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|
// File: Hermit.cxx
// Created: Wed Jan 15 16:24:52 1997
// Author: Stagiaire Francois DUMONT
// <dum@brunox.paris1.matra-dtv.fr>
#include <Hermit.ixx>
#include <Geom_BSplineCurve.hxx>
#include <Geom2d_BSplineCurve.hxx>
#include <BSplCLib.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_HArray1OfReal.hxx>
#include <TColStd_Array1OfInteger.hxx>
#include <TColStd_HArray1OfInteger.hxx>
#include <PLib.hxx>
#include <Standard_Boolean.hxx>
#include <gp_Pnt2d.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <Standard_DimensionError.hxx>
#include <Standard_Real.hxx>
#include <TCollection_CompareOfReal.hxx>
#include <SortTools_QuickSortOfReal.hxx>
#include <Precision.hxx>
//=======================================================================
//function : HermiteCoeff
//purpose : calculate the Hermite coefficients of degree 3 from BS and
// store them in TAB(4 coefficients)
//=======================================================================
static void HermiteCoeff(const Handle(Geom_BSplineCurve)& BS,
TColStd_Array1OfReal& TAB)
{
TColStd_Array1OfReal Knots(1,BS->NbKnots());
TColStd_Array1OfReal Weights(1,BS->NbPoles());
TColStd_Array1OfInteger Mults(1,BS->NbKnots());
Standard_Integer Degree,Index0,Index1; // denominateur value for u=0 & u=1
Standard_Real Denom0,Denom1, // denominator value for u=0 & u=1
Deriv0,Deriv1 ; // derivative denominator value for u=0 & 1
Standard_Boolean Periodic;
BS->Knots(Knots);
BSplCLib::Reparametrize(0.0,1.0,Knots); //affinity on the nodal vector
BS->Weights(Weights);
BS->Multiplicities(Mults);
Degree = BS->Degree();
Periodic = BS->IsPeriodic();
Index0 = BS->FirstUKnotIndex();
Index1 = BS->LastUKnotIndex()-1;
BSplCLib::D1(0.0,Index0,Degree,Periodic,Weights,BSplCLib::NoWeights(),Knots,Mults,Denom0,Deriv0);
BSplCLib::D1(1.0,Index1,Degree,Periodic,Weights,BSplCLib::NoWeights(),Knots,Mults,Denom1,Deriv1);
TAB(0) = 1/Denom0; //Hermit coefficients
TAB(1) = -Deriv0/(Denom0*Denom0);
TAB(2) = -Deriv1/(Denom1*Denom1);
TAB(3) = 1/Denom1;
}
//=======================================================================
//function : HermiteCoeff
//purpose : calculate the Hermite coefficients of degree 3 from BS and
// store them in TAB(4 coefficients)
//=======================================================================
static void HermiteCoeff(const Handle(Geom2d_BSplineCurve)& BS,
TColStd_Array1OfReal& TAB)
{
TColStd_Array1OfReal Knots(1,BS->NbKnots());
TColStd_Array1OfReal Weights(1,BS->NbPoles());
TColStd_Array1OfInteger Mults(1,BS->NbKnots());
Standard_Integer Degree,Index0,Index1;
Standard_Real Denom0,Denom1, // denominateur value for u=0 & u=1
Deriv0,Deriv1 ; // denominator value for u=0 & u=1
Standard_Boolean Periodic; // derivative denominatur value for u=0 & 1
BS->Knots(Knots);
BSplCLib::Reparametrize(0.0,1.0,Knots); //affinity on the nodal vector
BS->Weights(Weights);
BS->Multiplicities(Mults);
Degree = BS->Degree();
Periodic = BS->IsPeriodic();
Index0 = BS->FirstUKnotIndex();
Index1 = BS->LastUKnotIndex()-1;
BSplCLib::D1(0.0,Index0,Degree,Periodic,Weights,BSplCLib::NoWeights(),Knots,Mults,Denom0,Deriv0);
BSplCLib::D1(1.0,Index1,Degree,Periodic,Weights,BSplCLib::NoWeights(),Knots,Mults,Denom1,Deriv1);
TAB(0) = 1/Denom0; //Hermit coefficients
TAB(1) = -Deriv0/(Denom0*Denom0);
TAB(2) = -Deriv1/(Denom1*Denom1);
TAB(3) = 1/Denom1;
}
//=======================================================================
//function : SignDenom
//purpose : give the sign of Herm(0) True=Positive
//=======================================================================
static Standard_Boolean SignDenom(const TColgp_Array1OfPnt2d& Poles)
{
Standard_Boolean Result;
if (Poles(0).Y()<0)
Result=Standard_False;
else Result=Standard_True;
return Result;
}
//=======================================================================
//function : Polemax
//purpose : give the max and the min of the Poles (by their index)
//=======================================================================
static void Polemax(const TColgp_Array1OfPnt2d& Poles,
Standard_Integer& min,
Standard_Integer& max)
{
// Standard_Integer i,index=0;
Standard_Integer i;
Standard_Real Max,Min; //intermediate value of max and min ordinates
min=0;max=0; //initialisation of the indices
Min=Poles(0).Y(); //initialisation of the intermediate value
Max=Poles(0).Y();
for (i=1;i<=(Poles.Length()-1);i++){
if (Poles(i).Y()<Min){
Min=Poles(i).Y();
min=i;
}
if (Poles(i).Y()>Max){
Max=Poles(i).Y();
max=i;
}
}
}
//=======================================================================
//function : PolyTest
//purpose : give the knots U4 and U5 to insert to a(u)
//=======================================================================
static void PolyTest(const TColStd_Array1OfReal& Herm,
const Handle(Geom_BSplineCurve)& BS,
Standard_Real& U4,
Standard_Real& U5,
Standard_Integer& boucle,
const Standard_Real TolPoles,
// const Standard_Real TolKnots,
const Standard_Real ,
const Standard_Real Ux,
const Standard_Real Uy)
{
Standard_Integer index,i,
I1=0,I2=0,I3=0,I4=0; //knots index
TColgp_Array1OfPnt2d Polesinit(0,3) ;
Handle(TColStd_HArray1OfReal) Knots; //array of the BSpline knots + the ones inserted
Standard_Integer cas=0,mark=0,dercas=0, //loop marks
min,max; //Pole min and max indices
Standard_Real Us1,Us2,a; //bounderies value of the knots to be inserted
// gp_Pnt2d P ;
TCollection_CompareOfReal Comp;
U4=0.0;U5=1.0; //default value
if (Ux!=1.0){
BS->LocateU(Ux,0.0,I1,I2); //localization of the inserted knots
if (Uy!=0.0)
BS->LocateU(Uy,0.0,I3,I4);
}
if (I1==I2) //definition and filling of the
if((I3==I4)||(I3==0)){ //array of knots
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots());
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
}
else{
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots()+1);
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
Knots->SetValue(BS->NbKnots()+1,Uy);
}
else{
if((I3==I4)||(I3==0)){
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots()+1);
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
Knots->SetValue(BS->NbKnots()+1,Ux);
}
else{
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots()+2);
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
Knots->SetValue(BS->NbKnots()+1,Ux);
Knots->SetValue(BS->NbKnots()+2,Uy);
}
}
TColStd_Array1OfReal knots(1,Knots->Length());
knots=Knots->ChangeArray1();
SortTools_QuickSortOfReal::Sort(knots,Comp); //sort of the array of knots
Polesinit(0).SetCoord(0.0,Herm(0)); //poles of the Hermite polynome in the BSpline form
Polesinit(1).SetCoord(0.0,Herm(0)+Herm(1)/3.0);
Polesinit(2).SetCoord(0.0,Herm(3)-Herm(2)/3.0);
Polesinit(3).SetCoord(0.0,Herm(3));
//loop to check the tolerances on poles
if (TolPoles!=0.0){
Polemax(Polesinit,min,max);
Standard_Real Polemin=Polesinit(min).Y();
Standard_Real Polemax=Polesinit(max).Y();
if (((Polemax)>=((1/TolPoles)*Polemin))||((Polemin==0.0)&&(Polemax>=(1/TolPoles)))){
if (Polesinit(0).Y()>=(1/TolPoles)*Polesinit(3).Y()||Polesinit(0).Y()<=TolPoles*Polesinit(3).Y())
Standard_DimensionError::Raise("Hermit Impossible Tolerance");
if ((max==0)||(max==3))
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-TolPoles*Polemax));
if ((max==1)||(max==2)) {
if ((min==0)||(min==3))
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-(1/TolPoles)*Polemin));
else{
if ((TolPoles*Polemax<Polesinit(0).Y())&&(TolPoles*Polemax<Polesinit(3).Y())){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-TolPoles*Polemax));
mark=1;
}
if ((1/TolPoles*Polemin>Polesinit(0).Y())&&(1/TolPoles*Polemin>Polesinit(3).Y())&&(mark==0)){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-1/TolPoles*Polemin));
mark=1;
}
if (mark==0){
Standard_Real Pole0,Pole3;
Pole0=Polesinit(0).Y();
Pole3=Polesinit(3).Y();
if (Pole0<3){
a=Log10(Pole3/Pole0);
if (boucle==2)
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole3*(Pow(10.0,(-0.5*Log10(TolPoles)-a/2.0)))));
if (boucle==1){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole0*(Pow(10.0,(a/2.0+0.5*Log10(TolPoles))))));
dercas=1;
}
}
if (Pole0>Pole3){
a=Log10(Pole0/Pole3);
if (boucle==2)
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole0*(Pow(10.0,(-0.5*Log10(TolPoles)-a/2.0)))));
if (boucle==1){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole3*(Pow(10.0,(a/2.0+0.5*Log10(TolPoles))))));
dercas=1;
}
}
}
}
}
}
} //end of the loop
if (!SignDenom(Polesinit)) //invertion of the polynome sign
for (index=0;index<=3;index++)
Polesinit(index).SetCoord(0.0,-Polesinit(index).Y());
//loop of positivity
if ((Polesinit(1).Y()<0.0)&&(Polesinit(2).Y()>=0.0)){
Us1=Polesinit(0).Y()/(Polesinit(0).Y()-Polesinit(1).Y());
if (boucle==2)
Us1=Us1*knots(2);
if (boucle==1)
if (Ux!=0.0)
Us1=Us1*Ux;
BSplCLib::LocateParameter(3,knots,Us1,Standard_False,1,knots.Length(),I1,Us1);
if (I1<2)
U4=Us1;
else
U4=knots(I1);
}
if ((Polesinit(1).Y()>=0.0)&&(Polesinit(2).Y()<0.0)){
Us2=Polesinit(2).Y()/(Polesinit(2).Y()-Polesinit(3).Y());
if (boucle==2)
Us2=knots(knots.Length()-1)+Us2*(1-knots(knots.Length()-1));
if (boucle==1)
if (Ux!=0.0)
Us2=Uy+Us2*(1-Uy);
BSplCLib::LocateParameter(3,knots,Us2,Standard_False,1,knots.Length(),I1,Us2);
if (I1>=(knots.Length()-1))
U5=Us2;
else
U5=knots(I1+1);
}
if (dercas==1)
boucle++;
if ((Polesinit(1).Y()<0.0)&&(Polesinit(2).Y()<0.0)){
Us1=Polesinit(0).Y()/(Polesinit(0).Y()-Polesinit(1).Y());
Us2=Polesinit(2).Y()/(Polesinit(2).Y()-Polesinit(3).Y());
if (boucle!=0)
if (Ux!=0.0){
Us1=Us1*Ux;
Us2=Uy+Us2*(1-Uy);
}
if (Us2<=Us1){
BSplCLib::LocateParameter(3,knots,Us1,Standard_False,1,knots.Length(),I1,Us1);
if (knots(I1)>=Us2) //insertion of one knot for the two poles
U4=knots(I1);
else{
if (I1>=2){ //insertion to the left and
U4=knots(I1); //to the right without a new knot
BSplCLib::LocateParameter(3,knots,Us2,Standard_False,1,knots.Length(),I3,Us2);
if (I3<(BS->NbKnots()-1)){
U5=knots(I3+1);
cas=1;
}
}
if(cas==0) //insertion of only one new knot
U4=(Us1+Us2)/2;
}
}
else{ //insertion of two knots
BSplCLib::LocateParameter(3,knots,Us1,Standard_False,1,knots.Length(),I1,Us1);
if (I1>=2)
U4=knots(I1);
else
U4=Us1;
BSplCLib::LocateParameter(3,knots,Us2,Standard_False,1,knots.Length(),I3,Us2);
if (I3<(BS->NbKnots()-1))
U5=knots(I3+1);
else
U5=Us2;
}
}
}
//=======================================================================
//function : PolyTest
//purpose : give the knots U4 and U5 to insert to a(u)
//=======================================================================
static void PolyTest(const TColStd_Array1OfReal& Herm,
const Handle(Geom2d_BSplineCurve)& BS,
Standard_Real& U4,
Standard_Real& U5,
Standard_Integer& boucle,
const Standard_Real TolPoles,
// const Standard_Real TolKnots,
const Standard_Real ,
const Standard_Real Ux,
const Standard_Real Uy)
{
Standard_Integer index,i,
I1=0,I2=0,I3=0,I4=0; //knots index
TColgp_Array1OfPnt2d Polesinit(0,3) ;
Handle(TColStd_HArray1OfReal) Knots; //array of the BSpline knots + the ones inserted
Standard_Integer cas=0,mark=0,dercas=0, //loop marks
min,max; //Pole min and max indices
Standard_Real Us1,Us2,a; //bounderies value of the knots to be inserted
// gp_Pnt2d P ;
TCollection_CompareOfReal Comp;
U4=0.0;U5=1.0; //default value
if (Ux!=1.0){
BS->LocateU(Ux,0.0,I1,I2); //localization of the inserted knots
if (Uy!=0.0)
BS->LocateU(Uy,0.0,I3,I4);
}
if (I1==I2) //definition and filling of the
if((I3==I4)||(I3==0)){ //array of knots
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots());
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
}
else{
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots()+1);
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
Knots->SetValue(BS->NbKnots()+1,Uy);
}
else{
if((I3==I4)||(I3==0)){
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots()+1);
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
Knots->SetValue(BS->NbKnots()+1,Ux);
}
else{
Knots=new TColStd_HArray1OfReal(1,BS->NbKnots()+2);
for (i=1;i<=BS->NbKnots();i++)
Knots->SetValue(i,BS->Knot(i));
Knots->SetValue(BS->NbKnots()+1,Ux);
Knots->SetValue(BS->NbKnots()+2,Uy);
}
}
TColStd_Array1OfReal knots(1,Knots->Length());
knots=Knots->ChangeArray1();
SortTools_QuickSortOfReal::Sort(knots,Comp); //sort of the array of knots
Polesinit(0).SetCoord(0.0,Herm(0)); //poles of the Hermite polynome in the BSpline form
Polesinit(1).SetCoord(0.0,Herm(0)+Herm(1)/3.0);
Polesinit(2).SetCoord(0.0,Herm(3)-Herm(2)/3.0);
Polesinit(3).SetCoord(0.0,Herm(3));
//loop to check the tolerances on poles
if (TolPoles!=0.0){
Polemax(Polesinit,min,max);
Standard_Real Polemin=Polesinit(min).Y();
Standard_Real Polemax=Polesinit(max).Y();
if (((Polemax)>=((1/TolPoles)*Polemin))||((Polemin==0.0)&&(Polemax>=(1/TolPoles)))){
if (Polesinit(0).Y()>=(1/TolPoles)*Polesinit(3).Y()||Polesinit(0).Y()<=TolPoles*Polesinit(3).Y())
Standard_DimensionError::Raise("Hermit Impossible Tolerance");
if ((max==0)||(max==3))
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-TolPoles*Polemax));
if ((max==1)||(max==2)) {
if ((min==0)||(min==3))
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-(1/TolPoles)*Polemin));
else{
if ((TolPoles*Polemax<Polesinit(0).Y())&&(TolPoles*Polemax<Polesinit(3).Y())){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-TolPoles*Polemax));
mark=1;
}
if ((1/TolPoles*Polemin>Polesinit(0).Y())&&(1/TolPoles*Polemin>Polesinit(3).Y())&&(mark==0)){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0,(Polesinit(i).Y()-1/TolPoles*Polemin));
mark=1;
}
if (mark==0){
Standard_Real Pole0,Pole3;
Pole0=Polesinit(0).Y();
Pole3=Polesinit(3).Y();
if (Pole0<3){
a=Log10(Pole3/Pole0);
if (boucle==2)
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole3*(Pow(10.0,(-0.5*Log10(TolPoles)-a/2.0)))));
if (boucle==1){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole0*(Pow(10.0,(a/2.0+0.5*Log10(TolPoles))))));
dercas=1;
}
}
if (Pole0>Pole3){
a=Log10(Pole0/Pole3);
if (boucle==2)
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole0*(Pow(10.0,(-0.5*Log10(TolPoles)-a/2.0)))));
if (boucle==1){
for (i=0;i<=3;i++)
Polesinit(i).SetCoord(0.0, Polesinit(i).Y()-(Pole3*(Pow(10.0,(a/2.0+0.5*Log10(TolPoles))))));
dercas=1;
}
}
}
}
}
}
} //end of the loop
if (!SignDenom(Polesinit)) //invertion of the polynome sign
for (index=0;index<=3;index++)
Polesinit(index).SetCoord(0.0,-Polesinit(index).Y());
//boucle de positivite
if ((Polesinit(1).Y()<0.0)&&(Polesinit(2).Y()>=0.0)){
Us1=Polesinit(0).Y()/(Polesinit(0).Y()-Polesinit(1).Y());
if (boucle==2)
Us1=Us1*knots(2);
if (boucle==1)
if (Ux!=0.0)
Us1=Us1*Ux;
BSplCLib::LocateParameter(3,knots,Us1,Standard_False,1,knots.Length(),I1,Us1);
if (I1<2)
U4=Us1;
else
U4=knots(I1);
}
if ((Polesinit(1).Y()>=0.0)&&(Polesinit(2).Y()<0.0)){
Us2=Polesinit(2).Y()/(Polesinit(2).Y()-Polesinit(3).Y());
if (boucle==2)
Us2=knots(knots.Length()-1)+Us2*(1-knots(knots.Length()-1));
if (boucle==1)
if (Ux!=0.0)
Us2=Uy+Us2*(1-Uy);
BSplCLib::LocateParameter(3,knots,Us2,Standard_False,1,knots.Length(),I1,Us2);
if (I1>=(knots.Length()-1))
U5=Us2;
else
U5=knots(I1+1);
}
if (dercas==1)
boucle++;
if ((Polesinit(1).Y()<0.0)&&(Polesinit(2).Y()<0.0)){
Us1=Polesinit(0).Y()/(Polesinit(0).Y()-Polesinit(1).Y());
Us2=Polesinit(2).Y()/(Polesinit(2).Y()-Polesinit(3).Y());
if (boucle!=0)
if (Ux!=0.0){
Us1=Us1*Ux;
Us2=Uy+Us2*(1-Uy);
}
if (Us2<=Us1){
BSplCLib::LocateParameter(3,knots,Us1,Standard_False,1,knots.Length(),I1,Us1);
if (knots(I1)>=Us2) //insertion of one knot for the two poles
U4=knots(I1);
else{
if (I1>=2){ //insertion to the left and
U4=knots(I1); //to the right without a new knot
BSplCLib::LocateParameter(3,knots,Us2,Standard_False,1,knots.Length(),I3,Us2);
if (I3<(BS->NbKnots()-1)){
U5=knots(I3+1);
cas=1;
}
}
if(cas==0) //insertion of only one new knot
U4=(Us1+Us2)/2;
}
}
else{ //insertion of two knots
BSplCLib::LocateParameter(3,knots,Us1,Standard_False,1,knots.Length(),I1,Us1);
if (I1>=2)
U4=knots(I1);
else
U4=Us1;
BSplCLib::LocateParameter(3,knots,Us2,Standard_False,1,knots.Length(),I3,Us2);
if (I3<(BS->NbKnots()-1))
U5=knots(I3+1);
else
U5=Us2;
}
}
}
//=======================================================================
//function : InsertKnots
//purpose : insert the knots in BS knot sequence if they are not null.
//=======================================================================
static void InsertKnots(Handle(Geom2d_BSplineCurve)& BS,
const Standard_Real U4,
const Standard_Real U5)
{
if (U4!=0.0) //insertion of :0 knot if U4=0
BS->InsertKnot(U4); // 1 knot if U4=U5
if ((U5!=1.0)&&(U5!=U4)) // 2 knots otherwise
BS->InsertKnot(U5);
}
//=======================================================================
//function : MovePoles
//purpose : move the poles above the x axis
//=======================================================================
static void MovePoles(Handle(Geom2d_BSplineCurve)& BS)
{
gp_Pnt2d P ;
// Standard_Integer i,index;
Standard_Integer i;
for (i=3;i<=(BS->NbPoles()-2);i++){
P.SetCoord(1,(BS->Pole(i).Coord(1))); //raising of the no constrained poles to
P.SetCoord(2,(BS->Pole(1).Coord(2))); //the first pole level
BS->SetPole(i,P);
}
}
//=======================================================================
//function : Solution
//purpose :
//=======================================================================
Handle(Geom2d_BSplineCurve) Hermit::Solution(const Handle(Geom_BSplineCurve)& BS,
const Standard_Real TolPoles,
const Standard_Real TolKnots)
{
TColStd_Array1OfReal Herm(0,3);
Standard_Real Upos1=0.0, Upos2=1.0, //positivity knots
Ux=0.0, Uy=1.0,
Utol1=0.0, Utol2=1.0, //tolerance knots
Uint1=0.0, Uint2=1.0; //tolerance knots for the first loop
Standard_Integer boucle=1; //loop mark
TColStd_Array1OfReal Knots(1,2);
TColStd_Array1OfInteger Multiplicities(1,2);
TColgp_Array1OfPnt2d Poles(1,4);
Standard_Integer zeroboucle = 0 ;
HermiteCoeff(BS,Herm); //computation of the Hermite coefficient
Poles(1).SetCoord(0.0,Herm(0)); //poles of the Hermite polynome in the BSpline form
Poles(2).SetCoord(0.0,Herm(0)+Herm(1)/3.0);
Poles(3).SetCoord(0.0,Herm(3)-Herm(2)/3.0);
Poles(4).SetCoord(0.0,Herm(3));
Knots(1)=0.0;
Knots(2)=1.0;
Multiplicities(1)=4;
Multiplicities(2)=4;
Handle(Geom2d_BSplineCurve) BS1=new Geom2d_BSplineCurve(Poles,Knots,Multiplicities,3);//creation of the basic
Handle(Geom2d_BSplineCurve) BS2=new Geom2d_BSplineCurve(Poles,Knots,Multiplicities,3);//BSpline without modif
PolyTest(Herm,BS,Upos1,Upos2,zeroboucle,Precision::Confusion(),Precision::Confusion(),1.0,0.0);//computation of the positivity knots
InsertKnots(BS2,Upos1,Upos2); //and insertion
if (Upos1!=0.0)
if (Upos2!=1.0){
Ux=Min(Upos1,Upos2);
Uy=Max(Upos1,Upos2);
}
else{
Ux=Upos1;
Uy=Upos1;
}
else{
Ux=Upos2;
Uy=Upos2;
}
Herm(0)=BS2->Pole(1).Y(); //computation of the Hermite coefficient on the
Herm(1)=3*(BS2->Pole(2).Y()-BS2->Pole(1).Y()); //positive BSpline
Herm(2)=3*(BS2->Pole(BS2->NbPoles()).Y()-BS2->Pole(BS2->NbPoles()-1).Y());
Herm(3)=BS2->Pole(BS2->NbPoles()).Y();
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Ux,Uy); //computation of the tolerance knots
InsertKnots(BS2,Utol1,Utol2); //and insertion
if (boucle==2){ //insertion of two knots
Herm(0)=BS2->Pole(1).Y();
Herm(1)=3*(BS2->Pole(2).Y()-BS2->Pole(1).Y());
Herm(2)=3*(BS2->Pole(BS2->NbPoles()).Y()-BS2->Pole(BS2->NbPoles()-1).Y());
Herm(3)=BS2->Pole(BS2->NbPoles()).Y();
if (Utol1==0.0){
Uint2=Utol2;
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Uint2,0.0);
}
else{
Uint1=Utol1;
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Uint1,0.0);
}
InsertKnots(BS2,Utol1,Utol2);
}
if ((BS2->Knot(2)<TolKnots)||(BS2->Knot(BS2->NbKnots()-1)>(1-TolKnots))) //checking of the knots tolerance
Standard_DimensionError::Raise("Hermit Impossible Tolerance");
else{
if ((Upos2==1.0)&&(Utol2==1.0)&&(Uint2==1.0)) //test on the final inserted knots
InsertKnots(BS1,BS2->Knot(2),1.0);
else{
if ((Upos1==0.0)&&(Utol1==0.0)&&(Uint1==0.0))
InsertKnots(BS1,BS2->Knot(BS2->NbKnots()-1),1.0);
else
InsertKnots(BS1,BS2->Knot(BS2->NbKnots()-1),BS2->Knot(2));
}
MovePoles(BS1); //relocation of the no-contrained knots
}
return BS1;
}
//=======================================================================
// Solution
//=======================================================================
Handle(Geom2d_BSplineCurve) Hermit::Solution(const Handle(Geom2d_BSplineCurve)& BS,
const Standard_Real TolPoles,
const Standard_Real TolKnots)
{
TColStd_Array1OfReal Herm(0,3);
Standard_Real Upos1=0.0, Upos2=1.0, //positivity knots
Ux=0.0, Uy=1.0,
Utol1=0.0, Utol2=1.0, //tolerance knots
Uint1=0.0, Uint2=1.0; //tolerance knots for the first loop
Standard_Integer boucle=1; //loop mark
TColStd_Array1OfReal Knots(1,2);
TColStd_Array1OfInteger Multiplicities(1,2);
TColgp_Array1OfPnt2d Poles(1,4);
Standard_Integer zeroboucle = 0 ;
HermiteCoeff(BS,Herm); //computation of the Hermite coefficient
Poles(1).SetCoord(0.0,Herm(0)); //poles of the Hermite polynome in the BSpline form
Poles(2).SetCoord(0.0,Herm(0)+Herm(1)/3.0);
Poles(3).SetCoord(0.0,Herm(3)-Herm(2)/3.0);
Poles(4).SetCoord(0.0,Herm(3));
Knots(1)=0.0;
Knots(2)=1.0;
Multiplicities(1)=4;
Multiplicities(2)=4;
Handle(Geom2d_BSplineCurve) BS1=new Geom2d_BSplineCurve(Poles,Knots,Multiplicities,3);//creation of the basic
Handle(Geom2d_BSplineCurve) BS2=new Geom2d_BSplineCurve(Poles,Knots,Multiplicities,3);//BSpline without modif
PolyTest(Herm,BS,Upos1,Upos2,zeroboucle,Precision::Confusion(),Precision::Confusion(),1.0,0.0);//computation of the positivity knots
InsertKnots(BS2,Upos1,Upos2); //and insertion
if (Upos1!=0.0)
if (Upos2!=1.0){
Ux=Min(Upos1,Upos2);
Uy=Max(Upos1,Upos2);
}
else{
Ux=Upos1;
Uy=Upos1;
}
else{
Ux=Upos2;
Uy=Upos2;
}
Herm(0)=BS2->Pole(1).Y(); //computation of the Hermite coefficient on the
Herm(1)=3*(BS2->Pole(2).Y()-BS2->Pole(1).Y()); //positive BSpline
Herm(2)=3*(BS2->Pole(BS2->NbPoles()).Y()-BS2->Pole(BS2->NbPoles()-1).Y());
Herm(3)=BS2->Pole(BS2->NbPoles()).Y();
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Ux,Uy); //computation of the tolerance knots
InsertKnots(BS2,Utol1,Utol2); //and insertion
if (boucle==2){ //insertion of two knots
Herm(0)=BS2->Pole(1).Y();
Herm(1)=3*(BS2->Pole(2).Y()-BS2->Pole(1).Y());
Herm(2)=3*(BS2->Pole(BS2->NbPoles()).Y()-BS2->Pole(BS2->NbPoles()-1).Y());
Herm(3)=BS2->Pole(BS2->NbPoles()).Y();
if (Utol1==0.0){
Uint2=Utol2;
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Uint2,0.0);
}
else{
Uint1=Utol1;
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Uint1,0.0);
}
InsertKnots(BS2,Utol1,Utol2);
}
if ((BS2->Knot(2)<TolKnots)||(BS2->Knot(BS2->NbKnots()-1)>(1-TolKnots))) //checking of the knots tolerance
Standard_DimensionError::Raise("Hermit Impossible Tolerance");
else{
if ((Upos2==1.0)&&(Utol2==1.0)&&(Uint2==1.0)) //test on the final inserted knots
InsertKnots(BS1,BS2->Knot(2),1.0);
else{
if ((Upos1==0.0)&&(Utol1==0.0)&&(Uint1==0.0))
InsertKnots(BS1,BS2->Knot(BS2->NbKnots()-1),1.0);
else
InsertKnots(BS1,BS2->Knot(BS2->NbKnots()-1),BS2->Knot(2));
}
MovePoles(BS1); //relocation of the no-contrained knots
}
return BS1;
}
//=======================================================================
//function : Solutionbis
//purpose :
//=======================================================================
void Hermit::Solutionbis(const Handle(Geom_BSplineCurve)& BS,
Standard_Real & Knotmin,
Standard_Real & Knotmax,
const Standard_Real TolPoles,
const Standard_Real TolKnots)
{
TColStd_Array1OfReal Herm(0,3);
Standard_Real Upos1=0.0, Upos2=1.0, //positivity knots
Ux=0.0, Uy=1.0,
Utol1=0.0, Utol2=1.0, //tolerance knots
Uint1=0.0, Uint2=1.0; //tolerance knots for the first loop
Standard_Integer boucle=1; //loop mark
TColStd_Array1OfReal Knots(1,2);
TColStd_Array1OfInteger Multiplicities(1,2);
TColgp_Array1OfPnt2d Poles(1,4);
Standard_Integer zeroboucle = 0 ;
HermiteCoeff(BS,Herm); //computation of the Hermite coefficient
Poles(1).SetCoord(0.0,Herm(0)); //poles of the Hermite polynome in the BSpline form
Poles(2).SetCoord(0.0,Herm(0)+Herm(1)/3.0);
Poles(3).SetCoord(0.0,Herm(3)-Herm(2)/3.0);
Poles(4).SetCoord(0.0,Herm(3));
Knots(1)=0.0;
Knots(2)=1.0;
Multiplicities(1)=4;
Multiplicities(2)=4;
Handle(Geom2d_BSplineCurve) BS2=new Geom2d_BSplineCurve(Poles,Knots,Multiplicities,3);//creation of the basic
//BSpline without modif
PolyTest(Herm,BS,Upos1,Upos2,zeroboucle,Precision::Confusion(),Precision::Confusion(),1.0,0.0);//computation of the positivity knots
InsertKnots(BS2,Upos1,Upos2); //and insertion
if (Upos1!=0.0)
if (Upos2!=1.0){
Ux=Min(Upos1,Upos2);
Uy=Max(Upos1,Upos2);
}
else{
Ux=Upos1;
Uy=Upos1;
}
else{
Ux=Upos2;
Uy=Upos2;
}
Herm(0)=BS2->Pole(1).Y(); //computation of the Hermite coefficient on the
Herm(1)=3*(BS2->Pole(2).Y()-BS2->Pole(1).Y()); //positive BSpline
Herm(2)=3*(BS2->Pole(BS2->NbPoles()).Y()-BS2->Pole(BS2->NbPoles()-1).Y());
Herm(3)=BS2->Pole(BS2->NbPoles()).Y();
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Ux,Uy); //computation of the tolerance knots
InsertKnots(BS2,Utol1,Utol2); //and insertion
if (boucle==2){ //insertion of two knots
Herm(0)=BS2->Pole(1).Y();
Herm(1)=3*(BS2->Pole(2).Y()-BS2->Pole(1).Y());
Herm(2)=3*(BS2->Pole(BS2->NbPoles()).Y()-BS2->Pole(BS2->NbPoles()-1).Y());
Herm(3)=BS2->Pole(BS2->NbPoles()).Y();
if (Utol1==0.0){
Uint2=Utol2;
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Uint2,0.0);
}
else{
Uint1=Utol1;
PolyTest(Herm,BS,Utol1,Utol2,boucle,TolPoles,TolKnots,Uint1,0.0);
}
InsertKnots(BS2,Utol1,Utol2);
}
if ((BS2->Knot(2)<TolKnots)||(BS2->Knot(BS2->NbKnots()-1)>(1-TolKnots))) //checking of the knots tolerance
Standard_DimensionError::Raise("Hermit Impossible Tolerance");
else{
if ((Upos2==1.0)&&(Utol2==1.0)&&(Uint2==1.0)) //test on the final inserted knots
Knotmin=BS2->Knot(2);
else{
if ((Upos1==0.0)&&(Utol1==0.0)&&(Uint1==0.0))
Knotmax=BS2->Knot(BS2->NbKnots()-1);
else{
Knotmin=BS2->Knot(2);
Knotmax=BS2->Knot(BS2->NbKnots()-1);
}
}
}
}
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