Open CASCADE Technology  7.7.0.dev
Static Public Member Functions

BSplSLib Class Reference

BSplSLib B-spline surface Library This package provides an implementation of geometric functions for rational and non rational, periodic and non periodic B-spline surface computation. More...

#include <BSplSLib.hxx>

Static Public Member Functions

static void RationalDerivative (const Standard_Integer UDeg, const Standard_Integer VDeg, const Standard_Integer N, const Standard_Integer M, Standard_Real &Ders, Standard_Real &RDers, const Standard_Boolean All=Standard_True)
 this is a one dimensional function typedef void (*EvaluatorFunction) ( Standard_Integer // Derivative Request Standard_Real * // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end Standard_Real // UParameter Standard_Real // VParamerer Standard_Real & // Result Standard_Integer &) ;// 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>. More...
 
static void D0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P)
 
static void D1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer Degree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
 
static void D2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
 
static void D3 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
 
static void DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Vec &Vn)
 
static void Iso (const Standard_Real Param, const Standard_Boolean IsU, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, const Standard_Integer Degree, const Standard_Boolean Periodic, TColgp_Array1OfPnt &CPoles, TColStd_Array1OfReal *CWeights)
 Computes the poles and weights of an isoparametric curve at parameter (UIso if <IsU> is True, VIso else). More...
 
static void Reverse (TColgp_Array2OfPnt &Poles, const Standard_Integer Last, const Standard_Boolean UDirection)
 Reverses the array of poles. Last is the Index of the new first Row( Col) of Poles. On a non periodic surface Last is Poles.Upper(). On a periodic curve last is (number of flat knots - degree - 1) or (sum of multiplicities(but for the last) + degree. More...
 
static void HomogeneousD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, Standard_Real &W, gp_Pnt &P)
 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. More...
 
static void HomogeneousD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &N, gp_Vec &Nu, gp_Vec &Nv, Standard_Real &D, Standard_Real &Du, Standard_Real &Dv)
 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. More...
 
static void Reverse (TColStd_Array2OfReal &Weights, const Standard_Integer Last, const Standard_Boolean UDirection)
 Reverses the array of weights. More...
 
static Standard_Boolean IsRational (const TColStd_Array2OfReal &Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer J1, const Standard_Integer J2, const Standard_Real Epsilon=0.0)
 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. More...
 
static void SetPoles (const TColgp_Array2OfPnt &Poles, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection)
 Copy in FP the coordinates of the poles. More...
 
static void SetPoles (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection)
 Copy in FP the coordinates of the poles. More...
 
static void GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, const Standard_Boolean UDirection)
 Get from FP the coordinates of the poles. More...
 
static void GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &Weights, const Standard_Boolean UDirection)
 Get from FP the coordinates of the poles. More...
 
static void MovePoint (const Standard_Real U, const Standard_Real V, const gp_Vec &Displ, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean Rational, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, Standard_Integer &UFirstIndex, Standard_Integer &ULastIndex, Standard_Integer &VFirstIndex, Standard_Integer &VLastIndex, TColgp_Array2OfPnt &NewPoles)
 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. More...
 
static void InsertKnots (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger *AddMults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True)
 
static Standard_Boolean RemoveKnot (const Standard_Boolean UDirection, const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance)
 
static void IncreaseDegree (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults)
 
static void Unperiodize (const Standard_Boolean UDirection, const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal *NewWeights)
 
static TColStd_Array2OfRealNoWeights ()
 Used as argument for a non rational curve. More...
 
static void BuildCache (const Standard_Real U, const Standard_Real V, const Standard_Real USpanDomain, const Standard_Real VSpanDomain, const Standard_Boolean UPeriodicFlag, const Standard_Boolean VPeriodicFlag, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, TColgp_Array2OfPnt &CachePoles, TColStd_Array2OfReal *CacheWeights)
 Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles. More...
 
static void BuildCache (const Standard_Real theU, const Standard_Real theV, const Standard_Real theUSpanDomain, const Standard_Real theVSpanDomain, const Standard_Boolean theUPeriodic, const Standard_Boolean theVPeriodic, const Standard_Integer theUDegree, const Standard_Integer theVDegree, const Standard_Integer theUIndex, const Standard_Integer theVIndex, const TColStd_Array1OfReal &theUFlatKnots, const TColStd_Array1OfReal &theVFlatKnots, const TColgp_Array2OfPnt &thePoles, const TColStd_Array2OfReal *theWeights, TColStd_Array2OfReal &theCacheArray)
 Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplSLib_Cache. More...
 
static void CacheD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point)
 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. More...
 
static void CoefsD0 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point)
 Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!! More...
 
static void CacheD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV)
 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. More...
 
static void CoefsD1 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV)
 Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!! More...
 
static void CacheD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV, gp_Vec &VecUU, gp_Vec &VecUV, gp_Vec &VecVV)
 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. More...
 
static void CoefsD2 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV, gp_Vec &VecUU, gp_Vec &VecUV, gp_Vec &VecVV)
 Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!! More...
 
static void PolesCoefficients (const TColgp_Array2OfPnt &Poles, TColgp_Array2OfPnt &CachePoles)
 Warning! To be used for BezierSurfaces ONLY!!! More...
 
static void PolesCoefficients (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, TColgp_Array2OfPnt &CachePoles, TColStd_Array2OfReal *CacheWeights)
 Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziersurfaces at parameters 0.,0.; Warning: To be used for BezierSurfaces ONLY!!! More...
 
static void Resolution (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &VTolerance)
 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. More...
 
static void Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColStd_Array1OfReal &UParameters, const TColStd_Array1OfReal &VParameters, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &Weights, Standard_Integer &InversionProblem)
 Performs the interpolation of the data points given in the Poles array in the form [1,...,RL][1,...,RC][1...PolesDimension] . The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1. More...
 
static void Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColStd_Array1OfReal &UParameters, const TColStd_Array1OfReal &VParameters, TColgp_Array2OfPnt &Poles, Standard_Integer &InversionProblem)
 Performs the interpolation of the data points given in the Poles array. The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1. More...
 
static void FunctionMultiply (const BSplSLib_EvaluatorFunction &Function, const Standard_Integer UBSplineDegree, const Standard_Integer VBSplineDegree, const TColStd_Array1OfReal &UBSplineKnots, const TColStd_Array1OfReal &VBSplineKnots, const TColStd_Array1OfInteger *UMults, const TColStd_Array1OfInteger *VMults, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const Standard_Integer UNewDegree, const Standard_Integer VNewDegree, TColgp_Array2OfPnt &NewNumerator, TColStd_Array2OfReal &NewDenominator, Standard_Integer &theStatus)
 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 More...
 

Detailed Description

BSplSLib B-spline surface Library This package provides an implementation of geometric functions for rational and non rational, periodic and non periodic B-spline surface computation.

this package uses the multi-dimensions splines methods provided in the package BSplCLib.

In this package the B-spline surface is defined with : . its control points : Array2OfPnt Poles . its weights : Array2OfReal Weights . its knots and their multiplicity in the two parametric direction U and V : Array1OfReal UKnots, VKnots and Array1OfInteger UMults, VMults. . the degree of the normalized Spline functions : UDegree, VDegree

. the Booleans URational, VRational to know if the weights are constant in the U or V direction.

. the Booleans UPeriodic, VRational to know if the the surface is periodic in the U or V direction.

Warnings : The bounds of UKnots and UMults should be the same, the bounds of VKnots and VMults should be the same, the bounds of Poles and Weights should be the same.

The Control points representation is : Poles(Uorigin,Vorigin) ...................Poles(Uorigin,Vend) . . . . Poles(Uend, Vorigin) .....................Poles(Uend, Vend)

For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction.

Note: weight and multiplicity arrays can be passed by pointer for some functions so that NULL pointer is valid. That means no weights/no multiplicities passed.

KeyWords : B-spline surface, Functions, Library

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

Member Function Documentation

◆ BuildCache() [1/2]

static void BSplSLib::BuildCache ( const Standard_Real  theU,
const Standard_Real  theV,
const Standard_Real  theUSpanDomain,
const Standard_Real  theVSpanDomain,
const Standard_Boolean  theUPeriodic,
const Standard_Boolean  theVPeriodic,
const Standard_Integer  theUDegree,
const Standard_Integer  theVDegree,
const Standard_Integer  theUIndex,
const Standard_Integer  theVIndex,
const TColStd_Array1OfReal theUFlatKnots,
const TColStd_Array1OfReal theVFlatKnots,
const TColgp_Array2OfPnt thePoles,
const TColStd_Array2OfReal theWeights,
TColStd_Array2OfReal theCacheArray 
)
static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplSLib_Cache.

◆ BuildCache() [2/2]

static void BSplSLib::BuildCache ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Real  USpanDomain,
const Standard_Real  VSpanDomain,
const Standard_Boolean  UPeriodicFlag,
const Standard_Boolean  VPeriodicFlag,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColStd_Array1OfReal UFlatKnots,
const TColStd_Array1OfReal VFlatKnots,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
TColgp_Array2OfPnt CachePoles,
TColStd_Array2OfReal CacheWeights 
)
static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles.

◆ CacheD0()

static void BSplSLib::CacheD0 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Real  UCacheParameter,
const Standard_Real  VCacheParameter,
const Standard_Real  USpanLenght,
const Standard_Real  VSpanLength,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point 
)
static

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.

◆ CacheD1()

static void BSplSLib::CacheD1 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Real  UCacheParameter,
const Standard_Real  VCacheParameter,
const Standard_Real  USpanLenght,
const Standard_Real  VSpanLength,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point,
gp_Vec VecU,
gp_Vec VecV 
)
static

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.

◆ CacheD2()

static void BSplSLib::CacheD2 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Real  UCacheParameter,
const Standard_Real  VCacheParameter,
const Standard_Real  USpanLenght,
const Standard_Real  VSpanLength,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point,
gp_Vec VecU,
gp_Vec VecV,
gp_Vec VecUU,
gp_Vec VecUV,
gp_Vec VecVV 
)
static

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.

◆ CoefsD0()

static void BSplSLib::CoefsD0 ( const Standard_Real  U,
const Standard_Real  V,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point 
)
static

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

◆ CoefsD1()

static void BSplSLib::CoefsD1 ( const Standard_Real  U,
const Standard_Real  V,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point,
gp_Vec VecU,
gp_Vec VecV 
)
static

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

◆ CoefsD2()

static void BSplSLib::CoefsD2 ( const Standard_Real  U,
const Standard_Real  V,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point,
gp_Vec VecU,
gp_Vec VecV,
gp_Vec VecUU,
gp_Vec VecUV,
gp_Vec VecVV 
)
static

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

◆ D0()

static void BSplSLib::D0 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
gp_Pnt P 
)
static

◆ D1()

static void BSplSLib::D1 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  Degree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
gp_Pnt P,
gp_Vec Vu,
gp_Vec Vv 
)
static

◆ D2()

static void BSplSLib::D2 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
gp_Pnt P,
gp_Vec Vu,
gp_Vec Vv,
gp_Vec Vuu,
gp_Vec Vvv,
gp_Vec Vuv 
)
static

◆ D3()

static void BSplSLib::D3 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
gp_Pnt P,
gp_Vec Vu,
gp_Vec Vv,
gp_Vec Vuu,
gp_Vec Vvv,
gp_Vec Vuv,
gp_Vec Vuuu,
gp_Vec Vvvv,
gp_Vec Vuuv,
gp_Vec Vuvv 
)
static

◆ DN()

static void BSplSLib::DN ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  Nu,
const Standard_Integer  Nv,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
gp_Vec Vn 
)
static

◆ FunctionMultiply()

static void BSplSLib::FunctionMultiply ( const BSplSLib_EvaluatorFunction Function,
const Standard_Integer  UBSplineDegree,
const Standard_Integer  VBSplineDegree,
const TColStd_Array1OfReal UBSplineKnots,
const TColStd_Array1OfReal VBSplineKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UFlatKnots,
const TColStd_Array1OfReal VFlatKnots,
const Standard_Integer  UNewDegree,
const Standard_Integer  VNewDegree,
TColgp_Array2OfPnt NewNumerator,
TColStd_Array2OfReal NewDenominator,
Standard_Integer theStatus 
)
static

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)

◆ GetPoles() [1/2]

static void BSplSLib::GetPoles ( const TColStd_Array1OfReal FP,
TColgp_Array2OfPnt Poles,
const Standard_Boolean  UDirection 
)
static

Get from FP the coordinates of the poles.

◆ GetPoles() [2/2]

static void BSplSLib::GetPoles ( const TColStd_Array1OfReal FP,
TColgp_Array2OfPnt Poles,
TColStd_Array2OfReal Weights,
const Standard_Boolean  UDirection 
)
static

Get from FP the coordinates of the poles.

◆ HomogeneousD0()

static void BSplSLib::HomogeneousD0 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
Standard_Real W,
gp_Pnt P 
)
static

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.

◆ HomogeneousD1()

static void BSplSLib::HomogeneousD1 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  UIndex,
const Standard_Integer  VIndex,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
gp_Pnt N,
gp_Vec Nu,
gp_Vec Nv,
Standard_Real D,
Standard_Real Du,
Standard_Real Dv 
)
static

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.

◆ IncreaseDegree()

static void BSplSLib::IncreaseDegree ( const Standard_Boolean  UDirection,
const Standard_Integer  Degree,
const Standard_Integer  NewDegree,
const Standard_Boolean  Periodic,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Mults,
TColgp_Array2OfPnt NewPoles,
TColStd_Array2OfReal NewWeights,
TColStd_Array1OfReal NewKnots,
TColStd_Array1OfInteger NewMults 
)
static

◆ InsertKnots()

static void BSplSLib::InsertKnots ( const Standard_Boolean  UDirection,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Mults,
const TColStd_Array1OfReal AddKnots,
const TColStd_Array1OfInteger AddMults,
TColgp_Array2OfPnt NewPoles,
TColStd_Array2OfReal NewWeights,
TColStd_Array1OfReal NewKnots,
TColStd_Array1OfInteger NewMults,
const Standard_Real  Epsilon,
const Standard_Boolean  Add = Standard_True 
)
static

◆ Interpolate() [1/2]

static void BSplSLib::Interpolate ( const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const TColStd_Array1OfReal UFlatKnots,
const TColStd_Array1OfReal VFlatKnots,
const TColStd_Array1OfReal UParameters,
const TColStd_Array1OfReal VParameters,
TColgp_Array2OfPnt Poles,
Standard_Integer InversionProblem 
)
static

Performs the interpolation of the data points given in the Poles array. The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1.

The RowLength RL and the Length of VParameters must be the same. The length of VFlatKnots is Degree + RL + 1.

Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot

◆ Interpolate() [2/2]

static void BSplSLib::Interpolate ( const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const TColStd_Array1OfReal UFlatKnots,
const TColStd_Array1OfReal VFlatKnots,
const TColStd_Array1OfReal UParameters,
const TColStd_Array1OfReal VParameters,
TColgp_Array2OfPnt Poles,
TColStd_Array2OfReal Weights,
Standard_Integer InversionProblem 
)
static

Performs the interpolation of the data points given in the Poles array in the form [1,...,RL][1,...,RC][1...PolesDimension] . The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1.

The RowLength RL and the Length of VParameters must be the same. The length of VFlatKnots is Degree + RL + 1.

Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot

◆ Iso()

static void BSplSLib::Iso ( const Standard_Real  Param,
const Standard_Boolean  IsU,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Mults,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic,
TColgp_Array1OfPnt CPoles,
TColStd_Array1OfReal CWeights 
)
static

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

◆ IsRational()

static Standard_Boolean BSplSLib::IsRational ( const TColStd_Array2OfReal Weights,
const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  J1,
const Standard_Integer  J2,
const Standard_Real  Epsilon = 0.0 
)
static

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.

◆ MovePoint()

static void BSplSLib::MovePoint ( const Standard_Real  U,
const Standard_Real  V,
const gp_Vec Displ,
const Standard_Integer  UIndex1,
const Standard_Integer  UIndex2,
const Standard_Integer  VIndex1,
const Standard_Integer  VIndex2,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  Rational,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UFlatKnots,
const TColStd_Array1OfReal VFlatKnots,
Standard_Integer UFirstIndex,
Standard_Integer ULastIndex,
Standard_Integer VFirstIndex,
Standard_Integer VLastIndex,
TColgp_Array2OfPnt NewPoles 
)
static

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.

◆ NoWeights()

static TColStd_Array2OfReal* BSplSLib::NoWeights ( )
static

Used as argument for a non rational curve.

◆ PolesCoefficients() [1/2]

static void BSplSLib::PolesCoefficients ( const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
TColgp_Array2OfPnt CachePoles,
TColStd_Array2OfReal CacheWeights 
)
static

Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziersurfaces at parameters 0.,0.; Warning: To be used for BezierSurfaces ONLY!!!

◆ PolesCoefficients() [2/2]

static void BSplSLib::PolesCoefficients ( const TColgp_Array2OfPnt Poles,
TColgp_Array2OfPnt CachePoles 
)
static

Warning! To be used for BezierSurfaces ONLY!!!

◆ RationalDerivative()

static void BSplSLib::RationalDerivative ( const Standard_Integer  UDeg,
const Standard_Integer  VDeg,
const Standard_Integer  N,
const Standard_Integer  M,
Standard_Real Ders,
Standard_Real RDers,
const Standard_Boolean  All = Standard_True 
)
static

this is a one dimensional function typedef void (*EvaluatorFunction) ( Standard_Integer // Derivative Request Standard_Real * // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end Standard_Real // UParameter Standard_Real // VParamerer Standard_Real & // Result Standard_Integer &) ;// 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 Min(<N>,<UDeg>), 0 to 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 <= 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 dimensionned properly.

◆ RemoveKnot()

static Standard_Boolean BSplSLib::RemoveKnot ( const Standard_Boolean  UDirection,
const Standard_Integer  Index,
const Standard_Integer  Mult,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Mults,
TColgp_Array2OfPnt NewPoles,
TColStd_Array2OfReal NewWeights,
TColStd_Array1OfReal NewKnots,
TColStd_Array1OfInteger NewMults,
const Standard_Real  Tolerance 
)
static

◆ Resolution()

static void BSplSLib::Resolution ( const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
const TColStd_Array1OfReal UKnots,
const TColStd_Array1OfReal VKnots,
const TColStd_Array1OfInteger UMults,
const TColStd_Array1OfInteger VMults,
const Standard_Integer  UDegree,
const Standard_Integer  VDegree,
const Standard_Boolean  URat,
const Standard_Boolean  VRat,
const Standard_Boolean  UPer,
const Standard_Boolean  VPer,
const Standard_Real  Tolerance3D,
Standard_Real UTolerance,
Standard_Real VTolerance 
)
static

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.

◆ Reverse() [1/2]

static void BSplSLib::Reverse ( TColgp_Array2OfPnt Poles,
const Standard_Integer  Last,
const Standard_Boolean  UDirection 
)
static

Reverses the array of poles. Last is the Index of the new first Row( Col) of Poles. On a non periodic surface Last is Poles.Upper(). On a periodic curve last is (number of flat knots - degree - 1) or (sum of multiplicities(but for the last) + degree.

  • 1)

◆ Reverse() [2/2]

static void BSplSLib::Reverse ( TColStd_Array2OfReal Weights,
const Standard_Integer  Last,
const Standard_Boolean  UDirection 
)
static

Reverses the array of weights.

◆ SetPoles() [1/2]

static void BSplSLib::SetPoles ( const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
TColStd_Array1OfReal FP,
const Standard_Boolean  UDirection 
)
static

Copy in FP the coordinates of the poles.

◆ SetPoles() [2/2]

static void BSplSLib::SetPoles ( const TColgp_Array2OfPnt Poles,
TColStd_Array1OfReal FP,
const Standard_Boolean  UDirection 
)
static

Copy in FP the coordinates of the poles.

◆ Unperiodize()

static void BSplSLib::Unperiodize ( const Standard_Boolean  UDirection,
const Standard_Integer  Degree,
const TColStd_Array1OfInteger Mults,
const TColStd_Array1OfReal Knots,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
TColStd_Array1OfInteger NewMults,
TColStd_Array1OfReal NewKnots,
TColgp_Array2OfPnt NewPoles,
TColStd_Array2OfReal NewWeights 
)
static

The documentation for this class was generated from the following file: