BSplSLib

this is a one dimensional function typedef void (*EvaluatorFunction) ( int // Derivative Request double * // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end double // UParameter double // VParamerer double & // Result int &) ;// Error Code serves to multiply a given vectorial BSpline by a function Computes the derivatives of a ratio of two-variables functions x(u,v) / w(u,v) at orders <N,M>, x(u,v) is a vector in dimension <3>.
<Ders> is an array containing the values of the input derivatives from 0 to std::min(<N>,<UDeg>), 0 to std::min(<M>,<VDeg>). For orders higher than <UDeg,VDeg> the input derivatives are assumed to be 0.
The <Ders> is a 2d array and the dimension of the lines is always (<VDeg>+1) * (<3>+1), even if <N> is smaller than <Udeg> (the derivatives higher than <N> are not used).
Content of <Ders>:
x(i,j)[k] means: the composant k of x derivated (i) times in u and (j) times in v.
... First line ...
x[1],x[2],...,x[3],w x(0,1)[1],...,x(0,1)[3],w(1,0) ... x(0,VDeg)[1],...,x(0,VDeg)[3],w(0,VDeg)
... Then second line ...
x(1,0)[1],...,x(1,0)[3],w(1,0) x(1,1)[1],...,x(1,1)[3],w(1,1) ... x(1,VDeg)[1],...,x(1,VDeg)[3],w(1,VDeg)
...
... Last line ...
x(UDeg,0)[1],...,x(UDeg,0)[3],w(UDeg,0) x(UDeg,1)[1],...,x(UDeg,1)[3],w(UDeg,1) ... x(Udeg,VDeg)[1],...,x(UDeg,VDeg)[3],w(Udeg,VDeg)
If <All> is false, only the derivative at order <N,M> is computed. <RDers> is an array of length 3 which will contain the result :
x(1)/w , x(2)/w , ... derivated <N> <M> times
If <All> is true multiples derivatives are computed. All the derivatives (i,j) with 0 <= i+j <= std::max(N,M) are computed. <RDers> is an array of length 3 * (<N>+1) * (<M>+1) which will contains:
x(1)/w , x(2)/w , ... x(1)/w , x(2)/w , ... derivated <0,1> times x(1)/w , x(2)/w , ... derivated <0,2> times ... x(1)/w , x(2)/w , ... derivated <0,N> times
x(1)/w , x(2)/w , ... derivated <1,0> times x(1)/w , x(2)/w , ... derivated <1,1> times ... x(1)/w , x(2)/w , ... derivated <1,N> times
x(1)/w , x(2)/w , ... derivated <N,0> times .... Warning: <RDers> must be dimensioned properly.

Computes the poles and weights of an isoparametric curve at parameter (UIso if <IsU> is True, VIso else).

Makes an homogeneous evaluation of Poles and Weights any and returns in P the Numerator value and in W the Denominator value if Weights are present otherwise returns 1.0e0.

Makes an homogeneous evaluation of Poles and Weights any and returns in P the Numerator value and in W the Denominator value if Weights are present otherwise returns 1.0e0.

Returns False if all the weights of the array <Weights> in the area [I1,I2] * [J1,J2] are identic. Epsilon is used for comparing weights. If Epsilon is 0. the Epsilon of the first weight is used.

Find the new poles which allows an old point (with a given u,v as parameters) to reach a new position UIndex1,UIndex2 indicate the range of poles we can move for U (1, UNbPoles-1) or (2, UNbPoles) -> no constraint for one side in U (2, UNbPoles-1) -> the ends are enforced for U don't enter (1,NbPoles) and (1,VNbPoles) -> error: rigid move if problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0.

Used as argument for a non rational curve.

Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.

Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!

Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.

Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!

Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.

Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!

Given a tolerance in 3D space returns two tolerances, one in U one in V such that for all (u1,v1) and (u0,v0) in the domain of the surface f(u,v) we have : | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance we have |f (u1,v1) - f (u0,v0)| < Tolerance3D.

this will multiply a given BSpline numerator N(u,v) and denominator D(u,v) defined by its U/VBSplineDegree and U/VBSplineKnots, and U/VMults. Its Poles and Weights are arrays which are coded as array2 of the form [1..UNumPoles][1..VNumPoles] by a function a(u,v) which is assumed to satisfy the following:

1. a(u,v) * N(u,v) and a(u,v) * D(u,v) is a polynomial BSpline that can be expressed exactly as a BSpline of degree U/VNewDegree on the knots U/VFlatKnots
2. the range of a(u,v) is the same as the range of N(u,v) or D(u,v) Warning: it is the caller's responsibility to insure that conditions 1. and 2. above are satisfied no check whatsoever is made in this method theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(u,v)* N(u,v) and a(u,v) * D(u,v) theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline: the method used is interpolation at Schoenenberg
   *points of a(u,v)F(u,v)

Returns an NCollection_Array2<double> filled with 1.0 values. If theNbUPoles * theNbVPoles <= BSplCLib::MaxUnitWeightsSize(), references a pre-allocated global array (zero allocation). Otherwise, allocates a new array and fills with 1.0.

Constructor for caching of the span for the surface.

Verifies validity of the cache using parameters of the point.

Recomputes the cache data. Does not verify validity of the cache.

Calculates the point on the surface for specified parameters.

Calculates the point on the surface and its first derivative.

Calculates the point on the surface and derivatives till second order.

Calculates the point using pre-computed local parameters in [-1, 1] range. This bypasses periodic normalization and local parameter calculation.

Calculates the point and first derivatives using pre-computed local parameters in [-1, 1] range. This bypasses periodic normalization and local parameter calculation.

Calculates the point and derivatives till second order using pre-computed local parameters. This bypasses periodic normalization and local parameter calculation.

Function evaluation method to be defined by descendant.