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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.

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 shoud 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.

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

#include <BSplSLib.hxx>

Static Public Member Functions

static DEFINE_STANDARD_ALLOC 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 <br>

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.

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).

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

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


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


static void Reverse (TColStd_Array2OfReal &Weights, const Standard_Integer Last, const Standard_Boolean UDirection)
 Reverses the array of weights.

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.

static void SetPoles (const TColgp_Array2OfPnt &Poles, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection)
 Copy in FP the coordinates of the poles.

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.

static void GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, const Standard_Boolean UDirection)
 Get from FP the coordinates of the poles.

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.

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

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.


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



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


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!!!

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


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!!!

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


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!!!

static void PolesCoefficients (const TColgp_Array2OfPnt &Poles, TColgp_Array2OfPnt &CachePoles)
 Warning! To be used for BezierSurfaces ONLY!!!

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!!!


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

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.

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

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.

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

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 &Status)
 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 responsability to
insure that conditions 1. and 2. above are satisfied
: no check whatsoever is made in this method --
Status 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)
Status 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)
--



Member Function Documentation

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]
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]
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]
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]
static void BSplSLib::CoefsD0 ( const Standard_Real  U,
const Standard_Real  V,
const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
gp_Pnt Point 
) [static]
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]
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]
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]
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 Status 
) [static]
static void BSplSLib::GetPoles ( const TColStd_Array1OfReal FP,
TColgp_Array2OfPnt Poles,
const Standard_Boolean  UDirection 
) [static]
static void BSplSLib::GetPoles ( const TColStd_Array1OfReal FP,
TColgp_Array2OfPnt Poles,
TColStd_Array2OfReal Weights,
const Standard_Boolean  UDirection 
) [static]
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]
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]
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]
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]
static void BSplSLib::PolesCoefficients ( const TColgp_Array2OfPnt Poles,
TColgp_Array2OfPnt CachePoles 
) [static]
static void BSplSLib::PolesCoefficients ( const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
TColgp_Array2OfPnt CachePoles,
TColStd_Array2OfReal CacheWeights 
) [static]
static void BSplSLib::Reverse ( TColgp_Array2OfPnt Poles,
const Standard_Integer  Last,
const Standard_Boolean  UDirection 
) [static]
  • 1)
static void BSplSLib::Reverse ( TColStd_Array2OfReal Weights,
const Standard_Integer  Last,
const Standard_Boolean  UDirection 
) [static]
static void BSplSLib::SetPoles ( const TColgp_Array2OfPnt Poles,
TColStd_Array1OfReal FP,
const Standard_Boolean  UDirection 
) [static]
static void BSplSLib::SetPoles ( const TColgp_Array2OfPnt Poles,
const TColStd_Array2OfReal Weights,
TColStd_Array1OfReal FP,
const Standard_Boolean  UDirection 
) [static]
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: