SplineBasisfunction::SplineBasisfunction
(TColStd_Array1OfReal& vKnots,
TColStd_Array1OfInteger& vMults,
int iSize,
int iOrder)
: _vKnotVector(0,iSize-1)
{
int sum = 0;
for (int h=vMults.Lower(); h<=vMults.Upper(); h++)
sum += vMults(h);
if (vKnots.Length() != vMults.Length() || iSize != sum)
{
// Werfe Exception
Standard_ConstructionError::Raise("BSplineBasis");
}
int k=0;
for (int i=vMults.Lower(); i<=vMults.Upper(); i++)
{
for (int j=0; j<vMults(i); j++)
{
_vKnotVector(k) = vKnots(i);
k++;
}
}
_iOrder = iOrder;
}
void BSplineBasis::AllBasisFunctions(double fParam, TColStd_Array1OfReal& vFuncVals)
{
if (vFuncVals.Length() != _iOrder)
Standard_RangeError::Raise("BSplineBasis");
int iIndex = FindSpan(fParam);
TColStd_Array1OfReal zaehler_left(1,_iOrder-1);
TColStd_Array1OfReal zaehler_right(1,_iOrder-1);
vFuncVals(0) = 1.0f;
for (int j=1; j<_iOrder; j++)
{
zaehler_left(j) = fParam - _vKnotVector(iIndex+1-j);
zaehler_right(j) = _vKnotVector(iIndex+j) - fParam;
double saved = 0.0f;
for (int r=0; r<j; r++)
{
double tmp = vFuncVals(r)/(zaehler_right(r+1) + zaehler_left(j-r));
vFuncVals(r) = saved + zaehler_right(r+1)*tmp;
saved = zaehler_left(j-r)*tmp;
}
vFuncVals(j) = saved;
}
}
void SplineBasisfunction::SetKnots(TColStd_Array1OfReal& vKnots, int iOrder)
{
if (_vKnotVector.Length() != vKnots.Length())
Standard_RangeError::Raise("BSplineBasis");
_vKnotVector = vKnots;
_iOrder = iOrder;
}
SplineBasisfunction::SplineBasisfunction(TColStd_Array1OfReal& vKnots, int iOrder)
: _vKnotVector(0,vKnots.Length()-1)
{
_vKnotVector = vKnots;
_iOrder = iOrder;
}
void BSplineBasis::GenerateRootsAndWeights(TColStd_Array1OfReal& vRoots, TColStd_Array1OfReal& vWeights)
{
int iSize = vRoots.Length();
//Nullstellen der Legendre-Polynome und die zugeh. Gewichte
if (iSize == 1)
{
vRoots(0) = 0.0f; vWeights(0) = 2.0f;
}
else if (iSize == 2)
{
vRoots(0) = 0.57735f; vWeights(0) = 1.0f;
vRoots(1) = -vRoots(0); vWeights(1) = vWeights(0);
}
else if (iSize == 4)
{
vRoots(0) = 0.33998f; vWeights(0) = 0.65214f;
vRoots(1) = 0.86113f; vWeights(1) = 0.34785f;
vRoots(2) = -vRoots(0); vWeights(2) = vWeights(0);
vRoots(3) = -vRoots(1); vWeights(3) = vWeights(1);
}
else if (iSize == 6)
{
vRoots(0) = 0.23861f; vWeights(0) = 0.46791f;
vRoots(1) = 0.66120f; vWeights(1) = 0.36076f;
vRoots(2) = 0.93246f; vWeights(2) = 0.17132f;
vRoots(3) = -vRoots(0); vWeights(3) = vWeights(0);
vRoots(4) = -vRoots(1); vWeights(4) = vWeights(1);
vRoots(5) = -vRoots(2); vWeights(5) = vWeights(2);
}
else if (iSize == 8)
{
vRoots(0) = 0.18343f; vWeights(0) = 0.36268f;
vRoots(1) = 0.52553f; vWeights(1) = 0.31370f;
vRoots(2) = 0.79666f; vWeights(2) = 0.22238f;
vRoots(3) = 0.96028f; vWeights(3) = 0.10122f;
vRoots(4) = -vRoots(0); vWeights(4) = vWeights(0);
vRoots(5) = -vRoots(1); vWeights(5) = vWeights(1);
vRoots(6) = -vRoots(2); vWeights(6) = vWeights(2);
vRoots(7) = -vRoots(3); vWeights(7) = vWeights(3);
}
else if (iSize == 10)
{
vRoots(0) = 0.14887f; vWeights(0) = 0.29552f;
vRoots(1) = 0.43339f; vWeights(1) = 0.26926f;
vRoots(2) = 0.67940f; vWeights(2) = 0.21908f;
vRoots(3) = 0.86506f; vWeights(3) = 0.14945f;
vRoots(4) = 0.97390f; vWeights(4) = 0.06667f;
vRoots(5) = -vRoots(0); vWeights(5) = vWeights(0);
vRoots(6) = -vRoots(1); vWeights(6) = vWeights(1);
vRoots(7) = -vRoots(2); vWeights(7) = vWeights(2);
vRoots(8) = -vRoots(3); vWeights(8) = vWeights(3);
vRoots(9) = -vRoots(4); vWeights(9) = vWeights(4);
}
else
{
vRoots(0) = 0.12523f; vWeights(0) = 0.24914f;
vRoots(1) = 0.36783f; vWeights(1) = 0.23349f;
vRoots(2) = 0.58731f; vWeights(2) = 0.20316f;
vRoots(3) = 0.76990f; vWeights(3) = 0.16007f;
vRoots(4) = 0.90411f; vWeights(4) = 0.10693f;
vRoots(5) = 0.98156f; vWeights(5) = 0.04717f;
vRoots(6) = -vRoots(0); vWeights(6) = vWeights(0);
vRoots(7) = -vRoots(1); vWeights(7) = vWeights(1);
vRoots(8) = -vRoots(2); vWeights(8) = vWeights(2);
vRoots(9) = -vRoots(3); vWeights(9) = vWeights(3);
vRoots(10)= -vRoots(4); vWeights(10)= vWeights(4);
vRoots(11)= -vRoots(5); vWeights(11)= vWeights(5);
}
}
void BSplineBasis::DerivativesOfBasisFunction(int iIndex, int iMaxDer, double fParam,
TColStd_Array1OfReal& Derivat)
{
int iMax = iMaxDer;
if (Derivat.Length() != iMax+1)
Standard_RangeError::Raise("BSplineBasis");
//k-te Ableitungen (k>Grad) sind Null
if (iMax >= _iOrder)
{
for (int i=_iOrder; i<=iMaxDer; i++)
Derivat(i) = 0.0f;
iMax = _iOrder - 1;
}
TColStd_Array1OfReal ND(0, iMax);
int p = _iOrder-1;
math_Matrix N(0,p,0,p);
double saved;
// falls Wert außerhalb Intervall, dann Funktionswert und alle Ableitungen gleich Null
if (fParam < _vKnotVector(iIndex) || fParam >= _vKnotVector(iIndex+p+1))
{
for (int k=0; k<=iMax; k++)
Derivat(k) = 0.0f;
return;
}
// Berechne die Basisfunktionen der Ordnung 1
for (int j=0; j<_iOrder; j++)
{
if (fParam >= _vKnotVector(iIndex+j) && fParam < _vKnotVector(iIndex+j+1))
N(j,0) = 1.0f;
else
N(j,0) = 0.0f;
}
// Berechne Dreieckstabelle der Funktionswerte
for (int k=1; k<_iOrder; k++)
{
if (N(0,k-1) == 0.0f)
saved = 0.0f;
else
saved = ((fParam - _vKnotVector(iIndex))*N(0,k-1))/(_vKnotVector(iIndex+k)-_vKnotVector(iIndex));
for (int j=0; j<p-k+1; j++)
{
double Tleft = _vKnotVector(iIndex+j+1);
double Tright = _vKnotVector(iIndex+j+k+1);
if (N(j+1,k-1) == 0.0)
{
N(j,k) = saved;
saved = 0.0f;
}
else
{
double tmp = N(j+1,k-1)/(Tright-Tleft);
N(j,k) = saved + (Tright-fParam)*tmp;
saved = (fParam-Tleft)*tmp;
}
}
}
// Funktionswert
Derivat(0) = N(0,p);
// Berechne aus der Dreieckstabelle die Ableitungen
for (int k=1; k<=iMax; k++)
{
for (int j=0; j<=k; j++)
{
// Lade (p-k)-te Spalte
ND(j) = N(j,p-k);
}
for (int jj=1; jj<=k; jj++)
{
if (ND(0) == 0.0f)
saved = 0.0f;
else
saved = ND(0)/(_vKnotVector(iIndex+p-k+jj) - _vKnotVector(iIndex));
for (int j=0; j<k-jj+1; j++)
{
double Tleft = _vKnotVector(iIndex+j+1);
double Tright = _vKnotVector(iIndex+j+p-k+jj+1);
if (ND(j+1) == 0.0f)
{
ND(j) = (p-k+jj)*saved;
saved = 0.0f;
}
else
{
double tmp = ND(j+1)/(Tright-Tleft);
ND(j) = (p-k+jj)*(saved-tmp);
saved = tmp;
}
}
}
Derivat(k) = ND(0); //k-te Ableitung
}
return;
}
