Geom

The abstract class BoundedCurve describes the common behavior of bounded curves in 3D space. A bounded curve is limited by two finite values of the parameter, termed respectively "first parameter" and "last parameter". The "first parameter" gives the "start point" of the bounded curve, and the "last parameter" gives the "end point" of the bounded curve. The length of a bounded curve is finite. The Geom package provides three concrete classes of bounded curves:

two frequently used mathematical formulations of complex curves:
Geom_BezierCurve,
Geom_BSplineCurve, and
Geom_TrimmedCurve to trim a curve, i.e. to only take part of the curve limited by two values of the parameter of the basis curve.

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(3)

EndPoint(): gp_Pnt
Returns the end point of the curve.
StartPoint(): gp_Pnt
Returns the start point of the curve.
DynamicType(): Standard_Type

Geom_BoundedSurface

Geom_BoundedSurfaceGeom_SurfaceGeom_GeometryStandard_Transient

The root class for bounded surfaces in 3D space. A bounded surface is defined by a rectangle in its 2D parametric space, i.e.

its u parameter, which ranges between two finite values u0 and u1, referred to as "First u parameter" and "Last u parameter" respectively, and
its v parameter, which ranges between two finite values v0 and v1, referred to as "First v parameter" and the "Last v parameter" respectively. The surface is limited by four curves which are the boundaries of the surface:
its u0 and u1 isoparametric curves in the u parametric direction, and
its v0 and v1 isoparametric curves in the v parametric direction. A bounded surface is finite. The common behavior of all bounded surfaces is described by the Geom_Surface class. The Geom package provides three concrete implementations of bounded surfaces:
Geom_BezierSurface,
Geom_BSplineSurface, and
Geom_RectangularTrimmedSurface. The first two of these implement well known mathematical definitions of complex surfaces, the third trims a surface using four isoparametric curves, i.e. it limits the variation of its parameters to a rectangle in 2D parametric space.

Definition of the B_spline curve. A B-spline curve can be Uniform or non-uniform Rational or non-rational Periodic or non-periodic.
a b-spline curve is defined by : its degree; the degree for a Geom_BSplineCurve is limited to a value (25) which is defined and controlled by the system. This value is returned by the function MaxDegree;

its periodic or non-periodic nature;
a table of poles (also called control points), with their associated weights if the BSpline curve is rational. The poles of the curve are "control points" used to deform the curve. If the curve is non-periodic, the first pole is the start point of the curve, and the last pole is the end point of the curve.
The segment which joins the first pole to the second pole is the tangent to the curve at its start point, and the segment which joins the last pole to the second-from-last pole is the tangent to the curve at its end point. If the curve is periodic, these geometric properties are not verified. It is more difficult to give a geometric signification to the weights but are useful for providing exact representations of the arcs of a circle or ellipse. Moreover, if the weights of all the poles are equal, the curve has a polynomial equation; it is therefore a non-rational curve.
a table of knots with their multiplicities. For a Geom_BSplineCurve, the table of knots is an increasing sequence of reals without repetition; the multiplicities define the repetition of the knots. A BSpline curve is a piecewise polynomial or rational curve. The knots are the parameters of junction points between two pieces.
The multiplicity Mult(i) of the knot Knot(i) of the BSpline curve is related to the degree of continuity of the curve at the knot Knot(i), which is equal to Degree - Mult(i) where Degree is the degree of the BSpline curve. If the knots are regularly spaced (i.e. the difference between two consecutive knots is a constant), three specific and frequently used cases of knot distribution can be identified:
"uniform" if all multiplicities are equal to 1,
"quasi-uniform" if all multiplicities are equal to 1, except the first and the last knot which have a multiplicity of Degree + 1, where Degree is the degree of the BSpline curve,
"Piecewise Bezier" if all multiplicities are equal to Degree except the first and last knot which have a multiplicity of Degree + 1, where Degree is the degree of the BSpline curve. A curve of this type is a concatenation of arcs of Bezier curves. If the BSpline curve is not periodic:
the bounds of the Poles and Weights tables are 1 and NbPoles, where NbPoles is the number of poles of the BSpline curve,
the bounds of the Knots and Multiplicities tables are 1 and NbKnots, where NbKnots is the number of knots of the BSpline curve. If the BSpline curve is periodic, and if there are k periodic knots and p periodic poles, the period is: period = Knot(k + 1) - Knot(1) and the poles and knots tables can be considered as infinite tables, verifying:
Knot(i+k) = Knot(i) + period
Pole(i+p) = Pole(i) Note: data structures of a periodic BSpline curve are more complex than those of a non-periodic one. Warning In this class, weight value is considered to be zero if the weight is less than or equal to gp::Resolution().
References : . A survey of curve and surface methods in CADG Wolfgang BOHM CAGD 1 (1984) . On de Boor-like algorithms and blossoming Wolfgang BOEHM cagd 5 (1988) . Blossoming and knot insertion algorithms for B-spline curves Ronald N. GOLDMAN . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA . Curves and Surfaces for Computer Aided Geometric Design, a practical guide Gerald Farin

Constructors(3)

constructor(theOther: Geom_BSplineCurve): Geom_BSplineCurve
Copy constructor for optimized copying without validation.
Parameters (1)
- theOther —
  the BSpline curve to copy from
constructor(Poles: NCollection_Array1_gp_Pnt, Knots: NCollection_Array1_double, Multiplicities: NCollection_Array1_int, Degree: number, Periodic?: boolean): Geom_BSplineCurve
Creates a non-rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>.
Parameters (5)
- Poles
- Knots
- Multiplicities
- Degree
- Periodic
constructor(Poles: NCollection_Array1_gp_Pnt, Weights: NCollection_Array1_double, Knots: NCollection_Array1_double, Multiplicities: NCollection_Array1_int, Degree: number, Periodic?: boolean, CheckRational?: boolean): Geom_BSplineCurve
Creates a rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. Raises ConstructionError subject to the following conditions 0 < Degree <= MaxDegree.
Weights.Length() == Poles.Length()
Knots.Length() == Mults.Length() >= 2
Knots(i) < Knots(i+1) (Knots are increasing)
1 <= Mults(i) <= Degree
On a non periodic curve the first and last multiplicities may be Degree+1 (this is even recommended if you want the curve to start and finish on the first and last pole).
On a periodic curve the first and the last multicities must be the same.
on non-periodic curves
Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2
on periodic curves
Poles.Length() == Sum(Mults(i)) except the first or last
Parameters (7)
- Poles
- Weights
- Knots
- Multiplicities
- Degree
- Periodic
- CheckRational

Static methods(3)

MaxDegree(): number
Returns the value of the maximum degree of the normalized B-spline basis functions in this package.
get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(75)

HasEvalRepresentation(): boolean
Returns true if an evaluation representation is attached.
EvalRepresentation(): GeomEval_RepCurveDesc_Base
Returns the current evaluation representation descriptor (may be null).
SetEvalRepresentation(theDesc: GeomEval_RepCurveDesc_Base): void
Sets a new evaluation representation. Validates descriptor data and ensures no circular references.
Parameters (1)
- theDesc
ClearEvalRepresentation(): void
Removes the evaluation representation.
IncreaseDegree(Degree: number): void
Increases the degree of this BSpline curve to Degree. As a result, the poles, weights and multiplicities tables are modified; the knots table is not changed. Nothing is done if Degree is less than or equal to the current degree. Exceptions Standard_ConstructionError if Degree is greater than Geom_BSplineCurve::MaxDegree().
Parameters (1)
- Degree
IncreaseMultiplicity(Index: number, M: number): void
Increases the multiplicity of the knot <Index> to <M>.
If <M> is lower or equal to the current multiplicity nothing is done. If <M> is higher than the degree, the degree is used. If <Index> is not in [FirstUKnotIndex, LastUKnotIndex]
Parameters (2)
- Index
- M
IncreaseMultiplicity(I1: number, I2: number, M: number): void
Increases the multiplicities of the knots in [I1,I2] to <M>.
For each knot if <M> is lower or equal to the current multiplicity nothing is done. If <M> is higher than the degree the degree is used. If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
Parameters (3)
- I1
- I2
- M
IncrementMultiplicity(I1: number, I2: number, M: number): void
Increment the multiplicities of the knots in [I1,I2] by <M>.
If <M> is not positive nothing is done.
For each knot the resulting multiplicity is limited to the Degree. If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
Parameters (3)
- I1
- I2
- M
InsertKnot(U: number, M?: number, ParametricTolerance?: number, Add?: boolean): void
Inserts a knot value in the sequence of knots. If is an existing knot the multiplicity is increased by <M>.
If U is not on the parameter range nothing is done.
If the multiplicity is negative or null nothing is done. The new multiplicity is limited to the degree.
The tolerance criterion for knots equality is the max of Epsilon(U) and ParametricTolerance.
Parameters (4)
- U
- M
- ParametricTolerance
- Add
InsertKnots(Knots: NCollection_Array1_double, Mults: NCollection_Array1_int, ParametricTolerance?: number, Add?: boolean): void
Inserts a set of knots values in the sequence of knots.
For each U = Knots(i), M = Mults(i)
If is an existing knot the multiplicity is increased by <M> if <Add> is True, increased to <M> if <Add> is False.
If U is not on the parameter range nothing is done.
If the multiplicity is negative or null nothing is done. The new multiplicity is limited to the degree.
The tolerance criterion for knots equality is the max of Epsilon(U) and ParametricTolerance.
Parameters (4)
- Knots
- Mults
- ParametricTolerance
- Add
RemoveKnot(Index: number, M: number, Tolerance: number): boolean
Reduces the multiplicity of the knot of index Index to M. If M is equal to 0, the knot is removed. With a modification of this type, the array of poles is also modified. Two different algorithms are systematically used to compute the new poles of the curve.
If, for each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is less than Tolerance, this ensures that the curve is not modified by more than Tolerance. Under these conditions, true is returned; otherwise, false is returned. A low tolerance is used to prevent modification of the curve. A high tolerance is used to "smooth" the curve.
Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table. pole insertion and pole removing this operation is limited to the Uniform or QuasiUniform BSplineCurve. The knot values are modified. If the BSpline is NonUniform or Piecewise Bezier an exception Construction error is raised.
Parameters (3)
- Index
- M
- Tolerance
Reverse(): void
Changes the direction of parametrization of <me>. The Knot sequence is modified, the FirstParameter and the LastParameter are not modified. The StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve.
ReversedParameter(U: number): number
Returns the parameter on the reversed curve for the point of parameter U on <me>.
returns UFirst + ULast - U
Parameters (1)
- U
Segment(U1: number, U2: number, theTolerance?: number): void
Modifies this BSpline curve by segmenting it between U1 and U2. Either of these values can be outside the bounds of the curve, but U2 must be greater than U1. All data structure tables of this BSpline curve are modified, but the knots located between U1 and U2 are retained. The degree of the curve is not modified.
Parameter theTolerance defines the possible proximity of the segment boundaries and B-spline knots to treat them as equal.
Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the curve <me> or if the curve makes loop. After the segmentation the length of a curve can be null. raises if U2 < U1. Standard_DomainError if U2 - U1 exceeds the period for periodic curves. i.e. ((U2 - U1) - Period) > Precision::PConfusion().
Parameters (3)
- U1
- U2
- theTolerance
SetKnot(Index: number, K: number): void
Modifies this BSpline curve by assigning the value K to the knot of index Index in the knots table. This is a relatively local modification because K must be such that: Knots(Index - 1) < K < Knots(Index + 1) The second syntax allows you also to increase the multiplicity of the knot to M (but it is not possible to decrease the multiplicity of the knot with this function). Standard_ConstructionError if:
- K is not such that: Knots(Index - 1) < K < Knots(Index + 1)
- M is greater than the degree of this BSpline curve or lower than the previous multiplicity of knot of index Index in the knots table. Standard_OutOfRange if Index is outside the bounds of the knots table.
Parameters (2)
- Index
- K
SetKnot(Index: number, K: number, M: number): void
Changes the knot of range Index with its multiplicity. You can increase the multiplicity of a knot but it is not allowed to decrease the multiplicity of an existing knot.
Raised if K >= Knots(Index+1) or K <= Knots(Index-1). Raised if M is greater than Degree or lower than the previous multiplicity of knot of range Index. Raised if Index < 1 || Index > NbKnots
Parameters (3)
- Index
- K
- M
SetKnots(K: NCollection_Array1_double): void
Modifies this BSpline curve by assigning the array K to its knots table. The multiplicity of the knots is not modified. Exceptions Standard_ConstructionError if the values in the array K are not in ascending order. Standard_OutOfRange if the bounds of the array K are not respectively 1 and the number of knots of this BSpline curve.
Parameters (1)
- K
PeriodicNormalization(U: number): { U: number }
returns the parameter normalized within the period if the curve is periodic : otherwise does not do anything
Parameters (1)
- U
Returns
A result object with fields:
- U: updated value from the call.
SetPeriodic(): void
Changes this BSpline curve into a periodic curve. To become periodic, the curve must first be closed. Next, the knot sequence must be periodic. For this, FirstUKnotIndex and LastUKnotIndex are used to compute I1 and I2, the indexes in the knots array of the knots corresponding to the first and last parameters of this BSpline curve. The period is therefore: Knots(I2) - Knots(I1). Consequently, the knots and poles tables are modified. Exceptions Standard_ConstructionError if this BSpline curve is not closed.
SetOrigin(Index: number): void
Assigns the knot of index Index in the knots table as the origin of this periodic BSpline curve. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this curve is not periodic. Standard_DomainError if Index is outside the bounds of the knots table.
Parameters (1)
- Index
SetOrigin(U: number, Tol: number): void
Set the origin of a periodic curve at Knot U. If U is not a knot of the BSpline a new knot is inserted. KnotVector and poles are modified. Raised if the curve is not periodic.
Parameters (2)
- U
- Tol
SetNotPeriodic(): void
Changes this BSpline curve into a non-periodic curve. If this curve is already non-periodic, it is not modified. Note: the poles and knots tables are modified. Warning If this curve is periodic, as the multiplicity of the first and last knots is not modified, and is not equal to Degree + 1, where Degree is the degree of this BSpline curve, the start and end points of the curve are not its first and last poles.
SetPole(Index: number, P: gp_Pnt): void
Modifies this BSpline curve by assigning P to the pole of index Index in the poles table. Exceptions Standard_OutOfRange if Index is outside the bounds of the poles table. Standard_ConstructionError if Weight is negative or null.
Parameters (2)
- Index
- P
SetPole(Index: number, P: gp_Pnt, Weight: number): void
Modifies this BSpline curve by assigning P to the pole of index Index in the poles table. This syntax also allows you to modify the weight of the modified pole, which becomes Weight. In this case, if this BSpline curve is non-rational, it can become rational and vice versa. Exceptions Standard_OutOfRange if Index is outside the bounds of the poles table. Standard_ConstructionError if Weight is negative or null.
Parameters (3)
- Index
- P
- Weight
SetWeight(Index: number, Weight: number): void
Changes the weight for the pole of range Index. If the curve was non rational it can become rational. If the curve was rational it can become non rational.
Raised if Index < 1 || Index > NbPoles Raised if Weight <= 0.0
Parameters (2)
- Index
- Weight
MovePoint(U: number, P: gp_Pnt, Index1: number, Index2: number, FirstModifiedPole: number, LastModifiedPole: number): { FirstModifiedPole: number; LastModifiedPole: number }
Moves the point of parameter U of this BSpline curve to P. Index1 and Index2 are the indexes in the table of poles of this BSpline curve of the first and last poles designated to be moved. FirstModifiedPole and LastModifiedPole are the indexes of the first and last poles which are effectively modified. In the event of incompatibility between Index1, Index2 and the value U:
- no change is made to this BSpline curve, and
- the FirstModifiedPole and LastModifiedPole are returned null. Exceptions Standard_OutOfRange if:
- Index1 is greater than or equal to Index2, or
- Index1 or Index2 is less than 1 or greater than the number of poles of this BSpline curve.
Parameters (6)
- U
- P
- Index1
- Index2
- FirstModifiedPole
- LastModifiedPole
Returns
A result object with fields:
- FirstModifiedPole: updated value from the call.
- LastModifiedPole: updated value from the call.
MovePointAndTangent(U: number, P: gp_Pnt, Tangent: gp_Vec, Tolerance: number, StartingCondition: number, EndingCondition: number, ErrorStatus: number): { ErrorStatus: number }
Move a point with parameter U to P. and makes it tangent at U be Tangent. StartingCondition = -1 means first can move EndingCondition = -1 means last point can move StartingCondition = 0 means the first point cannot move EndingCondition = 0 means the last point cannot move StartingCondition = 1 means the first point and tangent cannot move EndingCondition = 1 means the last point and tangent cannot move and so forth ErrorStatus != 0 means that there are not enough degree of freedom with the constrain to deform the curve accordingly.
Parameters (7)
- U
- P
- Tangent
- Tolerance
- StartingCondition
- EndingCondition
- ErrorStatus
Returns
A result object with fields:
- ErrorStatus: updated value from the call.
IsCN(N: number): boolean
Returns the continuity of the curve, the curve is at least C0. Raised if N < 0.
Parameters (1)
- N
IsG1(theTf: number, theTl: number, theAngTol: number): boolean
Check if curve has at least G1 continuity in interval [theTf, theTl] Returns true if IsCN(1) or angle between "left" and "right" first derivatives at knots with C0 continuity is less then theAngTol only knots in interval [theTf, theTl] is checked.
Parameters (3)
- theTf
- theTl
- theAngTol
IsClosed(): boolean
Returns true if the distance between the first point and the last point of the curve is lower or equal to Resolution from package gp. Warnings : The first and the last point can be different from the first pole and the last pole of the curve.
IsPeriodic(): boolean
Returns True if the curve is periodic.
IsRational(): boolean
Returns True if the weights are not identical. The tolerance criterion is Epsilon of the class Real.
Continuity(): GeomAbs_Shape
Returns the global continuity of the curve : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, CN : the order of continuity is infinite. For a B-spline curve of degree d if a knot Ui has a multiplicity p the B-spline curve is only Cd-p continuous at Ui.
So the global continuity of the curve can't be greater than Cd-p where p is the maximum multiplicity of the interior Knots. In the interior of a knot span the curve is infinitely continuously differentiable.
Degree(): number
Returns the degree of this BSpline curve. The degree of a Geom_BSplineCurve curve cannot be greater than Geom_BSplineCurve::MaxDegree(). Computation of value and derivatives.
EvalD0(U: number): gp_Pnt
Returns the point of parameter U.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Raised if the continuity of the curve is not C1.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Raised if the continuity of the curve is not C2.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Raised if the continuity of the curve is not C3.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
For the point of parameter U of this BSpline curve, computes the vector corresponding to the Nth derivative. Warning On a point where the continuity of the curve is not the one requested, this function impacts the part defined by the parameter with a value greater than U, i.e. the part of the curve to the "right" of the singularity. Exceptions Standard_RangeError if N is less than 1.
The following functions compute the point of parameter U and the derivatives at this point on the B-spline curve arc defined between the knot FromK1 and the knot ToK2.
U can be out of bounds [Knot (FromK1), Knot (ToK2)] but for the computation we only use the definition of the curve between these two knots. This method is useful to compute local derivative, if the order of continuity of the whole curve is not greater enough.
Inside the parametric domain Knot (FromK1), Knot (ToK2) the evaluations are the same as if we consider the whole definition of the curve. Of course the evaluations are different outside this parametric domain.
Parameters (2)
- U
- N
LocalValue(U: number, FromK1: number, ToK2: number): gp_Pnt
Raised if FromK1 = ToK2.
Parameters (3)
- U
- FromK1
- ToK2
LocalD0(U: number, FromK1: number, ToK2: number, P: gp_Pnt): void
Raised if FromK1 = ToK2.
Parameters (4)
- U
- FromK1
- ToK2
- P —
  Mutated in place; read the updated value from this argument after the call.
LocalD1(U: number, FromK1: number, ToK2: number, P: gp_Pnt, V1: gp_Vec): void
Raised if the local continuity of the curve is not C1 between the knot K1 and the knot K2. Raised if FromK1 = ToK2.
Parameters (5)
- U
- FromK1
- ToK2
- P —
  Mutated in place; read the updated value from this argument after the call.
- V1 —
  Mutated in place; read the updated value from this argument after the call.
LocalD2(U: number, FromK1: number, ToK2: number, P: gp_Pnt, V1: gp_Vec, V2: gp_Vec): void
Raised if the local continuity of the curve is not C2 between the knot K1 and the knot K2. Raised if FromK1 = ToK2.
Parameters (6)
- U
- FromK1
- ToK2
- P —
  Mutated in place; read the updated value from this argument after the call.
- V1 —
  Mutated in place; read the updated value from this argument after the call.
- V2 —
  Mutated in place; read the updated value from this argument after the call.
LocalD3(U: number, FromK1: number, ToK2: number, P: gp_Pnt, V1: gp_Vec, V2: gp_Vec, V3: gp_Vec): void
Raised if the local continuity of the curve is not C3 between the knot K1 and the knot K2. Raised if FromK1 = ToK2.
Parameters (7)
- U
- FromK1
- ToK2
- P —
  Mutated in place; read the updated value from this argument after the call.
- V1 —
  Mutated in place; read the updated value from this argument after the call.
- V2 —
  Mutated in place; read the updated value from this argument after the call.
- V3 —
  Mutated in place; read the updated value from this argument after the call.
LocalDN(U: number, FromK1: number, ToK2: number, N: number): gp_Vec
Raised if the local continuity of the curve is not CN between the knot K1 and the knot K2. Raised if FromK1 = ToK2. Raised if N < 1.
Parameters (4)
- U
- FromK1
- ToK2
- N
EndPoint(): gp_Pnt
Returns the last point of the curve. Warnings : The last point of the curve is different from the last pole of the curve if the multiplicity of the last knot is lower than Degree.
FirstUKnotIndex(): number
Returns the index in the knot array of the knot corresponding to the first or last parameter of this BSpline curve. For a BSpline curve, the first (or last) parameter (which gives the start (or end) point of the curve) is a knot value. However, if the multiplicity of the first (or last) knot is less than Degree + 1, where Degree is the degree of the curve, it is not the first (or last) knot of the curve.
FirstParameter(): number
Returns the value of the first parameter of this BSpline curve. This is a knot value. The first parameter is the one of the start point of the BSpline curve.
Knot(Index: number): number
Returns the knot of range Index. When there is a knot with a multiplicity greater than 1 the knot is not repeated. The method Multiplicity can be used to get the multiplicity of the Knot. Raised if Index < 1 or Index > NbKnots.
Parameters (1)
- Index
Knots(K: NCollection_Array1_double): void
returns the knot values of the B-spline curve; Warning A knot with a multiplicity greater than 1 is not repeated in the knot table. The Multiplicity function can be used to obtain the multiplicity of each knot.
Raised K.Lower() is less than number of first knot or K.Upper() is more than number of last knot.
Deprecated
Parameters (1)
- K —
  Mutated in place; read the updated value from this argument after the call.
Knots(): NCollection_Array1_double
returns the knot values of the B-spline curve; Warning A knot with a multiplicity greater than 1 is not repeated in the knot table. The Multiplicity function can be used to obtain the multiplicity of each knot.
KnotSequence(K: NCollection_Array1_double): void
Returns K, the knots sequence of this BSpline curve. In this sequence, knots with a multiplicity greater than 1 are repeated.
In the case of a non-periodic curve the length of the sequence must be equal to the sum of the NbKnots multiplicities of the knots of the curve (where NbKnots is the number of knots of this BSpline curve).
This sum is also equal to : NbPoles + Degree + 1 where NbPoles is the number of poles and Degree the degree of this BSpline curve. In the case of a periodic curve, if there are k periodic knots, the period is Knot(k+1) - Knot(1).
The initial sequence is built by writing knots 1 to k+1, which are repeated according to their corresponding multiplicities.
If Degree is the degree of the curve, the degree of continuity of the curve at the knot of index 1 (or k+1) is equal to c = Degree + 1 - Mult(1). c knots are then inserted at the beginning and end of the initial sequence:
- the c values of knots preceding the first item Knot(k+1) in the initial sequence are inserted at the beginning; the period is subtracted from these c values;
- the c values of knots following the last item Knot(1) in the initial sequence are inserted at the end; the period is added to these c values. The length of the sequence must therefore be equal to: NbPoles + 2*Degree - Mult(1) + 2. Example For a non-periodic BSpline curve of degree 2 where:
- the array of knots is: { k1 k2 k3 k4 },
- with associated multiplicities: { 3 1 2 3 }, the knot sequence is: K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 } For a periodic BSpline curve of degree 4 , which is "C1" continuous at the first knot, and where :
- the periodic knots are: { k1 k2 k3 (k4) } (3 periodic knots: the points of parameter k1 and k4 are identical, the period is p = k4 - k1),
- with associated multiplicities: { 3 1 2 (3) }, the degree of continuity at knots k1 and k4 is: Degree + 1 - Mult(i) = 2. 2 supplementary knots are added at the beginning and end of the sequence:
- at the beginning: the 2 knots preceding k4 minus the period; in this example, this is k3 - p both times;
- at the end: the 2 knots following k1 plus the period; in this example, this is k2 + p and k3 + p. The knot sequence is therefore: K = { k3-p k3-p k1 k1 k1 k2 k3 k3 k4 k4 k4 k2+p k3+p } Exceptions Raised if K.Lower() is less than number of first knot in knot sequence with repetitions or K.Upper() is more than number of last knot in knot sequence with repetitions.
Deprecated
Parameters (1)
- K —
  Mutated in place; read the updated value from this argument after the call.
KnotSequence(): NCollection_Array1_double
returns the knots of the B-spline curve. Knots with multiplicit greater than 1 are repeated
KnotDistribution(): GeomAbs_BSplKnotDistribution
Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot the BSpline Curve can be :
- Uniform if all the knots are of multiplicity 1,
- QuasiUniform if all the knots are of multiplicity 1 except for the first and last knot which are of multiplicity Degree + 1,
- PiecewiseBezier if the first and last knots have multiplicity Degree + 1 and if interior knots have multiplicity Degree A piecewise Bezier with only two knots is a BezierCurve. else the curve is non uniform. The tolerance criterion is Epsilon from class Real.
LastUKnotIndex(): number
For a BSpline curve the last parameter (which gives the end point of the curve) is a knot value but if the multiplicity of the last knot index is lower than Degree + 1 it is not the last knot of the curve. This method computes the index of the knot corresponding to the last parameter.
LastParameter(): number
Computes the parametric value of the end point of the curve. It is a knot value.
LocateU(U: number, ParametricTolerance: number, I1: number, I2: number, WithKnotRepetition: boolean): { I1: number; I2: number }
Locates the parametric value U in the sequence of knots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values. Knots (I1) <= U <= Knots (I2) . if I1 = I2 U is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => U < Knots (1) - std::abs(ParametricTolerance) . if I2 > NbKnots => U > Knots (NbKnots) + std::abs(ParametricTolerance).
Parameters (5)
- U
- ParametricTolerance
- I1
- I2
- WithKnotRepetition
Returns
A result object with fields:
- I1: updated value from the call.
- I2: updated value from the call.
Multiplicity(Index: number): number
Returns the multiplicity of the knots of range Index. Raised if Index < 1 or Index > NbKnots.
Parameters (1)
- Index
Multiplicities(M: NCollection_Array1_int): void
Returns the multiplicity of the knots of the curve.
Raised if the length of M is not equal to NbKnots.
Deprecated
Parameters (1)
- M —
  Mutated in place; read the updated value from this argument after the call.
Multiplicities(): NCollection_Array1_int
returns the multiplicity of the knots of the curve.
NbKnots(): number
Returns the number of knots. This method returns the number of knot without repetition of multiple knots.
NbPoles(): number
Returns the number of poles.
Pole(Index: number): gp_Pnt
Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles.
Parameters (1)
- Index
Poles(P: NCollection_Array1_gp_Pnt): void
Returns the poles of the B-spline curve;.
Raised if the length of P is not equal to the number of poles.
Deprecated
Parameters (1)
- P —
  Mutated in place; read the updated value from this argument after the call.
Poles(): NCollection_Array1_gp_Pnt
Returns the poles of the B-spline curve;.
StartPoint(): gp_Pnt
Returns the start point of the curve. Warnings : This point is different from the first pole of the curve if the multiplicity of the first knot is lower than Degree.
Weight(Index: number): number
Returns the weight of the pole of range Index . Raised if Index < 1 or Index > NbPoles.
Parameters (1)
- Index
Weights(W: NCollection_Array1_double): void
Returns the weights of the B-spline curve;.
Raised if the length of W is not equal to NbPoles.
Deprecated
Parameters (1)
- W —
  Mutated in place; read the updated value from this argument after the call.
Weights(): NCollection_Array1_double
Returns the weights of the B-spline curve;.
WeightsArray(): NCollection_Array1_double
Returns a const reference to the weights array. For rational curves: the internal owning weights array. For non-rational curves: a non-owning view of unit weights from BSplCLib. The array is always sized to match NbPoles().
Remarks
Warning: Do NOT modify elements through the returned reference.
Transform(T: gp_Trsf): void
Applies the transformation T to this BSpline curve.
Parameters (1)
- T
Resolution(Tolerance3D: number, UTolerance: number): { UTolerance: number }
Computes for this BSpline curve the parametric tolerance UTolerance for a given 3D tolerance Tolerance3D. If f(t) is the equation of this BSpline curve, UTolerance ensures that: | t1 - t0| < Utolerance ===> |f(t1) - f(t0)| < Tolerance3D.
Parameters (2)
- Tolerance3D
- UTolerance
Returns
A result object with fields:
- UTolerance: updated value from the call.
Copy(): Geom_Geometry
Creates a new object which is a copy of this BSpline curve.
IsEqual(theOther: Geom_BSplineCurve, thePreci: number): boolean
Compare two Bspline curve on identity;.
Parameters (2)
- theOther
- thePreci
DynamicType(): Standard_Type

Geom_BSplineSurface

Describes a BSpline surface. In each parametric direction, a BSpline surface can be:

uniform or non-uniform,
rational or non-rational,
periodic or non-periodic. A BSpline surface is defined by:
its degrees, in the u and v parametric directions,
its periodic characteristic, in the u and v parametric directions,
a table of poles, also called control points (together with the associated weights if the surface is rational), and
a table of knots, together with the associated multiplicities. The degree of a Geom_BSplineSurface is limited to a value (25) which is defined and controlled by the system. This value is returned by the function MaxDegree. Poles and Weights Poles and Weights are manipulated using two associative double arrays:
the poles table, which is a double array of gp_Pnt points, and
the weights table, which is a double array of reals. The bounds of the poles and weights arrays are:
1 and NbUPoles for the row bounds (provided that the BSpline surface is not periodic in the u parametric direction), where NbUPoles is the number of poles of the surface in the u parametric direction, and
1 and NbVPoles for the column bounds (provided that the BSpline surface is not periodic in the v parametric direction), where NbVPoles is the number of poles of the surface in the v parametric direction. The poles of the surface are the points used to shape and reshape the surface. They comprise a rectangular network. If the surface is not periodic:
The points (1, 1), (NbUPoles, 1), (1, NbVPoles), and (NbUPoles, NbVPoles) are the four parametric "corners" of the surface.
The first column of poles and the last column of poles define two BSpline curves which delimit the surface in the v parametric direction. These are the v isoparametric curves corresponding to the two bounds of the v parameter.
The first row of poles and the last row of poles define two BSpline curves which delimit the surface in the u parametric direction. These are the u isoparametric curves corresponding to the two bounds of the u parameter. If the surface is periodic, these geometric properties are not verified. It is more difficult to define a geometrical significance for the weights. However they are useful for representing a quadric surface precisely.
Moreover, if the weights of all the poles are equal, the surface has a polynomial equation, and hence is a "non-rational surface". The non-rational surface is a special, but frequently used, case, where all poles have identical weights. The weights are defined and used only in the case of a rational surface. The rational characteristic is defined in each parametric direction. A surface can be rational in the u parametric direction, and non-rational in the v parametric direction.
Knots and Multiplicities For a Geom_BSplineSurface the table of knots is made up of two increasing sequences of reals, without repetition, one for each parametric direction. The multiplicities define the repetition of the knots. A BSpline surface comprises multiple contiguous patches, which are themselves polynomial or rational surfaces. The knots are the parameters of the isoparametric curves which limit these contiguous patches.
The multiplicity of a knot on a BSpline surface (in a given parametric direction) is related to the degree of continuity of the surface at that knot in that parametric direction: Degree of continuity at knot(i) = Degree - Multi(i) where:
Degree is the degree of the BSpline surface in the given parametric direction, and
Multi(i) is the multiplicity of knot number i in the given parametric direction. There are some special cases, where the knots are regularly spaced in one parametric direction (i.e. the difference between two consecutive knots is a constant).
"Uniform": all the multiplicities are equal to 1.
"Quasi-uniform": all the multiplicities are equal to 1, except for the first and last knots in this parametric direction, and these are equal to Degree + 1.
"Piecewise Bezier": all the multiplicities are equal to Degree except for the first and last knots, which are equal to Degree + 1. This surface is a concatenation of Bezier patches in the given parametric direction. If the BSpline surface is not periodic in a given parametric direction, the bounds of the knots and multiplicities tables are 1 and NbKnots, where NbKnots is the number of knots of the BSpline surface in that parametric direction. If the BSpline surface is periodic in a given parametric direction, and there are k periodic knots and p periodic poles in that parametric direction:
the period is such that: period = Knot(k+1) - Knot(1), and
the poles and knots tables in that parametric direction can be considered as infinite tables, such that: Knot(i+k) = Knot(i) + period, and Pole(i+p) = Pole(i) Note: The data structure tables for a periodic BSpline surface are more complex than those of a non-periodic one. References : . A survey of curve and surface methods in CADG Wolfgang BOHM CAGD 1 (1984) . On de Boor-like algorithms and blossoming Wolfgang BOEHM cagd 5 (1988) . Blossoming and knot insertion algorithms for B-spline curves Ronald N. GOLDMAN . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA . Curves and Surfaces for Computer Aided Geometric Design, a practical guide Gerald Farin

Constructors(3)

constructor(theOther: Geom_BSplineSurface): Geom_BSplineSurface
Copy constructor for optimized copying without validation.
Parameters (1)
- theOther —
  the BSpline surface to copy from
constructor(Poles: NCollection_Array2_gp_Pnt, UKnots: NCollection_Array1_double, VKnots: NCollection_Array1_double, UMults: NCollection_Array1_int, VMults: NCollection_Array1_int, UDegree: number, VDegree: number, UPeriodic?: boolean, VPeriodic?: boolean): Geom_BSplineSurface
Creates a non-rational b-spline surface (weights default value is 1.). The following conditions must be verified. 0 < UDegree <= MaxDegree. UKnots.Length() == UMults.Length() >= 2 UKnots(i) < UKnots(i+1) (Knots are increasing) 1 <= UMults(i) <= UDegree On a non uperiodic surface the first and last umultiplicities may be UDegree+1 (this is even recommended if you want the curve to start and finish on the first and last pole).
On a uperiodic surface the first and the last umultiplicities must be the same. on non-uperiodic surfaces Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2 on uperiodic surfaces Poles.ColLength() == Sum(UMults(i)) except the first or last The previous conditions for U holds also for V, with the RowLength of the poles.
Parameters (9)
- Poles
- UKnots
- VKnots
- UMults
- VMults
- UDegree
- VDegree
- UPeriodic
- VPeriodic
constructor(Poles: NCollection_Array2_gp_Pnt, Weights: NCollection_Array2_double, UKnots: NCollection_Array1_double, VKnots: NCollection_Array1_double, UMults: NCollection_Array1_int, VMults: NCollection_Array1_int, UDegree: number, VDegree: number, UPeriodic?: boolean, VPeriodic?: boolean): Geom_BSplineSurface
Creates a non-rational b-spline surface (weights default value is 1.).
The following conditions must be verified. 0 < UDegree <= MaxDegree.
UKnots.Length() == UMults.Length() >= 2
UKnots(i) < UKnots(i+1) (Knots are increasing) 1 <= UMults(i) <= UDegree
On a non uperiodic surface the first and last umultiplicities may be UDegree+1 (this is even recommended if you want the curve to start and finish on the first and last pole).
On a uperiodic surface the first and the last umultiplicities must be the same.
on non-uperiodic surfaces
Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2
on uperiodic surfaces
Poles.ColLength() == Sum(UMults(i)) except the first or last
The previous conditions for U holds also for V, with the RowLength of the poles.
Parameters (10)
- Poles
- Weights
- UKnots
- VKnots
- UMults
- VMults
- UDegree
- VDegree
- UPeriodic
- VPeriodic

Static methods(3)

MaxDegree(): number
Returns the value of the maximum degree of the normalized B-spline basis functions in the u and v directions.
get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(113)

HasEvalRepresentation(): boolean
Returns true if an evaluation representation is attached.
EvalRepresentation(): GeomEval_RepSurfaceDesc_Base
Returns the current evaluation representation descriptor (may be null).
SetEvalRepresentation(theDesc: GeomEval_RepSurfaceDesc_Base): void
Sets a new evaluation representation. Validates descriptor data and ensures no circular references.
Parameters (1)
- theDesc
ClearEvalRepresentation(): void
Removes the evaluation representation.
ExchangeUV(): void
Exchanges the u and v parametric directions on this BSpline surface. As a consequence:
- the poles and weights tables are transposed,
- the knots and multiplicities tables are exchanged,
- degrees of continuity, and rational, periodic and uniform characteristics are exchanged, and
- the orientation of the surface is inverted.
SetUPeriodic(): void
Sets the surface U periodic. Modifies this surface to be periodic in the U parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstUKnotIndex and LastUKnotIndex are used to compute I1 and I2.
These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this BSpline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Exceptions Standard_ConstructionError if the surface is not closed in the given parametric direction.
SetVPeriodic(): void
Sets the surface V periodic. Modifies this surface to be periodic in the V parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstVKnotIndex and LastVKnotIndex are used to compute I1 and I2.
These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this BSpline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Exceptions Standard_ConstructionError if the surface is not closed in the given parametric direction.
PeriodicNormalization(U: number, V: number): { U: number; V: number }
returns the parameter normalized within the period if the surface is periodic : otherwise does not do anything
Parameters (2)
- U
- V
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
SetUOrigin(Index: number): void
Assigns the knot of index Index in the knots table in the corresponding parametric direction to be the origin of this periodic BSpline surface. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this BSpline surface is not periodic in the given parametric direction. Standard_DomainError if Index is outside the bounds of the knots table in the given parametric direction.
Parameters (1)
- Index
SetVOrigin(Index: number): void
Assigns the knot of index Index in the knots table in the corresponding parametric direction to be the origin of this periodic BSpline surface. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this BSpline surface is not periodic in the given parametric direction. Standard_DomainError if Index is outside the bounds of the knots table in the given parametric direction.
Parameters (1)
- Index
SetUNotPeriodic(): void
Sets the surface U not periodic. Changes this BSpline surface into a non-periodic surface along U direction. If this surface is already non-periodic, it is not modified. Note: the poles and knots tables are modified.
SetVNotPeriodic(): void
Sets the surface V not periodic. Changes this BSpline surface into a non-periodic surface along V direction. If this surface is already non-periodic, it is not modified. Note: the poles and knots tables are modified.
UReverse(): void
Changes the orientation of this BSpline surface in the U parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed. Hence the orientation of the surface is reversed. The knots and poles tables are modified.
VReverse(): void
Changes the orientation of this BSpline surface in the V parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed. Hence the orientation of the surface is reversed. The knots and poles tables are modified.
UReversedParameter(U: number): number
Computes the u parameter on the modified surface, produced by reversing its U parametric direction, for the point of u parameter U, on this BSpline surface. For a BSpline surface, these functions return respectively:
- UFirst + ULast - U, where UFirst, ULast are the values of the first and last parameters of this BSpline surface, in the u parametric directions.
Parameters (1)
- U
VReversedParameter(V: number): number
Computes the v parameter on the modified surface, produced by reversing its V parametric direction, for the point of v parameter V on this BSpline surface. For a BSpline surface, these functions return respectively:
- VFirst + VLast - V, VFirst and VLast are the values of the first and last parameters of this BSpline surface, in the v pametric directions.
Parameters (1)
- V
IncreaseDegree(UDegree: number, VDegree: number): void
Increases the degrees of this BSpline surface to UDegree and VDegree in the u and v parametric directions respectively. As a result, the tables of poles, weights and multiplicities are modified. The tables of knots is not changed. Note: Nothing is done if the given degree is less than or equal to the current degree in the corresponding parametric direction. Exceptions Standard_ConstructionError if UDegree or VDegree is greater than Geom_BSplineSurface::MaxDegree().
Parameters (2)
- UDegree
- VDegree
InsertUKnots(Knots: NCollection_Array1_double, Mults: NCollection_Array1_int, ParametricTolerance?: number, Add?: boolean): void
Inserts into the knots table for the U parametric direction of this BSpline surface:
- the values of the array Knots, with their respective multiplicities, Mults. If the knot value to insert already exists in the table, its multiplicity is:
- increased by M, if Add is true (the default), or
- increased to M, if Add is false. The tolerance criterion used to check the equality of the knots is the larger of the values ParametricTolerance and double::Epsilon(val), where val is the knot value to be inserted. Warning
- If a given multiplicity coefficient is null, or negative, nothing is done.
- The new multiplicity of a knot is limited to the degree of this BSpline surface in the corresponding parametric direction. Exceptions Standard_ConstructionError if a knot value to insert is outside the bounds of this BSpline surface in the specified parametric direction. The comparison uses the precision criterion ParametricTolerance.
Parameters (4)
- Knots
- Mults
- ParametricTolerance
- Add
InsertVKnots(Knots: NCollection_Array1_double, Mults: NCollection_Array1_int, ParametricTolerance?: number, Add?: boolean): void
Inserts into the knots table for the V parametric direction of this BSpline surface:
- the values of the array Knots, with their respective multiplicities, Mults. If the knot value to insert already exists in the table, its multiplicity is:
- increased by M, if Add is true (the default), or
- increased to M, if Add is false. The tolerance criterion used to check the equality of the knots is the larger of the values ParametricTolerance and double::Epsilon(val), where val is the knot value to be inserted. Warning
- If a given multiplicity coefficient is null, or negative, nothing is done.
- The new multiplicity of a knot is limited to the degree of this BSpline surface in the corresponding parametric direction. Exceptions Standard_ConstructionError if a knot value to insert is outside the bounds of this BSpline surface in the specified parametric direction. The comparison uses the precision criterion ParametricTolerance.
Parameters (4)
- Knots
- Mults
- ParametricTolerance
- Add
RemoveUKnot(Index: number, M: number, Tolerance: number): boolean
Reduces to M the multiplicity of the knot of index Index in the U parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface.
For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance "smoothes" the surface. Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table of this BSpline surface.
Parameters (3)
- Index
- M
- Tolerance
RemoveVKnot(Index: number, M: number, Tolerance: number): boolean
Reduces to M the multiplicity of the knot of index Index in the V parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface.
For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance "smoothes" the surface. Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table of this BSpline surface.
Parameters (3)
- Index
- M
- Tolerance
IncreaseUMultiplicity(UIndex: number, M: number): void
Increases the multiplicity of the knot of range UIndex in the UKnots sequence. M is the new multiplicity. M must be greater than the previous multiplicity and lower or equal to the degree of the surface in the U parametric direction. Raised if M is not in the range [1, UDegree].
Raised if UIndex is not in the range [FirstUKnotIndex, LastUKnotIndex] given by the methods with the same name.
Parameters (2)
- UIndex
- M
IncreaseUMultiplicity(FromI1: number, ToI2: number, M: number): void
Increases until order M the multiplicity of the set of knots FromI1,...., ToI2 in the U direction. This method can be used to make a B_spline surface into a PiecewiseBezier B_spline surface. If <me> was uniform, it can become non uniform.
Raised if FromI1 or ToI2 is out of the range [FirstUKnotIndex, LastUKnotIndex].
M should be greater than the previous multiplicity of the all the knots FromI1,..., ToI2 and lower or equal to the Degree of the surface in the U parametric direction.
Parameters (3)
- FromI1
- ToI2
- M
IncrementUMultiplicity(FromI1: number, ToI2: number, Step: number): void
Increments the multiplicity of the consecutives uknots FromI1..ToI2 by step. The multiplicity of each knot FromI1,.....,ToI2 must be lower or equal to the UDegree of the B_spline.
Raised if FromI1 or ToI2 is not in the range [FirstUKnotIndex, LastUKnotIndex]
Raised if one knot has a multiplicity greater than UDegree.
Parameters (3)
- FromI1
- ToI2
- Step
IncreaseVMultiplicity(VIndex: number, M: number): void
Increases the multiplicity of a knot in the V direction. M is the new multiplicity.
M should be greater than the previous multiplicity and lower than the degree of the surface in the V parametric direction.
Raised if VIndex is not in the range [FirstVKnotIndex, LastVKnotIndex] given by the methods with the same name.
Parameters (2)
- VIndex
- M
IncreaseVMultiplicity(FromI1: number, ToI2: number, M: number): void
Increases until order M the multiplicity of the set of knots FromI1,...., ToI2 in the V direction. This method can be used to make a BSplineSurface into a PiecewiseBezier B_spline surface. If <me> was uniform, it can become non-uniform.
Raised if FromI1 or ToI2 is out of the range [FirstVKnotIndex, LastVKnotIndex] given by the methods with the same name.
M should be greater than the previous multiplicity of the all the knots FromI1,..., ToI2 and lower or equal to the Degree of the surface in the V parametric direction.
Parameters (3)
- FromI1
- ToI2
- M
IncrementVMultiplicity(FromI1: number, ToI2: number, Step: number): void
Increments the multiplicity of the consecutives vknots FromI1..ToI2 by step. The multiplicity of each knot FromI1,.....,ToI2 must be lower or equal to the VDegree of the B_spline.
Raised if FromI1 or ToI2 is not in the range [FirstVKnotIndex, LastVKnotIndex]
Raised if one knot has a multiplicity greater than VDegree.
Parameters (3)
- FromI1
- ToI2
- Step
InsertUKnot(U: number, M: number, ParametricTolerance: number, Add?: boolean): void
Inserts a knot value in the sequence of UKnots. If U is a knot value this method increases the multiplicity of the knot if the previous multiplicity was lower than M else it does nothing. The tolerance criterion is ParametricTolerance. ParametricTolerance should be greater or equal than Resolution from package gp.
Raised if U is out of the bounds [U1, U2] given by the methods Bounds, the criterion ParametricTolerance is used. Raised if M is not in the range [1, UDegree].
Parameters (4)
- U
- M
- ParametricTolerance
- Add
InsertVKnot(V: number, M: number, ParametricTolerance: number, Add?: boolean): void
Inserts a knot value in the sequence of VKnots. If V is a knot value this method increases the multiplicity of the knot if the previous multiplicity was lower than M otherwise it does nothing. The tolerance criterion is ParametricTolerance. ParametricTolerance should be greater or equal than Resolution from package gp.
raises if V is out of the Bounds [V1, V2] given by the methods Bounds, the criterion ParametricTolerance is used. raises if M is not in the range [1, VDegree].
Parameters (4)
- V
- M
- ParametricTolerance
- Add
Segment(U1: number, U2: number, V1: number, V2: number, theUTolerance?: number, theVTolerance?: number): void
Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction. The control points are modified, the first and the last point are not the same.
Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding direction of the segment boundaries and B-spline knots to treat them as equal.
Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the surface <me> or if the surface makes loop. raises if U2 < U1 or V2 < V1. Standard_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces. i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion(). Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces. i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).
Parameters (6)
- U1
- U2
- V1
- V2
- theUTolerance
- theVTolerance
CheckAndSegment(U1: number, U2: number, V1: number, V2: number, theUTolerance?: number, theVTolerance?: number): void
Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction.
same as Segment but do nothing if U1 and U2 (resp. V1 and V2) are equal to the bounds in U (resp. in V) of <me>. For example, if <me> is periodic in V, it will be always periodic in V after the segmentation if the bounds in V are unchanged
Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding direction of the segment boundaries and B-spline knots to treat them as equal.
Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the surface <me> or if the surface makes loop. raises if U2 < U1 or V2 < V1. Standard_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces. i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion(). Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces. i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).
Parameters (6)
- U1
- U2
- V1
- V2
- theUTolerance
- theVTolerance
SetUKnot(UIndex: number, K: number): void
Substitutes the UKnots of range UIndex with K.
Raised if UIndex < 1 or UIndex > NbUKnots
Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1)
Parameters (2)
- UIndex
- K
SetUKnot(UIndex: number, K: number, M: number): void
Changes the value of the UKnots of range UIndex and increases its multiplicity.
Raised if UIndex is not in the range [FirstUKnotIndex, LastUKnotIndex] given by the methods with the same name.
Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1) M must be lower than UDegree and greater than the previous multiplicity of the knot of range UIndex.
Parameters (3)
- UIndex
- K
- M
SetUKnots(UK: NCollection_Array1_double): void
Changes all the U-knots of the surface. The multiplicity of the knots are not modified.
Raised if there is an index such that UK (Index+1) <= UK (Index).
Raised if UK.Lower() < 1 or UK.Upper() > NbUKnots
Parameters (1)
- UK
SetVKnot(VIndex: number, K: number): void
Substitutes the VKnots of range VIndex with K.
Raised if VIndex < 1 or VIndex > NbVKnots
Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1)
Parameters (2)
- VIndex
- K
SetVKnot(VIndex: number, K: number, M: number): void
Changes the value of the VKnots of range VIndex and increases its multiplicity.
Raised if VIndex is not in the range [FirstVKnotIndex, LastVKnotIndex] given by the methods with the same name.
Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1) M must be lower than VDegree and greater than the previous multiplicity of the knot of range VIndex.
Parameters (3)
- VIndex
- K
- M
SetVKnots(VK: NCollection_Array1_double): void
Changes all the V-knots of the surface. The multiplicity of the knots are not modified.
Raised if there is an index such that VK (Index+1) <= VK (Index).
Raised if VK.Lower() < 1 or VK.Upper() > NbVKnots
Parameters (1)
- VK
LocateU(U: number, ParametricTolerance: number, I1: number, I2: number, WithKnotRepetition: boolean): { I1: number; I2: number }
Locates the parametric value U in the sequence of UKnots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values. UKnots (I1) <= U <= UKnots (I2) . if I1 = I2 U is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => U < UKnots(1) - std::abs(ParametricTolerance) . if I2 > NbUKnots => U > UKnots(NbUKnots)+std::abs(ParametricTolerance).
Parameters (5)
- U
- ParametricTolerance
- I1
- I2
- WithKnotRepetition
Returns
A result object with fields:
- I1: updated value from the call.
- I2: updated value from the call.
LocateV(V: number, ParametricTolerance: number, I1: number, I2: number, WithKnotRepetition: boolean): { I1: number; I2: number }
Locates the parametric value V in the sequence of knots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values.
VKnots (I1) <= V <= VKnots (I2) . if I1 = I2 V is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => V < VKnots(1) - std::abs(ParametricTolerance) . if I2 > NbVKnots => V > VKnots(NbVKnots)+std::abs(ParametricTolerance) poles insertion and removing The following methods are available only if the surface is Uniform or QuasiUniform in the considered direction The knot repartition is modified.
Parameters (5)
- V
- ParametricTolerance
- I1
- I2
- WithKnotRepetition
Returns
A result object with fields:
- I1: updated value from the call.
- I2: updated value from the call.
SetPole(UIndex: number, VIndex: number, P: gp_Pnt): void
Substitutes the pole of range (UIndex, VIndex) with P. If the surface is rational the weight of range (UIndex, VIndex) is not modified.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles.
Parameters (3)
- UIndex
- VIndex
- P
SetPole(UIndex: number, VIndex: number, P: gp_Pnt, Weight: number): void
Substitutes the pole and the weight of range (UIndex, VIndex) with P and W.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles. Raised if Weight <= Resolution from package gp.
Parameters (4)
- UIndex
- VIndex
- P
- Weight
SetPoleCol(VIndex: number, CPoles: NCollection_Array1_gp_Pnt): void
Changes a column of poles or a part of this column. Raised if Vindex < 1 or VIndex > NbVPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles.
Parameters (2)
- VIndex
- CPoles
SetPoleCol(VIndex: number, CPoles: NCollection_Array1_gp_Pnt, CPoleWeights: NCollection_Array1_double): void
Changes a column of poles or a part of this column with the corresponding weights. If the surface was rational it can become non rational. If the surface was non rational it can become rational. Raised if Vindex < 1 or VIndex > NbVPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles Raised if the bounds of CPoleWeights are not the same as the bounds of CPoles. Raised if one of the weight value of CPoleWeights is lower or equal to Resolution from package gp.
Parameters (3)
- VIndex
- CPoles
- CPoleWeights
SetPoleRow(UIndex: number, CPoles: NCollection_Array1_gp_Pnt, CPoleWeights: NCollection_Array1_double): void
Changes a row of poles or a part of this row with the corresponding weights. If the surface was rational it can become non rational. If the surface was non rational it can become rational. Raised if Uindex < 1 or UIndex > NbUPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles raises if the bounds of CPoleWeights are not the same as the bounds of CPoles. Raised if one of the weight value of CPoleWeights is lower or equal to Resolution from package gp.
Parameters (3)
- UIndex
- CPoles
- CPoleWeights
SetPoleRow(UIndex: number, CPoles: NCollection_Array1_gp_Pnt): void
Changes a row of poles or a part of this row. Raised if Uindex < 1 or UIndex > NbUPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles.
Parameters (2)
- UIndex
- CPoles
SetWeight(UIndex: number, VIndex: number, Weight: number): void
Changes the weight of the pole of range UIndex, VIndex. If the surface was non rational it can become rational. If the surface was rational it can become non rational.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles
Raised if weight is lower or equal to Resolution from package gp
Parameters (3)
- UIndex
- VIndex
- Weight
SetWeightCol(VIndex: number, CPoleWeights: NCollection_Array1_double): void
Changes a column of weights of a part of this column.
Raised if VIndex < 1 or VIndex > NbVPoles
Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() > NbUPoles. Raised if a weight value is lower or equal to Resolution from package gp.
Parameters (2)
- VIndex
- CPoleWeights
SetWeightRow(UIndex: number, CPoleWeights: NCollection_Array1_double): void
Changes a row of weights or a part of this row.
Raised if UIndex < 1 or UIndex > NbUPoles
Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() > NbVPoles. Raised if a weight value is lower or equal to Resolution from package gp.
Parameters (2)
- UIndex
- CPoleWeights
MovePoint(U: number, V: number, P: gp_Pnt, UIndex1: number, UIndex2: number, VIndex1: number, VIndex2: number, UFirstIndex: number, ULastIndex: number, VFirstIndex: number, VLastIndex: number): { UFirstIndex: number; ULastIndex: number; VFirstIndex: number; VLastIndex: number }
Move a point with parameter U and V to P. given u,v as parameters) to reach a new position UIndex1, UIndex2, VIndex1, VIndex2: indicates the poles which can be moved if Problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0.
Raised if UIndex1 < UIndex2 or VIndex1 < VIndex2 or UIndex1 < 1 || UIndex1 > NbUPoles or UIndex2 < 1 || UIndex2 > NbUPoles VIndex1 < 1 || VIndex1 > NbVPoles or VIndex2 < 1 || VIndex2 > NbVPoles characteristics of the surface
Parameters (11)
- U
- V
- P
- UIndex1
- UIndex2
- VIndex1
- VIndex2
- UFirstIndex
- ULastIndex
- VFirstIndex
- VLastIndex
Returns
A result object with fields:
- UFirstIndex: updated value from the call.
- ULastIndex: updated value from the call.
- VFirstIndex: updated value from the call.
- VLastIndex: updated value from the call.
IsUClosed(): boolean
Returns true if the first control points row and the last control points row are identical. The tolerance criterion is Resolution from package gp.
IsVClosed(): boolean
Returns true if the first control points column and the last last control points column are identical. The tolerance criterion is Resolution from package gp.
IsCNu(N: number): boolean
Returns True if the order of continuity of the surface in the U direction is N. Raised if N < 0.
Parameters (1)
- N
IsCNv(N: number): boolean
Returns True if the order of continuity of the surface in the V direction is N. Raised if N < 0.
Parameters (1)
- N
IsUPeriodic(): boolean
Returns True if the surface is closed in the U direction and if the B-spline has been turned into a periodic surface using the function SetUPeriodic.
IsURational(): boolean
Returns False if for each row of weights all the weights are identical. The tolerance criterion is resolution from package gp. Example : |1.0, 1.0, 1.0| if Weights = |0.5, 0.5, 0.5| returns False |2.0, 2.0, 2.0|.
IsVPeriodic(): boolean
Returns True if the surface is closed in the V direction and if the B-spline has been turned into a periodic surface using the function SetVPeriodic.
IsVRational(): boolean
Returns False if for each column of weights all the weights are identical. The tolerance criterion is resolution from package gp. Examples : |1.0, 2.0, 0.5| if Weights = |1.0, 2.0, 0.5| returns False |1.0, 2.0, 0.5|.
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds of the surface. Warnings : These parametric values are the bounds of the array of knots UKnots and VKnots only if the first knots and the last knots have a multiplicity equal to UDegree + 1 or VDegree + 1.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Continuity(): GeomAbs_Shape
Returns the continuity of the surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite.
A B-spline surface is infinitely continuously differentiable for the couple of parameters U, V such that U != UKnots(i) and V != VKnots(i). The continuity of the surface at a knot value depends on the multiplicity of this knot. Example : If the surface is C1 in the V direction and C2 in the U direction this function returns Shape = C1.
FirstUKnotIndex(): number
Computes the Index of the UKnots which gives the first parametric value of the surface in the U direction. The UIso curve corresponding to this value is a boundary curve of the surface.
FirstVKnotIndex(): number
Computes the Index of the VKnots which gives the first parametric value of the surface in the V direction. The VIso curve corresponding to this knot is a boundary curve of the surface.
LastUKnotIndex(): number
Computes the Index of the UKnots which gives the last parametric value of the surface in the U direction. The UIso curve corresponding to this knot is a boundary curve of the surface.
LastVKnotIndex(): number
Computes the Index of the VKnots which gives the last parametric value of the surface in the V direction. The VIso curve corresponding to this knot is a boundary curve of the surface.
NbUKnots(): number
Returns the number of knots in the U direction.
NbUPoles(): number
Returns number of poles in the U direction.
NbVKnots(): number
Returns the number of knots in the V direction.
NbVPoles(): number
Returns the number of poles in the V direction.
Pole(UIndex: number, VIndex: number): gp_Pnt
Returns the pole of range (UIndex, VIndex).
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles.
Parameters (2)
- UIndex
- VIndex
Poles(P: NCollection_Array2_gp_Pnt): void
Returns the poles of the B-spline surface.
Raised if the length of P in the U and V direction is not equal to NbUpoles and NbVPoles.
Deprecated
Parameters (1)
- P —
  Mutated in place; read the updated value from this argument after the call.
Poles(): NCollection_Array2_gp_Pnt
Returns the poles of the B-spline surface.
UDegree(): number
Returns the degree of the normalized B-splines Ni,n in the U direction.
UKnot(UIndex: number): number
Returns the Knot value of range UIndex. Raised if UIndex < 1 or UIndex > NbUKnots.
Parameters (1)
- UIndex
UKnotDistribution(): GeomAbs_BSplKnotDistribution
Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot in the U direction the B-spline surface can be :
- Uniform if all the knots are of multiplicity 1,
- QuasiUniform if all the knots are of multiplicity 1 except for the first and last knot which are of multiplicity Degree + 1,
- PiecewiseBezier if the first and last knots have multiplicity Degree + 1 and if interior knots have multiplicity Degree otherwise the surface is non uniform in the U direction The tolerance criterion is Resolution from package gp.
UKnots(Ku: NCollection_Array1_double): void
Returns the knots in the U direction.
Raised if the length of Ku is not equal to the number of knots in the U direction.
Deprecated
Parameters (1)
- Ku —
  Mutated in place; read the updated value from this argument after the call.
UKnots(): NCollection_Array1_double
Returns the knots in the U direction.
UKnotSequence(Ku: NCollection_Array1_double): void
Returns the uknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
Raised if the length of Ku is not equal to NbUPoles + UDegree + 1
Deprecated
Parameters (1)
- Ku —
  Mutated in place; read the updated value from this argument after the call.
UKnotSequence(): NCollection_Array1_double
Returns the uknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
UMultiplicity(UIndex: number): number
Returns the multiplicity value of knot of range UIndex in the u direction. Raised if UIndex < 1 or UIndex > NbUKnots.
Parameters (1)
- UIndex
UMultiplicities(Mu: NCollection_Array1_int): void
Returns the multiplicities of the knots in the U direction.
Raised if the length of Mu is not equal to the number of knots in the U direction.
Deprecated
Parameters (1)
- Mu —
  Mutated in place; read the updated value from this argument after the call.
UMultiplicities(): NCollection_Array1_int
Returns the multiplicities of the knots in the U direction.
VDegree(): number
Returns the degree of the normalized B-splines Ni,d in the V direction.
VKnot(VIndex: number): number
Returns the Knot value of range VIndex. Raised if VIndex < 1 or VIndex > NbVKnots.
Parameters (1)
- VIndex
VKnotDistribution(): GeomAbs_BSplKnotDistribution
Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot in the V direction the B-spline surface can be :
- Uniform if all the knots are of multiplicity 1,
- QuasiUniform if all the knots are of multiplicity 1 except for the first and last knot which are of multiplicity Degree + 1,
- PiecewiseBezier if the first and last knots have multiplicity Degree + 1 and if interior knots have multiplicity Degree otherwise the surface is non uniform in the V direction. The tolerance criterion is Resolution from package gp.
VKnots(Kv: NCollection_Array1_double): void
Returns the knots in the V direction.
Raised if the length of Kv is not equal to the number of knots in the V direction.
Deprecated
Parameters (1)
- Kv —
  Mutated in place; read the updated value from this argument after the call.
VKnots(): NCollection_Array1_double
Returns the knots in the V direction.
VKnotSequence(Kv: NCollection_Array1_double): void
Returns the vknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Kv = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
Raised if the length of Kv is not equal to NbVPoles + VDegree + 1
Deprecated
Parameters (1)
- Kv —
  Mutated in place; read the updated value from this argument after the call.
VKnotSequence(): NCollection_Array1_double
Returns the vknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
VMultiplicity(VIndex: number): number
Returns the multiplicity value of knot of range VIndex in the v direction. Raised if VIndex < 1 or VIndex > NbVKnots.
Parameters (1)
- VIndex
VMultiplicities(Mv: NCollection_Array1_int): void
Returns the multiplicities of the knots in the V direction.
Raised if the length of Mv is not equal to the number of knots in the V direction.
Deprecated
Parameters (1)
- Mv —
  Mutated in place; read the updated value from this argument after the call.
VMultiplicities(): NCollection_Array1_int
Returns the multiplicities of the knots in the V direction.
Weight(UIndex: number, VIndex: number): number
Returns the weight value of range UIndex, VIndex.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles.
Parameters (2)
- UIndex
- VIndex
Weights(W: NCollection_Array2_double): void
Returns the weights of the B-spline surface.
Raised if the length of W in the U and V direction is not equal to NbUPoles and NbVPoles.
Deprecated
Parameters (1)
- W —
  Mutated in place; read the updated value from this argument after the call.
Weights(): NCollection_Array2_double
Returns the weights of the B-spline surface. value and derivatives computation.
WeightsArray(): NCollection_Array2_double
Returns a const reference to the weights array. For rational surfaces: the internal owning weights array. For non-rational surfaces: a non-owning view of unit weights from BSplSLib. The array is always sized to match NbUPoles() x NbVPoles().
Remarks
Warning: Do NOT modify elements through the returned reference.
EvalD0(U: number, V: number): gp_Pnt
Computes the point of parameter (U, V) on the surface. Raises an exception on failure.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the point and first partial derivatives at (U, V). Raises an exception if the surface continuity is not C1.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the point and partial derivatives up to 2nd order at (U, V). Raises an exception if the surface continuity is not C2.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the point and partial derivatives up to 3rd order at (U, V). Raises an exception if the surface continuity is not C3.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V at (U, V). Raises an exception on failure.
Raised if the continuity of the surface is not CNu in the U direction and CNv in the V direction.
Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
The following functions computes the point for the parametric values (U, V) and the derivatives at this point on the B-spline surface patch delimited with the knots FromUK1, FromVK1 and the knots ToUK2, ToVK2. (U, V) can be out of these parametric bounds but for the computation we only use the definition of the surface between these knots.
This method is useful to compute local derivative, if the order of continuity of the whole surface is not greater enough.
Inside the parametric knot's domain previously defined the evaluations are the same as if we consider the whole definition of the surface. Of course the evaluations are different outside this parametric domain.
Parameters (4)
- U
- V
- Nu
- Nv
LocalD0(U: number, V: number, FromUK1: number, ToUK2: number, FromVK1: number, ToVK2: number, P: gp_Pnt): void
Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Parameters (7)
- U
- V
- FromUK1
- ToUK2
- FromVK1
- ToVK2
- P —
  Mutated in place; read the updated value from this argument after the call.
LocalD1(U: number, V: number, FromUK1: number, ToUK2: number, FromVK1: number, ToVK2: number, P: gp_Pnt, D1U: gp_Vec, D1V: gp_Vec): void
Raised if the local continuity of the surface is not C1 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Parameters (9)
- U
- V
- FromUK1
- ToUK2
- FromVK1
- ToVK2
- P —
  Mutated in place; read the updated value from this argument after the call.
- D1U —
  Mutated in place; read the updated value from this argument after the call.
- D1V —
  Mutated in place; read the updated value from this argument after the call.
LocalD2(U: number, V: number, FromUK1: number, ToUK2: number, FromVK1: number, ToVK2: number, P: gp_Pnt, D1U: gp_Vec, D1V: gp_Vec, D2U: gp_Vec, D2V: gp_Vec, D2UV: gp_Vec): void
Raised if the local continuity of the surface is not C2 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Parameters (12)
- U
- V
- FromUK1
- ToUK2
- FromVK1
- ToVK2
- P —
  Mutated in place; read the updated value from this argument after the call.
- D1U —
  Mutated in place; read the updated value from this argument after the call.
- D1V —
  Mutated in place; read the updated value from this argument after the call.
- D2U —
  Mutated in place; read the updated value from this argument after the call.
- D2V —
  Mutated in place; read the updated value from this argument after the call.
- D2UV —
  Mutated in place; read the updated value from this argument after the call.
LocalD3(U: number, V: number, FromUK1: number, ToUK2: number, FromVK1: number, ToVK2: number, P: gp_Pnt, D1U: gp_Vec, D1V: gp_Vec, D2U: gp_Vec, D2V: gp_Vec, D2UV: gp_Vec, D3U: gp_Vec, D3V: gp_Vec, D3UUV: gp_Vec, D3UVV: gp_Vec): void
Raised if the local continuity of the surface is not C3 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Parameters (16)
- U
- V
- FromUK1
- ToUK2
- FromVK1
- ToVK2
- P —
  Mutated in place; read the updated value from this argument after the call.
- D1U —
  Mutated in place; read the updated value from this argument after the call.
- D1V —
  Mutated in place; read the updated value from this argument after the call.
- D2U —
  Mutated in place; read the updated value from this argument after the call.
- D2V —
  Mutated in place; read the updated value from this argument after the call.
- D2UV —
  Mutated in place; read the updated value from this argument after the call.
- D3U —
  Mutated in place; read the updated value from this argument after the call.
- D3V —
  Mutated in place; read the updated value from this argument after the call.
- D3UUV —
  Mutated in place; read the updated value from this argument after the call.
- D3UVV —
  Mutated in place; read the updated value from this argument after the call.
LocalDN(U: number, V: number, FromUK1: number, ToUK2: number, FromVK1: number, ToVK2: number, Nu: number, Nv: number): gp_Vec
Raised if the local continuity of the surface is not CNu between the knots FromUK1, ToUK2 and CNv between the knots FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Parameters (8)
- U
- V
- FromUK1
- ToUK2
- FromVK1
- ToVK2
- Nu
- Nv
LocalValue(U: number, V: number, FromUK1: number, ToUK2: number, FromVK1: number, ToVK2: number): gp_Pnt
Computes the point of parameter U, V on the BSpline surface patch defines between the knots UK1 UK2, VK1, VK2. U can be out of the bounds [Knot UK1, Knot UK2] and V can be outof the bounds [Knot VK1, Knot VK2] but for the computation we only use the definition of the surface between these knot values. Raises if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Parameters (6)
- U
- V
- FromUK1
- ToUK2
- FromVK1
- ToVK2
UIso(U: number): Geom_Curve
Computes the U isoparametric curve. A B-spline curve is returned.
Parameters (1)
- U
UIso(U: number, CheckRational: boolean): Geom_Curve
Computes the U isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned.
Parameters (2)
- U
- CheckRational
VIso(V: number): Geom_Curve
Computes the V isoparametric curve. A B-spline curve is returned.
Parameters (1)
- V
VIso(V: number, CheckRational: boolean): Geom_Curve
Computes the V isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned. transformations.
Parameters (2)
- V
- CheckRational
Transform(T: gp_Trsf): void
Applies the transformation T to this BSpline surface.
Parameters (1)
- T
Resolution(Tolerance3D: number, UTolerance: number, VTolerance: number): { UTolerance: number; VTolerance: number }
Computes two tolerance values for this BSpline surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are:
- UTolerance in the u parametric direction, and
- VTolerance in the v parametric direction. If f(u,v) is the equation of this BSpline surface, UTolerance and VTolerance guarantee that : | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D
Parameters (3)
- Tolerance3D
- UTolerance
- VTolerance
Returns
A result object with fields:
- UTolerance: updated value from the call.
- VTolerance: updated value from the call.
Copy(): Geom_Geometry
Creates a new object which is a copy of this BSpline surface.
DynamicType(): Standard_Type

Geom_CartesianPoint

Geom_PointGeom_GeometryStandard_Transient

Describes a point in 3D space. A Geom_CartesianPoint is defined by a gp_Pnt point, with its three Cartesian coordinates X, Y and Z.

Constructors(2)

constructor(P: gp_Pnt): Geom_CartesianPoint
Returns a transient copy of P.
Parameters (1)
- P
constructor(X: number, Y: number, Z: number): Geom_CartesianPoint
Constructs a point defined by its three Cartesian coordinates X, Y and Z.
Parameters (3)
- X
- Y
- Z

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(13)

SetCoord(X: number, Y: number, Z: number): void
Assigns the coordinates X, Y and Z to this point.
Parameters (3)
- X
- Y
- Z
SetPnt(P: gp_Pnt): void
Set <me> to P.X(), P.Y(), P.Z() coordinates.
Parameters (1)
- P
SetX(X: number): void
Changes the X coordinate of <me>.
Parameters (1)
- X
SetY(Y: number): void
Changes the Y coordinate of <me>.
Parameters (1)
- Y
SetZ(Z: number): void
Changes the Z coordinate of <me>.
Parameters (1)
- Z
Coord(X: number, Y: number, Z: number): { X: number; Y: number; Z: number }
Returns the coordinates of <me>.
Parameters (3)
- X
- Y
- Z
Returns
A result object with fields:
- X: updated value from the call.
- Y: updated value from the call.
- Z: updated value from the call.
Pnt(): gp_Pnt
Returns a non transient cartesian point with the same coordinates as <me>.
X(): number
Returns the X coordinate of <me>.
Y(): number
Returns the Y coordinate of <me>.
Z(): number
Returns the Z coordinate of <me>.
Transform(T: gp_Trsf): void
Applies the transformation T to this point.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this point.
DynamicType(): Standard_Type

Geom_Circle

Geom_ConicGeom_CurveGeom_GeometryStandard_Transient

Describes a circle in 3D space. A circle is defined by its radius and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where:

the origin is the center of the circle, and
the origin, "X Direction" and "Y Direction" define the plane of the circle. This coordinate system is the local coordinate system of the circle. The "main Direction" of this coordinate system is the vector normal to the plane of the circle. The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the circle.
The "main Direction" of the local coordinate system gives an explicit orientation to the circle (definition of the trigonometric sense), determining the direction in which the parameter increases along the circle. The Geom_Circle circle is parameterized by an angle: P(U) = O + R*std::cos(U)XDir + RSin(U)*YDir, where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
R is the radius of the circle. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the circle. The parameter is the angle with this "X Direction". A circle is a closed and periodic curve. The period is 2.*Pi and the parameter range is [ 0, 2.*Pi [.

Constructors(2)

constructor(C: gp_Circ): Geom_Circle
Constructs a circle by conversion of the gp_Circ circle C.
Parameters (1)
- C
constructor(A2: gp_Ax2, Radius: number): Geom_Circle
Constructs a circle of radius Radius, where A2 locates the circle and defines its orientation in 3D space such that:
- the center of the circle is the origin of A2,
- the origin, "X Direction" and "Y Direction" of A2 define the plane of the circle,
- A2 is the local coordinate system of the circle. Note: It is possible to create a circle where Radius is equal to 0.0. raised if Radius < 0.
Parameters (2)
- A2
- Radius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(18)

SetCirc(C: gp_Circ): void
Set <me> so that <me> has the same geometric properties as C.
Parameters (1)
- C
SetRadius(R: number): void
Assigns the value R to the radius of this circle. Note: it is possible to have a circle with a radius equal to 0.0. Exceptions - Standard_ConstructionError if R is negative.
Parameters (1)
- R
Circ(): gp_Circ
returns the non transient circle from gp with the same geometric properties as <me>.
Radius(): number
Returns the radius of this circle.
ReversedParameter(U: number): number
Computes the parameter on the reversed circle for the point of parameter U on this circle. For a circle, the returned value is: 2.*Pi - U.
Parameters (1)
- U
Eccentricity(): number
Returns the eccentricity e = 0 for a circle.
FirstParameter(): number
Returns the value of the first parameter of this circle. This is 0.0, which gives the start point of this circle, or The start point and end point of a circle are coincident.
LastParameter(): number
Returns the value of the last parameter of this circle. This is 2.*Pi, which gives the end point of this circle. The start point and end point of a circle are coincident.
IsClosed(): boolean
returns True.
IsPeriodic(): boolean
returns True.
EvalD0(U: number): gp_Pnt
Returns the point of parameter U. P = C + R * Cos (U) * XDir + R * Sin (U) * YDir where C is the center of the circle , XDir the XDirection and YDir the YDirection of the circle's local coordinate system.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Returns the point of parameter U and the first derivative.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Returns the point of parameter U, the first and second derivatives.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Returns the point of parameter U, the first, second and third derivatives.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
Returns the vector corresponding to the derivative for the order of derivation N. Raised if N < 1.
Parameters (2)
- U
- N
Transform(T: gp_Trsf): void
Applies the transformation T to this circle.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this circle.
DynamicType(): Standard_Type

Geom_Conic

Geom_ElementarySurfaceGeom_SurfaceGeom_GeometryStandard_Transient

The abstract class Conic describes the common behavior of conic curves in 3D space and, in particular, their general characteristics. The Geom package provides four concrete classes of conics: Geom_Circle, Geom_Ellipse, Geom_Hyperbola and Geom_Parabola. A conic is positioned in space with a right-handed coordinate system (gp_Ax2 object), where:

the origin is the center of the conic (or the apex in the case of a parabola),
the origin, "X Direction" and "Y Direction" define the plane of the conic. This coordinate system is the local coordinate system of the conic. The "main Direction" of this coordinate system is the vector normal to the plane of the conic.
The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the conic.
The "main Direction" of the local coordinate system gives an explicit orientation to the conic, determining the direction in which the parameter increases along the conic. The "X Axis" of the local coordinate system also defines the origin of the parameter of the conic.

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(14)

SetAxis(theA1: gp_Ax1): void
Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed.
raised if the A1 is parallel to the XAxis of the conic.
Parameters (1)
- theA1
SetLocation(theP: gp_Pnt): void
changes the location point of the conic.
Parameters (1)
- theP
SetPosition(theA2: gp_Ax2): void
changes the local coordinate system of the conic.
Parameters (1)
- theA2
Axis(): gp_Ax1
Returns the "main Axis" of this conic. This axis is normal to the plane of the conic.
Location(): gp_Pnt
Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the Apex of the parabola.
Position(): gp_Ax2
Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u.
Eccentricity(): number
Returns the eccentricity value of the conic e. e = 0 for a circle 0 < e < 1 for an ellipse (e = 0 if MajorRadius = MinorRadius) e > 1 for a hyperbola e = 1 for a parabola Exceptions Standard_DomainError in the case of a hyperbola if its major radius is null.
XAxis(): gp_Ax1
Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic.
YAxis(): gp_Ax1
Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane of the conic.
Reverse(): void
Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified.
ReversedParameter(U: number): number
Returns the parameter on the reversed curve for the point of parameter U on <me>.
Parameters (1)
- U
Continuity(): GeomAbs_Shape
The continuity of the conic is Cn.
IsCN(N: number): boolean
Returns True. Raised if N < 0.
Parameters (1)
- N
DynamicType(): Standard_Type

Geom_ConicalSurface

Describes a cone. A cone is defined by the half-angle (can be negative) at its apex, and is positioned in space by a coordinate system (a gp_Ax3 object) and a reference radius as follows:

The "main Axis" of the coordinate system is the axis of revolution of the cone.
The plane defined by the origin, the "X Direction" and the "Y Direction" of the coordinate system is the reference plane of the cone. The intersection of the cone with this reference plane is a circle of radius equal to the reference radius.
The apex of the cone is on the negative side of the "main Axis" of the coordinate system if the half-angle is positive, and on the positive side if the half-angle is negative. This coordinate system is the "local coordinate system" of the cone. The following apply:
Rotation around its "main Axis", in the trigonometric sense given by the "X Direction" and the "Y Direction", defines the u parametric direction.
Its "X Axis" gives the origin for the u parameter.
Its "main Direction" is the v parametric direction of the cone.
Its origin is the origin of the v parameter. The parametric range of the two parameters is: -[0,2.*Pi]foru,and -]-infinity,+infinity[forv The parametric equation of the cone is: P(u,v)=O+(R+vsin(Ang))(cos(u)*XDir+sin(u)*YDir)+v*cos(Ang)*ZDir where:
O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of the cone's local coordinate system,
Ang is the half-angle at the apex of the cone, and
R is the reference radius.

Constructors(2)

constructor(C: gp_Cone): Geom_ConicalSurface
Creates a ConicalSurface from a non transient gp_Cone.
Parameters (1)
- C
constructor(A3: gp_Ax3, Ang: number, Radius: number): Geom_ConicalSurface
A3 defines the local coordinate system of the conical surface. Ang is the conical surface semi-angle. Its absolute value is in range ]0, PI/2[. Radius is the radius of the circle Viso in the placement plane of the conical surface defined with "XAxis" and "YAxis". The "ZDirection" of A3 defines the direction of the surface's axis of symmetry. If the location point of A3 is the apex of the surface Radius = 0 . At the creation the parametrization of the surface is defined such that the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface.
Raised if Radius < 0.0 or std::abs(Ang) < Resolution from gp or std::abs(Ang) >= PI/2 - Resolution
Parameters (3)
- A3
- Ang
- Radius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(28)

SetCone(C: gp_Cone): void
Set <me> so that <me> has the same geometric properties as C.
Parameters (1)
- C
SetRadius(R: number): void
Changes the radius of the conical surface in the placement plane (Z = 0, V = 0). The local coordinate system is not modified. Raised if R < 0.0.
Parameters (1)
- R
SetSemiAngle(Ang: number): void
Changes the semi angle of the conical surface. Semi-angle can be negative. Its absolute value std::abs(Ang) is in range ]0,PI/2[. Raises ConstructionError if std::abs(Ang) < Resolution from gp or std::abs(Ang) >= PI/2 - Resolution.
Parameters (1)
- Ang
Cone(): gp_Cone
Returns a non transient cone with the same geometric properties as <me>.
UReversedParameter(U: number): number
Eeturn 2.PI - U.
Parameters (1)
- U
VReversedParameter(V: number): number
Computes the u (or v) parameter on the modified surface, when reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this cone. In the case of a cone, these functions return respectively:
- 2.*Pi - U, -V.
Parameters (1)
- V
VReverse(): void
Changes the orientation of this cone in the v parametric direction. The bounds of the surface are not changed but the v parametric direction is reversed. As a consequence, for a cone:
- the "main Direction" of the local coordinate system is reversed, and
- the half-angle at the apex is inverted.
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method multiplies V by T.ScaleFactor()
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method returns a scale centered on the U axis with T.ScaleFactor
Parameters (1)
- T
Apex(): gp_Pnt
Computes the apex of this cone. It is on the negative side of the axis of revolution of this cone if the half-angle at the apex is positive, and on the positive side of the "main Axis" if the half-angle is negative.
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
The conical surface is infinite in the V direction so V1 = Realfirst from Standard and V2 = RealLast. U1 = 0 and U2 = 2*PI.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Coefficients(A1: number, A2: number, A3: number, B1: number, B2: number, B3: number, C1: number, C2: number, C3: number, D: number): { A1: number; A2: number; A3: number; B1: number; B2: number; B3: number; C1: number; C2: number; C3: number; D: number }
Returns the coefficients of the implicit equation of the quadric in the absolute cartesian coordinate system : These coefficients are normalized.
A1.X**2+A2.Y**2+A3.Z**2+2.(B1.X.Y+B2.X.Z+B3.Y.Z)+2.(C1.X+C2.Y+C3.Z)+D= 0.0
A1.X**2+A2.Y**2+A3.Z**2+2.(B1.X.Y+B2.X.Z+B3.Y.Z)+2.(C1.X+C2.Y+C3.Z)+D= 0.0
Parameters (10)
- A1
- A2
- A3
- B1
- B2
- B3
- C1
- C2
- C3
- D
Returns
A result object with fields:
- A1: updated value from the call.
- A2: updated value from the call.
- A3: updated value from the call.
- B1: updated value from the call.
- B2: updated value from the call.
- B3: updated value from the call.
- C1: updated value from the call.
- C2: updated value from the call.
- C3: updated value from the call.
- D: updated value from the call.
RefRadius(): number
Returns the reference radius of this cone. The reference radius is the radius of the circle formed by the intersection of this cone and its reference plane (i.e. the plane defined by the origin, "X Direction" and "Y Direction" of the local coordinate system of this cone). If the apex of this cone is on the origin of the local coordinate system of this cone, the returned value is 0.
SemiAngle(): number
Returns the semi-angle at the apex of this cone. Attention! Semi-angle can be negative.
IsUClosed(): boolean
returns True.
IsVClosed(): boolean
returns False.
IsUPeriodic(): boolean
Returns True.
IsVPeriodic(): boolean
Returns False.
UIso(U: number): Geom_Curve
Builds the U isoparametric line of this cone. The origin of this line is on the reference plane of this cone (i.e. the plane defined by the origin, "X Direction" and "Y Direction" of the local coordinate system of this cone).
Parameters (1)
- U
VIso(V: number): Geom_Curve
Builds the V isoparametric circle of this cone. It is the circle on this cone, located in the plane of Z coordinate V*cos(Semi-Angle) in the local coordinate system of this cone. The "Axis" of this circle is the axis of revolution of this cone. Its starting point is defined by the "X Direction" of this cone. Warning If the V isoparametric circle is close to the apex of this cone, the radius of the circle becomes very small. It is possible to have a circle with radius equal to 0.0.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on the surface.
P(U,V)=Loc+ (RefRadius+V*sin(Semi-Angle))*(cos(U)*XDir+sin(U)*YDir)+ V*cos(Semi-Angle)*ZDir
P(U,V)=Loc+ (RefRadius+V*sin(Semi-Angle))*(cos(U)*XDir+sin(U)*YDir)+ V*cos(Semi-Angle)*ZDir
where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the current point and the first derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the current point, the first and the second derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the current point, the first,the second and the third derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in the u parametric direction, and Nv in the v parametric direction at the point of parameters (U, V) of this cone. Exceptions Standard_RangeError if:
- Nu + Nv is less than 1,
- Nu or Nv is negative.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this cone.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this cone.
DynamicType(): Standard_Type

Geom_Curve

Geom_ElementarySurfaceGeom_SurfaceGeom_GeometryStandard_Transient

The abstract class Curve describes the common behavior of curves in 3D space. The Geom package provides numerous concrete classes of derived curves, including lines, circles, conics, Bezier or BSpline curves, etc. The main characteristic of these curves is that they are parameterized. The Geom_Curve class shows:

how to work with the parametric equation of a curve in order to calculate the point of parameter u, together with the vector tangent and the derivative vectors of order 2, 3,..., N at this point;
how to obtain general information about the curve (for example, level of continuity, closed characteristics, periodicity, bounds of the parameter field);
how the parameter changes when a geometric transformation is applied to the curve or when the orientation of the curve is inverted. All curves must have a geometric continuity: a curve is at least "C0". Generally, this property is checked at the time of construction or when the curve is edited. Where this is not the case, the documentation states so explicitly. Warning The Geom package does not prevent the construction of curves with null length or curves which self-intersect.

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(24)

Reverse(): void
Changes the direction of parametrization of <me>. The "FirstParameter" and the "LastParameter" are not changed but the orientation of the curve is modified. If the curve is bounded the StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve.
ReversedParameter(U: number): number
Returns the parameter on the reversed curve for the point of parameter U on <me>.
me->Reversed()->Value(me->ReversedParameter(U))
is the same point as
me->Value(U)
Parameters (1)
- U
TransformedParameter(U: number, T: gp_Trsf): number
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
me->Transformed(T)->Value(me->TransformedParameter(U,T))
is the same point as
me->Value(U).Transformed(T)
This methods returns
It can be redefined. For example on the Line.
Parameters (2)
- U
- T
ParametricTransformation(T: gp_Trsf): number
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)->Value(U * ParametricTransformation(T))
is the same point as
Value(U).Transformed(T)
This methods returns 1.
It can be redefined. For example on the Line.
Parameters (1)
- T
Reversed(): Geom_Curve
Returns a copy of <me> reversed.
FirstParameter(): number
Returns the value of the first parameter. Warnings : It can be RealFirst from package Standard if the curve is infinite.
LastParameter(): number
Returns the value of the last parameter. Warnings : It can be RealLast from package Standard if the curve is infinite.
IsClosed(): boolean
Returns true if the curve is closed. Some curves such as circle are always closed, others such as line are never closed (by definition). Some Curves such as OffsetCurve can be closed or not. These curves are considered as closed if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp which is a fixed criterion independent of the application.
IsPeriodic(): boolean
Is the parametrization of the curve periodic ? It is possible only if the curve is closed and if the following relation is satisfied : for each parametric value U the distance between the point P(u) and the point P (u + T) is lower or equal to Resolution from package gp, T is the period and must be a constant. There are three possibilities : . the curve is never periodic by definition (SegmentLine) . the curve is always periodic by definition (Circle) . the curve can be defined as periodic (BSpline). In this case a function SetPeriodic allows you to give the shape of the curve.
The general rule for this case is : if a curve can be periodic or not the default periodicity set is non periodic and you have to turn (explicitly) the curve into a periodic curve if you want the curve to be periodic.
Period(): number
Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic.
Continuity(): GeomAbs_Shape
It is the global continuity of the curve C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, G1 : tangency continuity all along the Curve, G2 : curvature continuity all along the Curve, CN : the order of continuity is infinite.
IsCN(N: number): boolean
Returns true if the degree of continuity of this curve is at least N. Exceptions - Standard_RangeError if N is less than 0.
Parameters (1)
- N
EvalD0(U: number): gp_Pnt
Computes the point of parameter U. Raises an exception on failure (e.g. OffsetCurve at singular point).
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Computes the point and first derivative at parameter U. Raises an exception if the curve continuity is not C1.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Computes the point and first two derivatives at parameter U. Raises an exception if the curve continuity is not C2.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Computes the point and first three derivatives at parameter U. Raises an exception if the curve continuity is not C3.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
Computes the Nth derivative at parameter U. Raises an exception if the curve continuity is not CN, or N < 1.
Parameters (2)
- U
- N
D0(U: number, P: gp_Pnt): void
Returns in P the point of parameter U.
Parameters (2)
- U
- P —
  Mutated in place; read the updated value from this argument after the call.
D1(U: number, P: gp_Pnt, V1: gp_Vec): void
Returns the point P of parameter U and the first derivative V1.
Parameters (3)
- U
- P —
  Mutated in place; read the updated value from this argument after the call.
- V1 —
  Mutated in place; read the updated value from this argument after the call.
D2(U: number, P: gp_Pnt, V1: gp_Vec, V2: gp_Vec): void
Returns the point P of parameter U, the first and second derivatives V1 and V2.
Parameters (4)
- U
- P —
  Mutated in place; read the updated value from this argument after the call.
- V1 —
  Mutated in place; read the updated value from this argument after the call.
- V2 —
  Mutated in place; read the updated value from this argument after the call.
D3(U: number, P: gp_Pnt, V1: gp_Vec, V2: gp_Vec, V3: gp_Vec): void
Returns the point P of parameter U, the first, the second and the third derivative.
Parameters (5)
- U
- P —
  Mutated in place; read the updated value from this argument after the call.
- V1 —
  Mutated in place; read the updated value from this argument after the call.
- V2 —
  Mutated in place; read the updated value from this argument after the call.
- V3 —
  Mutated in place; read the updated value from this argument after the call.
DN(U: number, N: number): gp_Vec
The returned vector gives the value of the derivative for the order of derivation N.
Parameters (2)
- U
- N
Value(U: number): gp_Pnt
Computes the point of parameter U on <me>.
Parameters (1)
- U
DynamicType(): Standard_Type

Geom_CylindricalSurface

This class defines the infinite cylindrical surface.
Every cylindrical surface is set by the following equation:

where R is cylinder radius.
The local coordinate system of the CylindricalSurface is defined with an axis placement (see class ElementarySurface).
The "ZAxis" is the symmetry axis of the CylindricalSurface, it gives the direction of increasing parametric value V.
The parametrization range is :

The "XAxis" and the "YAxis" define the placement plane of the surface (Z = 0, and parametric value V = 0) perpendicular to the symmetry axis. The "XAxis" defines the origin of the parameter U = 0. The trigonometric sense gives the positive orientation for the parameter U.
When you create a CylindricalSurface the U and V directions of parametrization are such that at each point of the surface the normal is oriented towards the "outside region".
The methods UReverse VReverse change the orientation of the surface.

Constructors(2)

constructor(C: gp_Cylinder): Geom_CylindricalSurface
Creates a CylindricalSurface from a non transient gp_Cylinder.
Parameters (1)
- C
constructor(A3: gp_Ax3, Radius: number): Geom_CylindricalSurface
A3 defines the local coordinate system of the cylindrical surface. The "ZDirection" of A3 defines the direction of the surface's axis of symmetry. At the creation the parametrization of the surface is defined such that the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface. Warnings: It is not forbidden to create a cylindrical surface with Radius = 0.0 Raised if Radius < 0.0.
Parameters (2)
- A3
- Radius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(24)

SetCylinder(C: gp_Cylinder): void
Set <me> so that <me> has the same geometric properties as C.
Parameters (1)
- C
SetRadius(R: number): void
Changes the radius of the cylinder. Raised if R < 0.0.
Parameters (1)
- R
Cylinder(): gp_Cylinder
returns a non transient cylinder with the same geometric properties as <me>.
UReversedParameter(U: number): number
Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.
Parameters (1)
- U
VReversedParameter(V: number): number
Return the parameter on the Vreversed surface for the point of parameter V on <me>. Return -V.
Parameters (1)
- V
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method multiplies V by T.ScaleFactor()
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method returns a scale centered on the U axis with T.ScaleFactor
Parameters (1)
- T
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
The CylindricalSurface is infinite in the V direction so V1 = Realfirst, V2 = RealLast from package Standard. U1 = 0 and U2 = 2*PI.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Coefficients(A1: number, A2: number, A3: number, B1: number, B2: number, B3: number, C1: number, C2: number, C3: number, D: number): { A1: number; A2: number; A3: number; B1: number; B2: number; B3: number; C1: number; C2: number; C3: number; D: number }
Returns the coefficients of the implicit equation of the quadric in the absolute cartesian coordinate system : These coefficients are normalized.
A1.X**2+A2.Y**2+A3.Z**2+2.(B1.X.Y+B2.X.Z+B3.Y.Z)+2.(C1.X+C2.Y+C3.Z)+D=0.0
A1.X**2+A2.Y**2+A3.Z**2+2.(B1.X.Y+B2.X.Z+B3.Y.Z)+2.(C1.X+C2.Y+C3.Z)+D=0.0
Parameters (10)
- A1
- A2
- A3
- B1
- B2
- B3
- C1
- C2
- C3
- D
Returns
A result object with fields:
- A1: updated value from the call.
- A2: updated value from the call.
- A3: updated value from the call.
- B1: updated value from the call.
- B2: updated value from the call.
- B3: updated value from the call.
- C1: updated value from the call.
- C2: updated value from the call.
- C3: updated value from the call.
- D: updated value from the call.
Radius(): number
Returns the radius of this cylinder.
IsUClosed(): boolean
Returns True.
IsVClosed(): boolean
Returns False.
IsUPeriodic(): boolean
Returns True.
IsVPeriodic(): boolean
Returns False.
UIso(U: number): Geom_Curve
The UIso curve is a Line. The location point of this line is on the placement plane (XAxis, YAxis) of the surface. This line is parallel to the axis of symmetry of the surface.
Parameters (1)
- U
VIso(V: number): Geom_Curve
The VIso curve is a circle. The start point of this circle (U = 0) is defined with the "XAxis" of the surface. The center of the circle is on the symmetry axis.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on the surface. P (U, V) = Loc + Radius * (cos (U) * XDir + sin (U) * YDir) + V * ZDir where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the current point and the first derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the current point, the first and the second derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the current point, the first, the second and the third derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this cylinder.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this cylinder.
DynamicType(): Standard_Type

Geom_Direction

Geom_VectorGeom_GeometryStandard_Transient

The class Direction specifies a vector that is never null. It is a unit vector.

Constructors(2)

constructor(V: gp_Dir): Geom_Direction
Creates a transient copy of <me>.
Parameters (1)
- V
constructor(X: number, Y: number, Z: number): Geom_Direction
Creates a unit vector with it 3 cartesian coordinates.
Raised if std::sqrt( XX + YY + Z*Z) <= Resolution from gp.
Parameters (3)
- X
- Y
- Z

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(15)

SetCoord(X: number, Y: number, Z: number): void
Sets <me> to X,Y,Z coordinates.
Raised if std::sqrt( XX + YY + Z*Z) <= Resolution from gp.
Parameters (3)
- X
- Y
- Z
SetDir(V: gp_Dir): void
Converts the gp_Dir unit vector V into this unit vector.
Parameters (1)
- V
SetX(X: number): void
Changes the X coordinate of <me>.
Raised if std::sqrt( XX + YY + Z*Z) <= Resolution from gp.
Parameters (1)
- X
SetY(Y: number): void
Changes the Y coordinate of <me>.
Raised if std::sqrt( XX + YY + Z*Z) <= Resolution from gp.
Parameters (1)
- Y
SetZ(Z: number): void
Changes the Z coordinate of <me>.
Raised if std::sqrt( XX + YY + Z*Z) <= Resolution from gp.
Parameters (1)
- Z
Dir(): gp_Dir
Returns the non transient direction with the same coordinates as <me>.
Magnitude(): number
returns 1.0 which is the magnitude of any unit vector.
SquareMagnitude(): number
returns 1.0 which is the square magnitude of any unit vector.
Cross(Other: Geom_Vector): void
Computes the cross product between <me> and <Other>.
Raised if the two vectors are parallel because it is not possible to have a direction with null length.
Parameters (1)
- Other
CrossCross(V1: Geom_Vector, V2: Geom_Vector): void
Computes the triple vector product <me> ^(V1 ^ V2).
Raised if V1 and V2 are parallel or <me> and (V1 ^ V2) are parallel
Parameters (2)
- V1
- V2
Crossed(Other: Geom_Vector): Geom_Vector
Computes the cross product between <me> and <Other>. A new direction is returned.
Raised if the two vectors are parallel because it is not possible to have a direction with null length.
Parameters (1)
- Other
CrossCrossed(V1: Geom_Vector, V2: Geom_Vector): Geom_Vector
Computes the triple vector product <me> ^(V1 ^ V2).
Raised if V1 and V2 are parallel or <me> and (V1 ^ V2) are parallel
Parameters (2)
- V1
- V2
Transform(T: gp_Trsf): void
Applies the transformation T to this unit vector, then normalizes it.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this unit vector.
DynamicType(): Standard_Type

Geom_ElementarySurface

Geom_ConicGeom_CurveGeom_GeometryStandard_Transient

Describes the common behavior of surfaces which have a simple parametric equation in a local coordinate system. The Geom package provides several implementations of concrete elementary surfaces:

the plane, and
four simple surfaces of revolution: the cylinder, the cone, the sphere and the torus. An elementary surface inherits the common behavior of Geom_Surface surfaces.
Furthermore, it is located in 3D space by a coordinate system (a gp_Ax3 object) which is also its local coordinate system.
Any elementary surface is oriented, i.e. the normal vector is always defined, and gives the same orientation to the surface, at any point on the surface. In topology this property is referred to as the "outside region of the surface". This orientation is related to the two parametric directions of the surface.
Rotation of a surface around the "main Axis" of its coordinate system, in the trigonometric sense given by the "X Direction" and the "Y Direction" of the coordinate system, defines the u parametric direction of that elementary surface of revolution. This is the default construction mode.
It is also possible, however, to change the orientation of a surface by reversing one of the two parametric directions: use the UReverse or VReverse functions to change the orientation of the normal at any point on the surface. Warning The local coordinate system of an elementary surface is not necessarily direct:
if it is direct, the trigonometric sense defined by its "main Direction" is the same as the trigonometric sense defined by its two vectors "X Direction" and "Y Direction": "main Direction" = "X Direction" ^ "Y Direction"
if it is indirect, the two definitions of trigonometric sense are opposite: "main Direction" = - "X Direction" ^ "Y Direction"

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(14)

SetAxis(theA1: gp_Ax1): void
Changes the main axis (ZAxis) of the elementary surface.
Raised if the direction of A1 is parallel to the XAxis of the coordinate system of the surface.
Parameters (1)
- theA1
SetLocation(theLoc: gp_Pnt): void
Changes the location of the local coordinates system of the surface.
Parameters (1)
- theLoc
SetPosition(theAx3: gp_Ax3): void
Changes the local coordinates system of the surface.
Parameters (1)
- theAx3
Axis(): gp_Ax1
Returns the main axis of the surface (ZAxis).
Location(): gp_Pnt
Returns the location point of the local coordinate system of the surface.
Position(): gp_Ax3
Returns the local coordinates system of the surface.
UReverse(): void
Reverses the U parametric direction of the surface.
UReversedParameter(U: number): number
Return the parameter on the Ureversed surface for the point of parameter U on <me>.
me->UReversed()->Value(me->UReversedParameter(U),V) is the same point as me->Value(U,V)
Parameters (1)
- U
VReverse(): void
Reverses the V parametric direction of the surface.
VReversedParameter(V: number): number
Return the parameter on the Vreversed surface for the point of parameter V on <me>.
me->VReversed()->Value(U,me->VReversedParameter(V)) is the same point as me->Value(U,V)
Parameters (1)
- V
Continuity(): GeomAbs_Shape
Returns GeomAbs_CN, the global continuity of any elementary surface.
IsCNu(N: number): boolean
Returns True.
Parameters (1)
- N
IsCNv(N: number): boolean
Returns True.
Parameters (1)
- N
DynamicType(): Standard_Type

Geom_Ellipse

Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where:

the origin is the center of the ellipse,
the "X Direction" defines the major axis, and
the "Y Direction" defines the minor axis. The origin, "X Direction" and "Y Direction" of this coordinate system define the plane of the ellipse. The coordinate system is the local coordinate system of the ellipse. The "main Direction" of this coordinate system is the vector normal to the plane of the ellipse. The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the ellipse.
The "main Direction" of the local coordinate system gives an explicit orientation to the ellipse (definition of the trigonometric sense), determining the direction in which the parameter increases along the ellipse. The Geom_Ellipse ellipse is parameterized by an angle: P(U) = O + MajorRad*std::cos(U)XDir + MinorRadSin(U)*YDir where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
MajorRad and MinorRad are the major and minor radii of the ellipse. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the ellipse. An ellipse is a closed and periodic curve. The period is 2.*Pi and the parameter range is [ 0, 2.*Pi [.

Constructors(2)

constructor(E: gp_Elips): Geom_Ellipse
Constructs an ellipse by conversion of the gp_Elips ellipse E.
Parameters (1)
- E
constructor(A2: gp_Ax2, MajorRadius: number, MinorRadius: number): Geom_Ellipse
Constructs an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the ellipse and defines its orientation in 3D space such that:
- the center of the ellipse is the origin of A2,
- the "X Direction" of A2 defines the major axis of the ellipse, i.e. the major radius MajorRadius is measured along this axis,
- the "Y Direction" of A2 defines the minor axis of the ellipse, i.e. the minor radius MinorRadius is measured along this axis,
- A2 is the local coordinate system of the ellipse. Exceptions Standard_ConstructionError if:
- MajorRadius is less than MinorRadius, or
- MinorRadius is less than 0. Warning The Geom package does not prevent the construction of an ellipse where MajorRadius and MinorRadius are equal.
Parameters (3)
- A2
- MajorRadius
- MinorRadius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(26)

SetElips(E: gp_Elips): void
Converts the gp_Elips ellipse E into this ellipse.
Parameters (1)
- E
SetMajorRadius(MajorRadius: number): void
Assigns a value to the major radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius.
Parameters (1)
- MajorRadius
SetMinorRadius(MinorRadius: number): void
Assigns a value to the minor radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius or if MinorRadius < 0.
Parameters (1)
- MinorRadius
Elips(): gp_Elips
returns the non transient ellipse from gp with the same
ReversedParameter(U: number): number
Computes the parameter on the reversed ellipse for the point of parameter U on this ellipse. For an ellipse, the returned value is: 2.*Pi - U.
Parameters (1)
- U
Directrix1(): gp_Ax1
This directrix is the line normal to the XAxis of the ellipse in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the ellipse, where e is the eccentricity of the ellipse. This line is parallel to the "YAxis". The intersection point between directrix1 and the "XAxis" is the "Location" point of the directrix1. This point is on the positive side of the "XAxis". Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle).
Directrix2(): gp_Ax1
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse.
Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle).
Eccentricity(): number
Returns the eccentricity of the ellipse between 0.0 and 1.0 If f is the distance between the center of the ellipse and the Focus1 then the eccentricity e = f / MajorRadius. Returns 0 if MajorRadius = 0.
Focal(): number
Computes the focal distance. It is the distance between the the two focus of the ellipse.
Focus1(): gp_Pnt
Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse.
Focus2(): gp_Pnt
Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse.
MajorRadius(): number
Returns the major radius of this ellipse.
MinorRadius(): number
Returns the minor radius of this ellipse.
Parameter(): number
Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0.
FirstParameter(): number
Returns the value of the first parameter of this ellipse. This is respectively:
- 0.0, which gives the start point of this ellipse, or The start point and end point of an ellipse are coincident.
LastParameter(): number
Returns the value of the last parameter of this ellipse. This is respectively:
- 2.*Pi, which gives the end point of this ellipse. The start point and end point of an ellipse are coincident.
IsClosed(): boolean
return True.
IsPeriodic(): boolean
return True.
EvalD0(U: number): gp_Pnt
Returns the point of parameter U. P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir where C is the center of the ellipse , XDir the direction of the "XAxis" and "YDir" the "YAxis" of the ellipse.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Returns the point of parameter U and the first derivative.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Returns the point of parameter U and the first and second derivatives.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Returns the point of parameter U, the first, second and third derivatives.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
For the point of parameter U of this ellipse, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.
Parameters (2)
- U
- N
Transform(T: gp_Trsf): void
Applies the transformation T to this ellipse.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this ellipse.
DynamicType(): Standard_Type

Geom_Geometry

Standard_Transient

The abstract class Geometry for 3D space is the root class of all geometric objects from the Geom package. It describes the common behavior of these objects when:

applying geometric transformations to objects, and
constructing objects by geometric transformation (including copying).
Warning Only transformations which do not modify the nature of the geometry can be applied to Geom objects: this is the case with translations, rotations, symmetries and scales; this is also the case with gp_Trsf composite transformations which are used to define the geometric transformations applied using the Transform or Transformed functions.
Note: Geometry defines the "prototype" of the abstract method Transform which is defined for each concrete type of derived object. All other transformations are implemented using the Transform method.

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(18)

Mirror(P: gp_Pnt): void
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry.
Parameters (1)
- P
Mirror(A1: gp_Ax1): void
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.
Parameters (1)
- A1
Mirror(A2: gp_Ax2): void
Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection).
Parameters (1)
- A2
Rotate(A1: gp_Ax1, Ang: number): void
Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.
Parameters (2)
- A1
- Ang
Scale(P: gp_Pnt, S: number): void
Scales a Geometry. S is the scaling value.
Parameters (2)
- P
- S
Translate(V: gp_Vec): void
Translates a Geometry. V is the vector of the translation.
Parameters (1)
- V
Translate(P1: gp_Pnt, P2: gp_Pnt): void
Translates a Geometry from the point P1 to the point P2.
Parameters (2)
- P1
- P2
Transform(T: gp_Trsf): void
Transformation of a geometric object. This transformation can be a translation, a rotation, a symmetry, a scaling or a complex transformation obtained by combination of the previous elementaries transformations. (see class Transformation of the package Geom).
Parameters (1)
- T
Mirrored(P: gp_Pnt): Geom_Geometry
Parameters (1)
- P
Mirrored(A1: gp_Ax1): Geom_Geometry
Parameters (1)
- A1
Mirrored(A2: gp_Ax2): Geom_Geometry
Parameters (1)
- A2
Rotated(A1: gp_Ax1, Ang: number): Geom_Geometry
Parameters (2)
- A1
- Ang
Scaled(P: gp_Pnt, S: number): Geom_Geometry
Parameters (2)
- P
- S
Transformed(T: gp_Trsf): Geom_Geometry
Parameters (1)
- T
Translated(V: gp_Vec): Geom_Geometry
Parameters (1)
- V
Translated(P1: gp_Pnt, P2: gp_Pnt): Geom_Geometry
Parameters (2)
- P1
- P2
Copy(): Geom_Geometry
Creates a new object which is a copy of this geometric object.
DynamicType(): Standard_Type

Geom_Hyperbola

Geom_ConicGeom_CurveGeom_GeometryStandard_Transient

Describes a branch of a hyperbola in 3D space. A hyperbola is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where:

the origin is the center of the hyperbola,
the "X Direction" defines the major axis, and
the "Y Direction" defines the minor axis. The origin, "X Direction" and "Y Direction" of this coordinate system define the plane of the hyperbola. The coordinate system is the local coordinate system of the hyperbola. The branch of the hyperbola described is the one located on the positive side of the major axis. The "main Direction" of the local coordinate system is a vector normal to the plane of the hyperbola.
The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the hyperbola.
The "main Direction" of the local coordinate system gives an explicit orientation to the hyperbola, determining the direction in which the parameter increases along the hyperbola.
The Geom_Hyperbola hyperbola is parameterized as follows: P(U) = O + MajRad*std::cosh(U)XDir + MinRadstd::sinh(U)*YDir, where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
MajRad and MinRad are the major and minor radii of the hyperbola. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the hyperbola. The parameter range is ] -infinite, +infinite [.
The following diagram illustrates the respective positions, in the plane of the hyperbola, of the three branches of hyperbolas constructed using the functions OtherBranch, ConjugateBranch1 and ConjugateBranch2: Defines the main branch of an hyperbola. ^YAxis | FirstConjugateBranch | Other | Main -------------------- C ------------------------------>XAxis Branch | Branch | SecondConjugateBranch | Warning The value of the major radius (on the major axis) can be less than the value of the minor radius (on the minor axis).

Constructors(2)

constructor(H: gp_Hypr): Geom_Hyperbola
Constructs a hyperbola by conversion of the gp_Hypr hyperbola H.
Parameters (1)
- H
constructor(A2: gp_Ax2, MajorRadius: number, MinorRadius: number): Geom_Hyperbola
Constructs a hyperbola defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the hyperbola and defines its orientation in 3D space such that:
- the center of the hyperbola is the origin of A2,
- the "X Direction" of A2 defines the major axis of the hyperbola, i.e. the major radius MajorRadius is measured along this axis,
- the "Y Direction" of A2 defines the minor axis of the hyperbola, i.e. the minor radius MinorRadius is measured along this axis,
- A2 is the local coordinate system of the hyperbola. Exceptions Standard_ConstructionError if:
- MajorRadius is less than 0.0,
- MinorRadius is less than 0.0.
Parameters (3)
- A2
- MajorRadius
- MinorRadius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(31)

SetHypr(H: gp_Hypr): void
Converts the gp_Hypr hyperbola H into this hyperbola.
Parameters (1)
- H
SetMajorRadius(MajorRadius: number): void
Assigns a value to the major radius of this hyperbola. Exceptions Standard_ConstructionError if:
- MajorRadius is less than 0.0, or
- MinorRadius is less than 0.0.Raised if MajorRadius < 0.0
Parameters (1)
- MajorRadius
SetMinorRadius(MinorRadius: number): void
Assigns a value to the minor radius of this hyperbola. Exceptions Standard_ConstructionError if:
- MajorRadius is less than 0.0, or
- MinorRadius is less than 0.0.Raised if MajorRadius < 0.0
Parameters (1)
- MinorRadius
Hypr(): gp_Hypr
returns the non transient parabola from gp with the same geometric properties as <me>.
ReversedParameter(U: number): number
Computes the parameter on the reversed hyperbola, for the point of parameter U on this hyperbola. For a hyperbola, the returned value is: -U.
Parameters (1)
- U
FirstParameter(): number
Returns RealFirst from Standard.
LastParameter(): number
returns RealLast from Standard.
IsClosed(): boolean
Returns False.
IsPeriodic(): boolean
return False for an hyperbola.
Asymptote1(): gp_Ax1
In the local coordinate system of the hyperbola the equation of the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = (B/A)*X. Raises ConstructionError if MajorRadius = 0.0.
Asymptote2(): gp_Ax1
In the local coordinate system of the hyperbola the equation of the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X. Raises ConstructionError if MajorRadius = 0.0.
ConjugateBranch1(): gp_Hypr
This branch of hyperbola is on the positive side of the YAxis of <me>.
ConjugateBranch2(): gp_Hypr
This branch of hyperbola is on the negative side of the YAxis of <me>. Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola.
Directrix1(): gp_Ax1
This directrix is the line normal to the XAxis of the hyperbola in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the hyperbola, where e is the eccentricity of the hyperbola. This line is parallel to the YAxis. The intersection point between directrix1 and the XAxis is the location point of the directrix1. This point is on the positive side of the XAxis.
Directrix2(): gp_Ax1
This line is obtained by the symmetrical transformation of "directrix1" with respect to the YAxis of the hyperbola.
Eccentricity(): number
Returns the eccentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. raised if MajorRadius = 0.0.
Focal(): number
Computes the focal distance. It is the distance between the two focus of the hyperbola.
Focus1(): gp_Pnt
Returns the first focus of the hyperbola. This focus is on the positive side of the XAxis of the hyperbola.
Focus2(): gp_Pnt
Returns the second focus of the hyperbola. This focus is on the negative side of the XAxis of the hyperbola.
MajorRadius(): number
Returns the major or minor radius of this hyperbola. The major radius is also the distance between the center of the hyperbola and the apex of the main branch (located on the "X Axis" of the hyperbola).
MinorRadius(): number
Returns the major or minor radius of this hyperbola. The minor radius is also the distance between the center of the hyperbola and the apex of a conjugate branch (located on the "Y Axis" of the hyperbola).
OtherBranch(): gp_Hypr
Computes the "other" branch of this hyperbola. This is the symmetrical branch with respect to the center of this hyperbola. Note: The diagram given under the class purpose indicates where the "other" branch is positioned in relation to this branch of the hyperbola.
Parameter(): number
Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. raised if MajorRadius = 0.0.
EvalD0(U: number): gp_Pnt
Returns the point of parameter U. P = C + MajorRadius * std::cosh(U) * XDir + MinorRadius * std::sinh(U) * YDir where C is the center of the hyperbola , XDir the XDirection and YDir the YDirection of the hyperbola's local coordinate system.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Returns the point of parameter U and the first derivative.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Returns the point of parameter U, the first and second derivatives.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Returns the point of parameter U, the first, second and third derivatives.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
Returns the vector corresponding to the derivative for the order of derivation N. Raised if N < 1.
Parameters (2)
- U
- N
Transform(T: gp_Trsf): void
Applies the transformation T to this hyperbola.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this hyperbola.
DynamicType(): Standard_Type

Geom_Line

Describes an infinite line. A line is defined and positioned in space with an axis (gp_Ax1 object) which gives it an origin and a unit vector. The Geom_Line line is parameterized: P (U) = O + U*Dir, where:

P is the point of parameter U,
O is the origin and Dir the unit vector of its positioning axis. The parameter range is ] -infinite, +infinite [. The orientation of the line is given by the unit vector of its positioning axis.

Constructors(3)

constructor(A1: gp_Ax1): Geom_Line
Creates a line located in 3D space with the axis placement A1. The Location of A1 is the origin of the line.
Parameters (1)
- A1
constructor(L: gp_Lin): Geom_Line
Creates a line from a non transient line from package gp.
Parameters (1)
- L
constructor(P: gp_Pnt, V: gp_Dir): Geom_Line
Constructs a line passing through point P and parallel to vector V (P and V are, respectively, the origin and the unit vector of the positioning axis of the line).
Parameters (2)
- P
- V

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(24)

SetLin(L: gp_Lin): void
Set <me> so that <me> has the same geometric properties as L.
Parameters (1)
- L
SetDirection(V: gp_Dir): void
changes the direction of the line.
Parameters (1)
- V
SetLocation(P: gp_Pnt): void
changes the "Location" point (origin) of the line.
Parameters (1)
- P
SetPosition(A1: gp_Ax1): void
changes the "Location" and a the "Direction" of <me>.
Parameters (1)
- A1
Lin(): gp_Lin
Returns non transient line from gp with the same geometric properties as <me>.
Position(): gp_Ax1
Returns the positioning axis of this line; this is also its local coordinate system.
Reverse(): void
Changes the orientation of this line. As a result, the unit vector of the positioning axis of this line is reversed.
ReversedParameter(U: number): number
Computes the parameter on the reversed line for the point of parameter U on this line. For a line, the returned value is -U.
Parameters (1)
- U
FirstParameter(): number
Returns the value of the first parameter of this line. This is double::RealFirst().
LastParameter(): number
Returns the value of the last parameter of this line. This is double::RealLast().
IsClosed(): boolean
returns False
IsPeriodic(): boolean
returns False
Continuity(): GeomAbs_Shape
Returns GeomAbs_CN, which is the global continuity of any line.
IsCN(N: number): boolean
returns True. Raised if N < 0.
Parameters (1)
- N
EvalD0(U: number): gp_Pnt
Returns the point of parameter U. P (U) = O + U * Dir where O is the "Location" point of the line and Dir the direction of the line.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Returns the point of parameter U and the first derivative.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Returns the point of parameter U, the first and second derivatives. The second derivative is a vector with null magnitude for a line.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Returns the point of parameter U, the first, second and third derivatives. The second and third derivatives are vectors with null magnitude for a line.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
Returns the vector corresponding to the derivative for the order of derivation N. Raised if N < 1.
Parameters (2)
- U
- N
Transform(T: gp_Trsf): void
Applies the transformation T to this line.
Parameters (1)
- T
TransformedParameter(U: number, T: gp_Trsf): number
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
me->Transformed(T)->Value(me->TransformedParameter(U,T))
is the same point as
me->Value(U).Transformed(T)
This methods returns * T.ScaleFactor()
Parameters (2)
- U
- T
ParametricTransformation(T: gp_Trsf): number
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)->Value(U * ParametricTransformation(T))
is the same point as
Value(U).Transformed(T)
This methods returns T.ScaleFactor()
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this line.
DynamicType(): Standard_Type

Geom_OffsetCurve

This class implements the basis services for an offset curve in 3D space. The Offset curve in this package can be a self intersecting curve even if the basis curve does not self-intersect. The self intersecting portions are not deleted at the construction time. An offset curve is a curve at constant distance (Offset) from a basis curve in a reference direction V. The offset curve takes its parametrization from the basis curve.
The Offset curve is in the direction of the normal N defined with the cross product T^V, where the vector T is given by the first derivative on the basis curve with non zero length.
The distance offset may be positive or negative to indicate the preferred side of the curve : . distance offset >0 => the curve is in the direction of N . distance offset <0 => the curve is in the direction of - N.
On the Offset curve : Value (U) = BasisCurve.Value(U) + (Offset * (T ^ V)) / ||T ^ V||
At any point the Offset direction V must not be parallel to the vector T and the vector T must not have null length else the offset curve is not defined. So the offset curve has not the same continuity as the basis curve.
Warnings :
In this package we suppose that the continuity of the offset curve is one degree less than the continuity of the basis curve and we don't check that at any point ||T^V|| != 0.0
So to evaluate the curve it is better to check that the offset curve is well defined at any point because an exception could be raised. The check is not done in this package at the creation of the offset curve because the control needs the use of an algorithm which cannot be implemented in this package.
The OffsetCurve is closed if the first point and the last point are the same (The distance between these two points is lower or equal to the Resolution sea package gp) . The OffsetCurve can be closed even if the basis curve is not closed.

Constructors(2)

constructor(theOther: Geom_OffsetCurve): Geom_OffsetCurve
Copy constructor for optimized copying without validation.
Parameters (1)
- theOther —
  the offset curve to copy from
constructor(C: Geom_Curve, Offset: number, V: gp_Dir, isNotCheckC0?: boolean): Geom_OffsetCurve
C is the basis curve, Offset is the distance between <me> and the basis curve at any point. V defines the fixed reference direction (offset direction).
If P is a point on the basis curve and T the first derivative with non zero length at this point, the corresponding point on the offset curve is in the direction of the vector-product N = V ^ T where N is a unitary vector. If isNotCheckC0 = TRUE checking if basis curve has C0-continuity is not made. Warnings : In this package the entities are not shared. The OffsetCurve is built with a copy of the curve C. So when C is modified the OffsetCurve is not modified.
Raised if the basis curve C is not at least C1. Warnings : No check is done to know if ||V^T|| != 0.0 at any point.
Parameters (4)
- C
- Offset
- V
- isNotCheckC0

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(30)

HasEvalRepresentation(): boolean
Returns true if an evaluation representation is attached.
EvalRepresentation(): GeomEval_RepCurveDesc_Base
Returns the current evaluation representation descriptor (may be null).
SetEvalRepresentation(theDesc: GeomEval_RepCurveDesc_Base): void
Sets a new evaluation representation. Validates descriptor data and ensures no circular references.
Parameters (1)
- theDesc
ClearEvalRepresentation(): void
Removes the evaluation representation.
Reverse(): void
Changes the orientation of this offset curve. As a result:
- the basis curve is reversed,
- the start point of the initial curve becomes the end point of the reversed curve,
- the end point of the initial curve becomes the start point of the reversed curve, and
- the first and last parameters are recomputed.
ReversedParameter(U: number): number
Computes the parameter on the reversed curve for the point of parameter U on this offset curve.
Parameters (1)
- U
SetBasisCurve(C: Geom_Curve, isNotCheckC0?: boolean): void
Changes this offset curve by assigning C as the basis curve from which it is built. If isNotCheckC0 = TRUE checking if basis curve has C0-continuity is not made. Exceptions Standard_ConstructionError if the curve C is not at least "C1" continuous.
Parameters (2)
- C
- isNotCheckC0
SetDirection(V: gp_Dir): void
Changes this offset curve by assigning V as the reference vector used to compute the offset direction.
Parameters (1)
- V
SetOffsetValue(D: number): void
Changes this offset curve by assigning D as the offset value.
Parameters (1)
- D
BasisCurve(): Geom_Curve
Returns the basis curve of this offset curve. Note: The basis curve can be an offset curve.
Continuity(): GeomAbs_Shape
Returns the global continuity of this offset curve as a value of the GeomAbs_Shape enumeration. The degree of continuity of this offset curve is equal to the degree of continuity of the basis curve minus 1.
Continuity of the Offset curve : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, G1 : tangency continuity all along the Curve, G2 : curvature continuity all along the Curve, CN : the order of continuity is infinite. Warnings : Returns the continuity of the basis curve - 1. The offset curve must have a unique offset direction defined at any point.
Direction(): gp_Dir
Returns the reference vector of this offset curve. Value and derivatives Warnings : The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction. If T is the first derivative with not null length and V the offset direction the relation ||T(U) ^ V|| != 0 must be satisfied to evaluate the offset curve. No check is done at the creation time and we suppose in this package that the offset curve is well defined.
EvalD0(U: number): gp_Pnt
Warning! this should not be called if the basis curve is not at least C1. Nevertheless if used on portion where the curve is C1, it is OK.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Warning! this should not be called if the continuity of the basis curve is not C2. Nevertheless, it's OK to use it on a portion where the curve is C2.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Warning! this should not be called if the continuity of the basis curve is not C3. Nevertheless, it's OK to use it on a portion where the curve is C3.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Computes the point and first three derivatives at parameter U. Raises an exception if the curve continuity is not C3.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
The returned vector gives the value of the derivative for the order of derivation N.
The following functions compute the value and derivatives on the offset curve and returns the derivatives on the basis curve too. The computation of the value and derivatives on the basis curve are used to evaluate the offset curve
Warning: The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction. Raised if N < 1.
Parameters (2)
- U
- N
FirstParameter(): number
Returns the value of the first parameter of this offset curve. The first parameter corresponds to the start point of the curve. Note: the first and last parameters of this offset curve are also the ones of its basis curve.
LastParameter(): number
Returns the value of the last parameter of this offset curve. The last parameter corresponds to the end point. Note: the first and last parameters of this offset curve are also the ones of its basis curve.
Offset(): number
Returns the offset value of this offset curve.
IsClosed(): boolean
Returns True if the distance between the start point and the end point of the curve is lower or equal to Resolution from package gp.
IsCN(N: number): boolean
Returns true if the degree of continuity of the basis curve of this offset curve is at least N + 1. This method answer True if the continuity of the basis curve is N + 1. We suppose in this class that a normal direction to the basis curve (used to compute the offset curve) is defined at any point on the basis curve. Raised if N < 0.
Parameters (1)
- N
IsPeriodic(): boolean
Returns true if this offset curve is periodic, i.e. if the basis curve of this offset curve is periodic.
Period(): number
Returns the period of this offset curve, i.e. the period of the basis curve of this offset curve. Exceptions Standard_NoSuchObject if the basis curve is not periodic.
Transform(T: gp_Trsf): void
Applies the transformation T to this offset curve. Note: the basis curve is also modified.
Parameters (1)
- T
TransformedParameter(U: number, T: gp_Trsf): number
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>. me->Transformed(T)->Value(me->TransformedParameter(U,T)) is the same point as me->Value(U).Transformed(T) This methods calls the basis curve method.
Parameters (2)
- U
- T
ParametricTransformation(T: gp_Trsf): number
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)->Value(U * ParametricTransformation(T)) is the same point as Value(U).Transformed(T) This methods calls the basis curve method.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this offset curve.
GetBasisCurveContinuity(): GeomAbs_Shape
Returns continuity of the basis curve.
DynamicType(): Standard_Type

Geom_OffsetSurface

Geom_ConicGeom_CurveGeom_GeometryStandard_Transient

Describes an offset surface in 3D space. An offset surface is defined by:

the basis surface to which it is parallel, and
the distance between the offset surface and its basis surface.
A point on the offset surface is built by measuring the offset value along the normal vector at a point on the basis surface.
This normal vector is given by the cross product D1u^D1v, where D1u and D1v are the vectors tangential to the basis surface in the u and v parametric directions at this point. The side of the basis surface on which the offset is measured depends on the sign of the offset value.
A Geom_OffsetSurface surface can be self-intersecting, even if the basis surface does not self-intersect. The self-intersecting portions are not deleted at the time of construction. Warning There must be only one normal vector defined at any point on the basis surface.
This must be verified by the user as no check is made at the time of construction to detect points with multiple possible normal directions (for example, the top of a conical surface).

Constructors(2)

constructor(theOther: Geom_OffsetSurface): Geom_OffsetSurface
Copy constructor for optimized copying without validation.
Parameters (1)
- theOther —
  the offset surface to copy from
constructor(S: Geom_Surface, Offset: number, isNotCheckC0?: boolean): Geom_OffsetSurface
Constructs a surface offset from the basis surface S, where Offset is the distance between the offset surface and the basis surface at any point. A point on the offset surface is built by measuring the offset value along a normal vector at a point on S.
This normal vector is given by the cross product D1u^D1v, where D1u and D1v are the vectors tangential to the basis surface in the u and v parametric directions at this point.
The side of S on which the offset value is measured is indicated by this normal vector if Offset is positive, or is the inverse sense if Offset is negative. If isNotCheckC0 = TRUE checking if basis surface has C0-continuity is not made. Warnings :
- The offset surface is built with a copy of the surface S. Therefore, when S is modified the offset surface is not modified.
- No check is made at the time of construction to detect points on S with multiple possible normal directions. Raised if S is not at least C1. Warnings : No check is done to verify that a unique normal direction is defined at any point of the basis surface S.
Parameters (3)
- S
- Offset
- isNotCheckC0

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(38)

HasEvalRepresentation(): boolean
Returns true if an evaluation representation is attached.
EvalRepresentation(): GeomEval_RepSurfaceDesc_Base
Returns the current evaluation representation descriptor (may be null).
SetEvalRepresentation(theDesc: GeomEval_RepSurfaceDesc_Base): void
Sets a new evaluation representation. Validates descriptor data and ensures no circular references.
Parameters (1)
- theDesc
ClearEvalRepresentation(): void
Removes the evaluation representation.
SetBasisSurface(S: Geom_Surface, isNotCheckC0?: boolean): void
Raised if S is not at least C1. Warnings : No check is done to verify that a unique normal direction is defined at any point of the basis surface S. If isNotCheckC0 = TRUE checking if basis surface has C0-continuity is not made. Exceptions Standard_ConstructionError if the surface S is not at least "C1" continuous.
Parameters (2)
- S
- isNotCheckC0
SetOffsetValue(D: number): void
Changes this offset surface by assigning D as the offset value.
Parameters (1)
- D
Offset(): number
Returns the offset value of this offset surface.
BasisSurface(): Geom_Surface
Returns the basis surface of this offset surface. Note: The basis surface can be an offset surface.
UReverse(): void
Changes the orientation of this offset surface in the u parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed.
UReversedParameter(U: number): number
Computes the u parameter on the modified surface, produced by reversing the u parametric direction of this offset surface, for any point of u parameter U on this offset surface.
Parameters (1)
- U
VReverse(): void
Changes the orientation of this offset surface in the v parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed.
VReversedParameter(V: number): number
Computes the v parameter on the modified surface, produced by reversing the or v parametric direction of this offset surface, for any point of v parameter V on this offset surface.
Parameters (1)
- V
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this offset surface. If the surface is infinite, this function can return:
- double::RealFirst(), or
- double::RealLast().
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Continuity(): GeomAbs_Shape
This method returns the continuity of the basis surface - 1. Continuity of the Offset surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite. Example : If the basis surface is C2 in the V direction and C3 in the U direction Shape = C1.
Warnings : If the basis surface has a unique normal direction defined at any point this method gives the continuity of the offset surface otherwise the effective continuity can be lower than the continuity of the basis surface - 1.
IsCNu(N: number): boolean
This method answer True if the continuity of the basis surface is N + 1 in the U parametric direction. We suppose in this class that a unique normal is defined at any point on the basis surface. Raised if N <0.
Parameters (1)
- N
IsCNv(N: number): boolean
This method answer True if the continuity of the basis surface is N + 1 in the V parametric direction. We suppose in this class that a unique normal is defined at any point on the basis surface. Raised if N <0.
Parameters (1)
- N
IsUClosed(): boolean
Checks whether this offset surface is closed in the u parametric direction. Returns true if, taking uFirst and uLast as the parametric bounds in the u parametric direction, the distance between the points P(uFirst,v) and P(uLast,v) is less than or equal to gp::Resolution() for each value of the parameter v.
IsVClosed(): boolean
Checks whether this offset surface is closed in the u or v parametric direction. Returns true if taking vFirst and vLast as the parametric bounds in the v parametric direction, the distance between the points P(u,vFirst) and P(u,vLast) is less than or equal to gp::Resolution() for each value of the parameter u.
IsUPeriodic(): boolean
Returns true if this offset surface is periodic in the u parametric direction, i.e. if the basis surface of this offset surface is periodic in this direction.
UPeriod(): number
Returns the period of this offset surface in the u parametric direction respectively, i.e. the period of the basis surface of this offset surface in this parametric direction. raises if the surface is not uperiodic.
IsVPeriodic(): boolean
Returns true if this offset surface is periodic in the v parametric direction, i.e. if the basis surface of this offset surface is periodic in this direction.
VPeriod(): number
Returns the period of this offset surface in the v parametric direction respectively, i.e. the period of the basis surface of this offset surface in this parametric direction. raises if the surface is not vperiodic.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve.
The following methods compute value and derivatives.
Warnings An exception is raised if a unique normal vector is not defined on the basis surface for the parametric value (U,V). No check is done at the creation time and we suppose in this package that the offset surface can be defined at any point.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
P(U,V)=Pbasis+Offset*Ndir
P(U,V)=Pbasis+Offset*Ndir
where
Ndir=D1Ubasis^D1Vbasis/||D1Ubasis^D1Vbasis||
Ndir=D1Ubasis^D1Vbasis/||D1Ubasis^D1Vbasis||
is the normal direction of the basis surface. Pbasis, D1Ubasis, D1Vbasis are the point and the first derivatives on the basis surface. If Ndir is undefined this method computes an approached normal direction using the following limited development:
Ndir=N0+DNdir/DU+DNdir/DV+Eps
Ndir=N0+DNdir/DU+DNdir/DV+Eps
with Eps->0 which requires to compute the second derivatives on the basis surface. If the normal direction cannot be approximate for this order of derivation the exception UndefinedValue is raised.
Raised if the continuity of the basis surface is not C1. Raised if the order of derivation required to compute the normal direction is greater than the second order. Raises an exception on failure.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the point and first partial derivatives at (U, V). Raises an exception if the continuity of the basis surface is not C2.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the point and partial derivatives up to 2nd order at (U, V). Raises an exception if the continuity of the basis surface is not C3.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the point and partial derivatives up to 3rd order at (U, V). Raises an exception if the continuity of the basis surface is not C4.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V at (U, V). Raises an exception on failure.
Raised if the continuity of the basis surface is not CNu + 1 in the U direction and CNv + 1 in the V direction. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Warnings: The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this offset surface. Note: the basis surface is also modified.
Parameters (1)
- T
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method calls the basis surface method.
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method calls the basis surface method.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this offset surface.
Surface(): Geom_Surface
returns an equivalent surface of the offset surface when the basis surface is a canonic surface or a rectangular limited surface on canonic surface or if the offset is null.
UOsculatingSurface(U: number, V: number, IsOpposite: boolean): { returnValue: boolean; IsOpposite: boolean; UOsculSurf: Geom_BSplineSurface; [Symbol.dispose](): void }
if true, L is the local osculating surface along U at the point U,V. It means that DL/DU is collinear to DS/DU. If IsOpposite == true these vectors have opposite direction.
Parameters (3)
- U
- V
- IsOpposite
Returns
A result object with fields:
- returnValue: the C++ return value
- IsOpposite: updated value from the call.
- UOsculSurf: owned by the returned envelope.
  Dispose the returned envelope to release owned Handle fields.
VOsculatingSurface(U: number, V: number, IsOpposite: boolean): { returnValue: boolean; IsOpposite: boolean; VOsculSurf: Geom_BSplineSurface; [Symbol.dispose](): void }
if true, L is the local osculating surface along V at the point U,V. It means that DL/DV is collinear to DS/DV. If IsOpposite == true these vectors have opposite direction.
Parameters (3)
- U
- V
- IsOpposite
Returns
A result object with fields:
- returnValue: the C++ return value
- IsOpposite: updated value from the call.
- VOsculSurf: owned by the returned envelope.
  Dispose the returned envelope to release owned Handle fields.
GetBasisSurfContinuity(): GeomAbs_Shape
Returns continuity of the basis surface.
DynamicType(): Standard_Type

Geom_Parabola

Describes a parabola in 3D space. A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in space with a coordinate system (gp_Ax2 object) where:

the origin is the apex of the parabola,
the "X Axis" defines the axis of symmetry; the parabola is on the positive side of this axis,
the origin, "X Direction" and "Y Direction" define the plane of the parabola. This coordinate system is the local coordinate system of the parabola. The "main Direction" of this coordinate system is a vector normal to the plane of the parabola.
The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the parabola.
The "main Direction" of the local coordinate system gives an explicit orientation to the parabola, determining the direction in which the parameter increases along the parabola.
The Geom_Parabola parabola is parameterized as follows: P(U) = O + U*U/(4.*F)XDir + UYDir where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
F is the focal length of the parabola. The parameter of the parabola is therefore its Y coordinate in the local coordinate system, with the "X Axis" of the local coordinate system defining the origin of the parameter. The parameter range is ] -infinite, +infinite [.

Constructors(3)

constructor(Prb: gp_Parab): Geom_Parabola
Creates a parabola from a non transient one.
Parameters (1)
- Prb
constructor(A2: gp_Ax2, Focal: number): Geom_Parabola
Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0.
Parameters (2)
- A2
- Focal
constructor(D: gp_Ax1, F: gp_Pnt): Geom_Parabola
D is the directrix of the parabola and F the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point F, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to D and its location point is the vertex of the parabola. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis.
Parameters (2)
- D
- F

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(23)

SetFocal(Focal: number): void
Assigns the value Focal to the focal distance of this parabola. Exceptions Standard_ConstructionError if Focal is negative.
Parameters (1)
- Focal
SetParab(Prb: gp_Parab): void
Converts the gp_Parab parabola Prb into this parabola.
Parameters (1)
- Prb
Parab(): gp_Parab
Returns the non transient parabola from gp with the same geometric properties as <me>.
ReversedParameter(U: number): number
Computes the parameter on the reversed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is: -U.
Parameters (1)
- U
FirstParameter(): number
Returns the value of the first or last parameter of this parabola. This is, respectively:
- double::RealFirst(), or
- double::RealLast().
LastParameter(): number
Returns the value of the first or last parameter of this parabola. This is, respectively:
- double::RealFirst(), or
- double::RealLast().
IsClosed(): boolean
Returns False.
IsPeriodic(): boolean
Returns False.
Directrix(): gp_Ax1
Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola.
Eccentricity(): number
Returns 1. (which is the eccentricity of any parabola).
Focus(): gp_Pnt
Computes the focus of this parabola. The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola.
Focal(): number
Computes the focal distance of this parabola The focal distance is the distance between the apex and the focus of the parabola.
Parameter(): number
Computes the parameter of this parabola which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y**2 = 2.PX.
EvalD0(U: number): gp_Pnt
Returns the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system.
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Returns the point of parameter U and the first derivative.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Returns the point of parameter U, the first and second derivatives.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Returns the point of parameter U, the first, second and third derivatives.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
For the point of parameter U of this parabola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.
Parameters (2)
- U
- N
Transform(T: gp_Trsf): void
Applies the transformation T to this parabola.
Parameters (1)
- T
TransformedParameter(U: number, T: gp_Trsf): number
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
me->Transformed(T)->Value(me->TransformedParameter(U,T))
is the same point as
me->Value(U).Transformed(T)
This methods returns * T.ScaleFactor()
Parameters (2)
- U
- T
ParametricTransformation(T: gp_Trsf): number
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)->Value(U * ParametricTransformation(T))
is the same point as
Value(U).Transformed(T)
This methods returns T.ScaleFactor()
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this parabola.
DynamicType(): Standard_Type

Geom_Plane

Geom_ElementarySurfaceGeom_SurfaceGeom_GeometryStandard_Transient

Describes a plane in 3D space. A plane is positioned in space by a coordinate system (a gp_Ax3 object) such that the plane is defined by the origin, "X Direction" and "Y Direction" of this coordinate system. This coordinate system is the "local coordinate system" of the plane. The following apply:

Its "X Direction" and "Y Direction" are respectively the u and v parametric directions of the plane.
Its origin is the origin of the u and v parameters (also called the "origin" of the plane).
Its "main Direction" is a vector normal to the plane. This normal vector gives the orientation of the plane only if the local coordinate system is "direct". (The orientation of the plane is always defined by the "X Direction" and the "Y Direction" of its local coordinate system.) The parametric equation of the plane is: P(u,v)=O+u*XDir+v*YDir where O, XDir and YDir are respectively the origin, the "X Direction" and the "Y Direction" of the local coordinate system of the plane. The parametric range of the two parameters u and v is ] -infinity, +infinity [.

Constructors(4)

constructor(A3: gp_Ax3): Geom_Plane
Creates a plane located in 3D space with an axis placement three axis. The "ZDirection" of "A3" is the direction normal to the plane. The "Location" point of "A3" is the origin of the plane. The "XDirection" and "YDirection" of "A3" define the directions of the U isoparametric and V isoparametric curves.
Parameters (1)
- A3
constructor(Pl: gp_Pln): Geom_Plane
Creates a plane from a non transient plane from package gp.
Parameters (1)
- Pl
constructor(P: gp_Pnt, V: gp_Dir): Geom_Plane
P is the "Location" point or origin of the plane. V is the direction normal to the plane.
Parameters (2)
- P
- V
constructor(A: number, B: number, C: number, D: number): Geom_Plane
Creates a plane from its cartesian equation:
Ax+By+Cz+D=0.0
Ax+By+Cz+D=0.0
Raised if std::sqrt(AA + BB + C*C) <= Resolution from gp
Parameters (4)
- A
- B
- C
- D

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(24)

SetPln(Pl: gp_Pln): void
Set <me> so that <me> has the same geometric properties as Pl.
Parameters (1)
- Pl
Pln(): gp_Pln
Converts this plane into a gp_Pln plane.
UReverse(): void
Changes the orientation of this plane in the u (or v) parametric direction. The bounds of the plane are not changed but the given parametric direction is reversed. Hence the orientation of the surface is reversed.
UReversedParameter(U: number): number
Computes the u parameter on the modified plane, produced when reversing the u parametric of this plane, for any point of u parameter U on this plane. In the case of a plane, these methods return - -U.
Parameters (1)
- U
VReverse(): void
Changes the orientation of this plane in the u (or v) parametric direction. The bounds of the plane are not changed but the given parametric direction is reversed. Hence the orientation of the surface is reversed.
VReversedParameter(V: number): number
Computes the v parameter on the modified plane, produced when reversing the v parametric of this plane, for any point of v parameter V on this plane. In the case of a plane, these methods return -V.
Parameters (1)
- V
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method multiplies U and V by T.ScaleFactor()
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method returns a scale centered on the origin with T.ScaleFactor
Parameters (1)
- T
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this plane. Because a plane is an infinite surface, the following is always true:
- U1 = V1 = double::RealFirst()
- U2 = V2 = double::RealLast().
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Coefficients(A: number, B: number, C: number, D: number): { A: number; B: number; C: number; D: number }
Computes the normalized coefficients of the plane's cartesian equation:
Ax+By+Cz+D=0.0
Ax+By+Cz+D=0.0
Parameters (4)
- A
- B
- C
- D
Returns
A result object with fields:
- A: updated value from the call.
- B: updated value from the call.
- C: updated value from the call.
- D: updated value from the call.
IsUClosed(): boolean
return False
IsVClosed(): boolean
return False
IsUPeriodic(): boolean
return False.
IsVPeriodic(): boolean
return False.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve. This is a Line parallel to the YAxis of the plane.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve. This is a Line parallel to the XAxis of the plane.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on <me>.
P=O+U*XDir+V*YDir.
P=O+U*XDir+V*YDir.
where O is the "Location" point of the plane, XDir the "XDirection" and YDir the "YDirection" of the plane's local coordinate system.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the current point and the first derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the current point, the first and the second derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the current point, the first,the second and the third derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this plane.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this plane.
DynamicType(): Standard_Type

Geom_Point

Geom_BoundedSurfaceGeom_SurfaceGeom_GeometryStandard_Transient

The abstract class Point describes the common behavior of geometric points in 3D space. The Geom package also provides the concrete class Geom_CartesianPoint.

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(8)

Coord(X: number, Y: number, Z: number): { X: number; Y: number; Z: number }
returns the Coordinates of <me>.
Parameters (3)
- X
- Y
- Z
Returns
A result object with fields:
- X: updated value from the call.
- Y: updated value from the call.
- Z: updated value from the call.
Pnt(): gp_Pnt
returns a non transient copy of <me>
X(): number
returns the X coordinate of <me>.
Y(): number
returns the Y coordinate of <me>.
Z(): number
returns the Z coordinate of <me>.
Distance(Other: Geom_Point): number
Computes the distance between <me> and <Other>.
Parameters (1)
- Other
SquareDistance(Other: Geom_Point): number
Computes the square distance between <me> and <Other>.
Parameters (1)
- Other
DynamicType(): Standard_Type

Geom_RectangularTrimmedSurface

Describes a portion of a surface (a patch) limited by two values of the u parameter in the u parametric direction, and two values of the v parameter in the v parametric direction. The domain of the trimmed surface must be within the domain of the surface being trimmed. The trimmed surface is defined by:

the basis surface, and
the values (umin, umax) and (vmin, vmax) which limit it in the u and v parametric directions. The trimmed surface is built from a copy of the basis surface. Therefore, when the basis surface is modified the trimmed surface is not changed. Consequently, the trimmed surface does not necessarily have the same orientation as the basis surface. Warning: The case of surface being trimmed is periodic and parametrics values are outside the domain is possible. But, domain of the trimmed surface can be translated by (n X) the period.

Constructors(2)

constructor(S: Geom_Surface, Param1: number, Param2: number, UTrim: boolean, Sense?: boolean): Geom_RectangularTrimmedSurface
The basis surface S is only trim in one parametric direction.
If UTrim = True the surface is trimmed in the U parametric direction else the surface is trimmed in the V parametric direction. In the considered parametric direction the resulting surface is oriented from Param1 to Param2. If S is periodic Sense gives the available part of the surface.
By default the trimmed surface has the same orientation as the basis surface S in the considered parametric direction (Sense = True).
If the basis surface S is closed or periodic in the parametric direction opposite to the trimming direction the trimmed surface has the same characteristics as the surface S in this direction. Warnings : In this package the entities are not shared. The RectangularTrimmedSurface is built with a copy of the surface S.
So when S is modified the RectangularTrimmedSurface is not modified Raised if S is not periodic in the considered parametric direction and Param1 or Param2 are out of the bounds of S. Param1 = Param2.
Parameters (5)
- S
- Param1
- Param2
- UTrim
- Sense
constructor(S: Geom_Surface, U1: number, U2: number, V1: number, V2: number, USense?: boolean, VSense?: boolean): Geom_RectangularTrimmedSurface
The U parametric direction of the surface is oriented from U1 to U2. The V parametric direction of the surface is oriented from V1 to V2. These two directions define the orientation of the surface (normal). If the surface is not periodic USense and VSense are not used for the construction. If the surface S is periodic in one direction USense and VSense give the available part of the surface. By default in this case the surface has the same orientation as the basis surface S. The returned surface is not closed and not periodic. ConstructionError Raised if S is not periodic in the UDirection and U1 or U2 are out of the bounds of S. S is not periodic in the VDirection and V1 or V2 are out of the bounds of S. U1 = U2 or V1 = V2.
Parameters (7)
- S
- U1
- U2
- V1
- V2
- USense
- VSense

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(29)

SetTrim(U1: number, U2: number, V1: number, V2: number, USense: boolean, VSense: boolean): void
Modifies this patch by changing the trim values applied to the original surface The u parametric direction of this patch is oriented from U1 to U2. The v parametric direction of this patch is oriented from V1 to V2.
USense and VSense are used for the construction only if the surface is periodic in the corresponding parametric direction, and define the available part of the surface; by default in this case, this patch has the same orientation as the basis surface. Raised if The BasisSurface is not periodic in the UDirection and U1 or U2 are out of the bounds of the BasisSurface. The BasisSurface is not periodic in the VDirection and V1 or V2 are out of the bounds of the BasisSurface. U1 = U2 or V1 = V2.
Parameters (6)
- U1
- U2
- V1
- V2
- USense
- VSense
SetTrim(Param1: number, Param2: number, UTrim: boolean, Sense: boolean): void
Modifies this patch by changing the trim values applied to the original surface The basis surface is trimmed only in one parametric direction: if UTrim is true, the surface is trimmed in the u parametric direction; if it is false, it is trimmed in the v parametric direction. In the "trimmed" direction, this patch is oriented from Param1 to Param2. If the basis surface is periodic in the "trimmed" direction, Sense defines its available part. By default in this case, this patch has the same orientation as the basis surface in this parametric direction.
If the basis surface is closed or periodic in the other parametric direction (i.e. not the "trimmed" direction), this patch has the same characteristics as the basis surface in that parametric direction. Raised if The BasisSurface is not periodic in the considered direction and Param1 or Param2 are out of the bounds of the BasisSurface. Param1 = Param2.
Parameters (4)
- Param1
- Param2
- UTrim
- Sense
BasisSurface(): Geom_Surface
Returns the Basis surface of <me>.
UReverse(): void
Changes the orientation of this patch in the u parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence the orientation of the surface is reversed.
UReversedParameter(U: number): number
Computes the u parameter on the modified surface, produced by when reversing its u parametric direction, for any point of u parameter U on this patch.
Parameters (1)
- U
VReverse(): void
Changes the orientation of this patch in the v parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence the orientation of the surface is reversed.
VReversedParameter(V: number): number
Computes the v parameter on the modified surface, produced by when reversing its v parametric direction, for any point of v parameter V on this patch.
Parameters (1)
- V
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this patch.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Continuity(): GeomAbs_Shape
Returns the continuity of the surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite.
IsUClosed(): boolean
Returns true if this patch is closed in U: either not trimmed in U and the basis surface is U-closed, or trimmed with a length that is an integer multiple of the U period of a U-periodic basis surface.
IsVClosed(): boolean
Returns true if this patch is closed in V: either not trimmed in V and the basis surface is V-closed, or trimmed with a length that is an integer multiple of the V period of a V-periodic basis surface.
IsCNu(N: number): boolean
Returns true if the order of derivation in the U parametric direction is N. Raised if N < 0.
Parameters (1)
- N
IsCNv(N: number): boolean
Returns true if the order of derivation in the V parametric direction is N. Raised if N < 0.
Parameters (1)
- N
IsUPeriodic(): boolean
Returns true if the basis surface is U-periodic and either not trimmed in U, or the trim spans an integer multiple of the U period.
UPeriod(): number
Returns the period of this patch in the u parametric direction. raises if the surface is not uperiodic.
IsVPeriodic(): boolean
Returns true if the basis surface is V-periodic and either not trimmed in V, or the trim spans an integer multiple of the V period.
VPeriod(): number
Returns the period of this patch in the v parametric direction. raises if the surface is not vperiodic. value and derivatives.
UIso(U: number): Geom_Curve
computes the U isoparametric curve.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point of parameter (U, V) on the surface. Can be raised if the basis surface is an OffsetSurface. Raises an exception on failure.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the point and first partial derivatives at (U, V). The returned derivatives have the same orientation as the derivatives of the basis surface even if the trimmed surface has not the same parametric orientation. Raises an exception if the surface continuity is not C1.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the point and partial derivatives up to 2nd order at (U, V). The returned derivatives have the same orientation as the derivatives of the basis surface even if the trimmed surface has not the same parametric orientation. Raises an exception if the surface continuity is not C2.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the point and partial derivatives up to 3rd order at (U, V). The returned derivatives have the same orientation as the derivatives of the basis surface even if the trimmed surface has not the same parametric orientation. Raises an exception if the surface continuity is not C3.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V at (U, V). The returned derivative has the same orientation as the derivative of the basis surface even if the trimmed surface has not the same parametric orientation. Raises an exception on failure. RangeError Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this patch. Warning As a consequence, the basis surface included in the data structure of this patch is also modified.
Parameters (1)
- T
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method calls the basis surface method.
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method calls the basis surface method.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this patch.
DynamicType(): Standard_Type

Geom_SphericalSurface

Geom_ElementarySurfaceGeom_SurfaceGeom_GeometryStandard_Transient

Describes a sphere. A sphere is defined by its radius, and is positioned in space by a coordinate system (a gp_Ax3 object), the origin of which is the center of the sphere. This coordinate system is the "local coordinate system" of the sphere. The following apply:

Rotation around its "main Axis", in the trigonometric sense given by the "X Direction" and the "Y Direction", defines the u parametric direction.
Its "X Axis" gives the origin for the u parameter.
The "reference meridian" of the sphere is a half-circle, of radius equal to the radius of the sphere. It is located in the plane defined by the origin, "X Direction" and "main Direction", centered on the origin, and positioned on the positive side of the "X Axis".
Rotation around the "Y Axis" gives the v parameter on the reference meridian.
The "X Axis" gives the origin of the v parameter on the reference meridian.
The v parametric direction is oriented by the "main Direction", i.e. when v increases, the Z coordinate increases. (This implies that the "Y Direction" orients the reference meridian only when the local coordinate system is indirect.)
The u isoparametric curve is a half-circle obtained by rotating the reference meridian of the sphere through an angle u around the "main Axis", in the trigonometric sense defined by the "X Direction" and the "Y Direction". The parametric equation of the sphere is: P(u,v) = O + Rcos(v)(cos(u)*XDir + sin(u)YDir)+Rsin(v)*ZDir where:
O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of its local coordinate system, and
R is the radius of the sphere. The parametric range of the two parameters is:
[ 0, 2.*Pi ] for u, and
[ - Pi/2., + Pi/2. ] for v.

Constructors(2)

constructor(S: gp_Sphere): Geom_SphericalSurface
Creates a SphericalSurface from a non persistent Sphere from package gp.
Parameters (1)
- S
constructor(A3: gp_Ax3, Radius: number): Geom_SphericalSurface
A3 is the local coordinate system of the surface. At the creation the parametrization of the surface is defined such as the normal Vector (N = D1U ^ D1V) is directed away from the center of the sphere. The direction of increasing parametric value V is defined by the rotation around the "YDirection" of A2 in the trigonometric sense and the orientation of increasing parametric value U is defined by the rotation around the main direction of A2 in the trigonometric sense. Warnings : It is not forbidden to create a spherical surface with Radius = 0.0 Raised if Radius < 0.0.
Parameters (2)
- A3
- Radius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(24)

SetRadius(R: number): void
Assigns the value R to the radius of this sphere. Exceptions Standard_ConstructionError if R is less than 0.0.
Parameters (1)
- R
SetSphere(S: gp_Sphere): void
Converts the gp_Sphere S into this sphere.
Parameters (1)
- S
Sphere(): gp_Sphere
Returns a non persistent sphere with the same geometric properties as <me>.
UReversedParameter(U: number): number
Computes the u parameter on the modified surface, when reversing its u parametric direction, for any point of u parameter U on this sphere. In the case of a sphere, these functions returns 2.PI - U.
Parameters (1)
- U
VReversedParameter(V: number): number
Computes the v parameter on the modified surface, when reversing its v parametric direction, for any point of v parameter V on this sphere. In the case of a sphere, these functions returns -U.
Parameters (1)
- V
Area(): number
Computes the area of the spherical surface.
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this sphere. For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Coefficients(A1: number, A2: number, A3: number, B1: number, B2: number, B3: number, C1: number, C2: number, C3: number, D: number): { A1: number; A2: number; A3: number; B1: number; B2: number; B3: number; C1: number; C2: number; C3: number; D: number }
Returns the coefficients of the implicit equation of the quadric in the absolute cartesian coordinates system : These coefficients are normalized. A1.X2 + A2.Y2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0.
Parameters (10)
- A1
- A2
- A3
- B1
- B2
- B3
- C1
- C2
- C3
- D
Returns
A result object with fields:
- A1: updated value from the call.
- A2: updated value from the call.
- A3: updated value from the call.
- B1: updated value from the call.
- B2: updated value from the call.
- B3: updated value from the call.
- C1: updated value from the call.
- C2: updated value from the call.
- C3: updated value from the call.
- D: updated value from the call.
Radius(): number
Computes the coefficients of the implicit equation of this quadric in the absolute Cartesian coordinate system: A1.X2 + A2.Y2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0 An implicit normalization is applied (i.e. A1 = A2 = 1. in the local coordinate system of this sphere).
Volume(): number
Computes the volume of the spherical surface.
IsUClosed(): boolean
Returns True.
IsVClosed(): boolean
Returns False.
IsUPeriodic(): boolean
Returns True.
IsVPeriodic(): boolean
Returns False.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve. The U isoparametric curves of the surface are defined by the section of the spherical surface with plane obtained by rotation of the plane (Location, XAxis, ZAxis) around ZAxis. This plane defines the origin of parametrization u. For a SphericalSurface the UIso curve is a Circle. Warnings : The radius of this circle can be zero.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve. The V isoparametric curves of the surface are defined by the section of the spherical surface with plane parallel to the plane (Location, XAxis, YAxis). This plane defines the origin of parametrization V. Be careful if V is close to PI/2 or 3*PI/2 the radius of the circle becomes tiny. It is not forbidden in this toolkit to create circle with radius = 0.0 For a SphericalSurface the VIso curve is a Circle. Warnings : The radius of this circle can be zero.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on the surface. P (U, V) = Loc + Radius * Sin (V) * Zdir + Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir) where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis and ZDir the direction of the ZAxis.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the current point and the first derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the current point, the first and the second derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the current point, the first,the second and the third derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this sphere.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this sphere.
DynamicType(): Standard_Type

Geom_Surface

Geom_SweptSurfaceGeom_SurfaceGeom_GeometryStandard_Transient

Describes the common behavior of surfaces in 3D space. The Geom package provides many implementations of concrete derived surfaces, such as planes, cylinders, cones, spheres and tori, surfaces of linear extrusion, surfaces of revolution, Bezier and BSpline surfaces, and so on. The key characteristic of these surfaces is that they are parameterized. Geom_Surface demonstrates:

how to work with the parametric equation of a surface to compute the point of parameters (u, v), and, at this point, the 1st, 2nd ... Nth derivative;
how to find global information about a surface in each parametric direction (for example, level of continuity, whether the surface is closed, its periodicity, the bounds of the parameters and so on);
how the parameters change when geometric transformations are applied to the surface, or the orientation is modified.
Note that all surfaces must have a geometric continuity, and any surface is at least "C0". Generally, continuity is checked at construction time or when the curve is edited. Where this is not the case, the documentation makes this explicit.
Warning The Geom package does not prevent the construction of surfaces with null areas, or surfaces which self-intersect.

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(32)

UReverse(): void
Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified.
UReversed(): Geom_Surface
Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.
UReversedParameter(U: number): number
Returns the parameter on the Ureversed surface for the point of parameter U on <me>.
me->UReversed()->Value(me->UReversedParameter(U),V)
me->UReversed()->Value(me->UReversedParameter(U),V)
is the same point as
me->Value(U,V)
me->Value(U,V)
Parameters (1)
- U
VReverse(): void
Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified.
VReversed(): Geom_Surface
Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.
VReversedParameter(V: number): number
Returns the parameter on the Vreversed surface for the point of parameter V on <me>.
me->VReversed()->Value(U,me->VReversedParameter(V))
me->VReversed()->Value(U,me->VReversedParameter(V))
is the same point as
me->Value(U,V)
me->Value(U,V)
Parameters (1)
- V
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method does not change and <V>
It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces.
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method returns an identity transformation
It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces.
Parameters (1)
- T
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this surface. If the surface is infinite, this function can return a value equal to Precision::Infinite: instead of double::LastReal.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
IsUClosed(): boolean
Checks whether this surface is closed in the u parametric direction. Returns true if, in the u parametric direction: taking uFirst and uLast as the parametric bounds in the u parametric direction, for each parameter v, the distance between the points P(uFirst, v) and P(uLast, v) is less than or equal to gp::Resolution().
IsVClosed(): boolean
Checks whether this surface is closed in the u parametric direction. Returns true if, in the v parametric direction: taking vFirst and vLast as the parametric bounds in the v parametric direction, for each parameter u, the distance between the points P(u, vFirst) and P(u, vLast) is less than or equal to gp::Resolution().
IsUPeriodic(): boolean
Checks if this surface is periodic in the u parametric direction. Returns true if:
- this surface is closed in the u parametric direction, and
- there is a constant T such that the distance between the points P (u, v) and P (u + T, v) (or the points P (u, v) and P (u, v + T)) is less than or equal to gp::Resolution().
  Note: T is the parametric period in the u parametric direction.
UPeriod(): number
Returns the period of this surface in the u parametric direction. Raises if the surface is not uperiodic.
IsVPeriodic(): boolean
Checks if this surface is periodic in the v parametric direction. Returns true if:
- this surface is closed in the v parametric direction, and
- there is a constant T such that the distance between the points P (u, v) and P (u + T, v) (or the points P (u, v) and P (u, v + T)) is less than or equal to gp::Resolution().
  Note: T is the parametric period in the v parametric direction.
VPeriod(): number
Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve.
Parameters (1)
- V
Continuity(): GeomAbs_Shape
Returns the Global Continuity of the surface in direction U and V :
- C0: only geometric continuity,
- C1: continuity of the first derivative all along the surface,
- C2: continuity of the second derivative all along the surface,
- C3: continuity of the third derivative all along the surface,
- G1: tangency continuity all along the surface,
- G2: curvature continuity all along the surface,
- CN: the order of continuity is infinite.
  Example: If the surface is C1 in the V parametric direction and C2 in the U parametric direction Shape = C1.
IsCNu(N: number): boolean
Returns the order of continuity of the surface in the U parametric direction. Raised if N < 0.
Parameters (1)
- N
IsCNv(N: number): boolean
Returns the order of continuity of the surface in the V parametric direction. Raised if N < 0.
Parameters (1)
- N
EvalD0(U: number, V: number): gp_Pnt
Computes the point of parameter (U, V) on the surface. Raises an exception on failure.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the point and first partial derivatives at (U, V). Raises an exception if the surface continuity is not C1.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the point and partial derivatives up to 2nd order at (U, V). Raises an exception if the surface continuity is not C2.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the point and partial derivatives up to 3rd order at (U, V). Raises an exception if the surface continuity is not C3.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V at the point (U, V). Raises an exception on failure.
Parameters (4)
- U
- V
- Nu
- Nv
D0(U: number, V: number, P: gp_Pnt): void
Computes the point of parameter (U, V).
Parameters (3)
- U
- V
- P —
  Mutated in place; read the updated value from this argument after the call.
D1(U: number, V: number, P: gp_Pnt, D1U: gp_Vec, D1V: gp_Vec): void
Computes the point and first partial derivatives.
Parameters (5)
- U
- V
- P —
  Mutated in place; read the updated value from this argument after the call.
- D1U —
  Mutated in place; read the updated value from this argument after the call.
- D1V —
  Mutated in place; read the updated value from this argument after the call.
D2(U: number, V: number, P: gp_Pnt, D1U: gp_Vec, D1V: gp_Vec, D2U: gp_Vec, D2V: gp_Vec, D2UV: gp_Vec): void
Computes the point and partial derivatives up to 2nd order.
Parameters (8)
- U
- V
- P —
  Mutated in place; read the updated value from this argument after the call.
- D1U —
  Mutated in place; read the updated value from this argument after the call.
- D1V —
  Mutated in place; read the updated value from this argument after the call.
- D2U —
  Mutated in place; read the updated value from this argument after the call.
- D2V —
  Mutated in place; read the updated value from this argument after the call.
- D2UV —
  Mutated in place; read the updated value from this argument after the call.
D3(U: number, V: number, P: gp_Pnt, D1U: gp_Vec, D1V: gp_Vec, D2U: gp_Vec, D2V: gp_Vec, D2UV: gp_Vec, D3U: gp_Vec, D3V: gp_Vec, D3UUV: gp_Vec, D3UVV: gp_Vec): void
Computes the point and partial derivatives up to 3rd order.
Parameters (12)
- U
- V
- P —
  Mutated in place; read the updated value from this argument after the call.
- D1U —
  Mutated in place; read the updated value from this argument after the call.
- D1V —
  Mutated in place; read the updated value from this argument after the call.
- D2U —
  Mutated in place; read the updated value from this argument after the call.
- D2V —
  Mutated in place; read the updated value from this argument after the call.
- D2UV —
  Mutated in place; read the updated value from this argument after the call.
- D3U —
  Mutated in place; read the updated value from this argument after the call.
- D3V —
  Mutated in place; read the updated value from this argument after the call.
- D3UUV —
  Mutated in place; read the updated value from this argument after the call.
- D3UVV —
  Mutated in place; read the updated value from this argument after the call.
DN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V.
Parameters (4)
- U
- V
- Nu
- Nv
Value(U: number, V: number): gp_Pnt
Computes the point of parameter (U, V) on the surface.
Parameters (2)
- U
- V
DynamicType(): Standard_Type

Geom_SurfaceOfLinearExtrusion

Describes a surface of linear extrusion ("extruded surface"), e.g. a generalized cylinder.
Such a surface is obtained by sweeping a curve (called the "extruded curve" or "basis") in a given direction (referred to as the "direction of extrusion" and defined by a unit vector). The u parameter is along the extruded curve. The v parameter is along the direction of extrusion. The parameter range for the u parameter is defined by the reference curve. The parameter range for the v parameter is ] - infinity, + infinity [. The position of the curve gives the origin of the v parameter. The surface is "CN" in the v parametric direction. The form of a surface of linear extrusion is generally a ruled surface (GeomAbs_RuledForm). It can be:

a cylindrical surface, if the extruded curve is a circle, or a trimmed circle, with an axis parallel to the direction of extrusion (GeomAbs_CylindricalForm), or
a planar surface, if the extruded curve is a line (GeomAbs_PlanarForm). Note: The surface of extrusion is built from a copy of the original basis curve, so the original curve is not modified when the surface is modified. Warning Degenerate surfaces are not detected. A degenerate surface is obtained, for example, when the extruded curve is a line and the direction of extrusion is parallel to that line.

Constructors(1)

constructor(C: Geom_Curve, V: gp_Dir): Geom_SurfaceOfLinearExtrusion
V is the direction of extrusion. C is the extruded curve. The form of a SurfaceOfLinearExtrusion can be : . ruled surface (RuledForm), . a cylindrical surface if the extruded curve is a circle or a trimmed circle (CylindricalForm), . a plane surface if the extruded curve is a Line (PlanarForm). Warnings : Degenerated surface cases are not detected. For example if the curve C is a line and V is parallel to the direction of this line.
Parameters (2)
- C
- V

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(29)

HasEvalRepresentation(): boolean
Returns true if an evaluation representation is attached.
EvalRepresentation(): GeomEval_RepSurfaceDesc_Base
Returns the current evaluation representation descriptor (may be null).
SetEvalRepresentation(theDesc: GeomEval_RepSurfaceDesc_Base): void
Sets a new evaluation representation. Validates descriptor data and ensures no circular references.
Parameters (1)
- theDesc
ClearEvalRepresentation(): void
Removes the evaluation representation.
SetDirection(V: gp_Dir): void
Assigns V as the "direction of extrusion" for this surface of linear extrusion.
Parameters (1)
- V
SetBasisCurve(C: Geom_Curve): void
Modifies this surface of linear extrusion by redefining its "basis curve" (the "extruded curve").
Parameters (1)
- C
UReverse(): void
Changes the orientation of this surface of linear extrusion in the u parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence the orientation of the surface is reversed. In the case of a surface of linear extrusion:
- UReverse reverses the basis curve, and
- VReverse reverses the direction of linear extrusion.
UReversedParameter(U: number): number
Computes the u parameter on the modified surface, produced by reversing its u parametric direction, for any point of u parameter U on this surface of linear extrusion. In the case of an extruded surface:
- UReverseParameter returns the reversed parameter given by the function ReversedParameter called with U on the basis curve,
Parameters (1)
- U
VReverse(): void
Changes the orientation of this surface of linear extrusion in the v parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence the orientation of the surface is reversed. In the case of a surface of linear extrusion:
- UReverse reverses the basis curve, and
- VReverse reverses the direction of linear extrusion.
VReversedParameter(V: number): number
Computes the v parameter on the modified surface, produced by reversing its u v parametric direction, for any point of v parameter V on this surface of linear extrusion. In the case of an extruded surface VReverse returns -V.
Parameters (1)
- V
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this surface of linear extrusion. A surface of linear extrusion is infinite in the v parametric direction, so:
- V1 = double::RealFirst()
- V2 = double::RealLast().
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
IsUClosed(): boolean
IsUClosed returns true if the "basis curve" of this surface of linear extrusion is closed.
IsVClosed(): boolean
IsVClosed always returns false.
IsCNu(N: number): boolean
IsCNu returns true if the degree of continuity for the "basis curve" of this surface of linear extrusion is at least N. Raises RangeError if N < 0.
Parameters (1)
- N
IsCNv(N: number): boolean
IsCNv always returns true.
Parameters (1)
- N
IsUPeriodic(): boolean
IsUPeriodic returns true if the "basis curve" of this surface of linear extrusion is periodic.
IsVPeriodic(): boolean
IsVPeriodic always returns false.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve of this surface of linear extrusion. This is the line parallel to the direction of extrusion, passing through the point of parameter U of the basis curve.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve of this surface of linear extrusion. This curve is obtained by translating the extruded curve in the direction of extrusion, with the magnitude V.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on the surface. The parameter U is the parameter on the extruded curve. The parametrization V is a linear parametrization, and the direction of parametrization is the direction of extrusion. If the point is on the extruded curve, V = 0.0 Raises an exception on failure.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the point and first partial derivatives at (U, V). Raises an exception if the surface continuity is not C1.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the point and partial derivatives up to 2nd order at (U, V). Raises an exception if the surface continuity is not C2.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the point and partial derivatives up to 3rd order at (U, V). Raises an exception if the surface continuity is not C3.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V at (U, V). Raises an exception on failure. Raises RangeError if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this surface of linear extrusion.
Parameters (1)
- T
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method multiplies: U by BasisCurve()->ParametricTransformation(T) V by T.ScaleFactor()
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method returns a scale U by BasisCurve()->ParametricTransformation(T) V by T.ScaleFactor()
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this surface of linear extrusion.
DynamicType(): Standard_Type

Geom_SurfaceOfRevolution

Geom_SweptSurfaceGeom_SurfaceGeom_GeometryStandard_Transient

Describes a surface of revolution (revolved surface).
Such a surface is obtained by rotating a curve (called the "meridian") through a complete revolution about an axis (referred to as the "axis of revolution"). The curve and the axis must be in the same plane (the "reference plane" of the surface). Rotation around the axis of revolution in the trigonometric sense defines the u parametric direction. So the u parameter is an angle, and its origin is given by the position of the meridian on the surface. The parametric range for the u parameter is: [ 0, 2.*Pi ] The v parameter is that of the meridian. Note: A surface of revolution is built from a copy of the original meridian. As a result the original meridian is not modified when the surface is modified. The form of a surface of revolution is typically a general revolution surface (GeomAbs_RevolutionForm). It can be:

a conical surface, if the meridian is a line or a trimmed line (GeomAbs_ConicalForm),
a cylindrical surface, if the meridian is a line or a trimmed line parallel to the axis of revolution (GeomAbs_CylindricalForm),
a planar surface if the meridian is a line or a trimmed line perpendicular to the axis of revolution of the surface (GeomAbs_PlanarForm),
a toroidal surface, if the meridian is a circle or a trimmed circle (GeomAbs_ToroidalForm), or
a spherical surface, if the meridian is a circle, the center of which is located on the axis of the revolved surface (GeomAbs_SphericalForm). Warning Be careful not to construct a surface of revolution where the curve and the axis or revolution are not defined in the same plane. If you do not have a correct configuration, you can correct your initial curve, using a cylindrical projection in the reference plane.

Constructors(1)

constructor(C: Geom_Curve, A1: gp_Ax1): Geom_SurfaceOfRevolution
C : is the meridian or the referenced curve. A1 is the axis of revolution.
The form of a SurfaceOfRevolution can be : . a general revolution surface (RevolutionForm), . a conical surface if the meridian is a line or a trimmed line (ConicalForm), . a cylindrical surface if the meridian is a line or a trimmed line parallel to the revolution axis (CylindricalForm), . a planar surface if the meridian is a line perpendicular to the revolution axis of the surface (PlanarForm). . a spherical surface, . a toroidal surface, . a quadric surface. Warnings : It is not checked that the curve C is planar and that the surface axis is in the plane of the curve. It is not checked that the revolved curve C doesn't self-intersects.
Parameters (2)
- C
- A1

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(34)

HasEvalRepresentation(): boolean
Returns true if an evaluation representation is attached.
EvalRepresentation(): GeomEval_RepSurfaceDesc_Base
Returns the current evaluation representation descriptor (may be null).
SetEvalRepresentation(theDesc: GeomEval_RepSurfaceDesc_Base): void
Sets a new evaluation representation. Validates descriptor data and ensures no circular references.
Parameters (1)
- theDesc
ClearEvalRepresentation(): void
Removes the evaluation representation.
SetAxis(A1: gp_Ax1): void
Changes the axis of revolution. Warnings : It is not checked that the axis is in the plane of the revolved curve.
Parameters (1)
- A1
SetDirection(V: gp_Dir): void
Changes the direction of the revolution axis. Warnings : It is not checked that the axis is in the plane of the revolved curve.
Parameters (1)
- V
SetBasisCurve(C: Geom_Curve): void
Changes the revolved curve of the surface. Warnings : It is not checked that the curve C is planar and that the surface axis is in the plane of the curve. It is not checked that the revolved curve C doesn't self-intersects.
Parameters (1)
- C
SetLocation(P: gp_Pnt): void
Changes the location point of the revolution axis. Warnings : It is not checked that the axis is in the plane of the revolved curve.
Parameters (1)
- P
Axis(): gp_Ax1
Returns the revolution axis of the surface.
Location(): gp_Pnt
Returns the location point of the axis of revolution.
ReferencePlane(): gp_Ax2
Computes the position of the reference plane of the surface defined by the basis curve and the symmetry axis. The location point is the location point of the revolution's axis, the XDirection of the plane is given by the revolution's axis and the orientation of the normal to the plane is given by the sense of revolution.
Raised if the revolved curve is not planar or if the revolved curve and the symmetry axis are not in the same plane or if the maximum of distance between the axis and the revolved curve is lower or equal to Resolution from gp.
UReverse(): void
Changes the orientation of this surface of revolution in the u parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed. Hence the orientation of the surface is reversed. As a consequence:
- UReverse reverses the direction of the axis of revolution of this surface,
UReversedParameter(U: number): number
Computes the u parameter on the modified surface, when reversing its u parametric direction, for any point of u parameter U on this surface of revolution. In the case of a revolved surface:
- UReversedParameter returns 2.*Pi - U
Parameters (1)
- U
VReverse(): void
Changes the orientation of this surface of revolution in the v parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed. Hence the orientation of the surface is reversed. As a consequence:
- VReverse reverses the meridian of this surface of revolution.
VReversedParameter(V: number): number
Computes the v parameter on the modified surface, when reversing its v parametric direction, for any point of v parameter V on this surface of revolution. In the case of a revolved surface:
- VReversedParameter returns the reversed parameter given by the function ReversedParameter called with V on the meridian.
Parameters (1)
- V
TransformParameters(U: number, V: number, T: gp_Trsf): { U: number; V: number }
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me->TransformParameters(U,V,T)
me->TransformParameters(U,V,T)
This method multiplies V by BasisCurve()->ParametricTransformation(T)
Parameters (3)
- U
- V
- T
Returns
A result object with fields:
- U: updated value from the call.
- V: updated value from the call.
ParametricTransformation(T: gp_Trsf): gp_GTrsf2d
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me->Transformed(T)->Value(U',V')
me->Transformed(T)->Value(U',V')
is the same point as
me->Value(U,V).Transformed(T)
me->Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with the 2d transformation returned by
me->ParametricTransformation(T)
me->ParametricTransformation(T)
This method returns a scale centered on the U axis with BasisCurve()->ParametricTransformation(T)
Parameters (1)
- T
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2 , V1 and V2 of this surface. A surface of revolution is always complete, so U1 = 0, U2 = 2*PI.
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
IsUClosed(): boolean
IsUClosed always returns true.
IsVClosed(): boolean
IsVClosed returns true if the meridian of this surface of revolution is closed.
IsCNu(N: number): boolean
IsCNu always returns true.
Parameters (1)
- N
IsCNv(N: number): boolean
IsCNv returns true if the degree of continuity of the meridian of this surface of revolution is at least N. Raised if N < 0.
Parameters (1)
- N
IsUPeriodic(): boolean
Returns True.
IsVPeriodic(): boolean
IsVPeriodic returns true if the meridian of this surface of revolution is periodic.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve of this surface of revolution. It is the curve obtained by rotating the meridian through an angle U about the axis of revolution.
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the U isoparametric curve of this surface of revolution. It is the curve obtained by rotating the meridian through an angle U about the axis of revolution.
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on the surface. U is the angle of the rotation around the revolution axis. The direction of this axis gives the sense of rotation. V is the parameter of the revolved curve. Raises an exception on failure.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the point and first partial derivatives at (U, V). Raises an exception if the surface continuity is not C1.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the point and partial derivatives up to 2nd order at (U, V). Raises an exception if the surface continuity is not C2.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the point and partial derivatives up to 3rd order at (U, V). Raises an exception if the surface continuity is not C3.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in U and Nv in V at (U, V). Raises an exception on failure.
Raised if the continuity of the surface is not CNu in the u direction and CNv in the v direction. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this surface of revolution.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this surface of revolution.
DynamicType(): Standard_Type

Geom_SweptSurface

Geom_ElementarySurfaceGeom_SurfaceGeom_GeometryStandard_Transient

Describes the common behavior for surfaces constructed by sweeping a curve with another curve. The Geom package provides two concrete derived surfaces: surface of revolution (a revolved surface), and surface of linear extrusion (an extruded surface).

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(4)

Continuity(): GeomAbs_Shape
returns the continuity of the surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the surface, C2 : continuity of the second derivative all along the surface, C3 : continuity of the third derivative all along the surface, G1 : tangency continuity all along the surface, G2 : curvature continuity all along the surface, CN : the order of continuity is infinite.
Direction(): gp_Dir
Returns the reference direction of the swept surface. For a surface of revolution it is the direction of the revolution axis, for a surface of linear extrusion it is the direction of extrusion.
BasisCurve(): Geom_Curve
Returns the referenced curve of the surface. For a surface of revolution it is the revolution curve, for a surface of linear extrusion it is the extruded curve.
DynamicType(): Standard_Type

Geom_ToroidalSurface

Describes a torus. A torus is defined by its major and minor radii, and positioned in space with a coordinate system (a gp_Ax3 object) as follows:

The origin is the center of the torus.
The surface is obtained by rotating a circle around the "main Direction". This circle has a radius equal to the minor radius, and is located in the plane defined by the origin, "X Direction" and "main Direction". It is centered on the "X Axis", on its positive side, and positioned at a distance from the origin equal to the major radius. This circle is the "reference circle" of the torus.
The plane defined by the origin, the "X Direction" and the "Y Direction" is called the "reference plane" of the torus. This coordinate system is the "local coordinate system" of the torus. The following apply:
Rotation around its "main Axis", in the trigonometric sense given by "X Direction" and "Y Direction", defines the u parametric direction.
The "X Axis" gives the origin for the u parameter.
Rotation around an axis parallel to the "Y Axis" and passing through the center of the "reference circle" gives the v parameter on the "reference circle".
The "X Axis" gives the origin of the v parameter on the "reference circle".
The v parametric direction is oriented by the inverse of the "main Direction", i.e. near 0, as v increases, the Z coordinate decreases. (This implies that the "Y Direction" orients the reference circle only when the local coordinate system is direct.)
The u isoparametric curve is a circle obtained by rotating the "reference circle" of the torus through an angle u about the "main Axis". The parametric equation of the torus is : P(u, v) = O + (R + r*cos(v)) * (cos(u)*XDir + sin(u)YDir ) + rsin(v)*ZDir, where:
O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of the local coordinate system,
r and R are, respectively, the minor and major radius. The parametric range of the two parameters is:
[ 0, 2.*Pi ] for u
[ 0, 2.*Pi ] for v

Constructors(2)

constructor(T: gp_Torus): Geom_ToroidalSurface
Creates a ToroidalSurface from a non transient Torus from package gp.
Parameters (1)
- T
constructor(A3: gp_Ax3, MajorRadius: number, MinorRadius: number): Geom_ToroidalSurface
A3 is the local coordinate system of the surface. The orientation of increasing V parametric value is defined by the rotation around the main axis (ZAxis) in the trigonometric sense. The parametrization of the surface in the U direction is defined such as the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface. Warnings : It is not forbidden to create a toroidal surface with MajorRadius = MinorRadius = 0.0.
Raised if MinorRadius < 0.0 or if MajorRadius < 0.0
Parameters (3)
- A3
- MajorRadius
- MinorRadius

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(26)

SetMajorRadius(MajorRadius: number): void
Modifies this torus by changing its major radius. Exceptions Standard_ConstructionError if:
- MajorRadius is negative, or
- MajorRadius - r is less than or equal to gp::Resolution(), where r is the minor radius of this torus.
Parameters (1)
- MajorRadius
SetMinorRadius(MinorRadius: number): void
Modifies this torus by changing its minor radius. Exceptions Standard_ConstructionError if:
- MinorRadius is negative, or
- R - MinorRadius is less than or equal to gp::Resolution(), where R is the major radius of this torus.
Parameters (1)
- MinorRadius
SetTorus(T: gp_Torus): void
Converts the gp_Torus torus T into this torus.
Parameters (1)
- T
Torus(): gp_Torus
Returns the non transient torus with the same geometric properties as <me>.
UReversedParameter(U: number): number
Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.
Parameters (1)
- U
VReversedParameter(V: number): number
Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.
Parameters (1)
- V
Area(): number
Computes the area of the surface.
Bounds(U1: number, U2: number, V1: number, V2: number): { U1: number; U2: number; V1: number; V2: number }
Returns the parametric bounds U1, U2, V1 and V2 of this torus. For a torus: U1 = V1 = 0 and U2 = V2 = 2*PI .
Parameters (4)
- U1
- U2
- V1
- V2
Returns
A result object with fields:
- U1: updated value from the call.
- U2: updated value from the call.
- V1: updated value from the call.
- V2: updated value from the call.
Coefficients(Coef: NCollection_Array1_double): void
Returns the coefficients of the implicit equation of the surface in the absolute cartesian coordinate system : Coef(1) * X4 + Coef(2) * Y4 + Coef(3) * Z4 + Coef(4) * X3 * Y + Coef(5) * X3 * Z + Coef(6) * Y3 * X + Coef(7) * Y3 * Z + Coef(8) * Z3 * X + Coef(9) * Z3 * Y + Coef(10) * X2 * Y2 + Coef(11) * X2 * Z2 + Coef(12) * Y2 * Z2 + Coef(13) * X3 + Coef(14) * Y3 + Coef(15) * Z3 + Coef(16) * X2 * Y + Coef(17) * X2 * Z + Coef(18) * Y2 * X + Coef(19) * Y2 * Z + Coef(20) * Z2 * X + Coef(21) * Z2 * Y + Coef(22) * X2 + Coef(23) * Y2 + Coef(24) * Z**2 + Coef(25) * X * Y + Coef(26) * X * Z + Coef(27) * Y * Z + Coef(28) * X + Coef(29) * Y + Coef(30) * Z + Coef(31) = 0.0 Raised if the length of Coef is lower than 31.
Parameters (1)
- Coef —
  Mutated in place; read the updated value from this argument after the call.
MajorRadius(): number
Returns the major radius, or the minor radius, of this torus.
MinorRadius(): number
Returns the major radius, or the minor radius, of this torus.
Volume(): number
Computes the volume.
IsUClosed(): boolean
Returns True.
IsVClosed(): boolean
Returns True.
IsUPeriodic(): boolean
Returns True.
IsVPeriodic(): boolean
Returns True.
UIso(U: number): Geom_Curve
Computes the U isoparametric curve.
For a toroidal surface the UIso curve is a circle. The center of the Uiso circle is at the distance MajorRadius from the location point of the toroidal surface. Warnings: The radius of the circle can be zero if for the surface MinorRadius = 0.0
Parameters (1)
- U
VIso(V: number): Geom_Curve
Computes the V isoparametric curve.
For a ToroidalSurface the VIso curve is a circle. The axis of the circle is the main axis (ZAxis) of the toroidal surface. Warnings: The radius of the circle can be zero if for the surface MajorRadius = MinorRadius
Parameters (1)
- V
EvalD0(U: number, V: number): gp_Pnt
Computes the point P (U, V) on the surface. P (U, V) = Loc + MinorRadius * Sin (V) * Zdir + (MajorRadius + MinorRadius * std::cos(V)) * (cos (U) * XDir + sin (U) * YDir) where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis and ZDir the direction of the ZAxis.
Parameters (2)
- U
- V
EvalD1(U: number, V: number): Geom_Surface_ResD1
Computes the current point and the first derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD2(U: number, V: number): Geom_Surface_ResD2
Computes the current point, the first and the second derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalD3(U: number, V: number): Geom_Surface_ResD3
Computes the current point, the first,the second and the third derivatives in the directions U and V.
Parameters (2)
- U
- V
EvalDN(U: number, V: number, Nu: number, Nv: number): gp_Vec
Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Parameters (4)
- U
- V
- Nu
- Nv
Transform(T: gp_Trsf): void
Applies the transformation T to this torus.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this torus.
DynamicType(): Standard_Type

Geom_Transformation

Standard_Transient

Describes how to construct the following elementary transformations.

translations,
rotations,
symmetries,
scales. The Transformation class can also be used to construct complex transformations by combining these elementary transformations. However, these transformations can never change the type of an object. For example, the projection transformation can change a circle into an ellipse, and therefore change the real type of the object. Such a transformation is forbidden in this environment and cannot be a Geom_Transformation. The transformation can be represented as follow :
V1 V2 V3 T | a11 a12 a13 a14 | | x | | x'| | a21 a22 a23 a24 | | y | | y'| | a31 a32 a33 a34 | | z | = | z'| | 0 0 0 1 | | 1 | | 1 |
where {V1, V2, V3} defines the vectorial part of the transformation and T defines the translation part of the transformation.
Note: Geom_Transformation transformations provide the same kind of "geometric" services as gp_Trsf ones but have more complex data structures.
The geometric objects provided by the Geom package use gp_Trsf transformations in the syntaxes Transform and Transformed. Geom_Transformation transformations are used in a context where they can be shared by several objects contained inside a common data structure.

Constructors(2)

constructor(): Geom_Transformation
Creates an identity transformation.
constructor(T: gp_Trsf): Geom_Transformation
Creates a transient copy of T.
Parameters (1)
- T

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(25)

DynamicType(): Standard_Type
SetMirror(thePnt: gp_Pnt): void
Makes the transformation into a symmetrical transformation with respect to a point P. P is the center of the symmetry.
Parameters (1)
- thePnt
SetMirror(theA1: gp_Ax1): void
Makes the transformation into a symmetrical transformation with respect to an axis A1. A1 is the center of the axial symmetry.
Parameters (1)
- theA1
SetMirror(theA2: gp_Ax2): void
Makes the transformation into a symmetrical transformation with respect to a plane. The plane of the symmetry is defined with the axis placement A2. It is the plane (Location, XDirection, YDirection).
Parameters (1)
- theA2
SetRotation(theA1: gp_Ax1, theAng: number): void
Makes the transformation into a rotation. A1 is the axis rotation and Ang is the angular value of the rotation in radians.
Parameters (2)
- theA1
- theAng
SetScale(thePnt: gp_Pnt, theScale: number): void
Makes the transformation into a scale. P is the center of the scale and S is the scaling value.
Parameters (2)
- thePnt
- theScale
SetTransformation(theFromSystem1: gp_Ax3, theToSystem2: gp_Ax3): void
Makes a transformation allowing passage from the coordinate system "FromSystem1" to the coordinate system "ToSystem2". Example : In a C++ implementation : Real x1, y1, z1; // are the coordinates of a point in the // local system FromSystem1 Real x2, y2, z2; // are the coordinates of a point in the // local system ToSystem2 gp_Pnt P1 (x1, y1, z1) Geom_Transformation T; T.SetTransformation (FromSystem1, ToSystem2); gp_Pnt P2 = P1.Transformed (T); P2.Coord (x2, y2, z2);.
Parameters (2)
- theFromSystem1
- theToSystem2
SetTransformation(theToSystem: gp_Ax3): void
Makes the transformation allowing passage from the basic coordinate system {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.), VZ (0., 0. ,1.) } to the local coordinate system defined with the Ax2 ToSystem. Same utilisation as the previous method. FromSystem1 is defaulted to the absolute coordinate system.
Parameters (1)
- theToSystem
SetTranslation(theVec: gp_Vec): void
Makes the transformation into a translation. V is the vector of the translation.
Parameters (1)
- theVec
SetTranslation(P1: gp_Pnt, P2: gp_Pnt): void
Makes the transformation into a translation from the point P1 to the point P2.
Parameters (2)
- P1
- P2
SetTrsf(theTrsf: gp_Trsf): void
Converts the gp_Trsf transformation T into this transformation.
Parameters (1)
- theTrsf
IsNegative(): boolean
Checks whether this transformation is an indirect transformation: returns true if the determinant of the matrix of the vectorial part of the transformation is less than 0.
Form(): gp_TrsfForm
Returns the nature of this transformation as a value of the gp_TrsfForm enumeration.
ScaleFactor(): number
Returns the scale value of the transformation.
Trsf(): gp_Trsf
Returns a non transient copy of <me>.
Value(theRow: number, theCol: number): number
Returns the coefficients of the global matrix of transformation. It is a 3 rows X 4 columns matrix.
Raised if Row < 1 or Row > 3 or Col < 1 or Col > 4
Parameters (2)
- theRow
- theCol
Invert(): void
Raised if the transformation is singular. This means that the ScaleFactor is lower or equal to Resolution from package gp.
Inverted(): Geom_Transformation
Raised if the transformation is singular. This means that the ScaleFactor is lower or equal to Resolution from package gp.
Multiplied(Other: Geom_Transformation): Geom_Transformation
Computes the transformation composed with Other and <me>. <me> * Other. Returns a new transformation.
Parameters (1)
- Other
Multiply(theOther: Geom_Transformation): void
Computes the transformation composed with Other and <me> . <me> = <me> * Other.
Parameters (1)
- theOther
Power(N: number): void
Computes the following composition of transformations if N > 0 <me> * <me> * .......* <me>. if N = 0 Identity if N < 0 <me>.Invert() * .........* <me>.Invert().
Raised if N < 0 and if the transformation is not inversible
Parameters (1)
- N
Powered(N: number): Geom_Transformation
Raised if N < 0 and if the transformation is not inversible.
Parameters (1)
- N
PreMultiply(Other: Geom_Transformation): void
Computes the matrix of the transformation composed with <me> and Other. <me> = Other * <me>.
Parameters (1)
- Other
Transforms(theX: number, theY: number, theZ: number): { theX: number; theY: number; theZ: number }
Applies the transformation <me> to the triplet {X, Y, Z}.
Parameters (3)
- theX
- theY
- theZ
Returns
A result object with fields:
- theX: updated value from the call.
- theY: updated value from the call.
- theZ: updated value from the call.
Copy(): Geom_Transformation
Creates a new object which is a copy of this transformation.

Geom_TrimmedCurve

Geom_BoundedCurveGeom_CurveGeom_GeometryStandard_Transient

Describes a portion of a curve (termed the "basis curve") limited by two parameter values inside the parametric domain of the basis curve. The trimmed curve is defined by:

the basis curve, and
the two parameter values which limit it. The trimmed curve can either have the same orientation as the basis curve or the opposite orientation.

Constructors(1)

constructor(C: Geom_Curve, U1: number, U2: number, Sense?: boolean, theAdjustPeriodic?: boolean): Geom_TrimmedCurve
Constructs a trimmed curve from the basis curve C which is limited between parameter values U1 and U2. Note: - U1 can be greater or less than U2; in both cases, the returned curve is oriented from U1 to U2.
- If the basis curve C is periodic, there is an ambiguity because two parts are available. In this case, the trimmed curve has the same orientation as the basis curve if Sense is true (default value) or the opposite orientation if Sense is false.
- If the curve is closed but not periodic, it is not possible to keep the part of the curve which includes the junction point (except if the junction point is at the beginning or at the end of the trimmed curve). If you tried to do this, you could alter the fundamental characteristics of the basis curve, which are used, for example, to compute the derivatives of the trimmed curve. The rules for a closed curve are therefore the same as those for an open curve. Warning: The trimmed curve is built from a copy of curve C. Therefore, when C is modified, the trimmed curve is not modified.
- If the basis curve is periodic and theAdjustPeriodic is True, the bounds of the trimmed curve may be different from U1 and U2 if the parametric origin of the basis curve is within the arc of the trimmed curve. In this case, the modified parameter will be equal to U1 or U2 plus or minus the period. When theAdjustPeriodic is False, parameters U1 and U2 will be the same, without adjustment into the first period. Exceptions Standard_ConstructionError if:
- C is not periodic and U1 or U2 is outside the bounds of C, or
- U1 is equal to U2.
Parameters (5)
- C
- U1
- U2
- Sense
- theAdjustPeriodic

Static methods(2)

get_type_name(): string
get_type_descriptor(): Standard_Type

Instance methods(23)

Reverse(): void
Changes the orientation of this trimmed curve. As a result:
- the basis curve is reversed,
- the start point of the initial curve becomes the end point of the reversed curve,
- the end point of the initial curve becomes the start point of the reversed curve,
- the first and last parameters are recomputed. If the trimmed curve was defined by:
- a basis curve whose parameter range is [ 0., 1. ],
- the two trim values U1 (first parameter) and U2 (last parameter), the reversed trimmed curve is defined by:
- the reversed basis curve, whose parameter range is still [ 0., 1. ],
- the two trim values 1. - U2 (first parameter) and 1. - U1 (last parameter).
ReversedParameter(U: number): number
Computes the parameter on the reversed curve for the point of parameter U on this trimmed curve.
Parameters (1)
- U
SetTrim(U1: number, U2: number, Sense?: boolean, theAdjustPeriodic?: boolean): void
Changes this trimmed curve, by redefining the parameter values U1 and U2 which limit its basis curve. Note: If the basis curve is periodic, the trimmed curve has the same orientation as the basis curve if Sense is true (default value) or the opposite orientation if Sense is false.
Warning If the basis curve is periodic and theAdjustPeriodic is True, the bounds of the trimmed curve may be different from U1 and U2 if the parametric origin of the basis curve is within the arc of the trimmed curve. In this case, the modified parameter will be equal to U1 or U2 plus or minus the period. When theAdjustPeriodic is False, parameters U1 and U2 will be the same, without adjustment into the first period. Exceptions Standard_ConstructionError if:
- the basis curve is not periodic, and either U1 or U2 are outside the bounds of the basis curve, or
- U1 is equal to U2.
Parameters (4)
- U1
- U2
- Sense
- theAdjustPeriodic
BasisCurve(): Geom_Curve
Returns the basis curve. Warning This function does not return a constant reference. Consequently, any modification of the returned value directly modifies the trimmed curve.
Continuity(): GeomAbs_Shape
Returns the continuity of the curve : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, CN : the order of continuity is infinite.
IsCN(N: number): boolean
Returns true if the degree of continuity of the basis curve of this trimmed curve is at least N. A trimmed curve is at least "C0" continuous. Warnings : The continuity of the trimmed curve can be greater than the continuity of the basis curve because you consider only a part of the basis curve. Raised if N < 0.
Parameters (1)
- N
EndPoint(): gp_Pnt
Returns the end point of <me>. This point is the evaluation of the curve for the "LastParameter".
FirstParameter(): number
Returns the value of the first parameter of <me>. The first parameter is the parameter of the "StartPoint" of the trimmed curve.
IsClosed(): boolean
Returns TRUE if the basis curve is periodic and the trim spans exactly one full period, or if the distance between the StartPoint and the EndPoint is within computational precision.
IsPeriodic(): boolean
Returns TRUE if the basis curve is periodic and the trim spans exactly one full period. Returns FALSE otherwise.
Period(): number
Returns the period of the basis curve of this trimmed curve. Exceptions Standard_NoSuchObject if the basis curve is not periodic.
LastParameter(): number
Returns the value of the last parameter of <me>. The last parameter is the parameter of the "EndPoint" of the trimmed curve.
StartPoint(): gp_Pnt
Returns the start point of <me>. This point is the evaluation of the curve from the "FirstParameter". value and derivatives Warnings : The returned derivatives have the same orientation as the derivatives of the basis curve even if the trimmed curve has not the same orientation as the basis curve.
EvalD0(U: number): gp_Pnt
Returns the point of parameter U.
If the basis curve is an OffsetCurve sometimes it is not possible to do the evaluation of the curve at the parameter U (see class OffsetCurve).
Parameters (1)
- U
EvalD1(U: number): Geom_Curve_ResD1
Raised if the continuity of the curve is not C1.
Parameters (1)
- U
EvalD2(U: number): Geom_Curve_ResD2
Raised if the continuity of the curve is not C2.
Parameters (1)
- U
EvalD3(U: number): Geom_Curve_ResD3
Raised if the continuity of the curve is not C3.
Parameters (1)
- U
EvalDN(U: number, N: number): gp_Vec
N is the order of derivation. Raised if the continuity of the curve is not CN. Raised if N < 1. geometric transformations.
Parameters (2)
- U
- N
Transform(T: gp_Trsf): void
Applies the transformation T to this trimmed curve. Warning The basis curve is also modified.
Parameters (1)
- T
TransformedParameter(U: number, T: gp_Trsf): number
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.
me->Transformed(T)->Value(me->TransformedParameter(U,T))
is the same point as
me->Value(U).Transformed(T)
This methods calls the basis curve method.
Parameters (2)
- U
- T
ParametricTransformation(T: gp_Trsf): number
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.
Transformed(T)->Value(U * ParametricTransformation(T))
is the same point as
Value(U).Transformed(T)
This methods calls the basis curve method.
Parameters (1)
- T
Copy(): Geom_Geometry
Creates a new object which is a copy of this trimmed curve.
DynamicType(): Standard_Type

Geom_UndefinedDerivative

Standard_DomainErrorStandard_Failureexception

Constructors(2)

constructor(theMessage: string): Geom_UndefinedDerivative
Parameters (1)
- theMessage
constructor(theMessage: string, theStackTrace: string): Geom_UndefinedDerivative
Parameters (2)
- theMessage
- theStackTrace

Instance methods(1)

ExceptionType(): string

Geom_UndefinedValue

Standard_DomainErrorStandard_Failureexception

Constructors(2)

constructor(theMessage: string): Geom_UndefinedValue
Parameters (1)
- theMessage
constructor(theMessage: string, theStackTrace: string): Geom_UndefinedValue
Parameters (2)
- theMessage
- theStackTrace

Instance methods(1)

ExceptionType(): string

Geom_Vector