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Geom2d

OCCT package Geom2d: Geom2d_AxisPlacement, Geom2d_BezierCurve, Geom2d_BoundedCurve, Geom2d_BSplineCurve, and 18 more bound classes.

Geom2d_AxisPlacement

Geom2d_GeometryStandard_Transient

Describes an axis in 2D space. An axis is defined by:

  • its origin, also termed the "Location point" of the axis,
  • its unit vector, termed the "Direction" of the axis. Note: Geom2d_AxisPlacement axes provide the same kind of "geometric" services as gp_Ax2d axes but have more complex data structures. The geometric objects provided by the Geom2d package use gp_Ax2d objects to include axes in their data structures, or to define an axis of symmetry or axis of rotation. Geom2d_AxisPlacement axes are used in a context where they can be shared by several objects contained inside a common data structure.

Constructors(2)

Static methods(2)

Instance methods(12)

Geom2d_BezierCurve

Geom2d_BoundedCurveGeom2d_CurveGeom2d_GeometryStandard_Transient

Describes a rational or non-rational Bezier curve.

  • a non-rational Bezier curve is defined by a table of poles (also called control points),
  • a rational Bezier curve is defined by a table of poles with varying weights. These data are manipulated by two parallel arrays:
  • the poles table, which is an array of gp_Pnt2d points, and
  • the weights table, which is an array of reals. The bounds of these arrays are 1 and "the number of poles" of the curve. The poles of the curve are "control points" used to deform the curve. 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.
    It is more difficult to give a geometric signification to the weights but they 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 is polynomial; it is therefore a non-rational curve. The non-rational curve is a special and frequently used case. The weights are defined and used only in case of a rational curve. The degree of a Bezier curve is equal to the number of poles, minus 1. It must be greater than or equal to 1.
    However, the degree of a Geom2d_BezierCurve curve is limited to a value (25) which is defined and controlled by the system. This value is returned by the function MaxDegree. The parameter range for a Bezier curve is [ 0, 1 ]. If the first and last control points of the Bezier curve are the same point then the curve is closed.
    For example, to create a closed Bezier curve with four control points, you have to give a set of control points P1, P2, P3 and P1. The continuity of a Bezier curve is infinite. It is not possible to build a Bezier curve with negative weights. We consider that a weight value is zero if it is less than or equal to gp::Resolution(). We also consider that two weight values W1 and W2 are equal if: |W2 - W1| <= gp::Resolution(). Warning
  • When considering the continuity of a closed Bezier curve at the junction point, remember that a curve of this type is never periodic. This means that the derivatives for the parameter u = 0 have no reason to be the same as the derivatives for the parameter u = 1 even if the curve is closed.
  • The length of a Bezier curve can be null.

Constructors(3)

  • constructor(CurvePoles: NCollection_Array1_gp_Pnt2d): Geom2d_BezierCurve

    Creates a non rational Bezier curve with a set of poles : CurvePoles. The weights are defaulted to all being 1. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2.

    Parameters (1)
    • CurvePoles
  • constructor(theOther: Geom2d_BezierCurve): Geom2d_BezierCurve

    Copy constructor for optimized copying without validation.

    Parameters (1)
    • theOther
  • constructor(CurvePoles: NCollection_Array1_gp_Pnt2d, PoleWeights: NCollection_Array1_double): Geom2d_BezierCurve

    Creates a rational Bezier curve with the set of poles CurvePoles and the set of weights PoleWeights. If all the weights are identical the curve is considered as non rational. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2 or CurvePoles and CurveWeights have not the same length or one weight value is lower or equal to Resolution from package gp.

    Parameters (2)
    • CurvePoles
    • PoleWeights

Static methods(3)

Instance methods(44)

  • HasEvalRepresentation(): boolean

    Returns true if an evaluation representation is attached.

  • EvalRepresentation(): Geom2dEval_RepCurveDesc_Base

    Returns the current evaluation representation descriptor (may be null).

  • SetEvalRepresentation(theDesc: Geom2dEval_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.

  • Increase(Degree: number): void

    Increases the degree of a bezier curve. Degree is the new degree of <me>. raises ConstructionError if Degree is greater than MaxDegree or lower than 2 or lower than the initial degree of <me>.

    Parameters (1)
    • Degree
  • InsertPoleAfter(Index: number, P: gp_Pnt2d, Weight?: number): void

    Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. Raised if Index is not in the range [0, NbPoles].
    Raised if the resulting number of poles is greater than MaxDegree + 1.

    Parameters (3)
    • Index
    • P
    • Weight
  • InsertPoleBefore(Index: number, P: gp_Pnt2d, Weight?: number): void

    Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. Raised if Index is not in the range [1, NbPoles+1].
    Raised if the resulting number of poles is greater than MaxDegree + 1.

    Parameters (3)
    • Index
    • P
    • Weight
  • RemovePole(Index: number): void

    Removes the pole of range Index. If the curve was rational it can become non rational. Raised if Index is not in the range [1, NbPoles].

    Parameters (1)
    • Index
  • Reverse(): void

    Reverses the direction of parametrization of <me> Value (NewU) = Value (1 - OldU).

  • ReversedParameter(U: number): number

    Returns the parameter on the reversed curve for the point of parameter U on <me>.
    returns 1-U

    Parameters (1)
    • U
  • Segment(U1: number, U2: number): void

    Segments the curve between U1 and U2 which can be out of the bounds of the curve. The curve is oriented from U1 to U2. The control points are modified, the first and the last point are not the same but the parametrization range is [0, 1] else it could not be a Bezier curve. 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.

    Parameters (2)
    • U1
    • U2
  • SetPole(Index: number, P: gp_Pnt2d): void

    Substitutes the pole of range index with P. If the curve <me> is rational the weight of range Index is not modified. raiseD if Index is not in the range [1, NbPoles].

    Parameters (2)
    • Index
    • P
  • SetPole(Index: number, P: gp_Pnt2d, Weight: number): void

    Substitutes the pole and the weights of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. Raised if Index is not in the range [1, NbPoles] Raised if Weight <= Resolution from package gp.

    Parameters (3)
    • Index
    • P
    • Weight
  • SetWeight(Index: number, Weight: number): void

    Changes the weight of the pole of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. Raised if Index is not in the range [1, NbPoles] Raised if Weight <= Resolution from package gp.

    Parameters (2)
    • Index
    • Weight
  • IsClosed(): boolean

    Returns True if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp.

  • IsCN(N: number): boolean

    Continuity of the curve, returns True.

    Parameters (1)
    • N
  • IsPeriodic(): boolean

    Returns False. A BezierCurve cannot be periodic in this package.

  • IsRational(): boolean

    Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp.

  • Continuity(): GeomAbs_Shape

    Returns GeomAbs_CN, which is the continuity of any Bezier curve.

  • Degree(): number

    Returns the polynomial degree of the curve. It is the number of poles less one. In this package the Degree of a Bezier curve cannot be greater than "MaxDegree".

  • EvalD0(U: number): gp_Pnt2d

    Computes the point of parameter U. Raises an exception on failure.

    Parameters (1)
    • U
  • EvalD1(U: number): Geom2d_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): Geom2d_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): Geom2d_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_Vec2d

    For this Bezier curve, computes.

    • the point P of parameter U, or
    • the point P and one or more of the following values:
    • V1, the first derivative vector,
    • V2, the second derivative vector,
    • V3, the third derivative vector. Note: the parameter U can be outside the bounds of the curve. Raises RangeError if N < 1.
    Parameters (2)
    • U
    • N
  • EndPoint(): gp_Pnt2d

    Returns the end point or start point of this Bezier curve.

  • FirstParameter(): number

    Returns the value of the first parameter of this Bezier curve. This is 0.0, which gives the start point of this Bezier curve.

  • LastParameter(): number

    Returns the value of the last parameter of this Bezier curve. This is 1.0, which gives the end point of this Bezier curve.

  • NbPoles(): number

    Returns the number of poles for this Bezier curve.

  • Pole(Index: number): gp_Pnt2d

    Returns the pole of range Index. Raised if Index is not in the range [1, NbPoles].

    Parameters (1)
    • Index
  • Poles(P: NCollection_Array1_gp_Pnt2d): void

    Returns all the poles of the 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_Pnt2d

    Returns all the poles of the curve.

  • StartPoint(): gp_Pnt2d

    Returns Value (U=1), it is the first control point of the curve.

  • Weight(Index: number): number

    Returns the weight of range Index. Raised if Index is not in the range [1, NbPoles].

    Parameters (1)
    • Index
  • Weights(W: NCollection_Array1_double): void

    Returns all the weights of the curve.
    Raised if the length of W is not equal to the number of poles.

    Deprecated
    Parameters (1)
    • W —
      Mutated in place; read the updated value from this argument after the call.
  • Weights(): NCollection_Array1_double

    Returns all the weights of the 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_Trsf2d): void

    Applies the transformation T to this Bezier curve.

    Parameters (1)
    • T
  • Resolution(ToleranceUV: number, UTolerance: number): { UTolerance: number }

    Computes for this Bezier curve the parametric tolerance UTolerance for a given tolerance Tolerance3D (relative to dimensions in the plane). If f(t) is the equation of this Bezier curve, UTolerance ensures that | t1 - t0| < Utolerance ===> |f(t1) - f(t0)| < ToleranceUV.

    Parameters (2)
    • ToleranceUV
    • UTolerance
    Returns

    A result object with fields:

    • UTolerance: updated value from the call.
  • Copy(): Geom2d_Geometry

    Creates a new object which is a copy of this Bezier curve.

  • Knots(): NCollection_Array1_double

    Returns Bezier knots {0.0, 1.0} as a static array.

  • Multiplicities(): NCollection_Array1_int

    Returns Bezier multiplicities for the current degree.

  • KnotSequence(): NCollection_Array1_double

    Returns Bezier flat knots for the current degree.

  • DynamicType(): Standard_Type

Geom2d_BoundedCurve

Geom2d_CurveGeom2d_GeometryStandard_Transient

The abstract class BoundedCurve describes the common behavior of bounded curves in 2D 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 Geom2d package provides three concrete classes of bounded curves:

Static methods(2)

Instance methods(3)

  • EndPoint(): gp_Pnt2d

    Returns the end point of the curve. The end point is the value of the curve for the "LastParameter" of the curve.

  • StartPoint(): gp_Pnt2d

    Returns the start point of the curve. The start point is the value of the curve for the "FirstParameter" of the curve.

  • DynamicType(): Standard_Type

Geom2d_BSplineCurve

Geom2d_BoundedCurveGeom2d_CurveGeom2d_GeometryStandard_Transient

Describes a BSpline curve. A BSpline curve can be:

  • uniform or non-uniform,
  • rational or non-rational,
  • periodic or non-periodic. A BSpline curve is defined by:
  • its degree; the degree for a Geom2d_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 they 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 Geom2d_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, such that:
  • 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. Warnings: In this class we consider that a weight value is zero if Weight <= Resolution from package gp. For two parametric values (or two knot values) U1, U2 we consider that U1 = U2 if Abs (U2 - U1) <= Epsilon (U1). For two weights values W1, W2 we consider that W1 = W2 if Abs (W2 - W1) <= Epsilon (W1). The method Epsilon is defined in the class Real from package Standard.
    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: Geom2d_BSplineCurve): Geom2d_BSplineCurve

    Copy constructor for optimized copying without validation.

    Parameters (1)
    • theOther
  • constructor(Poles: NCollection_Array1_gp_Pnt2d, Knots: NCollection_Array1_double, Multiplicities: NCollection_Array1_int, Degree: number, Periodic?: boolean): Geom2d_BSplineCurve

    Creates a non-rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. The following conditions must be verified. 0 < Degree <= MaxDegree.
    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 (5)
    • Poles
    • Knots
    • Multiplicities
    • Degree
    • Periodic
  • constructor(Poles: NCollection_Array1_gp_Pnt2d, Weights: NCollection_Array1_double, Knots: NCollection_Array1_double, Multiplicities: NCollection_Array1_int, Degree: number, Periodic?: boolean): Geom2d_BSplineCurve

    Creates a rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. The following conditions must be verified. 0 < Degree <= MaxDegree.
    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 (6)
    • Poles
    • Weights
    • Knots
    • Multiplicities
    • Degree
    • Periodic

Static methods(3)

Instance methods(76)

  • HasEvalRepresentation(): boolean

    Returns true if an evaluation representation is attached.

  • EvalRepresentation(): Geom2dEval_RepCurveDesc_Base

    Returns the current evaluation representation descriptor (may be null).

  • SetEvalRepresentation(theDesc: Geom2dEval_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 Geom2d_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. As a result, the poles and weights tables of this curve are modified. Warning It is forbidden to modify the multiplicity of the first or last knot of a non-periodic curve. Be careful as Geom2d does not protect against this. Exceptions Standard_OutOfRange if either Index, I1 or I2 is outside the bounds of the knots table.

    Parameters (3)
    • I1
    • I2
    • M
  • IncrementMultiplicity(I1: number, I2: number, M: number): void

    Increases by M the multiplicity of the knots of indexes I1 to I2 in the knots table of this BSpline curve. For each knot, the resulting multiplicity is limited to the degree of this curve. If M is negative, nothing is done. As a result, the poles and weights tables of this BSpline curve are modified. Warning It is forbidden to modify the multiplicity of the first or last knot of a non-periodic curve. Be careful as Geom2d does not protect against this. Exceptions Standard_OutOfRange if I1 or I2 is outside the bounds of the knots table.

    Parameters (3)
    • I1
    • I2
    • M
  • InsertKnot(U: number, M?: number, ParametricTolerance?: number): 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. Warning

    • If U is less than the first parameter or greater than the last parameter of this BSpline curve, nothing is done.
    • If M is negative or null, nothing is done.
    • The multiplicity of a knot is limited to the degree of this BSpline curve.
    Parameters (3)
    • U
    • M
    • ParametricTolerance
  • InsertKnots(Knots: NCollection_Array1_double, Mults: NCollection_Array1_int, ParametricTolerance?: number, Add?: boolean): void

    Inserts the values of the array Knots, with the respective multiplicities given by the array Mults, into the knots table of this BSpline curve. If a value of the array Knots is an existing knot, its multiplicity is:

    • increased by M, if Add is true, or
    • increased to M, if Add is false (default value). The tolerance criterion used for knot equality is the larger of the values ParametricTolerance (defaulted to 0.) and double::Epsilon(U), where U is the current knot value. Warning
    • For a value of the array Knots which is less than the first parameter or greater than the last parameter of this BSpline curve, nothing is done.
    • For a value of the array Mults which is negative or null, nothing is done.
    • The multiplicity of a knot is limited to the degree of this BSpline curve.
    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.

    Parameters (3)
    • Index
    • M
    • Tolerance
  • InsertPoleAfter(Index: number, P: gp_Pnt2d, Weight?: number): void

    The new pole is inserted after the pole of range Index. If the curve was non rational it can become rational.
    Raised if the B-spline is NonUniform or PiecewiseBezier or if Weight <= 0.0 Raised if Index is not in the range [1, Number of Poles]

    Parameters (3)
    • Index
    • P
    • Weight
  • InsertPoleBefore(Index: number, P: gp_Pnt2d, Weight?: number): void

    The new pole is inserted before the pole of range Index. If the curve was non rational it can become rational.
    Raised if the B-spline is NonUniform or PiecewiseBezier or if Weight <= 0.0 Raised if Index is not in the range [1, Number of Poles]

    Parameters (3)
    • Index
    • P
    • Weight
  • RemovePole(Index: number): void

    Removes the pole of range Index If the curve was rational it can become non rational.
    Raised if the B-spline is NonUniform or PiecewiseBezier. Raised if the number of poles of the B-spline curve is lower or equal to 2 before removing. Raised if Index is not in the range [1, Number of Poles]

    Parameters (1)
    • Index
  • Reverse(): void

    Reverses the orientation of this BSpline curve. As a result.

    • the knots and poles tables are modified;
    • 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.
  • ReversedParameter(U: number): number

    Computes the parameter on the reversed curve for the point of parameter U on this BSpline curve. The returned value is: UFirst + ULast - U, where UFirst and ULast are the values of the first and last parameters of this BSpline curve.

    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.

    • The segmentation of a periodic curve over an interval corresponding to its period generates a non-periodic curve with equivalent geometry. Exceptions Standard_DomainError if U2 is less than U1. 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) Exceptions 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

    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). Exceptions 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 (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 }

    Computes the parameter normalized within the "first" period of this BSpline curve, if it is periodic: the returned value is in the range Param1 and Param1 + Period, where:

    • Param1 is the "first parameter", and
    • Period the period of this BSpline curve. Note: If this curve is not periodic, U is not modified.
    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 Knot(I2) - Knot(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
  • SetNotPeriodic(): void

    Changes this BSpline curve into a non-periodic curve. If this curve is already non-periodic, it is not modified. Note that 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_Pnt2d): 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_Pnt2d, Weight: number): void

    Modifies this BSpline curve by assigning P to the pole of index Index in the poles table. The second 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

    Assigns the weight Weight to the pole of index Index of the poles table. If the curve was non rational it can become rational. If the curve was rational it can become non rational. Exceptions Standard_OutOfRange if Index is outside the bounds of the poles table. Standard_ConstructionError if Weight is negative or null.

    Parameters (2)
    • Index
    • Weight
  • MovePoint(U: number, P: gp_Pnt2d, 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_Pnt2d, Tangent: gp_Vec2d, 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 true if the degree of continuity of this BSpline curve is at least N. A BSpline curve is at least GeomAbs_C0. Exceptions Standard_RangeError if N is negative.

    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. In this class the degree of the basis normalized B-spline functions cannot be greater than "MaxDegree" Computation of value and derivatives.

  • EvalD0(U: number): gp_Pnt2d

    Computes the point of parameter U. Raises an exception on failure.

    Parameters (1)
    • U
  • EvalD1(U: number): Geom2d_Curve_ResD1

    Raised if the continuity of the curve is not C1.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_Curve_ResD2

    Raised if the continuity of the curve is not C2.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    For this BSpline curve, computes.

    • the point P of parameter U, or
    • the point P and one or more of the following values:
    • V1, the first derivative vector,
    • V2, the second derivative vector,
    • V3, the third derivative vector. Warning On a point where the continuity of the curve is not the one requested, these functions impact 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. Raises UndefinedDerivative if the continuity of the curve is not C3.
    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    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. Raises UndefinedDerivative if the continuity of the curve is not CN. RangeError if N < 1.
    The following functions computes 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_Pnt2d

    Raised if FromK1 = ToK2.

    Parameters (3)
    • U
    • FromK1
    • ToK2
  • LocalD0(U: number, FromK1: number, ToK2: number, P: gp_Pnt2d): 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_Pnt2d, V1: gp_Vec2d): 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_Pnt2d, V1: gp_Vec2d, V2: gp_Vec2d): 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_Pnt2d, V1: gp_Vec2d, V2: gp_Vec2d, V3: gp_Vec2d): 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_Vec2d

    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_Pnt2d

    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

    For a B-spline curve the first parameter (which gives the start point of the curve) is a knot value but if the multiplicity of the first knot index is lower than Degree + 1 it is not the first knot of the curve. This method computes the index of the knot corresponding to the first parameter.

  • FirstParameter(): number

    Computes the parametric value of the start point of the curve. It is a knot value.

  • 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;
    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;

  • KnotSequence(K: NCollection_Array1_double): void

    Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
    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 sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

  • 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_Pnt2d

    Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles.

    Parameters (1)
    • Index
  • Poles(P: NCollection_Array1_gp_Pnt2d): 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_Pnt2d

    Returns the poles of the B-spline curve;.

  • StartPoint(): gp_Pnt2d

    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_Trsf2d): void

    Applies the transformation T to this BSpline curve.

    Parameters (1)
    • T
  • Resolution(ToleranceUV: number, UTolerance: number): { UTolerance: number }

    Computes for this BSpline curve the parametric tolerance UTolerance for a given tolerance Tolerance3D (relative to dimensions in the plane). If f(t) is the equation of this BSpline curve, UTolerance ensures that: | t1 - t0| < Utolerance ===> |f(t1) - f(t0)| < ToleranceUV.

    Parameters (2)
    • ToleranceUV
    • UTolerance
    Returns

    A result object with fields:

    • UTolerance: updated value from the call.
  • Copy(): Geom2d_Geometry

    Creates a new object which is a copy of this BSpline curve.

  • DynamicType(): Standard_Type

Geom2d_CartesianPoint

Geom2d_PointGeom2d_GeometryStandard_Transient

Describes a point in 2D space. A Geom2d_CartesianPoint is defined by a gp_Pnt2d point, with its two Cartesian coordinates X and Y.

Constructors(2)

Static methods(2)

Instance methods(11)

  • SetCoord(X: number, Y: number): void

    Set <me> to X, Y coordinates.

    Parameters (2)
    • X
    • Y
  • SetPnt2d(P: gp_Pnt2d): void

    Set <me> to P.X(), P.Y() 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
  • Coord(X: number, Y: number): { X: number; Y: number }

    Returns the coordinates of <me>.

    Parameters (2)
    • X
    • Y
    Returns

    A result object with fields:

    • X: updated value from the call.
    • Y: updated value from the call.
  • Pnt2d(): gp_Pnt2d

    Returns a non persistent cartesian point with the same coordinates as <me>. -C++: return const&.

  • X(): number

    Returns the X coordinate of <me>.

  • Y(): number

    Returns the Y coordinate of <me>.

  • Transform(T: gp_Trsf2d): 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 Geom2d). The following transformations have the same properties as the previous ones but they don't modified the object itself. A copy of the object is returned.

    Parameters (1)
    • T
  • Copy(): Geom2d_Geometry
  • DynamicType(): Standard_Type

Geom2d_Circle

Geom2d_ConicGeom2d_CurveGeom2d_GeometryStandard_Transient

Describes a circle in the plane (2D space).
A circle is defined by its radius and, as with any conic curve, is positioned in the plane with a coordinate system (gp_Ax22d object) where the origin is the center of the circle. The coordinate system is the local coordinate system of the circle.
The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the circle, determining the direction in which the parameter increases along the circle.
The Geom2d_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 [. See Also GCE2d_MakeCircle which provides functions for more complex circle constructions gp_Ax22d and gp_Circ2d for an equivalent, non-parameterized data structure.

Constructors(3)

  • constructor(C: gp_Circ2d): Geom2d_Circle

    Constructs a circle by conversion of the gp_Circ2d circle C.

    Parameters (1)
    • C
  • constructor(A: gp_Ax22d, Radius: number): Geom2d_Circle

    Constructs a circle of radius Radius, where the coordinate system A locates the circle and defines its orientation in the plane such that:

    • the center of the circle is the origin of A,
    • the orientation (direct or indirect) of A gives the orientation of the circle.
    Parameters (2)
    • A
    • Radius
  • constructor(A: gp_Ax2d, Radius: number, Sense?: boolean): Geom2d_Circle

    Constructs a circle of radius Radius, whose center is the origin of axis A; A is the "X Axis" of the local coordinate system of the circle; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Note: It is possible to create a circle where Radius is equal to 0.0. Exceptions Standard_ConstructionError if Radius is negative.

    Parameters (3)
    • A
    • Radius
    • Sense

Static methods(2)

Instance methods(18)

  • SetCirc2d(C: gp_Circ2d): void

    Converts the gp_Circ2d circle C into this circle.

    Parameters (1)
    • C
  • SetRadius(R: number): void
    Parameters (1)
    • R
  • Circ2d(): gp_Circ2d

    Returns the non persistent 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 0., which is the eccentricity of any circle.

  • FirstParameter(): number

    Returns 0.0.

  • LastParameter(): number

    Returns 2*PI.

  • IsClosed(): boolean

    returns True.

  • IsPeriodic(): boolean

    returns True. The period of a circle is 2.*Pi.

  • EvalD0(U: number): gp_Pnt2d

    Returns in P 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): Geom2d_Curve_ResD1

    Returns the point P of parameter U and the first derivative V1.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_Curve_ResD2

    Returns the point P of parameter U, the first and second derivatives V1 and V2.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    Returns the point P of parameter u, the first second and third derivatives V1 V2 and V3.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    For the point of parameter U of this circle, computes the vector corresponding to the Nth derivative. Exceptions: Standard_RangeError if N is less than 1.

    Parameters (2)
    • U
    • N
  • Transform(T: gp_Trsf2d): void

    Applies the transformation T to this circle.

    Parameters (1)
    • T
  • Copy(): Geom2d_Geometry

    Creates a new object which is a copy of this circle.

  • DynamicType(): Standard_Type

Geom2d_Conic

Geom2d_CurveGeom2d_GeometryStandard_Transient

The abstract class Conic describes the common behavior of conic curves in 2D space and, in particular, their general characteristics.
The Geom2d package provides four specific classes of conics: Geom2d_Circle, Geom2d_Ellipse, Geom2d_Hyperbola and Geom2d_Parabola.
A conic is positioned in the plane with a coordinate system (gp_Ax22d object), where the origin is the center of the conic (or the apex in case of a parabola). This coordinate system is the local coordinate system of the conic. It gives the conic an explicit orientation, 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)

Instance methods(14)

  • SetAxis(theA: gp_Ax22d): void

    Modifies this conic, redefining its local coordinate system partially, by assigning theA as its axis.

    Parameters (1)
    • theA
  • SetXAxis(theAX: gp_Ax2d): void

    Assigns the origin and unit vector of axis theA to the origin of the local coordinate system of this conic and X Direction. The other unit vector of the local coordinate system of this conic is recomputed normal to theA, without changing the orientation of the local coordinate system (right-handed or left-handed).

    Parameters (1)
    • theAX
  • SetYAxis(theAY: gp_Ax2d): void

    Assigns the origin and unit vector of axis theA to the origin of the local coordinate system of this conic and Y Direction. The other unit vector of the local coordinate system of this conic is recomputed normal to theA, without changing the orientation of the local coordinate system (right-handed or left-handed).

    Parameters (1)
    • theAY
  • SetLocation(theP: gp_Pnt2d): void

    Modifies this conic, redefining its local coordinate system partially, by assigning theP as its origin.

    Parameters (1)
    • theP
  • XAxis(): gp_Ax2d

    Returns the "XAxis" of the conic. This axis defines the origin of parametrization of the conic. This axis and the "Yaxis" define the local coordinate system of the conic. -C++: return const&.

  • YAxis(): gp_Ax2d

    Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis".

  • 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

  • Location(): gp_Pnt2d

    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 vertex of the parabola.

  • Position(): gp_Ax22d

    Returns the local coordinates system 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

    Returns GeomAbs_CN which is the global continuity of any conic.

  • IsCN(N: number): boolean

    Returns True, the order of continuity of a conic is infinite.

    Parameters (1)
    • N
  • DynamicType(): Standard_Type

Geom2d_Curve

Geom2d_GeometryStandard_Transient

The abstract class Curve describes the common behavior of curves in 2D space. The Geom2d 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 Geom2d_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 explicitly states so. Warning The Geom2d package does not prevent the construction of curves with null length or curves which self-intersect.

Static methods(2)

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

    Computes the parameter on the reversed curve for the point of parameter U on this curve. Note: The point of parameter U on this curve is identical to the point of parameter ReversedParameter(U) on the reversed curve.

    Parameters (1)
    • U
  • TransformedParameter(U: number, T: gp_Trsf2d): number

    Computes the parameter on the curve transformed by T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line).

    Parameters (2)
    • U
    • T
  • ParametricTransformation(T: gp_Trsf2d): number

    Returns the coefficient required to compute the parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line).

    Parameters (1)
    • T
  • Reversed(): Geom2d_Curve

    Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded:

    • the start point of the initial curve becomes the end point of the reversed curve, and
    • the end point of the initial curve becomes the start point of the reversed curve.
    • Reversed creates a new curve.
  • FirstParameter(): number

    Returns the value of the first parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite.

  • LastParameter(): number

    Value of the last parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite.

  • IsClosed(): boolean

    Returns true if the curve is closed. Examples : 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

    Returns true if the parameter of the curve is 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. raises if the 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_Pnt2d

    Computes the point of parameter U. Raises an exception on failure.

    Parameters (1)
    • U
  • EvalD1(U: number): Geom2d_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): Geom2d_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): Geom2d_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_Vec2d

    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_Pnt2d): 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_Pnt2d, V1: gp_Vec2d): 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_Pnt2d, V1: gp_Vec2d, V2: gp_Vec2d): 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_Pnt2d, V1: gp_Vec2d, V2: gp_Vec2d, V3: gp_Vec2d): 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_Vec2d

    Computes the Nth derivative vector.

    Parameters (2)
    • U
    • N
  • Value(U: number): gp_Pnt2d

    Computes the point of parameter U on <me>. Implemented with D0.

    Parameters (1)
    • U
  • DynamicType(): Standard_Type

Geom2d_Direction

Geom2d_VectorGeom2d_GeometryStandard_Transient

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

Constructors(2)

Static methods(2)

Instance methods(11)

  • SetCoord(X: number, Y: number): void

    Assigns the coordinates X and Y to this unit vector, then normalizes it. Exceptions Standard_ConstructionError if std::sqrt(XX + YY) is less than or equal to gp::Resolution().

    Parameters (2)
    • X
    • Y
  • SetDir2d(V: gp_Dir2d): void

    Converts the gp_Dir2d unit vector V into this unit vector.

    Parameters (1)
    • V
  • SetX(X: number): void

    Assigns a value to the X coordinate of this unit vector, then normalizes it. Exceptions Standard_ConstructionError if the value assigned causes the magnitude of the vector to become less than or equal to gp::Resolution().

    Parameters (1)
    • X
  • SetY(Y: number): void

    Assigns a value to the Y coordinate of this unit vector, then normalizes it. Exceptions Standard_ConstructionError if the value assigned causes the magnitude of the vector to become less than or equal to gp::Resolution().

    Parameters (1)
    • Y
  • Dir2d(): gp_Dir2d

    Converts this unit vector into a gp_Dir2d unit vector.

  • Magnitude(): number

    returns 1.0

  • SquareMagnitude(): number

    returns 1.0

  • Crossed(Other: Geom2d_Vector): number

    Computes the cross product between <me> and <Other>.

    Parameters (1)
    • Other
  • Transform(T: gp_Trsf2d): void

    Applies the transformation T to this unit vector, then normalizes it.

    Parameters (1)
    • T
  • Copy(): Geom2d_Geometry

    Creates a new object which is a copy of this unit vector.

  • DynamicType(): Standard_Type

Geom2d_Ellipse

Geom2d_ConicGeom2d_CurveGeom2d_GeometryStandard_Transient

Describes an ellipse in the plane (2D space). An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in the plane with a coordinate system (gp_Ax22d 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. This coordinate system is the local coordinate system of the ellipse. The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the ellipse, determining the direction in which the parameter increases along the ellipse. The Geom2d_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 [. See Also GCE2d_MakeEllipse which provides functions for more complex ellipse constructions gp_Ax22d gp_Elips2d for an equivalent, non-parameterized data structure

Constructors(3)

  • constructor(E: gp_Elips2d): Geom2d_Ellipse

    Creates an ellipse by conversion of the gp_Elips2d ellipse E.

    Parameters (1)
    • E
  • constructor(Axis: gp_Ax22d, MajorRadius: number, MinorRadius: number): Geom2d_Ellipse

    Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where the coordinate system Axis locates the ellipse and defines its orientation in the plane such that:

    • the center of the ellipse is the origin of Axis,
    • the "X Direction" of Axis defines the major axis of the ellipse,
    • the "Y Direction" of Axis defines the minor axis of the ellipse,
    • the orientation of Axis (direct or indirect) gives the orientation of the ellipse. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if:
    • MajorRadius is less than MinorRadius, or
    • MinorRadius is less than 0.
    Parameters (3)
    • Axis
    • MajorRadius
    • MinorRadius
  • constructor(MajorAxis: gp_Ax2d, MajorRadius: number, MinorRadius: number, Sense?: boolean): Geom2d_Ellipse

    Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, and positioned in the plane by its major axis MajorAxis; the center of the ellipse is the origin of MajorAxis and the unit vector of MajorAxis is the "X Direction" of the local coordinate system of the ellipse; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if:

    • MajorRadius is less than MinorRadius, or
    • MinorRadius is less than 0.
    Parameters (4)
    • MajorAxis
    • MajorRadius
    • MinorRadius
    • Sense

Static methods(2)

Instance methods(26)

  • SetElips2d(E: gp_Elips2d): void

    Converts the gp_Elips2d ellipse E into this ellipse.

    Parameters (1)
    • E
  • SetMajorRadius(MajorRadius: number): void

    Assigns a value to the major radius of this ellipse. Exceptions Standard_ConstructionError if:

    • the major radius of this ellipse becomes less than the minor radius, or
    • MinorRadius is less than 0.
    Parameters (1)
    • MajorRadius
  • SetMinorRadius(MinorRadius: number): void

    Assigns a value to the minor radius of this ellipse. Exceptions Standard_ConstructionError if:

    • the major radius of this ellipse becomes less than the minor radius, or
    • MinorRadius is less than 0.
    Parameters (1)
    • MinorRadius
  • Elips2d(): gp_Elips2d

    Converts this ellipse into a gp_Elips2d ellipse.

  • 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_Ax2d

    Computes the directrices of this ellipse. 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". Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle).

  • Directrix2(): gp_Ax2d

    This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. Raises ConstructionError 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. The focal distance is the distance between the center and a focus of the ellipse.

  • Focus1(): gp_Pnt2d

    Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse.

  • Focus2(): gp_Pnt2d

    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

    Computes the parameter of this ellipse. This value is given by the formula 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 0.0, which gives the start point of this ellipse. 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 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_Pnt2d

    Returns in P 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): Geom2d_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): Geom2d_Curve_ResD2

    Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    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_Trsf2d): void

    Applies the transformation T to this ellipse.

    Parameters (1)
    • T
  • Copy(): Geom2d_Geometry

    Creates a new object which is a copy of this ellipse.

  • DynamicType(): Standard_Type

Geom2d_Geometry

Standard_Transient

The general abstract class Geometry in 2D space describes the common behaviour of all the geometric entities.
All the objects derived from this class can be move with a geometric transformation. Only the transformations which doesn't modify the nature of the geometry are available in this package. The method Transform which defines a general transformation is deferred. The other specifics transformations used the method Transform. All the following transformations modify the object itself.
Warning Only transformations which do not modify the nature of the geometry can be applied to Geom2d objects: this is the case with translations, rotations, symmetries and scales; this is also the case with gp_Trsf2d 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)

Instance methods(16)

Geom2d_Hyperbola

Geom2d_ConicGeom2d_CurveGeom2d_GeometryStandard_Transient

Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii and, as with any conic curve, is positioned in the plane with a coordinate system (gp_Ax22d 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. This 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 orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the hyperbola, determining the direction in which the parameter increases along the hyperbola. The Geom2d_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: ^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).
    See Also GCE2d_MakeHyperbola which provides functions for more complex hyperbola constructions gp_Ax22d gp_Hypr2d for an equivalent, non-parameterized data structure

Constructors(3)

  • constructor(H: gp_Hypr2d): Geom2d_Hyperbola

    Creates an Hyperbola from a non persistent one from package gp.

    Parameters (1)
    • H
  • constructor(Axis: gp_Ax22d, MajorRadius: number, MinorRadius: number): Geom2d_Hyperbola

    The XDirection of "Axis" is the "XAxis" of the hyperbola and the YDirection of "Axis" is the "YAxis". The major radius of the hyperbola is on this "XAxis" and the minor radius is on the "YAxis" of the hyperbola. Raised if MajorRadius < 0.0 or if MinorRadius < 0.0.

    Parameters (3)
    • Axis
    • MajorRadius
    • MinorRadius
  • constructor(MajorAxis: gp_Ax2d, MajorRadius: number, MinorRadius: number, Sense?: boolean): Geom2d_Hyperbola

    MajorAxis is the "XAxis" of the hyperbola. The YAxis is in the direct sense if "Sense" is True; The major radius of the hyperbola is on this "XAxis" and the minor radius is on the "YAxis" of the hyperbola. Raised if MajorRadius < 0.0 or if MinorRadius < 0.0.

    Parameters (4)
    • MajorAxis
    • MajorRadius
    • MinorRadius
    • Sense

Static methods(2)

Instance methods(31)

  • SetHypr2d(H: gp_Hypr2d): void

    Converts the gp_Hypr2d hyperbola H into this hyperbola.

    Parameters (1)
    • H
  • SetMajorRadius(MajorRadius: number): void

    Assigns a value to the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if:

    • MajorRadius is less than 0.0,
    • MinorRadius is less than 0.0.
    Parameters (1)
    • MajorRadius
  • SetMinorRadius(MinorRadius: number): void

    Assigns a value to the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if:

    • MajorRadius is less than 0.0,
    • MinorRadius is less than 0.0.
    Parameters (1)
    • MinorRadius
  • Hypr2d(): gp_Hypr2d

    Converts this hyperbola into a gp_Hypr2d one.

  • 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_Ax2d

    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 where A is the major radius of the hyperbola and B is the minor radius of the hyperbola. Raised if MajorRadius = 0.0.

  • Asymptote2(): gp_Ax2d

    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. where A is the major radius of the hyperbola and B is the minor radius of the hyperbola. raised if MajorRadius = 0.0.

  • ConjugateBranch1(): gp_Hypr2d

    Computes the first conjugate branch relative to this hyperbola. Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola.

  • ConjugateBranch2(): gp_Hypr2d

    Computes the second conjugate branch relative to this hyperbola. 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_Ax2d

    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_Ax2d

    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_Pnt2d

    Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola.

  • Focus2(): gp_Pnt2d

    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_Hypr2d

    Computes the "other" branch of this hyperbola. This is a 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. ^ YAxis | FirstConjugateBranch | Other | Main --------------------------- C -----------------------------------------&gtXAxis Branch | Branch | | SecondConjugateBranch | Warning The major radius can be less than the minor radius.

  • Parameter(): number

    Computes the parameter of this hyperbola. The parameter is: p = (e*e - 1) * MajorRadius where e is the eccentricity of this hyperbola and MajorRadius its major radius. Exceptions Standard_DomainError if the major radius of this hyperbola is null.

  • EvalD0(U: number): gp_Pnt2d

    Returns in P 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): Geom2d_Curve_ResD1

    Returns the point P of parameter U and the first derivative V1.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_Curve_ResD2

    Returns the point P of parameter U, the first and second derivatives V1 and V2.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    For the point of parameter U of this hyperbola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.

    Parameters (2)
    • U
    • N
  • Transform(T: gp_Trsf2d): void

    Applies the transformation T to this hyperbola.

    Parameters (1)
    • T
  • Copy(): Geom2d_Geometry

    Creates a new object which is a copy of this hyperbola.

  • DynamicType(): Standard_Type

Geom2d_Line

Geom2d_CurveGeom2d_GeometryStandard_Transient

Describes an infinite line in the plane (2D space). A line is defined and positioned in the plane with an axis (gp_Ax2d object) which gives it an origin and a unit vector. The Geom2d_Line line is parameterized as follows: 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. See Also GCE2d_MakeLine which provides functions for more complex line constructions gp_Ax2d gp_Lin2d for an equivalent, non-parameterized data structure.

Constructors(3)

Static methods(2)

Instance methods(27)

  • SetLin2d(L: gp_Lin2d): void

    Set <me> so that <me> has the same geometric properties as L.

    Parameters (1)
    • L
  • SetDirection(V: gp_Dir2d): void

    changes the direction of the line.

    Parameters (1)
    • V
  • Direction(): gp_Dir2d

    changes the direction of the line.

  • SetLocation(P: gp_Pnt2d): void

    Changes the "Location" point (origin) of the line.

    Parameters (1)
    • P
  • Location(): gp_Pnt2d

    Changes the "Location" point (origin) of the line.

  • SetPosition(A: gp_Ax2d): void

    Changes the "Location" and a the "Direction" of <me>.

    Parameters (1)
    • A
  • Position(): gp_Ax2d
  • Lin2d(): gp_Lin2d

    Returns non persistent line from gp with the same geometric properties as <me>.

  • 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 RealFirst from Standard.

  • LastParameter(): number

    Returns RealLast from Standard.

  • IsClosed(): boolean

    Returns False.

  • IsPeriodic(): boolean

    Returns False.

  • Continuity(): GeomAbs_Shape

    Returns GeomAbs_CN, which is the global continuity of any line.

  • Distance(P: gp_Pnt2d): number

    Computes the distance between <me> and the point P.

    Parameters (1)
    • P
  • IsCN(N: number): boolean

    Returns True.

    Parameters (1)
    • N
  • EvalD0(U: number): gp_Pnt2d

    Returns in P 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): Geom2d_Curve_ResD1

    Returns the point P of parameter u and the first derivative V1.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_Curve_ResD2

    Returns the point P of parameter U, the first and second derivatives V1 and V2. V2 is a vector with null magnitude for a line.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    V2 and V3 are vectors with null magnitude for a line.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    For the point of parameter U of this line, computes the vector corresponding to the Nth derivative. Note: if N is greater than or equal to 2, the result is a vector with null magnitude. Exceptions Standard_RangeError if N is less than 1.

    Parameters (2)
    • U
    • N
  • Transform(T: gp_Trsf2d): void

    Applies the transformation T to this line.

    Parameters (1)
    • T
  • TransformedParameter(U: number, T: gp_Trsf2d): number

    Computes the parameter on the line transformed by T for the point of parameter U on this line. For a line, the returned value is equal to U multiplied by the scale factor of transformation T.

    Parameters (2)
    • U
    • T
  • ParametricTransformation(T: gp_Trsf2d): number

    Returns the coefficient required to compute the parametric transformation of this line when transformation T is applied. This coefficient is the ratio between the parameter of a point on this line and the parameter of the transformed point on the new line transformed by T. For a line, the returned value is the scale factor of the transformation T.

    Parameters (1)
    • T
  • Copy(): Geom2d_Geometry

    Creates a new object, which is a copy of this line.

  • DynamicType(): Standard_Type

Geom2d_OffsetCurve

Geom2d_CurveGeom2d_GeometryStandard_Transient

This class implements the basis services for the creation, edition, modification and evaluation of planar offset curve. The offset curve is obtained by offsetting by distance along the normal to a basis curve defined in 2D 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 and the offset curve takes its parametrization from the basis curve. The Offset curve is in the direction of the normal to the basis curve N.
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 ^ Z)) / ||T ^ Z|| where T is the tangent vector to the basis curve and Z the direction of the normal vector to the plane of the curve, N = T ^ Z defines the offset direction and should not have null length.
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^Z|| != 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: Geom2d_OffsetCurve): Geom2d_OffsetCurve

    Copy constructor for optimized copying without validation.

    Parameters (1)
    • theOther
  • constructor(C: Geom2d_Curve, Offset: number, isNotCheckC0?: boolean): Geom2d_OffsetCurve

    Constructs a curve offset from the basis curve C, where Offset is the distance between the offset curve and the basis curve at any point. A point on the offset curve is built by measuring the offset value along a normal vector at a point on C. This normal vector is obtained by rotating the vector tangential to C at 90 degrees in the anti-trigonometric sense.
    The side of C on which the offset value is measured is indicated by this normal vector if Offset is positive, or in the inverse sense if Offset is negative. 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 Warning! if isNotCheckC0 = false, ConstructionError raised if the basis curve C is not at least C1. No check is done to know if ||V^Z|| != 0.0 at any point.

    Parameters (3)
    • C
    • Offset
    • isNotCheckC0

Static methods(2)

Instance methods(28)

  • HasEvalRepresentation(): boolean

    Returns true if an evaluation representation is attached.

  • EvalRepresentation(): Geom2dEval_RepCurveDesc_Base

    Returns the current evaluation representation descriptor (may be null).

  • SetEvalRepresentation(theDesc: Geom2dEval_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 direction of parametrization of <me>. 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: Geom2d_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 if isNotCheckC0 = false, Standard_ConstructionError if the curve C is not at least "C1" continuous.

    Parameters (2)
    • C
    • isNotCheckC0
  • SetOffsetValue(D: number): void

    Changes this offset curve by assigning D as the offset value.

    Parameters (1)
    • D
  • BasisCurve(): Geom2d_Curve

    Returns the basis curve of this offset curve. The basis curve can be an offset curve.

  • Continuity(): GeomAbs_Shape

    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 normal direction defined at any point. 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 Z the direction normal to the plane of the curve, the relation ||T(U) ^ Z|| != 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_Pnt2d

    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): Geom2d_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 portion where the curve is C2.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_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 portion where the curve is C3.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    Warning! This should not be called if the continuity of the basis curve is not C4. Nevertheless, it's OK to use it on portion where the curve is C4.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    The returned vector gives the value of the derivative for the order of derivation N. Warning! this should not be called raises UndefunedDerivative if the continuity of the basis curve is not CN+1. Nevertheless, it's OK to use it on portion where the curve is CN+1 raises RangeError if N < 1. raises NotImplemented if N > 3. 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 Warnings : The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction.

    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

    Is the order of continuity of the curve N ? Warnings : 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

    Is the parametrization of a curve is periodic ? If the basis curve is a circle or an ellipse the corresponding OffsetCurve is periodic. If the basis curve can't be periodic (for example BezierCurve) the OffsetCurve can't be 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_Trsf2d): void

    Applies the transformation T to this offset curve. Note: the basis curve is also modified.

    Parameters (1)
    • T
  • TransformedParameter(U: number, T: gp_Trsf2d): 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_Trsf2d): 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(): Geom2d_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

Geom2d_Parabola

Geom2d_ConicGeom2d_CurveGeom2d_GeometryStandard_Transient

Describes a parabola in the plane (2D space). A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in the plane with a coordinate system (gp_Ax22d object) where:

  • the origin is the apex of the parabola, and
  • the "X Axis" defines the axis of symmetry; the parabola is on the positive side of this axis. This coordinate system is the local coordinate system of the parabola. The orientation (direct or indirect) 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(4)

  • constructor(Prb: gp_Parab2d): Geom2d_Parabola

    Creates a parabola from a non persistent one.

    Parameters (1)
    • Prb
  • constructor(Axis: gp_Ax22d, Focal: number): Geom2d_Parabola

    Creates a parabola with its Axis and it's focal length "Focal". The XDirection of Axis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola. The "Location" point of "Axis" is the vertex of the parabola. Raised if Focal < 0.0.

    Parameters (2)
    • Axis
    • Focal
  • constructor(D: gp_Ax2d, F: gp_Pnt2d): Geom2d_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.

    Parameters (2)
    • D
    • F
  • constructor(MirrorAxis: gp_Ax2d, Focal: number, Sense?: boolean): Geom2d_Parabola

    Creates a parabola with its "MirrorAxis" and it's focal length "Focal". MirrorAxis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola and is in the direct sense if Sense is True. The "Location" point of "MirrorAxis" is the vertex of the parabola Raised if Focal < 0.0.

    Parameters (3)
    • MirrorAxis
    • Focal
    • Sense

Static methods(2)

Instance methods(23)

  • SetFocal(Focal: number): void

    Assigns the value Focal to the focal length of this parabola. Exceptions Standard_ConstructionError if Focal is negative.

    Parameters (1)
    • Focal
  • SetParab2d(Prb: gp_Parab2d): void

    Converts the gp_Parab2d parabola Prb into this parabola.

    Parameters (1)
    • Prb
  • Parab2d(): gp_Parab2d

    Returns the non persistent 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 RealFirst from Standard.

  • LastParameter(): number

    Returns RealLast from Standard.

  • IsClosed(): boolean

    Returns False.

  • IsPeriodic(): boolean

    Returns False.

  • Directrix(): gp_Ax2d

    The directrix is parallel to the "YAxis" of the parabola. The "Location" point of the directrix is the intersection point between the directrix and the symmetry axis ("XAxis") of the parabola.

  • Eccentricity(): number

    Returns the eccentricity e = 1.0.

  • Focus(): gp_Pnt2d

    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 length of this parabola. The focal length 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_Pnt2d

    Returns in P 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): Geom2d_Curve_ResD1

    Returns the point P of parameter U and the first derivative V1.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_Curve_ResD2

    Returns the point P of parameter U, the first and second derivatives V1 and V2.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    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_Trsf2d): void

    Applies the transformation T to this parabola.

    Parameters (1)
    • T
  • TransformedParameter(U: number, T: gp_Trsf2d): number

    Computes the parameter on the transformed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is equal to U multiplied by the scale factor of transformation T.

    Parameters (2)
    • U
    • T
  • ParametricTransformation(T: gp_Trsf2d): 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(): Geom2d_Geometry

    Creates a new object, which is a copy of this parabola.

  • DynamicType(): Standard_Type

Geom2d_Point

Geom2d_GeometryStandard_Transient

The abstract class Point describes the common behavior of geometric points in 2D space. The Geom2d package also provides the concrete class Geom2d_CartesianPoint.

Static methods(2)

Instance methods(7)

  • Coord(X: number, Y: number): { X: number; Y: number }

    returns the Coordinates of <me>.

    Parameters (2)
    • X
    • Y
    Returns

    A result object with fields:

    • X: updated value from the call.
    • Y: updated value from the call.
  • Pnt2d(): gp_Pnt2d

    returns a non persistent copy of <me>

  • X(): number

    returns the X coordinate of <me>.

  • Y(): number

    returns the Y coordinate of <me>.

  • Distance(Other: Geom2d_Point): number

    computes the distance between <me> and <Other>.

    Parameters (1)
    • Other
  • SquareDistance(Other: Geom2d_Point): number

    computes the square distance between <me> and <Other>.

    Parameters (1)
    • Other
  • DynamicType(): Standard_Type

Geom2d_Transformation

Standard_Transient

The class Transformation allows to create Translation, Rotation, Symmetry, Scaling and complex transformations obtained by combination of the previous elementary transformations.
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 Geom2d_Transformation. The transformation can be represented as follows:
V1 V2 T | a11 a12 a14 | | x | | x'| | a21 a22 a24 | | y | | y'| | 0 0 1 | | 1 | | 1 |
where {V1, V2} defines the vectorial part of the transformation and T defines the translation part of the transformation.

  • Geom2d_Transformation transformations provide the same kind of "geometric" services as gp_Trsf2d ones but have more complex data structures. The geometric objects provided by the Geom2d package use gp_Trsf2d transformations in the syntaxes Transform and Transformed.
  • Geom2d_Transformation transformations are used in a context where they can be shared by several objects contained inside a common data structure.

Constructors(2)

Static methods(2)

Instance methods(24)

  • SetMirror(P: gp_Pnt2d): void

    Makes the transformation into a symmetrical transformation with respect to a point P. P is the center of the symmetry.

    Parameters (1)
    • P
  • SetMirror(A: gp_Ax2d): void

    Makes the transformation into a symmetrical transformation with respect to an axis A. A is the center of the axial symmetry.

    Parameters (1)
    • A
  • SetRotation(P: gp_Pnt2d, Ang: number): void

    Assigns to this transformation the geometric properties of a rotation at angle Ang (in radians) about point P.

    Parameters (2)
    • P
    • Ang
  • SetScale(P: gp_Pnt2d, S: number): void

    Makes the transformation into a scale. P is the center of the scale and S is the scaling value.

    Parameters (2)
    • P
    • S
  • SetTransformation(FromSystem1: gp_Ax2d, ToSystem2: gp_Ax2d): void

    Makes a transformation allowing passage from the coordinate system "FromSystem1" to the coordinate system "ToSystem2".

    Parameters (2)
    • FromSystem1
    • ToSystem2
  • SetTransformation(ToSystem: gp_Ax2d): void

    Makes the transformation allowing passage from the basic coordinate system {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.)} to the local coordinate system defined with the Ax2d ToSystem.

    Parameters (1)
    • ToSystem
  • SetTranslation(V: gp_Vec2d): void

    Makes the transformation into a translation. V is the vector of the translation.

    Parameters (1)
    • V
  • SetTranslation(P1: gp_Pnt2d, P2: gp_Pnt2d): void

    Makes the transformation into a translation from the point P1 to the point P2.

    Parameters (2)
    • P1
    • P2
  • SetTrsf2d(T: gp_Trsf2d): void

    Makes the transformation into a transformation T from package gp.

    Parameters (1)
    • T
  • 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. Returns the nature of the transformation. It can be Identity, Rotation, Translation, PntMirror, Ax1Mirror, Scale, CompoundTrsf.

  • ScaleFactor(): number

    Returns the scale value of the transformation.

  • Trsf2d(): gp_Trsf2d

    Converts this transformation into a gp_Trsf2d transformation. Returns a non persistent copy of <me>. -C++: return const&.

  • Value(Row: number, Col: number): number

    Returns the coefficients of the global matrix of transformation. It is a 2 rows X 3 columns matrix.
    Raised if Row < 1 or Row > 2 or Col < 1 or Col > 2
    Computes the reverse transformation.

    Parameters (2)
    • Row
    • Col
  • Invert(): void

    Computes the inverse of this transformation and assigns the result to this transformation.
    Raised if the transformation is singular. This means that the ScaleFactor is lower or equal to Resolution from package gp.

  • Inverted(): Geom2d_Transformation

    Computes the inverse of this transformation and creates a new one. Raises ConstructionError if the transformation is singular. This means that the ScaleFactor is lower or equal to Resolution from package gp.

  • Multiplied(Other: Geom2d_Transformation): Geom2d_Transformation

    Computes the transformation composed with Other and <me>. <me> * Other. Returns a new transformation.

    Parameters (1)
    • Other
  • Multiply(Other: Geom2d_Transformation): void

    Computes the transformation composed with Other and <me> . <me> = <me> * Other.
    Computes the following composition of transformations if N > 0 <me> * <me> * .......* <me>. if N = 0 Identity if N < 0 <me>.Invert() * .........* <me>.Invert()

    Parameters (1)
    • Other
  • Power(N: number): void

    Raised if N < 0 and if the transformation is not inversible.

    Parameters (1)
    • N
  • Powered(N: number): Geom2d_Transformation

    Raised if N < 0 and if the transformation is not inversible.

    Parameters (1)
    • N
  • PreMultiply(Other: Geom2d_Transformation): void

    Computes the matrix of the transformation composed with <me> and Other. <me> = Other * <me>.

    Parameters (1)
    • Other
  • Transforms(X: number, Y: number): { X: number; Y: number }

    Applies the transformation <me> to the triplet {X, Y}.

    Parameters (2)
    • X
    • Y
    Returns

    A result object with fields:

    • X: updated value from the call.
    • Y: updated value from the call.
  • Copy(): Geom2d_Transformation

    Creates a new object, which is a copy of this transformation.

  • DynamicType(): Standard_Type

Geom2d_TrimmedCurve

Geom2d_BoundedCurveGeom2d_CurveGeom2d_GeometryStandard_Transient

Defines a portion of a curve limited by two values of parameters inside the parametric domain of the 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: Geom2d_Curve, U1: number, U2: number, Sense?: boolean, theAdjustPeriodic?: boolean): Geom2d_TrimmedCurve

    Creates a trimmed curve from the basis curve C limited between U1 and U2.
    . U1 can be greater or lower than U2. . 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 by default the trimmed curve has the same orientation as the basis curve (Sense = True). If Sense = False then the orientation of the trimmed curve is opposite to the orientation of the basis curve C.
    If the curve is closed but not periodic it is not possible to keep the part of the curve including the junction point (except if the junction point is at the beginning or at the end of the trimmed curve) because you could lose the fundamental characteristics of the basis curve which are used for example to compute the derivatives of the trimmed curve. So for a closed curve the rules are the same as for a open curve. Warnings : In this package the entities are not shared. The TrimmedCurve is built with a copy of the curve C.
    So when C is modified the TrimmedCurve is not modified Warnings : If is periodic and <theAdjustPeriodic> is True, parametrics bounds of the TrimmedCurve, can be different to [<U1>;<U2>}, if <U1> or <U2> are not in the principal period. Include : For more explanation see the scheme given with this class. Raises ConstructionError the C is not periodic and U1 or U2 are out of the bounds of C. Raised if U1 = U2.

    Parameters (5)
    • C
    • U1
    • U2
    • Sense
    • theAdjustPeriodic

Static methods(2)

Instance methods(23)

  • Reverse(): void

    Changes the direction of parametrization of <me>. The first and the last parametric values are 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. Example - If the trimmed curve is defined by:

    • a basis curve whose parameter range is [ 0.,1. ], and
    • 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. ], and
    • the two trim values 1. - U2 (first parameter) and 1. - U1 (last parameter).
  • 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
  • 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. If theAdjustPeriodic is False, parameters U1 and U2 will stay unchanged. 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(): Geom2d_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 global continuity of the basis curve of this trimmed 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

    -- Purpose Returns True if the order of continuity of the trimmed curve is 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_Pnt2d

    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_Pnt2d

    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.

  • EvalD0(U: number): gp_Pnt2d

    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): Geom2d_Curve_ResD1

    Raised if the continuity of the curve is not C1.

    Parameters (1)
    • U
  • EvalD2(U: number): Geom2d_Curve_ResD2

    Raised if the continuity of the curve is not C2.

    Parameters (1)
    • U
  • EvalD3(U: number): Geom2d_Curve_ResD3

    Raised if the continuity of the curve is not C3.

    Parameters (1)
    • U
  • EvalDN(U: number, N: number): gp_Vec2d

    For the point of parameter U of this trimmed curve, computes the vector corresponding to the Nth derivative. Warning The returned derivative vector has the same orientation as the derivative vector of the basis curve, even if the trimmed curve does not have the same orientation as the basis curve. Exceptions Standard_RangeError if N is less than 1. geometric transformations.

    Parameters (2)
    • U
    • N
  • Transform(T: gp_Trsf2d): void

    Applies the transformation T to this trimmed curve. Warning The basis curve is also modified.

    Parameters (1)
    • T
  • TransformedParameter(U: number, T: gp_Trsf2d): 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_Trsf2d): 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(): Geom2d_Geometry

    Creates a new object, which is a copy of this trimmed curve.

  • DynamicType(): Standard_Type

Geom2d_Vector

Geom2d_GeometryStandard_Transient

The abstract class Vector describes the common behavior of vectors in 2D space. The Geom2d package provides two concrete classes of vectors: Geom2d_Direction (unit vector) and Geom2d_VectorWithMagnitude.

Static methods(2)

Instance methods(12)

  • Reverse(): void

    Reverses the vector <me>.

  • Reversed(): Geom2d_Vector

    Returns a copy of <me> reversed.

  • Angle(Other: Geom2d_Vector): number

    Computes the angular value, in radians, between this vector and vector Other. The result is a value between -Pi and Pi. The orientation is from this vector to vector Other. Raises VectorWithNullMagnitude if one of the two vectors is a vector with null magnitude because the angular value is indefinite.

    Parameters (1)
    • Other
  • Coord(X: number, Y: number): { X: number; Y: number }

    Returns the coordinates of <me>.

    Parameters (2)
    • X
    • Y
    Returns

    A result object with fields:

    • X: updated value from the call.
    • Y: updated value from the call.
  • Magnitude(): number

    Returns the Magnitude of <me>.

  • SquareMagnitude(): number

    Returns the square magnitude of <me>.

  • X(): number

    Returns the X coordinate of <me>.

  • Y(): number

    Returns the Y coordinate of <me>.

  • Crossed(Other: Geom2d_Vector): number

    Cross product of <me> with the vector <Other>.

    Parameters (1)
    • Other
  • Dot(Other: Geom2d_Vector): number

    Returns the scalar product of 2 Vectors.

    Parameters (1)
    • Other
  • Vec2d(): gp_Vec2d

    Returns a non persistent copy of <me>.

  • DynamicType(): Standard_Type

Geom2d_VectorWithMagnitude

Geom2d_VectorGeom2d_GeometryStandard_Transient

Defines a vector with magnitude. A vector with magnitude can have a zero length.

Constructors(3)

Static methods(2)

Instance methods(20)

Adaptor2d

OCCT package Adaptor2d: Adaptor2d_Curve2d, Adaptor2d_Line2d, Adaptor2d_OffsetCurve.

Geom2dAdaptor

OCCT package Geom2dAdaptor: Geom2dAdaptor, Geom2dAdaptor_Curve.