// Created on: 1991-08-09
// Created by: JCV
// Copyright (c) 1991-1999 Matra Datavision
// Copyright (c) 1999-2012 OPEN CASCADE SAS
//
// The content of this file is subject to the Open CASCADE Technology Public
// License Version 6.5 (the "License"). You may not use the content of this file
// except in compliance with the License. Please obtain a copy of the License
// at http://www.opencascade.org and read it completely before using this file.
//
// The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
// main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
//
// The Original Code and all software distributed under the License is
// distributed on an "AS IS" basis, without warranty of any kind, and the
// Initial Developer hereby disclaims all such warranties, including without
// limitation, any warranties of merchantability, fitness for a particular
// purpose or non-infringement. Please see the License for the specific terms
// and conditions governing the rights and limitations under the License.
// Modified RLE 9 Sep 1993
// pmn : modified 28-01-97 : fixed a mistake in LocateParameter (PRO6973)
// pmn : modified 4-11-96 : fixed a mistake in BuildKnots (PRO6124)
// pmn : modified 28-Jun-96 : fixed a mistake in AntiBoorScheme
// xab : modified 15-Jun-95 : fixed a mistake in IsRational
// xab : modified 15-Mar-95 : removed Epsilon comparison in IsRational
// added RationalDerivatives.
// xab : 30-Mar-95 : fixed coupling with lti in RationalDerivatives
// xab : 15-Mar-96 : fixed a typo in Eval with extrapolation
// jct : 15-Apr-97 : added TangExtendToConstraint
// jct : 24-Apr-97 : correction on computation of Tbord and NewFlatKnots
// in TangExtendToConstraint; Continuity can be equal to 0
#include <BSplCLib.ixx>
#include <PLib.hxx>
#include <NCollection_LocalArray.hxx>
#include <Precision.hxx>
#include <Standard_NotImplemented.hxx>
typedef gp_Pnt Pnt;
typedef gp_Vec Vec;
typedef TColgp_Array1OfPnt Array1OfPnt;
typedef TColStd_Array1OfReal Array1OfReal;
typedef TColStd_Array1OfInteger Array1OfInteger;
//=======================================================================
//class : BSplCLib_LocalMatrix
//purpose: Auxiliary class optimizing creation of matrix buffer for
// evaluation of bspline (using stack allocation for main matrix)
//=======================================================================
class BSplCLib_LocalMatrix : public math_Matrix
{
public:
BSplCLib_LocalMatrix (Standard_Integer DerivativeRequest, Standard_Integer Order)
: math_Matrix (myBuffer, 1, DerivativeRequest + 1, 1, Order)
{
Standard_OutOfRange_Raise_if (DerivativeRequest > BSplCLib::MaxDegree() ||
Order > BSplCLib::MaxDegree()+1 || BSplCLib::MaxDegree() > 25,
"BSplCLib: bspline degree is greater than maximum supported");
}
private:
// local buffer, to be sufficient for addressing by index [Degree+1][Degree+1]
// (see math_Matrix implementation)
Standard_Real myBuffer[27*27];
};
//=======================================================================
//function : Hunt
//purpose :
//=======================================================================
void BSplCLib::Hunt (const Array1OfReal& XX,
const Standard_Real X,
Standard_Integer& Ilc)
{
// replaced by simple dichotomy (RLE)
Ilc = XX.Lower();
const Standard_Real *px = &XX(Ilc);
px -= Ilc;
if (X < px[Ilc]) {
Ilc--;
return;
}
Standard_Integer Ihi = XX.Upper();
if (X > px[Ihi]) {
Ilc = Ihi + 1;
return;
}
Standard_Integer Im;
while (Ihi - Ilc != 1) {
Im = (Ihi + Ilc) >> 1;
if (X > px[Im]) Ilc = Im;
else Ihi = Im;
}
}
//=======================================================================
//function : FirstUKnotIndex
//purpose :
//=======================================================================
Standard_Integer BSplCLib::FirstUKnotIndex (const Standard_Integer Degree,
const TColStd_Array1OfInteger& Mults)
{
Standard_Integer Index = Mults.Lower();
Standard_Integer SigmaMult = Mults(Index);
while (SigmaMult <= Degree) {
Index++;
SigmaMult += Mults (Index);
}
return Index;
}
//=======================================================================
//function : LastUKnotIndex
//purpose :
//=======================================================================
Standard_Integer BSplCLib::LastUKnotIndex (const Standard_Integer Degree,
const Array1OfInteger& Mults)
{
Standard_Integer Index = Mults.Upper();
Standard_Integer SigmaMult = Mults(Index);
while (SigmaMult <= Degree) {
Index--;
SigmaMult += Mults.Value (Index);
}
return Index;
}
//=======================================================================
//function : FlatIndex
//purpose :
//=======================================================================
Standard_Integer BSplCLib::FlatIndex
(const Standard_Integer Degree,
const Standard_Integer Index,
const TColStd_Array1OfInteger& Mults,
const Standard_Boolean Periodic)
{
Standard_Integer i, index = Index;
const Standard_Integer MLower = Mults.Lower();
const Standard_Integer *pmu = &Mults(MLower);
pmu -= MLower;
for (i = MLower + 1; i <= Index; i++)
index += pmu[i] - 1;
if ( Periodic)
index += Degree;
else
index += pmu[MLower] - 1;
return index;
}
//=======================================================================
//function : LocateParameter
//purpose : Processing of nodes with multiplicities
//pmn 28-01-97 -> compute eventual of the period.
//=======================================================================
void BSplCLib::LocateParameter
(const Standard_Integer , //Degree,
const Array1OfReal& Knots,
const Array1OfInteger& , //Mults,
const Standard_Real U,
const Standard_Boolean IsPeriodic,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
Standard_Integer& KnotIndex,
Standard_Real& NewU)
{
Standard_Real uf = 0, ul=1;
if (IsPeriodic) {
uf = Knots(Knots.Lower());
ul = Knots(Knots.Upper());
}
BSplCLib::LocateParameter(Knots,U,IsPeriodic,FromK1,ToK2,
KnotIndex,NewU, uf, ul);
}
//=======================================================================
//function : LocateParameter
//purpose : For plane nodes
// pmn 28-01-97 -> There is a need of the degre to calculate
// the eventual period
//=======================================================================
void BSplCLib::LocateParameter
(const Standard_Integer Degree,
const Array1OfReal& Knots,
const Standard_Real U,
const Standard_Boolean IsPeriodic,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
Standard_Integer& KnotIndex,
Standard_Real& NewU)
{
if (IsPeriodic)
BSplCLib::LocateParameter(Knots, U, IsPeriodic, FromK1, ToK2,
KnotIndex, NewU,
Knots(Knots.Lower() + Degree),
Knots(Knots.Upper() - Degree));
else
BSplCLib::LocateParameter(Knots, U, IsPeriodic, FromK1, ToK2,
KnotIndex, NewU,
0.,
1.);
}
//=======================================================================
//function : LocateParameter
//purpose : Effective computation
// pmn 28-01-97 : Add limits of the period as input argument,
// as it is imposible to produce them at this level.
//=======================================================================
void BSplCLib::LocateParameter
(const TColStd_Array1OfReal& Knots,
const Standard_Real U,
const Standard_Boolean IsPeriodic,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
Standard_Integer& KnotIndex,
Standard_Real& NewU,
const Standard_Real UFirst,
const Standard_Real ULast)
{
Standard_Integer First,Last;
if (FromK1 < ToK2) {
First = FromK1;
Last = ToK2;
}
else {
First = ToK2;
Last = FromK1;
}
Standard_Integer Last1 = Last - 1;
NewU = U;
if (IsPeriodic) {
Standard_Real Period = ULast - UFirst;
while (NewU > ULast )
NewU -= Period;
while (NewU < UFirst)
NewU += Period;
}
BSplCLib::Hunt (Knots, NewU, KnotIndex);
Standard_Real Eps = Epsilon(U);
Standard_Real val;
if (Eps < 0) Eps = - Eps;
Standard_Integer KLower = Knots.Lower();
const Standard_Real *knots = &Knots(KLower);
knots -= KLower;
if ( KnotIndex < Knots.Upper()) {
val = NewU - knots[KnotIndex + 1];
if (val < 0) val = - val;
// <= to be coherent with Segment where Eps corresponds to a bit of error.
if (val <= Eps) KnotIndex++;
}
if (KnotIndex < First) KnotIndex = First;
if (KnotIndex > Last1) KnotIndex = Last1;
if (KnotIndex != Last1) {
Standard_Real K1 = knots[KnotIndex];
Standard_Real K2 = knots[KnotIndex + 1];
val = K2 - K1;
if (val < 0) val = - val;
while (val <= Eps) {
KnotIndex++;
K1 = K2;
K2 = knots[KnotIndex + 1];
val = K2 - K1;
if (val < 0) val = - val;
}
}
}
//=======================================================================
//function : LocateParameter
//purpose : the index is recomputed only if out of range
//pmn 28-01-97 -> eventual computation of the period.
//=======================================================================
void BSplCLib::LocateParameter
(const Standard_Integer Degree,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
const Standard_Real U,
const Standard_Boolean Periodic,
Standard_Integer& KnotIndex,
Standard_Real& NewU)
{
Standard_Integer first,last;
if (&Mults) {
if (Periodic) {
first = Knots.Lower();
last = Knots.Upper();
}
else {
first = FirstUKnotIndex(Degree,Mults);
last = LastUKnotIndex (Degree,Mults);
}
}
else {
first = Knots.Lower() + Degree;
last = Knots.Upper() - Degree;
}
if ( KnotIndex < first || KnotIndex > last)
BSplCLib::LocateParameter(Knots, U, Periodic, first, last,
KnotIndex, NewU, Knots(first), Knots(last));
else
NewU = U;
}
//=======================================================================
//function : MaxKnotMult
//purpose :
//=======================================================================
Standard_Integer BSplCLib::MaxKnotMult
(const Array1OfInteger& Mults,
const Standard_Integer FromK1,
const Standard_Integer ToK2)
{
Standard_Integer MLower = Mults.Lower();
const Standard_Integer *pmu = &Mults(MLower);
pmu -= MLower;
Standard_Integer MaxMult = pmu[FromK1];
for (Standard_Integer i = FromK1; i <= ToK2; i++) {
if (MaxMult < pmu[i]) MaxMult = pmu[i];
}
return MaxMult;
}
//=======================================================================
//function : MinKnotMult
//purpose :
//=======================================================================
Standard_Integer BSplCLib::MinKnotMult
(const Array1OfInteger& Mults,
const Standard_Integer FromK1,
const Standard_Integer ToK2)
{
Standard_Integer MLower = Mults.Lower();
const Standard_Integer *pmu = &Mults(MLower);
pmu -= MLower;
Standard_Integer MinMult = pmu[FromK1];
for (Standard_Integer i = FromK1; i <= ToK2; i++) {
if (MinMult > pmu[i]) MinMult = pmu[i];
}
return MinMult;
}
//=======================================================================
//function : NbPoles
//purpose :
//=======================================================================
Standard_Integer BSplCLib::NbPoles(const Standard_Integer Degree,
const Standard_Boolean Periodic,
const TColStd_Array1OfInteger& Mults)
{
Standard_Integer i,sigma = 0;
Standard_Integer f = Mults.Lower();
Standard_Integer l = Mults.Upper();
const Standard_Integer * pmu = &Mults(f);
pmu -= f;
Standard_Integer Mf = pmu[f];
Standard_Integer Ml = pmu[l];
if (Mf <= 0) return 0;
if (Ml <= 0) return 0;
if (Periodic) {
if (Mf > Degree) return 0;
if (Ml > Degree) return 0;
if (Mf != Ml ) return 0;
sigma = Mf;
}
else {
Standard_Integer Deg1 = Degree + 1;
if (Mf > Deg1) return 0;
if (Ml > Deg1) return 0;
sigma = Mf + Ml - Deg1;
}
for (i = f + 1; i < l; i++) {
if (pmu[i] <= 0 ) return 0;
if (pmu[i] > Degree) return 0;
sigma += pmu[i];
}
return sigma;
}
//=======================================================================
//function : KnotSequenceLength
//purpose :
//=======================================================================
Standard_Integer BSplCLib::KnotSequenceLength
(const TColStd_Array1OfInteger& Mults,
const Standard_Integer Degree,
const Standard_Boolean Periodic)
{
Standard_Integer i,l = 0;
Standard_Integer MLower = Mults.Lower();
Standard_Integer MUpper = Mults.Upper();
const Standard_Integer * pmu = &Mults(MLower);
pmu -= MLower;
for (i = MLower; i <= MUpper; i++)
l += pmu[i];
if (Periodic) l += 2 * (Degree + 1 - pmu[MLower]);
return l;
}
//=======================================================================
//function : KnotSequence
//purpose :
//=======================================================================
void BSplCLib::KnotSequence
(const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
TColStd_Array1OfReal& KnotSeq)
{
BSplCLib::KnotSequence(Knots,Mults,0,Standard_False,KnotSeq);
}
//=======================================================================
//function : KnotSequence
//purpose :
//=======================================================================
void BSplCLib::KnotSequence
(const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
const Standard_Integer Degree,
const Standard_Boolean Periodic,
TColStd_Array1OfReal& KnotSeq)
{
Standard_Real K;
Standard_Integer Mult;
Standard_Integer MLower = Mults.Lower();
const Standard_Integer * pmu = &Mults(MLower);
pmu -= MLower;
Standard_Integer KLower = Knots.Lower();
Standard_Integer KUpper = Knots.Upper();
const Standard_Real * pkn = &Knots(KLower);
pkn -= KLower;
Standard_Integer M1 = Degree + 1 - pmu[MLower]; // for periodic
Standard_Integer i,j,index = Periodic ? M1 + 1 : 1;
for (i = KLower; i <= KUpper; i++) {
Mult = pmu[i];
K = pkn[i];
for (j = 1; j <= Mult; j++) {
KnotSeq (index) = K;
index++;
}
}
if (Periodic) {
Standard_Real period = pkn[KUpper] - pkn[KLower];
Standard_Integer m;
m = 1;
j = KUpper - 1;
for (i = M1; i >= 1; i--) {
KnotSeq(i) = pkn[j] - period;
m++;
if (m > pmu[j]) {
j--;
m = 1;
}
}
m = 1;
j = KLower + 1;
for (i = index; i <= KnotSeq.Upper(); i++) {
KnotSeq(i) = pkn[j] + period;
m++;
if (m > pmu[j]) {
j++;
m = 1;
}
}
}
}
//=======================================================================
//function : KnotsLength
//purpose :
//=======================================================================
Standard_Integer BSplCLib::KnotsLength(const TColStd_Array1OfReal& SeqKnots,
// const Standard_Boolean Periodic)
const Standard_Boolean )
{
Standard_Integer sizeMult = 1;
Standard_Real val = SeqKnots(1);
for (Standard_Integer jj=2;
jj<=SeqKnots.Length();jj++)
{
// test on strict equality on nodes
if (SeqKnots(jj)!=val)
{
val = SeqKnots(jj);
sizeMult++;
}
}
return sizeMult;
}
//=======================================================================
//function : Knots
//purpose :
//=======================================================================
void BSplCLib::Knots(const TColStd_Array1OfReal& SeqKnots,
TColStd_Array1OfReal &knots,
TColStd_Array1OfInteger &mult,
// const Standard_Boolean Periodic)
const Standard_Boolean )
{
Standard_Real val = SeqKnots(1);
Standard_Integer kk=1;
knots(kk) = val;
mult(kk) = 1;
for (Standard_Integer jj=2;jj<=SeqKnots.Length();jj++)
{
// test on strict equality on nodes
if (SeqKnots(jj)!=val)
{
val = SeqKnots(jj);
kk++;
knots(kk) = val;
mult(kk) = 1;
}
else
{
mult(kk)++;
}
}
}
//=======================================================================
//function : KnotForm
//purpose :
//=======================================================================
BSplCLib_KnotDistribution BSplCLib::KnotForm
(const Array1OfReal& Knots,
const Standard_Integer FromK1,
const Standard_Integer ToK2)
{
Standard_Real DU0,DU1,Ui,Uj,Eps0,val;
BSplCLib_KnotDistribution KForm = BSplCLib_Uniform;
Standard_Integer KLower = Knots.Lower();
const Standard_Real * pkn = &Knots(KLower);
pkn -= KLower;
Ui = pkn[FromK1];
if (Ui < 0) Ui = - Ui;
Uj = pkn[FromK1 + 1];
if (Uj < 0) Uj = - Uj;
DU0 = Uj - Ui;
if (DU0 < 0) DU0 = - DU0;
Eps0 = Epsilon (Ui) + Epsilon (Uj) + Epsilon (DU0);
Standard_Integer i = FromK1 + 1;
while (KForm != BSplCLib_NonUniform && i < ToK2) {
Ui = pkn[i];
if (Ui < 0) Ui = - Ui;
i++;
Uj = pkn[i];
if (Uj < 0) Uj = - Uj;
DU1 = Uj - Ui;
if (DU1 < 0) DU1 = - DU1;
val = DU1 - DU0;
if (val < 0) val = -val;
if (val > Eps0) KForm = BSplCLib_NonUniform;
DU0 = DU1;
Eps0 = Epsilon (Ui) + Epsilon (Uj) + Epsilon (DU0);
}
return KForm;
}
//=======================================================================
//function : MultForm
//purpose :
//=======================================================================
BSplCLib_MultDistribution BSplCLib::MultForm
(const Array1OfInteger& Mults,
const Standard_Integer FromK1,
const Standard_Integer ToK2)
{
Standard_Integer First,Last;
if (FromK1 < ToK2) {
First = FromK1;
Last = ToK2;
}
else {
First = ToK2;
Last = FromK1;
}
Standard_Integer MLower = Mults.Lower();
const Standard_Integer *pmu = &Mults(MLower);
pmu -= MLower;
Standard_Integer FirstMult = pmu[First];
BSplCLib_MultDistribution MForm = BSplCLib_Constant;
Standard_Integer i = First + 1;
Standard_Integer Mult = pmu[i];
// while (MForm != BSplCLib_NonUniform && i <= Last) { ???????????JR????????
while (MForm != BSplCLib_NonConstant && i <= Last) {
if (i == First + 1) {
if (Mult != FirstMult) MForm = BSplCLib_QuasiConstant;
}
else if (i == Last) {
if (MForm == BSplCLib_QuasiConstant) {
if (FirstMult != pmu[i]) MForm = BSplCLib_NonConstant;
}
else {
if (Mult != pmu[i]) MForm = BSplCLib_NonConstant;
}
}
else {
if (Mult != pmu[i]) MForm = BSplCLib_NonConstant;
Mult = pmu[i];
}
i++;
}
return MForm;
}
//=======================================================================
//function : KnotAnalysis
//purpose :
//=======================================================================
void BSplCLib::KnotAnalysis (const Standard_Integer Degree,
const Standard_Boolean Periodic,
const TColStd_Array1OfReal& CKnots,
const TColStd_Array1OfInteger& CMults,
GeomAbs_BSplKnotDistribution& KnotForm,
Standard_Integer& MaxKnotMult)
{
KnotForm = GeomAbs_NonUniform;
BSplCLib_KnotDistribution KSet =
BSplCLib::KnotForm (CKnots, 1, CKnots.Length());
if (KSet == BSplCLib_Uniform) {
BSplCLib_MultDistribution MSet =
BSplCLib::MultForm (CMults, 1, CMults.Length());
switch (MSet) {
case BSplCLib_NonConstant :
break;
case BSplCLib_Constant :
if (CKnots.Length() == 2) {
KnotForm = GeomAbs_PiecewiseBezier;
}
else {
if (CMults (1) == 1) KnotForm = GeomAbs_Uniform;
}
break;
case BSplCLib_QuasiConstant :
if (CMults (1) == Degree + 1) {
Standard_Real M = CMults (2);
if (M == Degree ) KnotForm = GeomAbs_PiecewiseBezier;
else if (M == 1) KnotForm = GeomAbs_QuasiUniform;
}
break;
}
}
Standard_Integer FirstKM =
Periodic ? CKnots.Lower() : BSplCLib::FirstUKnotIndex (Degree,CMults);
Standard_Integer LastKM =
Periodic ? CKnots.Upper() : BSplCLib::LastUKnotIndex (Degree,CMults);
MaxKnotMult = 0;
if (LastKM - FirstKM != 1) {
Standard_Integer Multi;
for (Standard_Integer i = FirstKM + 1; i < LastKM; i++) {
Multi = CMults (i);
MaxKnotMult = Max (MaxKnotMult, Multi);
}
}
}
//=======================================================================
//function : Reparametrize
//purpose :
//=======================================================================
void BSplCLib::Reparametrize
(const Standard_Real U1,
const Standard_Real U2,
Array1OfReal& Knots)
{
Standard_Integer Lower = Knots.Lower();
Standard_Integer Upper = Knots.Upper();
Standard_Real UFirst = Min (U1, U2);
Standard_Real ULast = Max (U1, U2);
Standard_Real NewLength = ULast - UFirst;
BSplCLib_KnotDistribution KSet = BSplCLib::KnotForm (Knots, Lower, Upper);
if (KSet == BSplCLib_Uniform) {
Standard_Real DU = NewLength / (Upper - Lower);
Knots (Lower) = UFirst;
for (Standard_Integer i = Lower + 1; i <= Upper; i++) {
Knots (i) = Knots (i-1) + DU;
}
}
else {
Standard_Real K2;
Standard_Real Ratio;
Standard_Real K1 = Knots (Lower);
Standard_Real Length = Knots (Upper) - Knots (Lower);
Knots (Lower) = UFirst;
for (Standard_Integer i = Lower + 1; i <= Upper; i++) {
K2 = Knots (i);
Ratio = (K2 - K1) / Length;
Knots (i) = Knots (i-1) + (NewLength * Ratio);
//for CheckCurveData
Standard_Real Eps = Epsilon( Abs(Knots(i-1)) );
if (Knots(i) - Knots(i-1) <= Eps)
Knots(i) = NextAfter (Knots(i-1) + Eps, RealLast());
K1 = K2;
}
}
}
//=======================================================================
//function : Reverse
//purpose :
//=======================================================================
void BSplCLib::Reverse(TColStd_Array1OfReal& Knots)
{
Standard_Integer first = Knots.Lower();
Standard_Integer last = Knots.Upper();
Standard_Real kfirst = Knots(first);
Standard_Real klast = Knots(last);
Standard_Real tfirst = kfirst;
Standard_Real tlast = klast;
first++;
last--;
while (first <= last) {
tfirst += klast - Knots(last);
tlast -= Knots(first) - kfirst;
kfirst = Knots(first);
klast = Knots(last);
Knots(first) = tfirst;
Knots(last) = tlast;
first++;
last--;
}
}
//=======================================================================
//function : Reverse
//purpose :
//=======================================================================
void BSplCLib::Reverse(TColStd_Array1OfInteger& Mults)
{
Standard_Integer first = Mults.Lower();
Standard_Integer last = Mults.Upper();
Standard_Integer temp;
while (first < last) {
temp = Mults(first);
Mults(first) = Mults(last);
Mults(last) = temp;
first++;
last--;
}
}
//=======================================================================
//function : Reverse
//purpose :
//=======================================================================
void BSplCLib::Reverse(TColStd_Array1OfReal& Weights,
const Standard_Integer L)
{
Standard_Integer i, l = L;
l = Weights.Lower()+(l-Weights.Lower())%(Weights.Upper()-Weights.Lower()+1);
TColStd_Array1OfReal temp(0,Weights.Length()-1);
for (i = Weights.Lower(); i <= l; i++)
temp(l-i) = Weights(i);
for (i = l+1; i <= Weights.Upper(); i++)
temp(l-Weights.Lower()+Weights.Upper()-i+1) = Weights(i);
for (i = Weights.Lower(); i <= Weights.Upper(); i++)
Weights(i) = temp(i-Weights.Lower());
}
//=======================================================================
//function : IsRational
//purpose :
//=======================================================================
Standard_Boolean BSplCLib::IsRational(const TColStd_Array1OfReal& Weights,
const Standard_Integer I1,
const Standard_Integer I2,
// const Standard_Real Epsi)
const Standard_Real )
{
Standard_Integer i, f = Weights.Lower(), l = Weights.Length();
Standard_Integer I3 = I2 - f;
const Standard_Real * WG = &Weights(f);
WG -= f;
for (i = I1 - f; i < I3; i++) {
if (WG[f + (i % l)] != WG[f + ((i + 1) % l)]) return Standard_True;
}
return Standard_False ;
}
//=======================================================================
//function : Eval
//purpose : evaluate point and derivatives
//=======================================================================
void BSplCLib::Eval(const Standard_Real U,
const Standard_Integer Degree,
Standard_Real& Knots,
const Standard_Integer Dimension,
Standard_Real& Poles)
{
Standard_Integer step,i,Dms,Dm1,Dpi,Sti;
Standard_Real X, Y, *poles, *knots = &Knots;
Dm1 = Dms = Degree;
Dm1--;
Dms++;
switch (Dimension) {
case 1 : {
for (step = - 1; step < Dm1; step++) {
Dms--;
poles = &Poles;
Dpi = Dm1;
Sti = step;
for (i = 0; i < Dms; i++) {
Dpi++;
Sti++;
X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
Y = 1 - X;
poles[0] *= X; poles[0] += Y * poles[1];
poles += 1;
}
}
break;
}
case 2 : {
for (step = - 1; step < Dm1; step++) {
Dms--;
poles = &Poles;
Dpi = Dm1;
Sti = step;
for (i = 0; i < Dms; i++) {
Dpi++;
Sti++;
X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
Y = 1 - X;
poles[0] *= X; poles[0] += Y * poles[2];
poles[1] *= X; poles[1] += Y * poles[3];
poles += 2;
}
}
break;
}
case 3 : {
for (step = - 1; step < Dm1; step++) {
Dms--;
poles = &Poles;
Dpi = Dm1;
Sti = step;
for (i = 0; i < Dms; i++) {
Dpi++;
Sti++;
X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
Y = 1 - X;
poles[0] *= X; poles[0] += Y * poles[3];
poles[1] *= X; poles[1] += Y * poles[4];
poles[2] *= X; poles[2] += Y * poles[5];
poles += 3;
}
}
break;
}
case 4 : {
for (step = - 1; step < Dm1; step++) {
Dms--;
poles = &Poles;
Dpi = Dm1;
Sti = step;
for (i = 0; i < Dms; i++) {
Dpi++;
Sti++;
X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
Y = 1 - X;
poles[0] *= X; poles[0] += Y * poles[4];
poles[1] *= X; poles[1] += Y * poles[5];
poles[2] *= X; poles[2] += Y * poles[6];
poles[3] *= X; poles[3] += Y * poles[7];
poles += 4;
}
}
break;
}
default : {
Standard_Integer k;
for (step = - 1; step < Dm1; step++) {
Dms--;
poles = &Poles;
Dpi = Dm1;
Sti = step;
for (i = 0; i < Dms; i++) {
Dpi++;
Sti++;
X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
Y = 1 - X;
for (k = 0; k < Dimension; k++) {
poles[k] *= X;
poles[k] += Y * poles[k + Dimension];
}
poles += Dimension;
}
}
}
}
}
//=======================================================================
//function : BoorScheme
//purpose :
//=======================================================================
void BSplCLib::BoorScheme(const Standard_Real U,
const Standard_Integer Degree,
Standard_Real& Knots,
const Standard_Integer Dimension,
Standard_Real& Poles,
const Standard_Integer Depth,
const Standard_Integer Length)
{
//
// Compute the values
//
// P(i,j) (U).
//
// for i = 0 to Depth,
// j = 0 to Length - i
//
// The Boor scheme is :
//
// P(0,j) = Pole(j)
// P(i,j) = x * P(i-1,j) + (1-x) * P(i-1,j+1)
//
// where x = (knot(i+j+Degree) - U) / (knot(i+j+Degree) - knot(i+j))
//
//
// The values are stored in the array Poles
// They are alternatively written if the odd and even positions.
//
// The successives contents of the array are
// ***** means unitialised, l = Degree + Length
//
// P(0,0) ****** P(0,1) ...... P(0,l-1) ******** P(0,l)
// P(0,0) P(1,0) P(0,1) ...... P(0,l-1) P(1,l-1) P(0,l)
// P(0,0) P(1,0) P(2,0) ...... P(2,l-1) P(1,l-1) P(0,l)
//
Standard_Integer i,k,step;
Standard_Real *knots = &Knots;
Standard_Real *pole, *firstpole = &Poles - 2 * Dimension;
// the steps of recursion
for (step = 0; step < Depth; step++) {
firstpole += Dimension;
pole = firstpole;
// compute the new row of poles
for (i = step; i < Length; i++) {
pole += 2 * Dimension;
// coefficient
Standard_Real X = (knots[i+Degree-step] - U)
/ (knots[i+Degree-step] - knots[i]);
Standard_Real Y = 1. - X;
// Value
// P(i,j) = X * P(i-1,j) + (1-X) * P(i-1,j+1)
for (k = 0; k < Dimension; k++)
pole[k] = X * pole[k - Dimension] + Y * pole[k + Dimension];
}
}
}
//=======================================================================
//function : AntiBoorScheme
//purpose :
//=======================================================================
Standard_Boolean BSplCLib::AntiBoorScheme(const Standard_Real U,
const Standard_Integer Degree,
Standard_Real& Knots,
const Standard_Integer Dimension,
Standard_Real& Poles,
const Standard_Integer Depth,
const Standard_Integer Length,
const Standard_Real Tolerance)
{
// do the Boor scheme reverted.
Standard_Integer i,k,step, half_length;
Standard_Real *knots = &Knots;
Standard_Real z,X,Y,*pole, *firstpole = &Poles + (Depth-1) * Dimension;
// Test the special case length = 1
// only verification of the central point
if (Length == 1) {
X = (knots[Degree] - U) / (knots[Degree] - knots[0]);
Y = 1. - X;
for (k = 0; k < Dimension; k++) {
z = X * firstpole[k] + Y * firstpole[k+2*Dimension];
if (Abs(z - firstpole[k+Dimension]) > Tolerance)
return Standard_False;
}
return Standard_True;
}
// General case
// the steps of recursion
for (step = Depth-1; step >= 0; step--) {
firstpole -= Dimension;
pole = firstpole;
// first step from left to right
for (i = step; i < Length-1; i++) {
pole += 2 * Dimension;
X = (knots[i+Degree-step] - U) / (knots[i+Degree-step] - knots[i]);
Y = 1. - X;
for (k = 0; k < Dimension; k++)
pole[k+Dimension] = (pole[k] - X*pole[k-Dimension]) / Y;
}
// second step from right to left
pole += 4* Dimension;
half_length = (Length - 1 + step) / 2 ;
//
// only do half of the way from right to left
// otherwise it start degenerating because of
// overflows
//
for (i = Length-1; i > half_length ; i--) {
pole -= 2 * Dimension;
// coefficient
X = (knots[i+Degree-step] - U) / (knots[i+Degree-step] - knots[i]);
Y = 1. - X;
for (k = 0; k < Dimension; k++) {
z = (pole[k] - Y * pole[k+Dimension]) / X;
if (Abs(z-pole[k-Dimension]) > Tolerance)
return Standard_False;
pole[k-Dimension] += z;
pole[k-Dimension] /= 2.;
}
}
}
return Standard_True;
}
//=======================================================================
//function : Derivative
//purpose :
//=======================================================================
void BSplCLib::Derivative(const Standard_Integer Degree,
Standard_Real& Knots,
const Standard_Integer Dimension,
const Standard_Integer Length,
const Standard_Integer Order,
Standard_Real& Poles)
{
Standard_Integer i,k,step,span = Degree;
Standard_Real *knot = &Knots;
for (step = 1; step <= Order; step++) {
Standard_Real* pole = &Poles;
for (i = step; i < Length; i++) {
Standard_Real coef = - span / (knot[i+span] - knot[i]);
for (k = 0; k < Dimension; k++) {
pole[k] -= pole[k+Dimension];
pole[k] *= coef;
}
pole += Dimension;
}
span--;
}
}
//=======================================================================
//function : Bohm
//purpose :
//=======================================================================
void BSplCLib::Bohm(const Standard_Real U,
const Standard_Integer Degree,
const Standard_Integer N,
Standard_Real& Knots,
const Standard_Integer Dimension,
Standard_Real& Poles)
{
// First phase independant of U, compute the poles of the derivatives
Standard_Integer i,j,iDim,min,Dmi,DDmi,jDmi,Degm1;
Standard_Real *knot = &Knots, *pole, coef, *tbis, *psav, *psDD, *psDDmDim;
psav = &Poles;
if (N < Degree) min = N;
else min = Degree;
Degm1 = Degree - 1;
DDmi = (Degree << 1) + 1;
switch (Dimension) {
case 1 : {
psDD = psav + Degree;
psDDmDim = psDD - 1;
for (i = 0; i < Degree; i++) {
DDmi--;
pole = psDD;
tbis = psDDmDim;
jDmi = DDmi;
for (j = Degm1; j >= i; j--) {
jDmi--;
*pole -= *tbis; *pole /= (knot[jDmi] - knot[j]);
pole--;
tbis--;
}
}
// Second phase, dependant of U
iDim = - 1;
for (i = 0; i < Degree; i++) {
iDim += 1;
pole = psav + iDim;
tbis = pole + 1;
coef = U - knot[i];
for (j = i; j >= 0; j--) {
*pole += coef * (*tbis);
pole--;
tbis--;
}
}
// multiply by the degrees
coef = Degree;
Dmi = Degree;
pole = psav + 1;
for (i = 1; i <= min; i++) {
*pole *= coef; pole++;
Dmi--;
coef *= Dmi;
}
break;
}
case 2 : {
psDD = psav + (Degree << 1);
psDDmDim = psDD - 2;
for (i = 0; i < Degree; i++) {
DDmi--;
pole = psDD;
tbis = psDDmDim;
jDmi = DDmi;
for (j = Degm1; j >= i; j--) {
jDmi--;
coef = 1. / (knot[jDmi] - knot[j]);
*pole -= *tbis; *pole *= coef; pole++; tbis++;
*pole -= *tbis; *pole *= coef;
pole -= 3;
tbis -= 3;
}
}
// Second phase, dependant of U
iDim = - 2;
for (i = 0; i < Degree; i++) {
iDim += 2;
pole = psav + iDim;
tbis = pole + 2;
coef = U - knot[i];
for (j = i; j >= 0; j--) {
*pole += coef * (*tbis); pole++; tbis++;
*pole += coef * (*tbis);
pole -= 3;
tbis -= 3;
}
}
// multiply by the degrees
coef = Degree;
Dmi = Degree;
pole = psav + 2;
for (i = 1; i <= min; i++) {
*pole *= coef; pole++;
*pole *= coef; pole++;
Dmi--;
coef *= Dmi;
}
break;
}
case 3 : {
psDD = psav + (Degree << 1) + Degree;
psDDmDim = psDD - 3;
for (i = 0; i < Degree; i++) {
DDmi--;
pole = psDD;
tbis = psDDmDim;
jDmi = DDmi;
for (j = Degm1; j >= i; j--) {
jDmi--;
coef = 1. / (knot[jDmi] - knot[j]);
*pole -= *tbis; *pole *= coef; pole++; tbis++;
*pole -= *tbis; *pole *= coef; pole++; tbis++;
*pole -= *tbis; *pole *= coef;
pole -= 5;
tbis -= 5;
}
}
// Second phase, dependant of U
iDim = - 3;
for (i = 0; i < Degree; i++) {
iDim += 3;
pole = psav + iDim;
tbis = pole + 3;
coef = U - knot[i];
for (j = i; j >= 0; j--) {
*pole += coef * (*tbis); pole++; tbis++;
*pole += coef * (*tbis); pole++; tbis++;
*pole += coef * (*tbis);
pole -= 5;
tbis -= 5;
}
}
// multiply by the degrees
coef = Degree;
Dmi = Degree;
pole = psav + 3;
for (i = 1; i <= min; i++) {
*pole *= coef; pole++;
*pole *= coef; pole++;
*pole *= coef; pole++;
Dmi--;
coef *= Dmi;
}
break;
}
case 4 : {
psDD = psav + (Degree << 2);
psDDmDim = psDD - 4;
for (i = 0; i < Degree; i++) {
DDmi--;
pole = psDD;
tbis = psDDmDim;
jDmi = DDmi;
for (j = Degm1; j >= i; j--) {
jDmi--;
coef = 1. / (knot[jDmi] - knot[j]);
*pole -= *tbis; *pole *= coef; pole++; tbis++;
*pole -= *tbis; *pole *= coef; pole++; tbis++;
*pole -= *tbis; *pole *= coef; pole++; tbis++;
*pole -= *tbis; *pole *= coef;
pole -= 7;
tbis -= 7;
}
}
// Second phase, dependant of U
iDim = - 4;
for (i = 0; i < Degree; i++) {
iDim += 4;
pole = psav + iDim;
tbis = pole + 4;
coef = U - knot[i];
for (j = i; j >= 0; j--) {
*pole += coef * (*tbis); pole++; tbis++;
*pole += coef * (*tbis); pole++; tbis++;
*pole += coef * (*tbis); pole++; tbis++;
*pole += coef * (*tbis);
pole -= 7;
tbis -= 7;
}
}
// multiply by the degrees
coef = Degree;
Dmi = Degree;
pole = psav + 4;
for (i = 1; i <= min; i++) {
*pole *= coef; pole++;
*pole *= coef; pole++;
*pole *= coef; pole++;
*pole *= coef; pole++;
Dmi--;
coef *= Dmi;
}
break;
}
default : {
Standard_Integer k;
Standard_Integer Dim2 = Dimension << 1;
psDD = psav + Degree * Dimension;
psDDmDim = psDD - Dimension;
for (i = 0; i < Degree; i++) {
DDmi--;
pole = psDD;
tbis = psDDmDim;
jDmi = DDmi;
for (j = Degm1; j >= i; j--) {
jDmi--;
coef = 1. / (knot[jDmi] - knot[j]);
for (k = 0; k < Dimension; k++) {
*pole -= *tbis; *pole *= coef; pole++; tbis++;
}
pole -= Dim2;
tbis -= Dim2;
}
}
// Second phase, dependant of U
iDim = - Dimension;
for (i = 0; i < Degree; i++) {
iDim += Dimension;
pole = psav + iDim;
tbis = pole + Dimension;
coef = U - knot[i];
for (j = i; j >= 0; j--) {
for (k = 0; k < Dimension; k++) {
*pole += coef * (*tbis); pole++; tbis++;
}
pole -= Dim2;
tbis -= Dim2;
}
}
// multiply by the degrees
coef = Degree;
Dmi = Degree;
pole = psav + Dimension;
for (i = 1; i <= min; i++) {
for (k = 0; k < Dimension; k++) {
*pole *= coef; pole++;
}
Dmi--;
coef *= Dmi;
}
}
}
}
//=======================================================================
//function : BuildKnots
//purpose :
//=======================================================================
void BSplCLib::BuildKnots(const Standard_Integer Degree,
const Standard_Integer Index,
const Standard_Boolean Periodic,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
Standard_Real& LK)
{
Standard_Integer KLower = Knots.Lower();
const Standard_Real * pkn = &Knots(KLower);
pkn -= KLower;
Standard_Real *knot = &LK;
if (&Mults == NULL) {
switch (Degree) {
case 1 : {
Standard_Integer j = Index ;
knot[0] = pkn[j]; j++;
knot[1] = pkn[j];
break;
}
case 2 : {
Standard_Integer j = Index - 1;
knot[0] = pkn[j]; j++;
knot[1] = pkn[j]; j++;
knot[2] = pkn[j]; j++;
knot[3] = pkn[j];
break;
}
case 3 : {
Standard_Integer j = Index - 2;
knot[0] = pkn[j]; j++;
knot[1] = pkn[j]; j++;
knot[2] = pkn[j]; j++;
knot[3] = pkn[j]; j++;
knot[4] = pkn[j]; j++;
knot[5] = pkn[j];
break;
}
case 4 : {
Standard_Integer j = Index - 3;
knot[0] = pkn[j]; j++;
knot[1] = pkn[j]; j++;
knot[2] = pkn[j]; j++;
knot[3] = pkn[j]; j++;
knot[4] = pkn[j]; j++;
knot[5] = pkn[j]; j++;
knot[6] = pkn[j]; j++;
knot[7] = pkn[j];
break;
}
case 5 : {
Standard_Integer j = Index - 4;
knot[0] = pkn[j]; j++;
knot[1] = pkn[j]; j++;
knot[2] = pkn[j]; j++;
knot[3] = pkn[j]; j++;
knot[4] = pkn[j]; j++;
knot[5] = pkn[j]; j++;
knot[6] = pkn[j]; j++;
knot[7] = pkn[j]; j++;
knot[8] = pkn[j]; j++;
knot[9] = pkn[j];
break;
}
case 6 : {
Standard_Integer j = Index - 5;
knot[ 0] = pkn[j]; j++;
knot[ 1] = pkn[j]; j++;
knot[ 2] = pkn[j]; j++;
knot[ 3] = pkn[j]; j++;
knot[ 4] = pkn[j]; j++;
knot[ 5] = pkn[j]; j++;
knot[ 6] = pkn[j]; j++;
knot[ 7] = pkn[j]; j++;
knot[ 8] = pkn[j]; j++;
knot[ 9] = pkn[j]; j++;
knot[10] = pkn[j]; j++;
knot[11] = pkn[j];
break;
}
default : {
Standard_Integer i,j;
Standard_Integer Deg2 = Degree << 1;
j = Index - Degree;
for (i = 0; i < Deg2; i++) {
j++;
knot[i] = pkn[j];
}
}
}
}
else {
Standard_Integer i;
Standard_Integer Deg1 = Degree - 1;
Standard_Integer KUpper = Knots.Upper();
Standard_Integer MLower = Mults.Lower();
Standard_Integer MUpper = Mults.Upper();
const Standard_Integer * pmu = &Mults(MLower);
pmu -= MLower;
Standard_Real dknot = 0;
Standard_Integer ilow = Index , mlow = 0;
Standard_Integer iupp = Index + 1, mupp = 0;
Standard_Real loffset = 0., uoffset = 0.;
Standard_Boolean getlow = Standard_True, getupp = Standard_True;
if (Periodic) {
dknot = pkn[KUpper] - pkn[KLower];
if (iupp > MUpper) {
iupp = MLower + 1;
uoffset = dknot;
}
}
// Find the knots around Index
for (i = 0; i < Degree; i++) {
if (getlow) {
mlow++;
if (mlow > pmu[ilow]) {
mlow = 1;
ilow--;
getlow = (ilow >= MLower);
if (Periodic && !getlow) {
ilow = MUpper - 1;
loffset = dknot;
getlow = Standard_True;
}
}
if (getlow)
knot[Deg1 - i] = pkn[ilow] - loffset;
}
if (getupp) {
mupp++;
if (mupp > pmu[iupp]) {
mupp = 1;
iupp++;
getupp = (iupp <= MUpper);
if (Periodic && !getupp) {
iupp = MLower + 1;
uoffset = dknot;
getupp = Standard_True;
}
}
if (getupp)
knot[Degree + i] = pkn[iupp] + uoffset;
}
}
}
}
//=======================================================================
//function : PoleIndex
//purpose :
//=======================================================================
Standard_Integer BSplCLib::PoleIndex(const Standard_Integer Degree,
const Standard_Integer Index,
const Standard_Boolean Periodic,
const TColStd_Array1OfInteger& Mults)
{
Standard_Integer i, pindex = 0;
for (i = Mults.Lower(); i <= Index; i++)
pindex += Mults(i);
if (Periodic)
pindex -= Mults(Mults.Lower());
else
pindex -= Degree + 1;
return pindex;
}
//=======================================================================
//function : BuildBoor
//purpose : builds the local array for boor
//=======================================================================
void BSplCLib::BuildBoor(const Standard_Integer Index,
const Standard_Integer Length,
const Standard_Integer Dimension,
const TColStd_Array1OfReal& Poles,
Standard_Real& LP)
{
Standard_Real *poles = &LP;
Standard_Integer i,k, ip = Poles.Lower() + Index * Dimension;
for (i = 0; i < Length+1; i++) {
for (k = 0; k < Dimension; k++) {
poles[k] = Poles(ip);
ip++;
if (ip > Poles.Upper()) ip = Poles.Lower();
}
poles += 2 * Dimension;
}
}
//=======================================================================
//function : BoorIndex
//purpose :
//=======================================================================
Standard_Integer BSplCLib::BoorIndex(const Standard_Integer Index,
const Standard_Integer Length,
const Standard_Integer Depth)
{
if (Index <= Depth) return Index;
if (Index <= Length) return 2 * Index - Depth;
return Length + Index - Depth;
}
//=======================================================================
//function : GetPole
//purpose :
//=======================================================================
void BSplCLib::GetPole(const Standard_Integer Index,
const Standard_Integer Length,
const Standard_Integer Depth,
const Standard_Integer Dimension,
Standard_Real& LP,
Standard_Integer& Position,
TColStd_Array1OfReal& Pole)
{
Standard_Integer k;
Standard_Real* pole = &LP + BoorIndex(Index,Length,Depth) * Dimension;
for (k = 0; k < Dimension; k++) {
Pole(Position) = pole[k];
Position++;
}
if (Position > Pole.Upper()) Position = Pole.Lower();
}
//=======================================================================
//function : PrepareInsertKnots
//purpose :
//=======================================================================
Standard_Boolean BSplCLib::PrepareInsertKnots
(const Standard_Integer Degree,
const Standard_Boolean Periodic,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
const TColStd_Array1OfReal& AddKnots,
const TColStd_Array1OfInteger& AddMults,
Standard_Integer& NbPoles,
Standard_Integer& NbKnots,
const Standard_Real Tolerance,
const Standard_Boolean Add)
{
Standard_Boolean addflat = &AddMults == NULL;
Standard_Integer first,last;
if (Periodic) {
first = Knots.Lower();
last = Knots.Upper();
}
else {
first = FirstUKnotIndex(Degree,Mults);
last = LastUKnotIndex(Degree,Mults);
}
Standard_Real adeltaK1 = Knots(first)-AddKnots(AddKnots.Lower());
Standard_Real adeltaK2 = AddKnots(AddKnots.Upper())-Knots(last);
if (adeltaK1 > Tolerance) return Standard_False;
if (adeltaK2 > Tolerance) return Standard_False;
Standard_Integer sigma = 0, mult, amult;
NbKnots = 0;
Standard_Integer k = Knots.Lower() - 1;
Standard_Integer ak = AddKnots.Lower();
if(Periodic && AddKnots.Length() > 1)
{
//gka for case when segments was produced on full period only one knot
//was added in the end of curve
if(fabs(adeltaK1) <= Precision::PConfusion() &&
fabs(adeltaK2) <= Precision::PConfusion())
ak++;
}
Standard_Real au,oldau = AddKnots(ak),Eps;
while (ak <= AddKnots.Upper()) {
au = AddKnots(ak);
if (au < oldau) return Standard_False;
oldau = au;
Eps = Max(Tolerance,Epsilon(au));
while ((k < Knots.Upper()) && (Knots(k+1) - au <= Eps)) {
k++;
NbKnots++;
sigma += Mults(k);
}
if (addflat) amult = 1;
else amult = Max(0,AddMults(ak));
while ((ak < AddKnots.Upper()) &&
(Abs(au - AddKnots(ak+1)) <= Eps)) {
ak++;
if (Add) {
if (addflat) amult++;
else amult += Max(0,AddMults(ak));
}
}
if (Abs(au - Knots(k)) <= Eps) {
// identic to existing knot
mult = Mults(k);
if (Add) {
if (mult + amult > Degree)
amult = Max(0,Degree - mult);
sigma += amult;
}
else if (amult > mult) {
if (amult > Degree) amult = Degree;
sigma += amult - mult;
}
/*
// on periodic curves if this is the last knot
// the multiplicity is added twice to account for the first knot
if (k == Knots.Upper() && Periodic) {
if (Add)
sigma += amult;
else
sigma += amult - mult;
}
*/
}
else {
// not identic to existing knot
if (amult > 0) {
if (amult > Degree) amult = Degree;
NbKnots++;
sigma += amult;
}
}
ak++;
}
// count the last knots
while (k < Knots.Upper()) {
k++;
NbKnots++;
sigma += Mults(k);
}
if (Periodic) {
//for periodic B-Spline the requirement is that multiplicites of the first
//and last knots must be equal (see Geom_BSplineCurve constructor for
//instance);
//respectively AddMults() must meet this requirement if AddKnots() contains
//knot(s) coincident with first or last
NbPoles = sigma - Mults(Knots.Upper());
}
else {
NbPoles = sigma - Degree - 1;
}
return Standard_True;
}
//=======================================================================
//function : Copy
//purpose : copy reals from an array to an other
//
// NbValues are copied from OldPoles(OldFirst)
// to NewPoles(NewFirst)
//
// Periodicity is handled.
// OldFirst and NewFirst are updated
// to the position after the last copied pole.
//
//=======================================================================
static void Copy(const Standard_Integer NbPoles,
Standard_Integer& OldFirst,
const TColStd_Array1OfReal& OldPoles,
Standard_Integer& NewFirst,
TColStd_Array1OfReal& NewPoles)
{
// reset the index in the range for periodicity
OldFirst = OldPoles.Lower() +
(OldFirst - OldPoles.Lower()) % (OldPoles.Upper() - OldPoles.Lower() + 1);
NewFirst = NewPoles.Lower() +
(NewFirst - NewPoles.Lower()) % (NewPoles.Upper() - NewPoles.Lower() + 1);
// copy
Standard_Integer i;
for (i = 1; i <= NbPoles; i++) {
NewPoles(NewFirst) = OldPoles(OldFirst);
OldFirst++;
if (OldFirst > OldPoles.Upper()) OldFirst = OldPoles.Lower();
NewFirst++;
if (NewFirst > NewPoles.Upper()) NewFirst = NewPoles.Lower();
}
}
//=======================================================================
//function : InsertKnots
//purpose : insert an array of knots and multiplicities
//=======================================================================
void BSplCLib::InsertKnots
(const Standard_Integer Degree,
const Standard_Boolean Periodic,
const Standard_Integer Dimension,
const TColStd_Array1OfReal& Poles,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
const TColStd_Array1OfReal& AddKnots,
const TColStd_Array1OfInteger& AddMults,
TColStd_Array1OfReal& NewPoles,
TColStd_Array1OfReal& NewKnots,
TColStd_Array1OfInteger& NewMults,
const Standard_Real Tolerance,
const Standard_Boolean Add)
{
Standard_Boolean addflat = &AddMults == NULL;
Standard_Integer i,k,mult,firstmult;
Standard_Integer index,kn,curnk,curk;
Standard_Integer p,np, curp, curnp, length, depth;
Standard_Real u;
Standard_Integer need;
Standard_Real Eps;
// -------------------
// create local arrays
// -------------------
Standard_Real *knots = new Standard_Real[2*Degree];
Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
//----------------------------
// loop on the knots to insert
//----------------------------
curk = Knots.Lower()-1; // current position in Knots
curnk = NewKnots.Lower()-1; // current position in NewKnots
curp = Poles.Lower(); // current position in Poles
curnp = NewPoles.Lower(); // current position in NewPoles
// NewKnots, NewMults, NewPoles contains the current state of the curve
// index is the first pole of the current curve for insertion schema
if (Periodic) index = -Mults(Mults.Lower());
else index = -Degree-1;
// on Periodic curves the first knot and the last knot are inserted later
// (they are the same knot)
firstmult = 0; // multiplicity of the first-last knot for periodic
// kn current knot to insert in AddKnots
for (kn = AddKnots.Lower(); kn <= AddKnots.Upper(); kn++) {
u = AddKnots(kn);
Eps = Max(Tolerance,Epsilon(u));
//-----------------------------------
// find the position in the old knots
// and copy to the new knots
//-----------------------------------
while (curk < Knots.Upper() && Knots(curk+1) - u <= Eps) {
curk++; curnk++;
NewKnots(curnk) = Knots(curk);
index += NewMults(curnk) = Mults(curk);
}
//-----------------------------------
// Slice the knots and the mults
// to the current size of the new curve
//-----------------------------------
i = curnk + Knots.Upper() - curk;
TColStd_Array1OfReal nknots(NewKnots(NewKnots.Lower()),NewKnots.Lower(),i);
TColStd_Array1OfInteger nmults(NewMults(NewMults.Lower()),NewMults.Lower(),i);
//-----------------------------------
// copy enough knots
// to compute the insertion schema
//-----------------------------------
k = curk;
i = curnk;
mult = 0;
while (mult < Degree && k < Knots.Upper()) {
k++; i++;
nknots(i) = Knots(k);
mult += nmults(i) = Mults(k);
}
// copy knots at the end for periodic curve
if (Periodic) {
mult = 0;
k = Knots.Upper();
i = nknots.Upper();
while (mult < Degree && i > curnk) {
nknots(i) = Knots(k);
mult += nmults(i) = Mults(k);
k--;
i--;
}
nmults(nmults.Upper()) = nmults(nmults.Lower());
}
//------------------------------------
// do the boor scheme on the new curve
// to insert the new knot
//------------------------------------
Standard_Boolean sameknot = (Abs(u-NewKnots(curnk)) <= Eps);
if (sameknot) length = Max(0,Degree - NewMults(curnk));
else length = Degree;
if (addflat) depth = 1;
else depth = Min(Degree,AddMults(kn));
if (sameknot) {
if (Add) {
if ((NewMults(curnk) + depth) > Degree)
depth = Degree - NewMults(curnk);
}
else {
depth = Max(0,depth-NewMults(curnk));
}
if (Periodic) {
// on periodic curve the first and last knot are delayed to the end
if (curk == Knots.Lower() || (curk == Knots.Upper())) {
firstmult += depth;
depth = 0;
}
}
}
if (depth <= 0) continue;
BuildKnots(Degree,curnk,Periodic,nknots,nmults,*knots);
// copy the poles
need = NewPoles.Lower()+(index+length+1)*Dimension - curnp;
need = Min(need,Poles.Upper() - curp + 1);
p = curp;
np = curnp;
Copy(need,p,Poles,np,NewPoles);
curp += need;
curnp += need;
// slice the poles to the current number of poles in case of periodic
TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
BuildBoor(index,length,Dimension,npoles,*poles);
BoorScheme(u,Degree,*knots,Dimension,*poles,depth,length);
//-------------------
// copy the new poles
//-------------------
curnp += depth * Dimension; // number of poles is increased by depth
TColStd_Array1OfReal ThePoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
np = NewKnots.Lower()+(index+1)*Dimension;
for (i = 1; i <= length + depth; i++)
GetPole(i,length,depth,Dimension,*poles,np,ThePoles);
//-------------------
// insert the knot
//-------------------
index += depth;
if (sameknot) {
NewMults(curnk) += depth;
}
else {
curnk++;
NewKnots(curnk) = u;
NewMults(curnk) = depth;
}
}
//------------------------------
// copy the last poles and knots
//------------------------------
Copy(Poles.Upper() - curp + 1,curp,Poles,curnp,NewPoles);
while (curk < Knots.Upper()) {
curk++; curnk++;
NewKnots(curnk) = Knots(curk);
NewMults(curnk) = Mults(curk);
}
//------------------------------
// process the first-last knot
// on periodic curves
//------------------------------
if (firstmult > 0) {
curnk = NewKnots.Lower();
if (NewMults(curnk) + firstmult > Degree) {
firstmult = Degree - NewMults(curnk);
}
if (firstmult > 0) {
length = Degree - NewMults(curnk);
depth = firstmult;
BuildKnots(Degree,curnk,Periodic,NewKnots,NewMults,*knots);
TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),
NewPoles.Lower(),
NewPoles.Upper()-depth*Dimension);
BuildBoor(0,length,Dimension,npoles,*poles);
BoorScheme(NewKnots(curnk),Degree,*knots,Dimension,*poles,depth,length);
//---------------------------
// copy the new poles
// but rotate them with depth
//---------------------------
np = NewPoles.Lower();
for (i = depth; i < length + depth; i++)
GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
np = NewPoles.Upper() - depth*Dimension + 1;
for (i = 0; i < depth; i++)
GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
NewMults(NewMults.Lower()) += depth;
NewMults(NewMults.Upper()) += depth;
}
}
// free local arrays
delete [] knots;
delete [] poles;
}
//=======================================================================
//function : RemoveKnot
//purpose :
//=======================================================================
Standard_Boolean BSplCLib::RemoveKnot
(const Standard_Integer Index,
const Standard_Integer Mult,
const Standard_Integer Degree,
const Standard_Boolean Periodic,
const Standard_Integer Dimension,
const TColStd_Array1OfReal& Poles,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
TColStd_Array1OfReal& NewPoles,
TColStd_Array1OfReal& NewKnots,
TColStd_Array1OfInteger& NewMults,
const Standard_Real Tolerance)
{
Standard_Integer index,i,j,k,p,np;
Standard_Integer TheIndex = Index;
// protection
Standard_Integer first,last;
if (Periodic) {
first = Knots.Lower();
last = Knots.Upper();
}
else {
first = BSplCLib::FirstUKnotIndex(Degree,Mults) + 1;
last = BSplCLib::LastUKnotIndex(Degree,Mults) - 1;
}
if (Index < first) return Standard_False;
if (Index > last) return Standard_False;
if ( Periodic && (Index == first)) TheIndex = last;
Standard_Integer depth = Mults(TheIndex) - Mult;
Standard_Integer length = Degree - Mult;
// -------------------
// create local arrays
// -------------------
Standard_Real *knots = new Standard_Real[4*Degree];
Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
// ------------------------------------
// build the knots for anti Boor Scheme
// ------------------------------------
// the new sequence of knots
// is obtained from the knots at Index-1 and Index
BSplCLib::BuildKnots(Degree,TheIndex-1,Periodic,Knots,Mults,*knots);
index = PoleIndex(Degree,TheIndex-1,Periodic,Mults);
BSplCLib::BuildKnots(Degree,TheIndex,Periodic,Knots,Mults,knots[2*Degree]);
index += Mult;
for (i = 0; i < Degree - Mult; i++)
knots[i] = knots[i+Mult];
for (i = Degree-Mult; i < 2*Degree; i++)
knots[i] = knots[2*Degree+i];
// ------------------------------------
// build the poles for anti Boor Scheme
// ------------------------------------
p = Poles.Lower()+index * Dimension;
for (i = 0; i <= length + depth; i++) {
j = Dimension * BoorIndex(i,length,depth);
for (k = 0; k < Dimension; k++) {
poles[j+k] = Poles(p+k);
}
p += Dimension;
if (p > Poles.Upper()) p = Poles.Lower();
}
// ----------------
// Anti Boor Scheme
// ----------------
Standard_Boolean result = AntiBoorScheme(Knots(TheIndex),Degree,*knots,
Dimension,*poles,
depth,length,Tolerance);
// ----------------
// copy the results
// ----------------
if (result) {
// poles
p = Poles.Lower();
np = NewPoles.Lower();
// unmodified poles before
Copy((index+1)*Dimension,p,Poles,np,NewPoles);
// modified
for (i = 1; i <= length; i++)
BSplCLib::GetPole(i,length,0,Dimension,*poles,np,NewPoles);
p += (length + depth) * Dimension ;
// unmodified poles after
if (p != Poles.Lower()) {
i = Poles.Upper() - p + 1;
Copy(i,p,Poles,np,NewPoles);
}
// knots and mults
if (Mult > 0) {
NewKnots = Knots;
NewMults = Mults;
NewMults(TheIndex) = Mult;
if (Periodic) {
if (TheIndex == first) NewMults(last) = Mult;
if (TheIndex == last) NewMults(first) = Mult;
}
}
else {
if (!Periodic || (TheIndex != first && TheIndex != last)) {
for (i = Knots.Lower(); i < TheIndex; i++) {
NewKnots(i) = Knots(i);
NewMults(i) = Mults(i);
}
for (i = TheIndex+1; i <= Knots.Upper(); i++) {
NewKnots(i-1) = Knots(i);
NewMults(i-1) = Mults(i);
}
}
else {
// The interesting case of a Periodic curve
// where the first and last knot is removed.
for (i = first; i < last-1; i++) {
NewKnots(i) = Knots(i+1);
NewMults(i) = Mults(i+1);
}
NewKnots(last-1) = NewKnots(first) + Knots(last) - Knots(first);
NewMults(last-1) = NewMults(first);
}
}
}
// free local arrays
delete [] knots;
delete [] poles;
return result;
}
//=======================================================================
//function : IncreaseDegreeCountKnots
//purpose :
//=======================================================================
Standard_Integer BSplCLib::IncreaseDegreeCountKnots
(const Standard_Integer Degree,
const Standard_Integer NewDegree,
const Standard_Boolean Periodic,
const TColStd_Array1OfInteger& Mults)
{
if (Periodic) return Mults.Length();
Standard_Integer f = FirstUKnotIndex(Degree,Mults);
Standard_Integer l = LastUKnotIndex(Degree,Mults);
Standard_Integer m,i,removed = 0, step = NewDegree - Degree;
i = Mults.Lower();
m = Degree + (f - i + 1) * step + 1;
while (m > NewDegree+1) {
removed++;
m -= Mults(i) + step;
i++;
}
if (m < NewDegree+1) removed--;
i = Mults.Upper();
m = Degree + (i - l + 1) * step + 1;
while (m > NewDegree+1) {
removed++;
m -= Mults(i) + step;
i--;
}
if (m < NewDegree+1) removed--;
return Mults.Length() - removed;
}
//=======================================================================
//function : IncreaseDegree
//purpose :
//=======================================================================
void BSplCLib::IncreaseDegree
(const Standard_Integer Degree,
const Standard_Integer NewDegree,
const Standard_Boolean Periodic,
const Standard_Integer Dimension,
const TColStd_Array1OfReal& Poles,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
TColStd_Array1OfReal& NewPoles,
TColStd_Array1OfReal& NewKnots,
TColStd_Array1OfInteger& NewMults)
{
// Degree elevation of a BSpline Curve
// This algorithms loops on degree incrementation from Degree to NewDegree.
// The variable curDeg is the current degree to increment.
// Before degree incrementations a "working curve" is created.
// It has the same knot, poles and multiplicities.
// If the curve is periodic knots are added on the working curve before
// and after the existing knots to make it a non-periodic curves.
// The poles are also copied.
// The first and last multiplicity of the working curve are set to Degree+1,
// null poles are added if necessary.
// Then the degree is incremented on the working curve.
// The knots are unchanged but all multiplicities will be incremented.
// Each degree incrementation is achieved by averaging curDeg+1 curves.
// See : Degree elevation of B-spline curves
// Hartmut PRAUTZSCH
// CAGD 1 (1984)
//-------------------------
// create the working curve
//-------------------------
Standard_Integer i,k,f,l,m,pf,pl,firstknot;
pf = 0; // number of null poles added at beginning
pl = 0; // number of null poles added at end
Standard_Integer nbwknots = Knots.Length();
f = FirstUKnotIndex(Degree,Mults);
l = LastUKnotIndex (Degree,Mults);
if (Periodic) {
// Periodic curves are transformed in non-periodic curves
nbwknots += f - Mults.Lower();
pf = -Degree - 1;
for (i = Mults.Lower(); i <= f; i++)
pf += Mults(i);
nbwknots += Mults.Upper() - l;
pl = -Degree - 1;
for (i = l; i <= Mults.Upper(); i++)
pl += Mults(i);
}
// copy the knots and multiplicities
TColStd_Array1OfReal wknots(1,nbwknots);
TColStd_Array1OfInteger wmults(1,nbwknots);
if (!Periodic) {
wknots = Knots;
wmults = Mults;
}
else {
// copy the knots for a periodic curve
Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
i = 0;
for (k = l; k < Knots.Upper(); k++) {
i++;
wknots(i) = Knots(k) - period;
wmults(i) = Mults(k);
}
for (k = Knots.Lower(); k <= Knots.Upper(); k++) {
i++;
wknots(i) = Knots(k);
wmults(i) = Mults(k);
}
for (k = Knots.Lower()+1; k <= f; k++) {
i++;
wknots(i) = Knots(k) + period;
wmults(i) = Mults(k);
}
}
// set the first and last mults to Degree+1
// and add null poles
pf += Degree + 1 - wmults(1);
wmults(1) = Degree + 1;
pl += Degree + 1 - wmults(nbwknots);
wmults(nbwknots) = Degree + 1;
//---------------------------
// poles of the working curve
//---------------------------
Standard_Integer nbwpoles = 0;
for (i = 1; i <= nbwknots; i++) nbwpoles += wmults(i);
nbwpoles -= Degree + 1;
// we provide space for degree elevation
TColStd_Array1OfReal
wpoles(1,(nbwpoles + (nbwknots-1) * (NewDegree - Degree)) * Dimension);
for (i = 1; i <= pf * Dimension; i++)
wpoles(i) = 0;
k = Poles.Lower();
for (i = pf * Dimension + 1; i <= (nbwpoles - pl) * Dimension; i++) {
wpoles(i) = Poles(k);
k++;
if (k > Poles.Upper()) k = Poles.Lower();
}
for (i = (nbwpoles-pl)*Dimension+1; i <= nbwpoles*Dimension; i++)
wpoles(i) = 0;
//-----------------------------------------------------------
// Declare the temporary arrays used in degree incrementation
//-----------------------------------------------------------
Standard_Integer nbwp = nbwpoles + (nbwknots-1) * (NewDegree - Degree);
// Arrays for storing the temporary curves
TColStd_Array1OfReal tempc1(1,nbwp * Dimension);
TColStd_Array1OfReal tempc2(1,nbwp * Dimension);
// Array for storing the knots to insert
TColStd_Array1OfReal iknots(1,nbwknots);
// Arrays for receiving the knots after insertion
TColStd_Array1OfReal nknots(1,nbwknots);
//------------------------------
// Loop on degree incrementation
//------------------------------
Standard_Integer step,curDeg;
Standard_Integer nbp = nbwpoles;
nbwp = nbp;
for (curDeg = Degree; curDeg < NewDegree; curDeg++) {
nbp = nbwp; // current number of poles
nbwp = nbp + nbwknots - 1; // new number of poles
// For the averaging
TColStd_Array1OfReal nwpoles(1,nbwp * Dimension);
nwpoles.Init(0.0e0) ;
for (step = 0; step <= curDeg; step++) {
// Compute the bspline of rank step.
// if not the first time, decrement the multiplicities back
if (step != 0) {
for (i = 1; i <= nbwknots; i++)
wmults(i)--;
}
// Poles are the current poles
// but the poles congruent to step are duplicated.
Standard_Integer offset = 0;
for (i = 0; i < nbp; i++) {
offset++;
for (k = 0; k < Dimension; k++) {
tempc1((offset-1)*Dimension+k+1) =
wpoles(NewPoles.Lower()+i*Dimension+k);
}
if (i % (curDeg+1) == step) {
offset++;
for (k = 0; k < Dimension; k++) {
tempc1((offset-1)*Dimension+k+1) =
wpoles(NewPoles.Lower()+i*Dimension+k);
}
}
}
// Knots multiplicities are increased
// For each knot where the sum of multiplicities is congruent to step
Standard_Integer stepmult = step+1;
Standard_Integer nbknots = 0;
Standard_Integer smult = 0;
for (k = 1; k <= nbwknots; k++) {
smult += wmults(k);
if (smult >= stepmult) {
// this knot is increased
stepmult += curDeg+1;
wmults(k)++;
}
else {
// this knot is inserted
nbknots++;
iknots(nbknots) = wknots(k);
}
}
// the curve is obtained by inserting the knots
// to raise the multiplicities
// we build "slices" of the arrays to set the correct size
if (nbknots > 0) {
TColStd_Array1OfReal aknots(iknots(1),1,nbknots);
TColStd_Array1OfReal curve (tempc1(1),1,offset * Dimension);
TColStd_Array1OfReal ncurve(tempc2(1),1,nbwp * Dimension);
// InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
// aknots,NoMults(),ncurve,nknots,wmults,Epsilon(1.));
InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
aknots,NoMults(),ncurve,nknots,wmults,0.0);
// add to the average
for (i = 1; i <= nbwp * Dimension; i++)
nwpoles(i) += ncurve(i);
}
else {
// add to the average
for (i = 1; i <= nbwp * Dimension; i++)
nwpoles(i) += tempc1(i);
}
}
// The result is the average
for (i = 1; i <= nbwp * Dimension; i++) {
wpoles(i) = nwpoles(i) / (curDeg+1);
}
}
//-----------------
// Copy the results
//-----------------
// index in new knots of the first knot of the curve
if (Periodic)
firstknot = Mults.Upper() - l + 1;
else
firstknot = f;
// the new curve starts at index firstknot
// so we must remove knots until the sum of multiplicities
// from the first to the start is NewDegree+1
// m is the current sum of multiplicities
m = 0;
for (k = 1; k <= firstknot; k++)
m += wmults(k);
// compute the new first knot (k), pf will be the index of the first pole
k = 1;
pf = 0;
while (m > NewDegree+1) {
k++;
m -= wmults(k);
pf += wmults(k);
}
if (m < NewDegree+1) {
k--;
wmults(k) += m - NewDegree - 1;
pf += m - NewDegree - 1;
}
// on a periodic curve the knots start with firstknot
if (Periodic)
k = firstknot;
// copy knots
for (i = NewKnots.Lower(); i <= NewKnots.Upper(); i++) {
NewKnots(i) = wknots(k);
NewMults(i) = wmults(k);
k++;
}
// copy poles
pf *= Dimension;
for (i = NewPoles.Lower(); i <= NewPoles.Upper(); i++) {
pf++;
NewPoles(i) = wpoles(pf);
}
}
//=======================================================================
//function : PrepareUnperiodize
//purpose :
//=======================================================================
void BSplCLib::PrepareUnperiodize
(const Standard_Integer Degree,
const TColStd_Array1OfInteger& Mults,
Standard_Integer& NbKnots,
Standard_Integer& NbPoles)
{
Standard_Integer i;
// initialize NbKnots and NbPoles
NbKnots = Mults.Length();
NbPoles = - Degree - 1;
for (i = Mults.Lower(); i <= Mults.Upper(); i++)
NbPoles += Mults(i);
Standard_Integer sigma, k;
// Add knots at the beginning of the curve to raise Multiplicities
// to Degre + 1;
sigma = Mults(Mults.Lower());
k = Mults.Upper() - 1;
while ( sigma < Degree + 1) {
sigma += Mults(k);
NbPoles += Mults(k);
k--;
NbKnots++;
}
// We must add exactly until Degree + 1 ->
// Supress the excedent.
if ( sigma > Degree + 1)
NbPoles -= sigma - Degree - 1;
// Add knots at the end of the curve to raise Multiplicities
// to Degre + 1;
sigma = Mults(Mults.Upper());
k = Mults.Lower() + 1;
while ( sigma < Degree + 1) {
sigma += Mults(k);
NbPoles += Mults(k);
k++;
NbKnots++;
}
// We must add exactly until Degree + 1 ->
// Supress the excedent.
if ( sigma > Degree + 1)
NbPoles -= sigma - Degree - 1;
}
//=======================================================================
//function : Unperiodize
//purpose :
//=======================================================================
void BSplCLib::Unperiodize
(const Standard_Integer Degree,
const Standard_Integer , // Dimension,
const TColStd_Array1OfInteger& Mults,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfReal& Poles,
TColStd_Array1OfInteger& NewMults,
TColStd_Array1OfReal& NewKnots,
TColStd_Array1OfReal& NewPoles)
{
Standard_Integer sigma, k, index = 0;
// evaluation of index : number of knots to insert before knot(1) to
// raise sum of multiplicities to <Degree + 1>
sigma = Mults(Mults.Lower());
k = Mults.Upper() - 1;
while ( sigma < Degree + 1) {
sigma += Mults(k);
k--;
index++;
}
Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
// set the 'interior' knots;
for ( k = 1; k <= Knots.Length(); k++) {
NewKnots ( k + index ) = Knots( k);
NewMults ( k + index ) = Mults( k);
}
// set the 'starting' knots;
for ( k = 1; k <= index; k++) {
NewKnots( k) = NewKnots( k + Knots.Length() - 1) - period;
NewMults( k) = NewMults( k + Knots.Length() - 1);
}
NewMults( 1) -= sigma - Degree -1;
// set the 'ending' knots;
sigma = NewMults( index + Knots.Length() );
for ( k = Knots.Length() + index + 1; k <= NewKnots.Length(); k++) {
NewKnots( k) = NewKnots( k - Knots.Length() + 1) + period;
NewMults( k) = NewMults( k - Knots.Length() + 1);
sigma += NewMults( k - Knots.Length() + 1);
}
NewMults(NewMults.Length()) -= sigma - Degree - 1;
for ( k = 1 ; k <= NewPoles.Length(); k++) {
NewPoles(k ) = Poles( (k-1) % Poles.Length() + 1);
}
}
//=======================================================================
//function : PrepareTrimming
//purpose :
//=======================================================================
void BSplCLib::PrepareTrimming(const Standard_Integer Degree,
const Standard_Boolean Periodic,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
const Standard_Real U1,
const Standard_Real U2,
Standard_Integer& NbKnots,
Standard_Integer& NbPoles)
{
Standard_Integer i;
Standard_Real NewU1, NewU2;
Standard_Integer index1 = 0, index2 = 0;
// Eval index1, index2 : position of U1 and U2 in the Array Knots
// such as Knots(index1-1) <= U1 < Knots(index1)
// Knots(index2-1) <= U2 < Knots(index2)
LocateParameter( Degree, Knots, Mults, U1, Periodic,
Knots.Lower(), Knots.Upper(), index1, NewU1);
LocateParameter( Degree, Knots, Mults, U2, Periodic,
Knots.Lower(), Knots.Upper(), index2, NewU2);
index1++;
if ( Abs(Knots(index2) - U2) <= Epsilon( U1))
index2--;
// eval NbKnots:
NbKnots = index2 - index1 + 3;
// eval NbPoles:
NbPoles = Degree + 1;
for ( i = index1; i <= index2; i++)
NbPoles += Mults(i);
}
//=======================================================================
//function : Trimming
//purpose :
//=======================================================================
void BSplCLib::Trimming(const Standard_Integer Degree,
const Standard_Boolean Periodic,
const Standard_Integer Dimension,
const TColStd_Array1OfReal& Knots,
const TColStd_Array1OfInteger& Mults,
const TColStd_Array1OfReal& Poles,
const Standard_Real U1,
const Standard_Real U2,
TColStd_Array1OfReal& NewKnots,
TColStd_Array1OfInteger& NewMults,
TColStd_Array1OfReal& NewPoles)
{
Standard_Integer i, nbpoles, nbknots;
Standard_Real kk[2];
Standard_Integer mm[2];
TColStd_Array1OfReal K( kk[0], 1, 2 );
TColStd_Array1OfInteger M( mm[0], 1, 2 );
K(1) = U1; K(2) = U2;
mm[0] = mm[1] = Degree;
if (!PrepareInsertKnots( Degree, Periodic, Knots, Mults, K, M,
nbpoles, nbknots, Epsilon( U1), 0))
Standard_OutOfRange::Raise();
TColStd_Array1OfReal TempPoles(1, nbpoles*Dimension);
TColStd_Array1OfReal TempKnots(1, nbknots);
TColStd_Array1OfInteger TempMults(1, nbknots);
//
// do not allow the multiplicities to Add : they must be less than Degree
//
InsertKnots(Degree, Periodic, Dimension, Poles, Knots, Mults,
K, M, TempPoles, TempKnots, TempMults, Epsilon(U1),
Standard_False);
// find in TempPoles the index of the pole corresponding to U1
Standard_Integer Kindex = 0, Pindex;
Standard_Real NewU1;
LocateParameter( Degree, TempKnots, TempMults, U1, Periodic,
TempKnots.Lower(), TempKnots.Upper(), Kindex, NewU1);
Pindex = PoleIndex ( Degree, Kindex, Periodic, TempMults);
Pindex *= Dimension;
for ( i = 1; i <= NewPoles.Length(); i++) NewPoles(i) = TempPoles(Pindex + i);
for ( i = 1; i <= NewKnots.Length(); i++) {
NewKnots(i) = TempKnots( Kindex+i-1);
NewMults(i) = TempMults( Kindex+i-1);
}
NewMults(1) = Min(Degree, NewMults(1)) + 1 ;
NewMults(NewMults.Length())= Min(Degree, NewMults(NewMults.Length())) + 1 ;
}
//=======================================================================
//function : Solves a LU factored Matrix
//purpose :
//=======================================================================
Standard_Integer
BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
const Standard_Integer UpperBandWidth,
const Standard_Integer LowerBandWidth,
const Standard_Integer ArrayDimension,
Standard_Real& Array)
{
Standard_Integer ii,
jj,
kk,
MinIndex,
MaxIndex,
ReturnCode = 0 ;
Standard_Real *PolesArray = &Array ;
Standard_Real Inverse ;
if (Matrix.LowerCol() != 1 ||
Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
ReturnCode = 1 ;
goto FINISH ;
}
for (ii = Matrix.LowerRow() + 1; ii <= Matrix.UpperRow() ; ii++) {
MinIndex = (ii - LowerBandWidth >= Matrix.LowerRow() ?
ii - LowerBandWidth : Matrix.LowerRow()) ;
for ( jj = MinIndex ; jj < ii ; jj++) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PolesArray[(ii-1) * ArrayDimension + kk] +=
PolesArray[(jj-1) * ArrayDimension + kk] * Matrix(ii, jj - ii + LowerBandWidth + 1) ;
}
}
}
for (ii = Matrix.UpperRow() ; ii >= Matrix.LowerRow() ; ii--) {
MaxIndex = (ii + UpperBandWidth <= Matrix.UpperRow() ?
ii + UpperBandWidth : Matrix.UpperRow()) ;
for (jj = MaxIndex ; jj > ii ; jj--) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PolesArray[(ii-1) * ArrayDimension + kk] -=
PolesArray[(jj - 1) * ArrayDimension + kk] *
Matrix(ii, jj - ii + LowerBandWidth + 1) ;
}
}
//fixing a bug PRO18577 to avoid divizion by zero
Standard_Real divizor = Matrix(ii,LowerBandWidth + 1) ;
Standard_Real Toler = 1.0e-16;
if ( Abs(divizor) > Toler )
Inverse = 1.0e0 / divizor ;
else {
Inverse = 1.0e0;
// cout << " BSplCLib::SolveBandedSystem() : zero determinant " << endl;
ReturnCode = 1;
goto FINISH;
}
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PolesArray[(ii-1) * ArrayDimension + kk] *= Inverse ;
}
}
FINISH :
return (ReturnCode) ;
}
//=======================================================================
//function : Solves a LU factored Matrix
//purpose :
//=======================================================================
Standard_Integer
BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
const Standard_Integer UpperBandWidth,
const Standard_Integer LowerBandWidth,
const Standard_Boolean HomogeneousFlag,
const Standard_Integer ArrayDimension,
Standard_Real& Poles,
Standard_Real& Weights)
{
Standard_Integer ii,
kk,
ErrorCode = 0,
ReturnCode = 0 ;
Standard_Real Inverse,
*PolesArray = &Poles,
*WeightsArray = &Weights ;
if (Matrix.LowerCol() != 1 ||
Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
ReturnCode = 1 ;
goto FINISH ;
}
if (HomogeneousFlag == Standard_False) {
for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1; ii++) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PolesArray[ii * ArrayDimension + kk] *=
WeightsArray[ii] ;
}
}
}
ErrorCode =
BSplCLib::SolveBandedSystem(Matrix,
UpperBandWidth,
LowerBandWidth,
ArrayDimension,
Poles) ;
if (ErrorCode != 0) {
ReturnCode = 2 ;
goto FINISH ;
}
ErrorCode =
BSplCLib::SolveBandedSystem(Matrix,
UpperBandWidth,
LowerBandWidth,
1,
Weights) ;
if (ErrorCode != 0) {
ReturnCode = 3 ;
goto FINISH ;
}
if (HomogeneousFlag == Standard_False) {
for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1 ; ii++) {
Inverse = 1.0e0 / WeightsArray[ii] ;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PolesArray[ii * ArrayDimension + kk] *= Inverse ;
}
}
}
FINISH : return (ReturnCode) ;
}
//=======================================================================
//function : BuildSchoenbergPoints
//purpose :
//=======================================================================
void BSplCLib::BuildSchoenbergPoints(const Standard_Integer Degree,
const TColStd_Array1OfReal& FlatKnots,
TColStd_Array1OfReal& Parameters)
{
Standard_Integer ii,
jj ;
Standard_Real Inverse ;
Inverse = 1.0e0 / (Standard_Real)Degree ;
for (ii = Parameters.Lower() ; ii <= Parameters.Upper() ; ii++) {
Parameters(ii) = 0.0e0 ;
for (jj = 1 ; jj <= Degree ; jj++) {
Parameters(ii) += FlatKnots(jj + ii) ;
}
Parameters(ii) *= Inverse ;
}
}
//=======================================================================
//function : Interpolate
//purpose :
//=======================================================================
void BSplCLib::Interpolate(const Standard_Integer Degree,
const TColStd_Array1OfReal& FlatKnots,
const TColStd_Array1OfReal& Parameters,
const TColStd_Array1OfInteger& ContactOrderArray,
const Standard_Integer ArrayDimension,
Standard_Real& Poles,
Standard_Integer& InversionProblem)
{
Standard_Integer ErrorCode,
UpperBandWidth,
LowerBandWidth ;
// Standard_Real *PolesArray = &Poles ;
math_Matrix InterpolationMatrix(1, Parameters.Length(),
1, 2 * Degree + 1) ;
ErrorCode =
BSplCLib::BuildBSpMatrix(Parameters,
ContactOrderArray,
FlatKnots,
Degree,
InterpolationMatrix,
UpperBandWidth,
LowerBandWidth) ;
Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
ErrorCode =
BSplCLib::FactorBandedMatrix(InterpolationMatrix,
UpperBandWidth,
LowerBandWidth,
InversionProblem) ;
Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
ErrorCode =
BSplCLib::SolveBandedSystem(InterpolationMatrix,
UpperBandWidth,
LowerBandWidth,
ArrayDimension,
Poles) ;
Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
}
//=======================================================================
//function : Interpolate
//purpose :
//=======================================================================
void BSplCLib::Interpolate(const Standard_Integer Degree,
const TColStd_Array1OfReal& FlatKnots,
const TColStd_Array1OfReal& Parameters,
const TColStd_Array1OfInteger& ContactOrderArray,
const Standard_Integer ArrayDimension,
Standard_Real& Poles,
Standard_Real& Weights,
Standard_Integer& InversionProblem)
{
Standard_Integer ErrorCode,
UpperBandWidth,
LowerBandWidth ;
math_Matrix InterpolationMatrix(1, Parameters.Length(),
1, 2 * Degree + 1) ;
ErrorCode =
BSplCLib::BuildBSpMatrix(Parameters,
ContactOrderArray,
FlatKnots,
Degree,
InterpolationMatrix,
UpperBandWidth,
LowerBandWidth) ;
Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
ErrorCode =
BSplCLib::FactorBandedMatrix(InterpolationMatrix,
UpperBandWidth,
LowerBandWidth,
InversionProblem) ;
Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
ErrorCode =
BSplCLib::SolveBandedSystem(InterpolationMatrix,
UpperBandWidth,
LowerBandWidth,
Standard_False,
ArrayDimension,
Poles,
Weights) ;
Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
}
//=======================================================================
//function : Evaluates a Bspline function : uses the ExtrapMode
//purpose : the function is extrapolated using the Taylor expansion
// of degree ExtrapMode[0] to the left and the Taylor
// expansion of degree ExtrapMode[1] to the right
// this evaluates the numerator by multiplying by the weights
// and evaluating it but does not call RationalDerivatives after
//=======================================================================
void BSplCLib::Eval
(const Standard_Real Parameter,
const Standard_Boolean PeriodicFlag,
const Standard_Integer DerivativeRequest,
Standard_Integer& ExtrapMode,
const Standard_Integer Degree,
const TColStd_Array1OfReal& FlatKnots,
const Standard_Integer ArrayDimension,
Standard_Real& Poles,
Standard_Real& Weights,
Standard_Real& PolesResults,
Standard_Real& WeightsResults)
{
Standard_Integer ii,
jj,
kk=0,
Index,
Index1,
Index2,
*ExtrapModeArray,
Modulus,
NewRequest,
ExtrapolatingFlag[2],
ErrorCode,
ReturnCode,
Order = Degree + 1,
FirstNonZeroBsplineIndex,
LocalRequest = DerivativeRequest ;
Standard_Real *PResultArray,
*WResultArray,
*PolesArray,
*WeightsArray,
LocalParameter,
Period,
Inverse,
Delta ;
PolesArray = &Poles ;
WeightsArray = &Weights ;
ExtrapModeArray = &ExtrapMode ;
PResultArray = &PolesResults ;
WResultArray = &WeightsResults ;
LocalParameter = Parameter ;
ExtrapolatingFlag[0] =
ExtrapolatingFlag[1] = 0 ;
//
// check if we are extrapolating to a degree which is smaller than
// the degree of the Bspline
//
if (PeriodicFlag) {
Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
LocalParameter -= Period ;
}
while (LocalParameter < FlatKnots(2)) {
LocalParameter += Period ;
}
}
if (Parameter < FlatKnots(2) &&
LocalRequest < ExtrapModeArray[0] &&
ExtrapModeArray[0] < Degree) {
LocalRequest = ExtrapModeArray[0] ;
LocalParameter = FlatKnots(2) ;
ExtrapolatingFlag[0] = 1 ;
}
if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
LocalRequest < ExtrapModeArray[1] &&
ExtrapModeArray[1] < Degree) {
LocalRequest = ExtrapModeArray[1] ;
LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
ExtrapolatingFlag[1] = 1 ;
}
Delta = Parameter - LocalParameter ;
if (LocalRequest >= Order) {
LocalRequest = Degree ;
}
if (PeriodicFlag) {
Modulus = FlatKnots.Length() - Degree -1 ;
}
else {
Modulus = FlatKnots.Length() - Degree ;
}
BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
ErrorCode =
BSplCLib::EvalBsplineBasis(1,
LocalRequest,
Order,
FlatKnots,
LocalParameter,
FirstNonZeroBsplineIndex,
BsplineBasis) ;
if (ErrorCode != 0) {
ReturnCode = 1 ;
goto FINISH ;
}
if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
Index = 0 ;
Index2 = 0 ;
for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
Index1 = FirstNonZeroBsplineIndex ;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PResultArray[Index + kk] = 0.0e0 ;
}
WResultArray[Index] = 0.0e0 ;
for (jj = 1 ; jj <= Order ; jj++) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
PResultArray[Index + kk] +=
PolesArray[(Index1-1) * ArrayDimension + kk]
* WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
}
WResultArray[Index2] += WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
Index1 = Index1 % Modulus ;
Index1 += 1 ;
}
Index += ArrayDimension ;
Index2 += 1 ;
}
}
else {
//
// store Taylor expansion in LocalRealArray
//
NewRequest = DerivativeRequest ;
if (NewRequest > Degree) {
NewRequest = Degree ;
}
NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
Index = 0 ;
Inverse = 1.0e0 ;
for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
Index1 = FirstNonZeroBsplineIndex ;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
LocalRealArray[Index + kk] = 0.0e0 ;
}
for (jj = 1 ; jj <= Order ; jj++) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
LocalRealArray[Index + kk] +=
PolesArray[(Index1-1)*ArrayDimension + kk] *
WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
}
Index1 = Index1 % Modulus ;
Index1 += 1 ;
}
for (kk = 0 ; kk < ArrayDimension ; kk++) {
LocalRealArray[Index + kk] *= Inverse ;
}
Index += ArrayDimension ;
Inverse /= (Standard_Real) ii ;
}
PLib::EvalPolynomial(Delta,
NewRequest,
Degree,
ArrayDimension,
LocalRealArray[0],
PolesResults) ;
Index = 0 ;
Inverse = 1.0e0 ;
for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
Index1 = FirstNonZeroBsplineIndex ;
LocalRealArray[Index] = 0.0e0 ;
for (jj = 1 ; jj <= Order ; jj++) {
LocalRealArray[Index] +=
WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
Index1 = Index1 % Modulus ;
Index1 += 1 ;
}
LocalRealArray[Index + kk] *= Inverse ;
Index += 1 ;
Inverse /= (Standard_Real) ii ;
}
PLib::EvalPolynomial(Delta,
NewRequest,
Degree,
1,
LocalRealArray[0],
WeightsResults) ;
}
FINISH : ;
}
//=======================================================================
//function : Evaluates a Bspline function : uses the ExtrapMode
//purpose : the function is extrapolated using the Taylor expansion
// of degree ExtrapMode[0] to the left and the Taylor
// expansion of degree ExtrapMode[1] to the right
// WARNING : the array Results is supposed to have at least
// (DerivativeRequest + 1) * ArrayDimension slots and the
//
//=======================================================================
void BSplCLib::Eval
(const Standard_Real Parameter,
const Standard_Boolean PeriodicFlag,
const Standard_Integer DerivativeRequest,
Standard_Integer& ExtrapMode,
const Standard_Integer Degree,
const TColStd_Array1OfReal& FlatKnots,
const Standard_Integer ArrayDimension,
Standard_Real& Poles,
Standard_Real& Results)
{
Standard_Integer ii,
jj,
kk,
Index,
Index1,
*ExtrapModeArray,
Modulus,
NewRequest,
ExtrapolatingFlag[2],
ErrorCode,
ReturnCode,
Order = Degree + 1,
FirstNonZeroBsplineIndex,
LocalRequest = DerivativeRequest ;
Standard_Real *ResultArray,
*PolesArray,
LocalParameter,
Period,
Inverse,
Delta ;
PolesArray = &Poles ;
ExtrapModeArray = &ExtrapMode ;
ResultArray = &Results ;
LocalParameter = Parameter ;
ExtrapolatingFlag[0] =
ExtrapolatingFlag[1] = 0 ;
//
// check if we are extrapolating to a degree which is smaller than
// the degree of the Bspline
//
if (PeriodicFlag) {
Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
LocalParameter -= Period ;
}
while (LocalParameter < FlatKnots(2)) {
LocalParameter += Period ;
}
}
if (Parameter < FlatKnots(2) &&
LocalRequest < ExtrapModeArray[0] &&
ExtrapModeArray[0] < Degree) {
LocalRequest = ExtrapModeArray[0] ;
LocalParameter = FlatKnots(2) ;
ExtrapolatingFlag[0] = 1 ;
}
if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
LocalRequest < ExtrapModeArray[1] &&
ExtrapModeArray[1] < Degree) {
LocalRequest = ExtrapModeArray[1] ;
LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
ExtrapolatingFlag[1] = 1 ;
}
Delta = Parameter - LocalParameter ;
if (LocalRequest >= Order) {
LocalRequest = Degree ;
}
if (PeriodicFlag) {
Modulus = FlatKnots.Length() - Degree -1 ;
}
else {
Modulus = FlatKnots.Length() - Degree ;
}
BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
ErrorCode =
BSplCLib::EvalBsplineBasis(1,
LocalRequest,
Order,
FlatKnots,
LocalParameter,
FirstNonZeroBsplineIndex,
BsplineBasis);
if (ErrorCode != 0) {
ReturnCode = 1 ;
goto FINISH ;
}
if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
Index = 0 ;
for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
Index1 = FirstNonZeroBsplineIndex ;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
ResultArray[Index + kk] = 0.0e0 ;
}
for (jj = 1 ; jj <= Order ; jj++) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
ResultArray[Index + kk] +=
PolesArray[(Index1-1) * ArrayDimension + kk] * BsplineBasis(ii,jj) ;
}
Index1 = Index1 % Modulus ;
Index1 += 1 ;
}
Index += ArrayDimension ;
}
}
else {
//
// store Taylor expansion in LocalRealArray
//
NewRequest = DerivativeRequest ;
if (NewRequest > Degree) {
NewRequest = Degree ;
}
NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
Index = 0 ;
Inverse = 1.0e0 ;
for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
Index1 = FirstNonZeroBsplineIndex ;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
LocalRealArray[Index + kk] = 0.0e0 ;
}
for (jj = 1 ; jj <= Order ; jj++) {
for (kk = 0 ; kk < ArrayDimension ; kk++) {
LocalRealArray[Index + kk] +=
PolesArray[(Index1-1)*ArrayDimension + kk] * BsplineBasis(ii,jj) ;
}
Index1 = Index1 % Modulus ;
Index1 += 1 ;
}
for (kk = 0 ; kk < ArrayDimension ; kk++) {
LocalRealArray[Index + kk] *= Inverse ;
}
Index += ArrayDimension ;
Inverse /= (Standard_Real) ii ;
}
PLib::EvalPolynomial(Delta,
NewRequest,
Degree,
ArrayDimension,
LocalRealArray[0],
Results) ;
}
FINISH : ;
}
//=======================================================================
//function : TangExtendToConstraint
//purpose : Extends a Bspline function using the tangency map
// WARNING :
//
//
//=======================================================================
void BSplCLib::TangExtendToConstraint
(const TColStd_Array1OfReal& FlatKnots,
const Standard_Real C1Coefficient,
const Standard_Integer NumPoles,
Standard_Real& Poles,
const Standard_Integer CDimension,
const Standard_Integer CDegree,
const TColStd_Array1OfReal& ConstraintPoint,
const Standard_Integer Continuity,
const Standard_Boolean After,
Standard_Integer& NbPolesResult,
Standard_Integer& NbKnotsResult,
Standard_Real& KnotsResult,
Standard_Real& PolesResult)
{
#if DEB
if (CDegree<Continuity+1) {
cout<<"The BSpline degree must be greater than the order of continuity"<<endl;
}
#endif
Standard_Real * Padr = &Poles ;
Standard_Real * KRadr = &KnotsResult ;
Standard_Real * PRadr = &PolesResult ;
////////////////////////////////////////////////////////////////////////
//
// 1. calculation of extension nD
//
////////////////////////////////////////////////////////////////////////
// Hermite matrix
Standard_Integer Csize = Continuity + 2;
math_Matrix MatCoefs(1,Csize, 1,Csize);
if (After) {
PLib::HermiteCoefficients(0, 1, // Limits
Continuity, 0, // Orders of constraints
MatCoefs);
}
else {
PLib::HermiteCoefficients(0, 1, // Limits
0, Continuity, // Orders of constraints
MatCoefs);
}
// position at the node of connection
Standard_Real Tbord ;
if (After) {
Tbord = FlatKnots(FlatKnots.Upper()-CDegree);
}
else {
Tbord = FlatKnots(FlatKnots.Lower()+CDegree);
}
Standard_Boolean periodic_flag = Standard_False ;
Standard_Integer ipos, extrap_mode[2], derivative_request = Max(Continuity,1);
extrap_mode[0] = extrap_mode[1] = CDegree;
TColStd_Array1OfReal EvalBS(1, CDimension * (derivative_request+1)) ;
Standard_Real * Eadr = (Standard_Real *) &EvalBS(1) ;
BSplCLib::Eval(Tbord,periodic_flag,derivative_request,extrap_mode[0],
CDegree,FlatKnots,CDimension,Poles,*Eadr);
// norm of the tangent at the node of connection
math_Vector Tgte(1,CDimension);
for (ipos=1;ipos<=CDimension;ipos++) {
Tgte(ipos) = EvalBS(ipos+CDimension);
}
Standard_Real L1=Tgte.Norm();
// matrix of constraints
math_Matrix Contraintes(1,Csize,1,CDimension);
if (After) {
for (ipos=1;ipos<=CDimension;ipos++) {
Contraintes(1,ipos) = EvalBS(ipos);
Contraintes(2,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
if(Continuity >= 2) Contraintes(3,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
if(Continuity >= 3) Contraintes(4,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
Contraintes(Continuity+2,ipos) = ConstraintPoint(ipos);
}
}
else {
for (ipos=1;ipos<=CDimension;ipos++) {
Contraintes(1,ipos) = ConstraintPoint(ipos);
Contraintes(2,ipos) = EvalBS(ipos);
if(Continuity >= 1) Contraintes(3,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
if(Continuity >= 2) Contraintes(4,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
if(Continuity >= 3) Contraintes(5,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
}
}
// calculate the coefficients of extension
Standard_Integer ii, jj, kk;
TColStd_Array1OfReal ExtraCoeffs(1,Csize*CDimension);
ExtraCoeffs.Init(0.);
for (ii=1; ii<=Csize; ii++) {
for (jj=1; jj<=Csize; jj++) {
for (kk=1; kk<=CDimension; kk++) {
ExtraCoeffs(kk+(jj-1)*CDimension) += MatCoefs(ii,jj)*Contraintes(ii,kk);
}
}
}
// calculate the poles of extension
TColStd_Array1OfReal ExtrapPoles(1,Csize*CDimension);
Standard_Real * EPadr = &ExtrapPoles(1) ;
PLib::CoefficientsPoles(CDimension,
ExtraCoeffs, PLib::NoWeights(),
ExtrapPoles, PLib::NoWeights());
// calculate the nodes of extension with multiplicities
TColStd_Array1OfReal ExtrapNoeuds(1,2);
ExtrapNoeuds(1) = 0.;
ExtrapNoeuds(2) = 1.;
TColStd_Array1OfInteger ExtrapMults(1,2);
ExtrapMults(1) = Csize;
ExtrapMults(2) = Csize;
// flat nodes of extension
TColStd_Array1OfReal FK2(1, Csize*2);
BSplCLib::KnotSequence(ExtrapNoeuds,ExtrapMults,FK2);
// norm of the tangent at the connection point
if (After) {
BSplCLib::Eval(0.,periodic_flag,1,extrap_mode[0],
Csize-1,FK2,CDimension,*EPadr,*Eadr);
}
else {
BSplCLib::Eval(1.,periodic_flag,1,extrap_mode[0],
Csize-1,FK2,CDimension,*EPadr,*Eadr);
}
for (ipos=1;ipos<=CDimension;ipos++) {
Tgte(ipos) = EvalBS(ipos+CDimension);
}
Standard_Real L2 = Tgte.Norm();
// harmonisation of degrees
TColStd_Array1OfReal NewP2(1, (CDegree+1)*CDimension);
TColStd_Array1OfReal NewK2(1, 2);
TColStd_Array1OfInteger NewM2(1, 2);
if (Csize-1<CDegree) {
BSplCLib::IncreaseDegree(Csize-1,CDegree,Standard_False,CDimension,
ExtrapPoles,ExtrapNoeuds,ExtrapMults,
NewP2,NewK2,NewM2);
}
else {
NewP2 = ExtrapPoles;
NewK2 = ExtrapNoeuds;
NewM2 = ExtrapMults;
}
// flat nodes of extension after harmonization of degrees
TColStd_Array1OfReal NewFK2(1, (CDegree+1)*2);
BSplCLib::KnotSequence(NewK2,NewM2,NewFK2);
////////////////////////////////////////////////////////////////////////
//
// 2. concatenation C0
//
////////////////////////////////////////////////////////////////////////
// ratio of reparametrization
Standard_Real Ratio=1, Delta;
if ( (L1 > Precision::Confusion()) && (L2 > Precision::Confusion()) ) {
Ratio = L2 / L1;
}
if ( (Ratio < 1.e-5) || (Ratio > 1.e5) ) Ratio = 1;
if (After) {
// do not touch the first BSpline
Delta = Ratio*NewFK2(NewFK2.Lower()) - FlatKnots(FlatKnots.Upper());
}
else {
// do not touch the second BSpline
Delta = Ratio*NewFK2(NewFK2.Upper()) - FlatKnots(FlatKnots.Lower());
}
// result of the concatenation
Standard_Integer NbP1 = NumPoles, NbP2 = CDegree+1;
Standard_Integer NbK1 = FlatKnots.Length(), NbK2 = 2*(CDegree+1);
TColStd_Array1OfReal NewPoles (1, (NbP1+ NbP2-1)*CDimension);
TColStd_Array1OfReal NewFlats (1, NbK1+NbK2-CDegree-2);
// poles
Standard_Integer indNP, indP, indEP;
if (After) {
for (ii=1; ii<=NbP1+NbP2-1; ii++) {
for (jj=1; jj<=CDimension; jj++) {
indNP = (ii-1)*CDimension+jj;
indP = (ii-1)*CDimension+jj-1;
indEP = (ii-NbP1)*CDimension+jj;
if (ii<NbP1) NewPoles(indNP) = Padr[indP];
else NewPoles(indNP) = NewP2(indEP);
}
}
}
else {
for (ii=1; ii<=NbP1+NbP2-1; ii++) {
for (jj=1; jj<=CDimension; jj++) {
indNP = (ii-1)*CDimension+jj;
indEP = (ii-1)*CDimension+jj;
indP = (ii-NbP2)*CDimension+jj-1;
if (ii<NbP2) NewPoles(indNP) = NewP2(indEP);
else NewPoles(indNP) = Padr[indP];
}
}
}
// flat nodes
if (After) {
// start with the nodes of the initial surface
for (ii=1; ii<NbK1; ii++) {
NewFlats(ii) = FlatKnots(FlatKnots.Lower()+ii-1);
}
// continue with the reparameterized nodes of the extension
for (ii=1; ii<=NbK2-CDegree-1; ii++) {
NewFlats(NbK1+ii-1) = Ratio*NewFK2(NewFK2.Lower()+ii+CDegree) - Delta;
}
}
else {
// start with the reparameterized nodes of the extension
for (ii=1; ii<NbK2-CDegree; ii++) {
NewFlats(ii) = Ratio*NewFK2(NewFK2.Lower()+ii-1) - Delta;
}
// continue with the nodes of the initial surface
for (ii=2; ii<=NbK1; ii++) {
NewFlats(NbK2+ii-CDegree-2) = FlatKnots(FlatKnots.Lower()+ii-1);
}
}
////////////////////////////////////////////////////////////////////////
//
// 3. reduction of multiplicite at the node of connection
//
////////////////////////////////////////////////////////////////////////
// number of separate nodes
Standard_Integer KLength = 1;
for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
if (NewFlats(ii) != NewFlats(ii-1)) KLength++;
}
// flat nodes --> nodes + multiplicities
TColStd_Array1OfReal NewKnots (1, KLength);
TColStd_Array1OfInteger NewMults (1, KLength);
NewMults.Init(1);
jj = 1;
NewKnots(jj) = NewFlats(1);
for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
if (NewFlats(ii) == NewFlats(ii-1)) NewMults(jj)++;
else {
jj++;
NewKnots(jj) = NewFlats(ii);
}
}
// reduction of multiplicity at the second or the last but one node
Standard_Integer Index = 2, M = CDegree;
if (After) Index = KLength-1;
TColStd_Array1OfReal ResultPoles (1, (NbP1+ NbP2-1)*CDimension);
TColStd_Array1OfReal ResultKnots (1, KLength);
TColStd_Array1OfInteger ResultMults (1, KLength);
Standard_Real Tol = 1.e-6;
Standard_Boolean Ok = Standard_True;
while ( (M>CDegree-Continuity) && Ok) {
Ok = RemoveKnot(Index, M-1, CDegree, Standard_False, CDimension,
NewPoles, NewKnots, NewMults,
ResultPoles, ResultKnots, ResultMults, Tol);
if (Ok) M--;
}
if (M == CDegree) {
// number of poles of the concatenation
NbPolesResult = NbP1 + NbP2 - 1;
// the poles of the concatenation
Standard_Integer PLength = NbPolesResult*CDimension;
for (jj=1; jj<=PLength; jj++) {
PRadr[jj-1] = NewPoles(jj);
}
// flat nodes of the concatenation
Standard_Integer ideb = 0;
for (jj=0; jj<NewKnots.Length(); jj++) {
for (ii=0; ii<NewMults(jj+1); ii++) {
KRadr[ideb+ii] = NewKnots(jj+1);
}
ideb += NewMults(jj+1);
}
NbKnotsResult = ideb;
}
else {
// number of poles of the result
NbPolesResult = NbP1 + NbP2 - 1 - CDegree + M;
// the poles of the result
Standard_Integer PLength = NbPolesResult*CDimension;
for (jj=0; jj<PLength; jj++) {
PRadr[jj] = ResultPoles(jj+1);
}
// flat nodes of the result
Standard_Integer ideb = 0;
for (jj=0; jj<ResultKnots.Length(); jj++) {
for (ii=0; ii<ResultMults(jj+1); ii++) {
KRadr[ideb+ii] = ResultKnots(jj+1);
}
ideb += ResultMults(jj+1);
}
NbKnotsResult = ideb;
}
}
//=======================================================================
//function : Resolution
//purpose :
// d
// Let C(t) = SUM Ci Bi(t) a Bspline curve of degree d
// i = 1,n
// with nodes tj for j = 1,n+d+1
//
//
// ' C1 - Ci-1 d-1
// Then C (t) = SUM d * --------- Bi (t)
// i = 2,n ti+d - ti
//
// d-1
// for the base of BSpline Bi (t) of degree d-1.
//
// Consequently the upper bound of the norm of the derivative from C is :
//
//
// | Ci - Ci-1 |
// d * Max | --------- |
// i = 2,n | ti+d - ti |
//
// N(t)
// In the rational case set C(t) = -----
// D(t)
//
//
// D(t) = SUM Di Bi(t)
// i=1,n
//
// N(t) = SUM Di * Ci Bi(t)
// i =1,n
//
// N'(t) - D'(t) C(t)
// C'(t) = -----------------------
// D(t)
//
//
// N'(t) - D'(t) C(t) =
//
// Di * (Ci - C(t)) - Di-1 * (Ci-1 - C(t)) d-1
// SUM d * ---------------------------------------- * Bi (t) =
// i=2,n ti+d - ti
//
//
// Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj) d-1
// SUM SUM d * ----------------------------------- * Betaj(t) * Bi (t)
//i=2,n j=1,n ti+d - ti
//
//
//
// Dj Bj(t)
// Betaj(t) = --------
// D(t)
//
// Betaj(t) form a partition >= 0 of the entity with support
// tj, tj+d+1. Consequently if Rj = {j-d, ...., j+d+d+1}
// obtain an upper bound of the derivative of C by taking :
//
//
//
//
//
//
// Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj)
// Max Max d * -----------------------------------
// j=1,n i dans Rj ti+d - ti
//
// --------------------------------------------------------
//
// Min Di
// i =1,n
//
//
//=======================================================================
void BSplCLib::Resolution( Standard_Real& Poles,
const Standard_Integer ArrayDimension,
const Standard_Integer NumPoles,
const TColStd_Array1OfReal& Weights,
const TColStd_Array1OfReal& FlatKnots,
const Standard_Integer Degree,
const Standard_Real Tolerance3D,
Standard_Real& UTolerance)
{
Standard_Integer ii,num_poles,ii_index,jj_index,ii_inDim;
Standard_Integer lower,upper,ii_minus,jj,ii_miDim;
Standard_Integer Deg1 = Degree + 1;
Standard_Integer Deg2 = (Degree << 1) + 1;
Standard_Real value,factor,W,min_weights,inverse;
Standard_Real pa_ii_inDim_0, pa_ii_inDim_1, pa_ii_inDim_2, pa_ii_inDim_3;
Standard_Real pa_ii_miDim_0, pa_ii_miDim_1, pa_ii_miDim_2, pa_ii_miDim_3;
Standard_Real wg_ii_index, wg_ii_minus;
Standard_Real *PA,max_derivative;
const Standard_Real * FK = &FlatKnots(FlatKnots.Lower());
PA = &Poles;
max_derivative = 0.0e0;
num_poles = FlatKnots.Length() - Deg1;
switch (ArrayDimension) {
case 2 : {
if (&Weights != NULL) {
const Standard_Real * WG = &Weights(Weights.Lower());
min_weights = WG[0];
for (ii = 1 ; ii < NumPoles ; ii++) {
W = WG[ii];
if (W < min_weights) min_weights = W;
}
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_inDim = ii_index << 1;
ii_minus = (ii - 1) % NumPoles;
ii_miDim = ii_minus << 1;
pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
pa_ii_inDim_1 = PA[ii_inDim];
pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
pa_ii_miDim_1 = PA[ii_miDim];
wg_ii_index = WG[ii_index];
wg_ii_minus = WG[ii_minus];
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
lower = ii - Deg1;
if (lower < 0) lower = 0;
upper = Deg2 + ii;
if (upper > num_poles) upper = num_poles;
for (jj = lower ; jj < upper ; jj++) {
jj_index = jj % NumPoles;
jj_index = jj_index << 1;
value = 0.0e0;
factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor; jj_index++;
factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor;
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
max_derivative /= min_weights;
}
else {
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_index = ii_index << 1;
ii_minus = (ii - 1) % NumPoles;
ii_minus = ii_minus << 1;
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
value = 0.0e0;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor; ii_index++; ii_minus++;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor;
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
break;
}
case 3 : {
if (&Weights != NULL) {
const Standard_Real * WG = &Weights(Weights.Lower());
min_weights = WG[0];
for (ii = 1 ; ii < NumPoles ; ii++) {
W = WG[ii];
if (W < min_weights) min_weights = W;
}
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_inDim = (ii_index << 1) + ii_index;
ii_minus = (ii - 1) % NumPoles;
ii_miDim = (ii_minus << 1) + ii_minus;
pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
pa_ii_inDim_1 = PA[ii_inDim]; ii_inDim++;
pa_ii_inDim_2 = PA[ii_inDim];
pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
pa_ii_miDim_1 = PA[ii_miDim]; ii_miDim++;
pa_ii_miDim_2 = PA[ii_miDim];
wg_ii_index = WG[ii_index];
wg_ii_minus = WG[ii_minus];
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
lower = ii - Deg1;
if (lower < 0) lower = 0;
upper = Deg2 + ii;
if (upper > num_poles) upper = num_poles;
for (jj = lower ; jj < upper ; jj++) {
jj_index = jj % NumPoles;
jj_index = (jj_index << 1) + jj_index;
value = 0.0e0;
factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor; jj_index++;
factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor; jj_index++;
factor = (((PA[jj_index] - pa_ii_inDim_2) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_2) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor;
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
max_derivative /= min_weights;
}
else {
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_index = (ii_index << 1) + ii_index;
ii_minus = (ii - 1) % NumPoles;
ii_minus = (ii_minus << 1) + ii_minus;
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
value = 0.0e0;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor; ii_index++; ii_minus++;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor; ii_index++; ii_minus++;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor;
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
break;
}
case 4 : {
if (&Weights != NULL) {
const Standard_Real * WG = &Weights(Weights.Lower());
min_weights = WG[0];
for (ii = 1 ; ii < NumPoles ; ii++) {
W = WG[ii];
if (W < min_weights) min_weights = W;
}
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_inDim = ii_index << 2;
ii_minus = (ii - 1) % NumPoles;
ii_miDim = ii_minus << 2;
pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
pa_ii_inDim_1 = PA[ii_inDim]; ii_inDim++;
pa_ii_inDim_2 = PA[ii_inDim]; ii_inDim++;
pa_ii_inDim_3 = PA[ii_inDim];
pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
pa_ii_miDim_1 = PA[ii_miDim]; ii_miDim++;
pa_ii_miDim_2 = PA[ii_miDim]; ii_miDim++;
pa_ii_miDim_3 = PA[ii_miDim];
wg_ii_index = WG[ii_index];
wg_ii_minus = WG[ii_minus];
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
lower = ii - Deg1;
if (lower < 0) lower = 0;
upper = Deg2 + ii;
if (upper > num_poles) upper = num_poles;
for (jj = lower ; jj < upper ; jj++) {
jj_index = jj % NumPoles;
jj_index = jj_index << 2;
value = 0.0e0;
factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor; jj_index++;
factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor; jj_index++;
factor = (((PA[jj_index] - pa_ii_inDim_2) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_2) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor; jj_index++;
factor = (((PA[jj_index] - pa_ii_inDim_3) * wg_ii_index) -
((PA[jj_index] - pa_ii_miDim_3) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor;
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
max_derivative /= min_weights;
}
else {
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_index = ii_index << 2;
ii_minus = (ii - 1) % NumPoles;
ii_minus = ii_minus << 2;
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
value = 0.0e0;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor; ii_index++; ii_minus++;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor; ii_index++; ii_minus++;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor; ii_index++; ii_minus++;
factor = PA[ii_index] - PA[ii_minus];
if (factor < 0) factor = - factor;
value += factor;
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
break;
}
default : {
Standard_Integer kk;
if (&Weights != NULL) {
const Standard_Real * WG = &Weights(Weights.Lower());
min_weights = WG[0];
for (ii = 1 ; ii < NumPoles ; ii++) {
W = WG[ii];
if (W < min_weights) min_weights = W;
}
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_inDim = ii_index * ArrayDimension;
ii_minus = (ii - 1) % NumPoles;
ii_miDim = ii_minus * ArrayDimension;
wg_ii_index = WG[ii_index];
wg_ii_minus = WG[ii_minus];
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
lower = ii - Deg1;
if (lower < 0) lower = 0;
upper = Deg2 + ii;
if (upper > num_poles) upper = num_poles;
for (jj = lower ; jj < upper ; jj++) {
jj_index = jj % NumPoles;
jj_index *= ArrayDimension;
value = 0.0e0;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
factor = (((PA[jj_index + kk] - PA[ii_inDim + kk]) * wg_ii_index) -
((PA[jj_index + kk] - PA[ii_miDim + kk]) * wg_ii_minus));
if (factor < 0) factor = - factor;
value += factor;
}
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
max_derivative /= min_weights;
}
else {
for (ii = 1 ; ii < num_poles ; ii++) {
ii_index = ii % NumPoles;
ii_index *= ArrayDimension;
ii_minus = (ii - 1) % NumPoles;
ii_minus *= ArrayDimension;
inverse = FK[ii + Degree] - FK[ii];
inverse = 1.0e0 / inverse;
value = 0.0e0;
for (kk = 0 ; kk < ArrayDimension ; kk++) {
factor = PA[ii_index + kk] - PA[ii_minus + kk];
if (factor < 0) factor = - factor;
value += factor;
}
value *= inverse;
if (max_derivative < value) max_derivative = value;
}
}
}
}
max_derivative *= Degree;
if (max_derivative > RealSmall())
UTolerance = Tolerance3D / max_derivative;
else
UTolerance = Tolerance3D / RealSmall();
}
//=======================================================================
// function: FlatBezierKnots
// purpose :
//=======================================================================
// array of flat knots for bezier curve of maximum 25 degree
static const Standard_Real knots[52] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
const Standard_Real& BSplCLib::FlatBezierKnots (const Standard_Integer Degree)
{
Standard_OutOfRange_Raise_if (Degree < 1 || Degree > MaxDegree() || MaxDegree() != 25,
"Bezier curve degree greater than maximal supported");
return knots[25-Degree];
}