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occt/src/PLib/PLib.cxx
abv 42cf5bc1ca 0024002: Overall code and build procedure refactoring -- automatic 
Automatic upgrade of OCCT code by command "occt_upgrade . -nocdl":
- WOK-generated header files from inc and sources from drv are moved to src
- CDL files removed
- All packages are converted to nocdlpack
2015-07-12 07:42:38 +03:00

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// Created on: 1995-08-28
// Created by: Laurent BOURESCHE
// Copyright (c) 1995-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.
// Modified: 28/02/1996 by PMN : HermiteCoefficients added
// Modified: 18/06/1996 by PMN : NULL reference.
// Modified: 19/02/1997 by JCT : EvalPoly2Var added
#include <GeomAbs_Shape.hxx>
#include <math.hxx>
#include <math_Gauss.hxx>
#include <math_Matrix.hxx>
#include <NCollection_LocalArray.hxx>
#include <PLib.hxx>
#include <Standard_ConstructionError.hxx>
// To convert points array into Real ..
// *********************************
//=======================================================================
//function : SetPoles
//purpose :
//=======================================================================
void PLib::SetPoles(const TColgp_Array1OfPnt2d& Poles,
TColStd_Array1OfReal& FP)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
const gp_Pnt2d& P = Poles(i);
FP(j) = P.Coord(1); j++;
FP(j) = P.Coord(2); j++;
}
}
//=======================================================================
//function : SetPoles
//purpose :
//=======================================================================
void PLib::SetPoles(const TColgp_Array1OfPnt2d& Poles,
const TColStd_Array1OfReal& Weights,
TColStd_Array1OfReal& FP)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
Standard_Real w = Weights(i);
const gp_Pnt2d& P = Poles(i);
FP(j) = P.Coord(1) * w; j++;
FP(j) = P.Coord(2) * w; j++;
FP(j) = w; j++;
}
}
//=======================================================================
//function : GetPoles
//purpose :
//=======================================================================
void PLib::GetPoles(const TColStd_Array1OfReal& FP,
TColgp_Array1OfPnt2d& Poles)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
gp_Pnt2d& P = Poles(i);
P.SetCoord(1,FP(j)); j++;
P.SetCoord(2,FP(j)); j++;
}
}
//=======================================================================
//function : GetPoles
//purpose :
//=======================================================================
void PLib::GetPoles(const TColStd_Array1OfReal& FP,
TColgp_Array1OfPnt2d& Poles,
TColStd_Array1OfReal& Weights)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
Standard_Real w = FP(j + 2);
Weights(i) = w;
gp_Pnt2d& P = Poles(i);
P.SetCoord(1,FP(j) / w); j++;
P.SetCoord(2,FP(j) / w); j++;
j++;
}
}
//=======================================================================
//function : SetPoles
//purpose :
//=======================================================================
void PLib::SetPoles(const TColgp_Array1OfPnt& Poles,
TColStd_Array1OfReal& FP)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
const gp_Pnt& P = Poles(i);
FP(j) = P.Coord(1); j++;
FP(j) = P.Coord(2); j++;
FP(j) = P.Coord(3); j++;
}
}
//=======================================================================
//function : SetPoles
//purpose :
//=======================================================================
void PLib::SetPoles(const TColgp_Array1OfPnt& Poles,
const TColStd_Array1OfReal& Weights,
TColStd_Array1OfReal& FP)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
Standard_Real w = Weights(i);
const gp_Pnt& P = Poles(i);
FP(j) = P.Coord(1) * w; j++;
FP(j) = P.Coord(2) * w; j++;
FP(j) = P.Coord(3) * w; j++;
FP(j) = w; j++;
}
}
//=======================================================================
//function : GetPoles
//purpose :
//=======================================================================
void PLib::GetPoles(const TColStd_Array1OfReal& FP,
TColgp_Array1OfPnt& Poles)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
gp_Pnt& P = Poles(i);
P.SetCoord(1,FP(j)); j++;
P.SetCoord(2,FP(j)); j++;
P.SetCoord(3,FP(j)); j++;
}
}
//=======================================================================
//function : GetPoles
//purpose :
//=======================================================================
void PLib::GetPoles(const TColStd_Array1OfReal& FP,
TColgp_Array1OfPnt& Poles,
TColStd_Array1OfReal& Weights)
{
Standard_Integer j = FP .Lower();
Standard_Integer PLower = Poles.Lower();
Standard_Integer PUpper = Poles.Upper();
for (Standard_Integer i = PLower; i <= PUpper; i++) {
Standard_Real w = FP(j + 3);
Weights(i) = w;
gp_Pnt& P = Poles(i);
P.SetCoord(1,FP(j) / w); j++;
P.SetCoord(2,FP(j) / w); j++;
P.SetCoord(3,FP(j) / w); j++;
j++;
}
}
// specialized allocator
namespace
{
class BinomAllocator
{
public:
//! Main constructor
BinomAllocator (const Standard_Integer theMaxBinom)
: myBinom (NULL),
myMaxBinom (theMaxBinom)
{
Standard_Integer i, im1, ip1, id2, md2, md3, j, k;
Standard_Integer np1 = myMaxBinom + 1;
myBinom = new Standard_Integer*[np1];
myBinom[0] = new Standard_Integer[1];
myBinom[0][0] = 1;
for (i = 1; i < np1; ++i)
{
im1 = i - 1;
ip1 = i + 1;
id2 = i >> 1;
md2 = im1 >> 1;
md3 = ip1 >> 1;
k = 0;
myBinom[i] = new Standard_Integer[ip1];
for (j = 0; j < id2; ++j)
{
myBinom[i][j] = k + myBinom[im1][j];
k = myBinom[im1][j];
}
j = id2;
if (j > md2) j = im1 - j;
myBinom[i][id2] = k + myBinom[im1][j];
for (j = ip1 - md3; j < ip1; j++)
{
myBinom[i][j] = myBinom[i][i - j];
}
}
}
//! Destructor
~BinomAllocator()
{
// free memory
for (Standard_Integer i = 0; i <= myMaxBinom; ++i)
{
delete[] myBinom[i];
}
delete[] myBinom;
}
Standard_Real Value (const Standard_Integer N,
const Standard_Integer P) const
{
Standard_OutOfRange_Raise_if (N > myMaxBinom,
"PLib, BinomAllocator: requested degree is greater than maximum supported");
return Standard_Real (myBinom[N][P]);
}
private:
BinomAllocator (const BinomAllocator&);
BinomAllocator& operator= (const BinomAllocator&);
private:
Standard_Integer** myBinom;
Standard_Integer myMaxBinom;
};
// we do not call BSplCLib here to avoid Cyclic dependency detection by WOK
//static BinomAllocator THE_BINOM (BSplCLib::MaxDegree() + 1);
static BinomAllocator THE_BINOM (25 + 1);
}
//=======================================================================
//function : Bin
//purpose :
//=======================================================================
Standard_Real PLib::Bin(const Standard_Integer N,
const Standard_Integer P)
{
return THE_BINOM.Value (N, P);
}
//=======================================================================
//function : RationalDerivative
//purpose :
//=======================================================================
void PLib::RationalDerivative(const Standard_Integer Degree,
const Standard_Integer DerivativeRequest,
const Standard_Integer Dimension,
Standard_Real& Ders,
Standard_Real& RDers,
const Standard_Boolean All)
{
//
// Our purpose is to compute f = (u/v) derivated N = DerivativeRequest times
//
// We Write u = fv
// Let C(N,P) be the binomial
//
// then we have
//
// (q) (p) (q-p)
// u = SUM C (q,p) f v
// p = 0 to q
//
//
// Therefore
//
//
// (q) ( (q) (p) (q-p) )
// f = (1/v) ( u - SUM C (q,p) f v )
// ( p = 0 to q-1 )
//
//
// make arrays for the binomial since computing it each time could raise a performance
// issue
// As oppose to the method below the <Der> array is organized in the following
// fashion :
//
// u (1) u (2) .... u (Dimension) v (1)
//
// (1) (1) (1) (1)
// u (1) u (2) .... u (Dimension) v (1)
//
// ............................................
//
// (Degree) (Degree) (Degree) (Degree)
// u (1) u (2) .... u (Dimension) v (1)
//
//
Standard_Real Inverse;
Standard_Real *PolesArray = &Ders;
Standard_Real *RationalArray = &RDers;
Standard_Real Factor ;
Standard_Integer ii, Index, OtherIndex, Index1, Index2, jj;
NCollection_LocalArray<Standard_Real> binomial_array;
NCollection_LocalArray<Standard_Real> derivative_storage;
if (Dimension == 3) {
Standard_Integer DeRequest1 = DerivativeRequest + 1;
Standard_Integer MinDegRequ = DerivativeRequest;
if (MinDegRequ > Degree) MinDegRequ = Degree;
binomial_array.Allocate (DeRequest1);
for (ii = 0 ; ii < DeRequest1 ; ii++) {
binomial_array[ii] = 1.0e0 ;
}
if (!All) {
Standard_Integer DimDeRequ1 = (DeRequest1 << 1) + DeRequest1;
derivative_storage.Allocate (DimDeRequ1);
RationalArray = derivative_storage ;
}
Inverse = 1.0e0 / PolesArray[3] ;
Index = 0 ;
Index2 = - 6;
OtherIndex = 0 ;
for (ii = 0 ; ii <= MinDegRequ ; ii++) {
Index2 += 3;
Index1 = Index2;
RationalArray[Index] = PolesArray[OtherIndex]; Index++; OtherIndex++;
RationalArray[Index] = PolesArray[OtherIndex]; Index++; OtherIndex++;
RationalArray[Index] = PolesArray[OtherIndex];
Index -= 2;
OtherIndex += 2;
for (jj = ii - 1 ; jj >= 0 ; jj--) {
Factor = binomial_array[jj] * PolesArray[((ii-jj) << 2) + 3];
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
RationalArray[Index] -= Factor * RationalArray[Index1];
Index -= 2;
Index1 -= 5;
}
for (jj = ii ; jj >= 1 ; jj--) {
binomial_array[jj] += binomial_array[jj - 1] ;
}
RationalArray[Index] *= Inverse ; Index++;
RationalArray[Index] *= Inverse ; Index++;
RationalArray[Index] *= Inverse ; Index++;
}
for (ii= MinDegRequ + 1; ii <= DerivativeRequest ; ii++){
Index2 += 3;
Index1 = Index2;
RationalArray[Index] = 0.0e0; Index++;
RationalArray[Index] = 0.0e0; Index++;
RationalArray[Index] = 0.0e0;
Index -= 2;
for (jj = ii - 1 ; jj >= ii - MinDegRequ ; jj--) {
Factor = binomial_array[jj] * PolesArray[((ii-jj) << 2) + 3];
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
RationalArray[Index] -= Factor * RationalArray[Index1];
Index -= 2;
Index1 -= 5;
}
for (jj = ii ; jj >= 1 ; jj--) {
binomial_array[jj] += binomial_array[jj - 1] ;
}
RationalArray[Index] *= Inverse; Index++;
RationalArray[Index] *= Inverse; Index++;
RationalArray[Index] *= Inverse; Index++;
}
if (!All) {
RationalArray = &RDers ;
Standard_Integer DimDeRequ = (DerivativeRequest << 1) + DerivativeRequest;
RationalArray[0] = derivative_storage[DimDeRequ]; DimDeRequ++;
RationalArray[1] = derivative_storage[DimDeRequ]; DimDeRequ++;
RationalArray[2] = derivative_storage[DimDeRequ];
}
}
else {
Standard_Integer kk;
Standard_Integer Dimension1 = Dimension + 1;
Standard_Integer Dimension2 = Dimension << 1;
Standard_Integer DeRequest1 = DerivativeRequest + 1;
Standard_Integer MinDegRequ = DerivativeRequest;
if (MinDegRequ > Degree) MinDegRequ = Degree;
binomial_array.Allocate (DeRequest1);
for (ii = 0 ; ii < DeRequest1 ; ii++) {
binomial_array[ii] = 1.0e0 ;
}
if (!All) {
Standard_Integer DimDeRequ1 = Dimension * DeRequest1;
derivative_storage.Allocate (DimDeRequ1);
RationalArray = derivative_storage ;
}
Inverse = 1.0e0 / PolesArray[Dimension] ;
Index = 0 ;
Index2 = - Dimension2;
OtherIndex = 0 ;
for (ii = 0 ; ii <= MinDegRequ ; ii++) {
Index2 += Dimension;
Index1 = Index2;
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] = PolesArray[OtherIndex]; Index++; OtherIndex++;
}
Index -= Dimension;
OtherIndex ++;;
for (jj = ii - 1 ; jj >= 0 ; jj--) {
Factor = binomial_array[jj] * PolesArray[(ii-jj) * Dimension1 + Dimension];
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
}
Index -= Dimension ;
Index1 -= Dimension2 ;
}
for (jj = ii ; jj >= 1 ; jj--) {
binomial_array[jj] += binomial_array[jj - 1] ;
}
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] *= Inverse ; Index++;
}
}
for (ii= MinDegRequ + 1; ii <= DerivativeRequest ; ii++){
Index2 += Dimension;
Index1 = Index2;
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] = 0.0e0 ; Index++;
}
Index -= Dimension;
for (jj = ii - 1 ; jj >= ii - MinDegRequ ; jj--) {
Factor = binomial_array[jj] * PolesArray[(ii-jj) * Dimension1 + Dimension];
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
}
Index -= Dimension ;
Index1 -= Dimension2 ;
}
for (jj = ii ; jj >= 1 ; jj--) {
binomial_array[jj] += binomial_array[jj - 1] ;
}
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] *= Inverse; Index++;
}
}
if (!All) {
RationalArray = &RDers ;
Standard_Integer DimDeRequ = Dimension * DerivativeRequest;
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[kk] = derivative_storage[DimDeRequ]; DimDeRequ++;
}
}
}
}
//=======================================================================
//function : RationalDerivatives
//purpose : Uses Homogeneous Poles Derivatives and Deivatives of Weights
//=======================================================================
void PLib::RationalDerivatives(const Standard_Integer DerivativeRequest,
const Standard_Integer Dimension,
Standard_Real& PolesDerivates,
// must be an array with
// (DerivativeRequest + 1) * Dimension slots
Standard_Real& WeightsDerivates,
// must be an array with
// (DerivativeRequest + 1) slots
Standard_Real& RationalDerivates)
{
//
// Our purpose is to compute f = (u/v) derivated N times
//
// We Write u = fv
// Let C(N,P) be the binomial
//
// then we have
//
// (q) (p) (q-p)
// u = SUM C (q,p) f v
// p = 0 to q
//
//
// Therefore
//
//
// (q) ( (q) (p) (q-p) )
// f = (1/v) ( u - SUM C (q,p) f v )
// ( p = 0 to q-1 )
//
//
// make arrays for the binomial since computing it each time could
// raize a performance issue
//
Standard_Real Inverse;
Standard_Real *PolesArray = &PolesDerivates;
Standard_Real *WeightsArray = &WeightsDerivates;
Standard_Real *RationalArray = &RationalDerivates;
Standard_Real Factor ;
Standard_Integer ii, Index, Index1, Index2, jj;
Standard_Integer DeRequest1 = DerivativeRequest + 1;
NCollection_LocalArray<Standard_Real> binomial_array (DeRequest1);
NCollection_LocalArray<Standard_Real> derivative_storage;
for (ii = 0 ; ii < DeRequest1 ; ii++) {
binomial_array[ii] = 1.0e0 ;
}
Inverse = 1.0e0 / WeightsArray[0] ;
if (Dimension == 3) {
Index = 0 ;
Index2 = - 6 ;
for (ii = 0 ; ii < DeRequest1 ; ii++) {
Index2 += 3;
Index1 = Index2;
RationalArray[Index] = PolesArray[Index] ; Index++;
RationalArray[Index] = PolesArray[Index] ; Index++;
RationalArray[Index] = PolesArray[Index] ;
Index -= 2;
for (jj = ii - 1 ; jj >= 0 ; jj--) {
Factor = binomial_array[jj] * WeightsArray[ii - jj] ;
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
RationalArray[Index] -= Factor * RationalArray[Index1];
Index -= 2;
Index1 -= 5;
}
for (jj = ii ; jj >= 1 ; jj--) {
binomial_array[jj] += binomial_array[jj - 1] ;
}
RationalArray[Index] *= Inverse ; Index++;
RationalArray[Index] *= Inverse ; Index++;
RationalArray[Index] *= Inverse ; Index++;
}
}
else {
Standard_Integer kk;
Standard_Integer Dimension2 = Dimension << 1;
Index = 0 ;
Index2 = - Dimension2;
for (ii = 0 ; ii < DeRequest1 ; ii++) {
Index2 += Dimension;
Index1 = Index2;
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] = PolesArray[Index]; Index++;
}
Index -= Dimension;
for (jj = ii - 1 ; jj >= 0 ; jj--) {
Factor = binomial_array[jj] * WeightsArray[ii - jj] ;
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++;
}
Index -= Dimension;
Index1 -= Dimension2;
}
for (jj = ii ; jj >= 1 ; jj--) {
binomial_array[jj] += binomial_array[jj - 1] ;
}
for (kk = 0 ; kk < Dimension ; kk++) {
RationalArray[Index] *= Inverse ; Index++;
}
}
}
}
//=======================================================================
// Auxiliary template functions used for optimized evaluation of polynome
// and its derivatives for smaller dimensions of the polynome
//=======================================================================
namespace {
// recursive template for evaluating value or first derivative
template<int dim>
inline void eval_step1 (double* poly, double par, double* coef)
{
eval_step1<dim - 1> (poly, par, coef);
poly[dim] = poly[dim] * par + coef[dim];
}
// recursion end
template<>
inline void eval_step1<-1> (double*, double, double*)
{
}
// recursive template for evaluating second derivative
template<int dim>
inline void eval_step2 (double* poly, double par, double* coef)
{
eval_step2<dim - 1> (poly, par, coef);
poly[dim] = poly[dim] * par + coef[dim] * 2.;
}
// recursion end
template<>
inline void eval_step2<-1> (double*, double, double*)
{
}
// evaluation of only value
template<int dim>
inline void eval_poly0 (double* aRes, double* aCoeffs, int Degree, double Par)
{
Standard_Real* aRes0 = aRes;
memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * dim);
for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++)
{
aCoeffs -= dim;
// Calculating the value of the polynomial
eval_step1<dim-1> (aRes0, Par, aCoeffs);
}
}
// evaluation of value and first derivative
template<int dim>
inline void eval_poly1 (double* aRes, double* aCoeffs, int Degree, double Par)
{
Standard_Real* aRes0 = aRes;
Standard_Real* aRes1 = aRes + dim;
memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * dim);
memset(aRes1, 0, sizeof(Standard_Real) * dim);
for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++)
{
aCoeffs -= dim;
// Calculating derivatives of the polynomial
eval_step1<dim-1> (aRes1, Par, aRes0);
// Calculating the value of the polynomial
eval_step1<dim-1> (aRes0, Par, aCoeffs);
}
}
// evaluation of value and first and second derivatives
template<int dim>
inline void eval_poly2 (double* aRes, double* aCoeffs, int Degree, double Par)
{
Standard_Real* aRes0 = aRes;
Standard_Real* aRes1 = aRes + dim;
Standard_Real* aRes2 = aRes + 2 * dim;
memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * dim);
memset(aRes1, 0, sizeof(Standard_Real) * dim);
memset(aRes2, 0, sizeof(Standard_Real) * dim);
for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++)
{
aCoeffs -= dim;
// Calculating second derivatives of the polynomial
eval_step2<dim-1> (aRes2, Par, aRes1);
// Calculating derivatives of the polynomial
eval_step1<dim-1> (aRes1, Par, aRes0);
// Calculating the value of the polynomial
eval_step1<dim-1> (aRes0, Par, aCoeffs);
}
}
}
//=======================================================================
//function : This evaluates a polynomial and its derivatives
//purpose : up to the requested order
//=======================================================================
void PLib::EvalPolynomial(const Standard_Real Par,
const Standard_Integer DerivativeRequest,
const Standard_Integer Degree,
const Standard_Integer Dimension,
Standard_Real& PolynomialCoeff,
Standard_Real& Results)
//
// the polynomial coefficients are assumed to be stored as follows :
// 0
// [0] [Dimension -1] X coefficient
// 1
// [Dimension] [Dimension + Dimension -1] X coefficient
// 2
// [2 * Dimension] [2 * Dimension + Dimension-1] X coefficient
//
// ...................................................
//
//
// d
// [d * Dimension] [d * Dimension + Dimension-1] X coefficient
//
// where d is the Degree
//
{
Standard_Real* aCoeffs = &PolynomialCoeff + Degree * Dimension;
Standard_Real* aRes = &Results;
Standard_Real* anOriginal;
Standard_Integer ind = 0;
switch (DerivativeRequest)
{
case 1:
{
switch (Dimension)
{
case 1: eval_poly1<1> (aRes, aCoeffs, Degree, Par); break;
case 2: eval_poly1<2> (aRes, aCoeffs, Degree, Par); break;
case 3: eval_poly1<3> (aRes, aCoeffs, Degree, Par); break;
case 4: eval_poly1<4> (aRes, aCoeffs, Degree, Par); break;
case 5: eval_poly1<5> (aRes, aCoeffs, Degree, Par); break;
case 6: eval_poly1<6> (aRes, aCoeffs, Degree, Par); break;
case 7: eval_poly1<7> (aRes, aCoeffs, Degree, Par); break;
case 8: eval_poly1<8> (aRes, aCoeffs, Degree, Par); break;
case 9: eval_poly1<9> (aRes, aCoeffs, Degree, Par); break;
case 10: eval_poly1<10> (aRes, aCoeffs, Degree, Par); break;
case 11: eval_poly1<11> (aRes, aCoeffs, Degree, Par); break;
case 12: eval_poly1<12> (aRes, aCoeffs, Degree, Par); break;
case 13: eval_poly1<13> (aRes, aCoeffs, Degree, Par); break;
case 14: eval_poly1<14> (aRes, aCoeffs, Degree, Par); break;
case 15: eval_poly1<15> (aRes, aCoeffs, Degree, Par); break;
default:
{
Standard_Real* aRes0 = aRes;
Standard_Real* aRes1 = aRes + Dimension;
memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * Dimension);
memset(aRes1, 0, sizeof(Standard_Real) * Dimension);
for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++)
{
aCoeffs -= Dimension;
// Calculating derivatives of the polynomial
for (ind = 0; ind < Dimension; ind++)
aRes1[ind] = aRes1[ind] * Par + aRes0[ind];
// Calculating the value of the polynomial
for (ind = 0; ind < Dimension; ind++)
aRes0[ind] = aRes0[ind] * Par + aCoeffs[ind];
}
}
}
break;
}
case 2:
{
switch (Dimension)
{
case 1: eval_poly2<1> (aRes, aCoeffs, Degree, Par); break;
case 2: eval_poly2<2> (aRes, aCoeffs, Degree, Par); break;
case 3: eval_poly2<3> (aRes, aCoeffs, Degree, Par); break;
case 4: eval_poly2<4> (aRes, aCoeffs, Degree, Par); break;
case 5: eval_poly2<5> (aRes, aCoeffs, Degree, Par); break;
case 6: eval_poly2<6> (aRes, aCoeffs, Degree, Par); break;
case 7: eval_poly2<7> (aRes, aCoeffs, Degree, Par); break;
case 8: eval_poly2<8> (aRes, aCoeffs, Degree, Par); break;
case 9: eval_poly2<9> (aRes, aCoeffs, Degree, Par); break;
case 10: eval_poly2<10> (aRes, aCoeffs, Degree, Par); break;
case 11: eval_poly2<11> (aRes, aCoeffs, Degree, Par); break;
case 12: eval_poly2<12> (aRes, aCoeffs, Degree, Par); break;
case 13: eval_poly2<13> (aRes, aCoeffs, Degree, Par); break;
case 14: eval_poly2<14> (aRes, aCoeffs, Degree, Par); break;
case 15: eval_poly2<15> (aRes, aCoeffs, Degree, Par); break;
default:
{
Standard_Real* aRes0 = aRes;
Standard_Real* aRes1 = aRes + Dimension;
Standard_Real* aRes2 = aRes1 + Dimension;
// Nullify the results
Standard_Integer aSize = 2 * Dimension;
memcpy(aRes, aCoeffs, sizeof(Standard_Real) * Dimension);
memset(aRes1, 0, sizeof(Standard_Real) * aSize);
for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++)
{
aCoeffs -= Dimension;
// Calculating derivatives of the polynomial
for (ind = 0; ind < Dimension; ind++)
aRes2[ind] = aRes2[ind] * Par + aRes1[ind] * 2.0;
for (ind = 0; ind < Dimension; ind++)
aRes1[ind] = aRes1[ind] * Par + aRes0[ind];
// Calculating the value of the polynomial
for (ind = 0; ind < Dimension; ind++)
aRes0[ind] = aRes0[ind] * Par + aCoeffs[ind];
}
break;
}
}
break;
}
default:
{
// Nullify the results
Standard_Integer aResSize = (1 + DerivativeRequest) * Dimension;
memset(aRes, 0, sizeof(Standard_Real) * aResSize);
for (Standard_Integer aDeg = 0; aDeg <= Degree; aDeg++)
{
aRes = &Results + aResSize - Dimension;
// Calculating derivatives of the polynomial
for (Standard_Integer aDeriv = DerivativeRequest; aDeriv > 0; aDeriv--)
{
anOriginal = aRes - Dimension; // pointer to the derivative minus 1
for (ind = 0; ind < Dimension; ind++)
aRes[ind] = aRes[ind] * Par + anOriginal[ind] * aDeriv;
aRes = anOriginal;
}
// Calculating the value of the polynomial
for (ind = 0; ind < Dimension; ind++)
aRes[ind] = aRes[ind] * Par + aCoeffs[ind];
aCoeffs -= Dimension;
}
}
}
}
//=======================================================================
//function : This evaluates a polynomial without derivative
//purpose :
//=======================================================================
void PLib::NoDerivativeEvalPolynomial(const Standard_Real Par,
const Standard_Integer Degree,
const Standard_Integer Dimension,
const Standard_Integer DegreeDimension,
Standard_Real& PolynomialCoeff,
Standard_Real& Results)
{
Standard_Real* aCoeffs = &PolynomialCoeff + DegreeDimension;
Standard_Real* aRes = &Results;
switch (Dimension)
{
case 1: eval_poly0<1> (aRes, aCoeffs, Degree, Par); break;
case 2: eval_poly0<2> (aRes, aCoeffs, Degree, Par); break;
case 3: eval_poly0<3> (aRes, aCoeffs, Degree, Par); break;
case 4: eval_poly0<4> (aRes, aCoeffs, Degree, Par); break;
case 5: eval_poly0<5> (aRes, aCoeffs, Degree, Par); break;
case 6: eval_poly0<6> (aRes, aCoeffs, Degree, Par); break;
case 7: eval_poly0<7> (aRes, aCoeffs, Degree, Par); break;
case 8: eval_poly0<8> (aRes, aCoeffs, Degree, Par); break;
case 9: eval_poly0<9> (aRes, aCoeffs, Degree, Par); break;
case 10: eval_poly0<10> (aRes, aCoeffs, Degree, Par); break;
case 11: eval_poly0<11> (aRes, aCoeffs, Degree, Par); break;
case 12: eval_poly0<12> (aRes, aCoeffs, Degree, Par); break;
case 13: eval_poly0<13> (aRes, aCoeffs, Degree, Par); break;
case 14: eval_poly0<14> (aRes, aCoeffs, Degree, Par); break;
case 15: eval_poly0<15> (aRes, aCoeffs, Degree, Par); break;
default:
{
memcpy(aRes, aCoeffs, sizeof(Standard_Real) * Dimension);
for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++)
{
aCoeffs -= Dimension;
for (Standard_Integer ind = 0; ind < Dimension; ind++)
aRes[ind] = aRes[ind] * Par + aCoeffs[ind];
}
}
}
}
//=======================================================================
//function : This evaluates a polynomial of 2 variables
//purpose : or its derivative at the requested orders
//=======================================================================
void PLib::EvalPoly2Var(const Standard_Real UParameter,
const Standard_Real VParameter,
const Standard_Integer UDerivativeRequest,
const Standard_Integer VDerivativeRequest,
const Standard_Integer UDegree,
const Standard_Integer VDegree,
const Standard_Integer Dimension,
Standard_Real& PolynomialCoeff,
Standard_Real& Results)
//
// the polynomial coefficients are assumed to be stored as follows :
// 0 0
// [0] [Dimension -1] U V coefficient
// 1 0
// [Dimension] [Dimension + Dimension -1] U V coefficient
// 2 0
// [2 * Dimension] [2 * Dimension + Dimension-1] U V coefficient
//
// ...................................................
//
//
// m 0
// [m * Dimension] [m * Dimension + Dimension-1] U V coefficient
//
// where m = UDegree
//
// 0 1
// [(m+1) * Dimension] [(m+1) * Dimension + Dimension-1] U V coefficient
//
// ...................................................
//
// m 1
// [2*m * Dimension] [2*m * Dimension + Dimension-1] U V coefficient
//
// ...................................................
//
// m n
// [m*n * Dimension] [m*n * Dimension + Dimension-1] U V coefficient
//
// where n = VDegree
{
Standard_Integer Udim = (VDegree+1)*Dimension,
index = Udim*UDerivativeRequest;
TColStd_Array1OfReal Curve(1, Udim*(UDerivativeRequest+1));
TColStd_Array1OfReal Point(1, Dimension*(VDerivativeRequest+1));
Standard_Real * Result = (Standard_Real *) &Curve.ChangeValue(1);
Standard_Real * Digit = (Standard_Real *) &Point.ChangeValue(1);
Standard_Real * ResultArray ;
ResultArray = &Results ;
PLib::EvalPolynomial(UParameter,
UDerivativeRequest,
UDegree,
Udim,
PolynomialCoeff,
Result[0]);
PLib::EvalPolynomial(VParameter,
VDerivativeRequest,
VDegree,
Dimension,
Result[index],
Digit[0]);
index = Dimension*VDerivativeRequest;
for (Standard_Integer i=0;i<Dimension;i++) {
ResultArray[i] = Digit[index+i];
}
}
//=======================================================================
//function : This evaluates the lagrange polynomial and its derivatives
//purpose : up to the requested order that interpolates a series of
//points of dimension <Dimension> with given assigned parameters
//=======================================================================
Standard_Integer
PLib::EvalLagrange(const Standard_Real Parameter,
const Standard_Integer DerivativeRequest,
const Standard_Integer Degree,
const Standard_Integer Dimension,
Standard_Real& Values,
Standard_Real& Parameters,
Standard_Real& Results)
{
//
// the points are assumed to be stored as follows in the Values array :
//
// [0] [Dimension -1] first point coefficients
//
// [Dimension] [Dimension + Dimension -1] second point coefficients
//
// [2 * Dimension] [2 * Dimension + Dimension-1] third point coefficients
//
// ...................................................
//
//
//
// [d * Dimension] [d * Dimension + Dimension-1] d + 1 point coefficients
//
// where d is the Degree
//
// The ParameterArray stores the parameter value assign to each point in
// order described above, that is
// [0] is assign to first point
// [1] is assign to second point
//
Standard_Integer ii, jj, kk, Index, Index1, ReturnCode=0;
Standard_Integer local_request = DerivativeRequest;
Standard_Real *ParameterArray;
Standard_Real difference;
Standard_Real *PointsArray;
Standard_Real *ResultArray ;
PointsArray = &Values ;
ParameterArray = &Parameters ;
ResultArray = &Results ;
if (local_request >= Degree) {
local_request = Degree ;
}
NCollection_LocalArray<Standard_Real> divided_differences_array ((Degree + 1) * Dimension);
//
// Build the divided differences array
//
for (ii = 0 ; ii < (Degree + 1) * Dimension ; ii++) {
divided_differences_array[ii] = PointsArray[ii] ;
}
for (ii = Degree ; ii >= 0 ; ii--) {
for (jj = Degree ; jj > Degree - ii ; jj--) {
Index = jj * Dimension ;
Index1 = Index - Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
divided_differences_array[Index + kk] -=
divided_differences_array[Index1 + kk] ;
}
difference =
ParameterArray[jj] - ParameterArray[jj - Degree -1 + ii] ;
if (Abs(difference) < RealSmall()) {
ReturnCode = 1 ;
goto FINISH ;
}
difference = 1.0e0 / difference ;
for (kk = 0 ; kk < Dimension ; kk++) {
divided_differences_array[Index + kk] *= difference ;
}
}
}
//
//
// Evaluate the divided difference array polynomial which expresses as
//
// P(t) = [t1] P + (t - t1) [t1,t2] P + (t - t1)(t - t2)[t1,t2,t3] P + ...
// + (t - t1)(t - t2)(t - t3)...(t - td) [t1,t2,...,td+1] P
//
// The ith slot in the divided_differences_array is [t1,t2,...,ti+1]
//
//
Index = Degree * Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
ResultArray[kk] = divided_differences_array[Index + kk] ;
}
for (ii = Dimension ; ii < (local_request + 1) * Dimension ; ii++) {
ResultArray[ii] = 0.0e0 ;
}
for (ii = Degree ; ii >= 1 ; ii--) {
difference = Parameter - ParameterArray[ii - 1] ;
for (jj = local_request ; jj > 0 ; jj--) {
Index = jj * Dimension ;
Index1 = Index - Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
ResultArray[Index + kk] *= difference ;
ResultArray[Index + kk] += ResultArray[Index1+kk]*(Standard_Real) jj ;
}
}
Index = (ii -1) * Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
ResultArray[kk] *= difference ;
ResultArray[kk] += divided_differences_array[Index+kk] ;
}
}
FINISH :
return (ReturnCode) ;
}
//=======================================================================
//function : This evaluates the hermite polynomial and its derivatives
//purpose : up to the requested order that interpolates a series of
//points of dimension <Dimension> with given assigned parameters
//=======================================================================
Standard_Integer PLib::EvalCubicHermite
(const Standard_Real Parameter,
const Standard_Integer DerivativeRequest,
const Standard_Integer Dimension,
Standard_Real& Values,
Standard_Real& Derivatives,
Standard_Real& theParameters,
Standard_Real& Results)
{
//
// the points are assumed to be stored as follows in the Values array :
//
// [0] [Dimension -1] first point coefficients
//
// [Dimension] [Dimension + Dimension -1] last point coefficients
//
//
// the derivatives are assumed to be stored as follows in
// the Derivatives array :
//
// [0] [Dimension -1] first point coefficients
//
// [Dimension] [Dimension + Dimension -1] last point coefficients
//
// The ParameterArray stores the parameter value assign to each point in
// order described above, that is
// [0] is assign to first point
// [1] is assign to last point
//
Standard_Integer ii, jj, kk, pp, Index, Index1, Degree, ReturnCode;
Standard_Integer local_request = DerivativeRequest ;
ReturnCode = 0 ;
Degree = 3 ;
Standard_Real ParametersArray[4];
Standard_Real difference;
Standard_Real inverse;
Standard_Real *FirstLast;
Standard_Real *PointsArray;
Standard_Real *DerivativesArray;
Standard_Real *ResultArray ;
DerivativesArray = &Derivatives ;
PointsArray = &Values ;
FirstLast = &theParameters ;
ResultArray = &Results ;
if (local_request >= Degree) {
local_request = Degree ;
}
NCollection_LocalArray<Standard_Real> divided_differences_array ((Degree + 1) * Dimension);
for (ii = 0, jj = 0 ; ii < 2 ; ii++, jj+= 2) {
ParametersArray[jj] =
ParametersArray[jj+1] = FirstLast[ii] ;
}
//
// Build the divided differences array
//
//
// initialise it at the stage 2 of the building algorithm
// for devided differences
//
inverse = FirstLast[1] - FirstLast[0] ;
inverse = 1.0e0 / inverse ;
for (ii = 0, jj = Dimension, kk = 2 * Dimension, pp = 3 * Dimension ;
ii < Dimension ;
ii++, jj++, kk++, pp++) {
divided_differences_array[ii] = PointsArray[ii] ;
divided_differences_array[kk] = inverse *
(PointsArray[jj] - PointsArray[ii]) ;
divided_differences_array[jj] = DerivativesArray[ii] ;
divided_differences_array[pp] = DerivativesArray[jj] ;
}
for (ii = 1 ; ii <= Degree ; ii++) {
for (jj = Degree ; jj >= ii+1 ; jj--) {
Index = jj * Dimension ;
Index1 = Index - Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
divided_differences_array[Index + kk] -=
divided_differences_array[Index1 + kk] ;
}
for (kk = 0 ; kk < Dimension ; kk++) {
divided_differences_array[Index + kk] *= inverse ;
}
}
}
//
//
// Evaluate the divided difference array polynomial which expresses as
//
// P(t) = [t1] P + (t - t1) [t1,t2] P + (t - t1)(t - t2)[t1,t2,t3] P + ...
// + (t - t1)(t - t2)(t - t3)...(t - td) [t1,t2,...,td+1] P
//
// The ith slot in the divided_differences_array is [t1,t2,...,ti+1]
//
//
Index = Degree * Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
ResultArray[kk] = divided_differences_array[Index + kk] ;
}
for (ii = Dimension ; ii < (local_request + 1) * Dimension ; ii++) {
ResultArray[ii] = 0.0e0 ;
}
for (ii = Degree ; ii >= 1 ; ii--) {
difference = Parameter - ParametersArray[ii - 1] ;
for (jj = local_request ; jj > 0 ; jj--) {
Index = jj * Dimension ;
Index1 = Index - Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
ResultArray[Index + kk] *= difference ;
ResultArray[Index + kk] += ResultArray[Index1+kk]*(Standard_Real) jj;
}
}
Index = (ii -1) * Dimension ;
for (kk = 0 ; kk < Dimension ; kk++) {
ResultArray[kk] *= difference ;
ResultArray[kk] += divided_differences_array[Index+kk] ;
}
}
// FINISH :
return (ReturnCode) ;
}
//=======================================================================
//function : HermiteCoefficients
//purpose : calcul des polynomes d'Hermite
//=======================================================================
Standard_Boolean PLib::HermiteCoefficients(const Standard_Real FirstParameter,
const Standard_Real LastParameter,
const Standard_Integer FirstOrder,
const Standard_Integer LastOrder,
math_Matrix& MatrixCoefs)
{
Standard_Integer NbCoeff = FirstOrder + LastOrder + 2, Ordre[2];
Standard_Integer ii, jj, pp, cote, iof=0;
Standard_Real Prod, TBorne = FirstParameter;
math_Vector Coeff(1,NbCoeff), B(1, NbCoeff, 0.0);
math_Matrix MAT(1,NbCoeff, 1,NbCoeff, 0.0);
// Test de validites
if ((FirstOrder < 0) || (LastOrder < 0)) return Standard_False;
Standard_Real D1 = fabs(FirstParameter), D2 = fabs(LastParameter);
if (D1 > 100 || D2 > 100) return Standard_False;
D2 += D1;
if (D2 < 0.01) return Standard_False;
if (fabs(LastParameter - FirstParameter) / D2 < 0.01) return Standard_False;
// Calcul de la matrice a inverser (MAT)
Ordre[0] = FirstOrder+1;
Ordre[1] = LastOrder+1;
for (cote=0; cote<=1; cote++) {
Coeff.Init(1);
for (pp=1; pp<=Ordre[cote]; pp++) {
ii = pp + iof;
Prod = 1;
for (jj=pp; jj<=NbCoeff; jj++) {
// tout se passe dans les 3 lignes suivantes
MAT(ii, jj) = Coeff(jj) * Prod;
Coeff(jj) *= jj - pp;
Prod *= TBorne;
}
}
TBorne = LastParameter;
iof = Ordre[0];
}
// resolution du systemes
math_Gauss ResolCoeff(MAT, 1.0e-10);
if (!ResolCoeff.IsDone()) return Standard_False;
for (ii=1; ii<=NbCoeff; ii++) {
B(ii) = 1;
ResolCoeff.Solve(B, Coeff);
MatrixCoefs.SetRow( ii, Coeff);
B(ii) = 0;
}
return Standard_True;
}
//=======================================================================
//function : CoefficientsPoles
//purpose :
//=======================================================================
void PLib::CoefficientsPoles (const TColgp_Array1OfPnt& Coefs,
const TColStd_Array1OfReal& WCoefs,
TColgp_Array1OfPnt& Poles,
TColStd_Array1OfReal& Weights)
{
TColStd_Array1OfReal tempC(1,3*Coefs.Length());
PLib::SetPoles(Coefs,tempC);
TColStd_Array1OfReal tempP(1,3*Poles.Length());
PLib::SetPoles(Coefs,tempP);
PLib::CoefficientsPoles(3,tempC,WCoefs,tempP,Weights);
PLib::GetPoles(tempP,Poles);
}
//=======================================================================
//function : CoefficientsPoles
//purpose :
//=======================================================================
void PLib::CoefficientsPoles (const TColgp_Array1OfPnt2d& Coefs,
const TColStd_Array1OfReal& WCoefs,
TColgp_Array1OfPnt2d& Poles,
TColStd_Array1OfReal& Weights)
{
TColStd_Array1OfReal tempC(1,2*Coefs.Length());
PLib::SetPoles(Coefs,tempC);
TColStd_Array1OfReal tempP(1,2*Poles.Length());
PLib::SetPoles(Coefs,tempP);
PLib::CoefficientsPoles(2,tempC,WCoefs,tempP,Weights);
PLib::GetPoles(tempP,Poles);
}
//=======================================================================
//function : CoefficientsPoles
//purpose :
//=======================================================================
void PLib::CoefficientsPoles (const TColStd_Array1OfReal& Coefs,
const TColStd_Array1OfReal& WCoefs,
TColStd_Array1OfReal& Poles,
TColStd_Array1OfReal& Weights)
{
PLib::CoefficientsPoles(1,Coefs,WCoefs,Poles,Weights);
}
//=======================================================================
//function : CoefficientsPoles
//purpose :
//=======================================================================
void PLib::CoefficientsPoles (const Standard_Integer dim,
const TColStd_Array1OfReal& Coefs,
const TColStd_Array1OfReal& WCoefs,
TColStd_Array1OfReal& Poles,
TColStd_Array1OfReal& Weights)
{
Standard_Boolean rat = &WCoefs != NULL;
Standard_Integer loc = Coefs.Lower();
Standard_Integer lop = Poles.Lower();
Standard_Integer lowc=0;
Standard_Integer lowp=0;
Standard_Integer upc = Coefs.Upper();
Standard_Integer upp = Poles.Upper();
Standard_Integer upwc=0;
Standard_Integer upwp=0;
Standard_Integer reflen = Coefs.Length()/dim;
Standard_Integer i,j,k;
//Les Extremites.
if (rat) {
lowc = WCoefs.Lower(); lowp = Weights.Lower();
upwc = WCoefs.Upper(); upwp = Weights.Upper();
}
for (i = 0; i < dim; i++){
Poles (lop + i) = Coefs (loc + i);
Poles (upp - i) = Coefs (upc - i);
}
if (rat) {
Weights (lowp) = WCoefs (lowc);
Weights (upwp) = WCoefs (upwc);
}
Standard_Real Cnp;
for (i = 2; i < reflen; i++ ) {
Cnp = PLib::Bin(reflen - 1, i - 1);
if (rat) Weights (lowp + i - 1) = WCoefs (lowc + i - 1) / Cnp;
for(j = 0; j < dim; j++){
Poles(lop + dim * (i-1) + j)= Coefs(loc + dim * (i-1) + j) / Cnp;
}
}
for (i = 1; i <= reflen - 1; i++) {
for (j = reflen - 1; j >= i; j--) {
if (rat) Weights (lowp + j) += Weights (lowp + j -1);
for(k = 0; k < dim; k++){
Poles(lop + dim * j + k) += Poles(lop + dim * (j - 1) + k);
}
}
}
if (rat) {
for (i = 1; i <= reflen; i++) {
for(j = 0; j < dim; j++){
Poles(lop + dim * (i-1) + j) /= Weights(lowp + i -1);
}
}
}
}
//=======================================================================
//function : Trimming
//purpose :
//=======================================================================
void PLib::Trimming(const Standard_Real U1,
const Standard_Real U2,
TColgp_Array1OfPnt& Coefs,
TColStd_Array1OfReal& WCoefs)
{
TColStd_Array1OfReal temp(1,3*Coefs.Length());
PLib::SetPoles(Coefs,temp);
PLib::Trimming(U1,U2,3,temp,WCoefs);
PLib::GetPoles(temp,Coefs);
}
//=======================================================================
//function : Trimming
//purpose :
//=======================================================================
void PLib::Trimming(const Standard_Real U1,
const Standard_Real U2,
TColgp_Array1OfPnt2d& Coefs,
TColStd_Array1OfReal& WCoefs)
{
TColStd_Array1OfReal temp(1,2*Coefs.Length());
PLib::SetPoles(Coefs,temp);
PLib::Trimming(U1,U2,2,temp,WCoefs);
PLib::GetPoles(temp,Coefs);
}
//=======================================================================
//function : Trimming
//purpose :
//=======================================================================
void PLib::Trimming(const Standard_Real U1,
const Standard_Real U2,
TColStd_Array1OfReal& Coefs,
TColStd_Array1OfReal& WCoefs)
{
PLib::Trimming(U1,U2,1,Coefs,WCoefs);
}
//=======================================================================
//function : Trimming
//purpose :
//=======================================================================
void PLib::Trimming(const Standard_Real U1,
const Standard_Real U2,
const Standard_Integer dim,
TColStd_Array1OfReal& Coefs,
TColStd_Array1OfReal& WCoefs)
{
// principe :
// on fait le changement de variable v = (u-U1) / (U2-U1)
// on exprime u = f(v) que l'on remplace dans l'expression polynomiale
// decomposee sous la forme du schema iteratif de horner.
Standard_Real lsp = U2 - U1;
Standard_Integer indc, indw=0;
Standard_Integer upc = Coefs.Upper() - dim + 1, upw=0;
Standard_Integer len = Coefs.Length()/dim;
Standard_Boolean rat = &WCoefs != NULL;
if (rat) {
if(len != WCoefs.Length())
Standard_Failure::Raise("PLib::Trimming : nbcoefs/dim != nbweights !!!");
upw = WCoefs.Upper();
}
len --;
for (Standard_Integer i = 1; i <= len; i++) {
Standard_Integer j ;
indc = upc - dim*(i-1);
if (rat) indw = upw - i + 1;
//calcul du coefficient de degre le plus faible a l'iteration i
for( j = 0; j < dim; j++){
Coefs(indc - dim + j) += U1 * Coefs(indc + j);
}
if (rat) WCoefs(indw - 1) += U1 * WCoefs(indw);
//calcul des coefficients intermediaires :
while (indc < upc){
indc += dim;
for(Standard_Integer k = 0; k < dim; k++){
Coefs(indc - dim + k) =
U1 * Coefs(indc + k) + lsp * Coefs(indc - dim + k);
}
if (rat) {
indw ++;
WCoefs(indw - 1) = U1 * WCoefs(indw) + lsp * WCoefs(indw - 1);
}
}
//calcul du coefficient de degre le plus eleve :
for(j = 0; j < dim; j++){
Coefs(upc + j) *= lsp;
}
if (rat) WCoefs(upw) *= lsp;
}
}
//=======================================================================
//function : CoefficientsPoles
//purpose :
// Modified: 21/10/1996 by PMN : PolesCoefficient (PRO5852).
// on ne bidouille plus les u et v c'est a l'appelant de savoir ce qu'il
// fait avec BuildCache ou plus simplement d'utiliser PolesCoefficients
//=======================================================================
void PLib::CoefficientsPoles (const TColgp_Array2OfPnt& Coefs,
const TColStd_Array2OfReal& WCoefs,
TColgp_Array2OfPnt& Poles,
TColStd_Array2OfReal& Weights)
{
Standard_Boolean rat = (&WCoefs != NULL);
Standard_Integer LowerRow = Poles.LowerRow();
Standard_Integer UpperRow = Poles.UpperRow();
Standard_Integer LowerCol = Poles.LowerCol();
Standard_Integer UpperCol = Poles.UpperCol();
Standard_Integer ColLength = Poles.ColLength();
Standard_Integer RowLength = Poles.RowLength();
// Bidouille pour retablir u et v pour les coefs calcules
// par buildcache
// Standard_Boolean inv = Standard_False; //ColLength != Coefs.ColLength();
Standard_Integer Row, Col;
Standard_Real W, Cnp;
Standard_Integer I1, I2;
Standard_Integer NPoleu , NPolev;
gp_XYZ Temp;
for (NPoleu = LowerRow; NPoleu <= UpperRow; NPoleu++){
Poles (NPoleu, LowerCol) = Coefs (NPoleu, LowerCol);
if (rat) {
Weights (NPoleu, LowerCol) = WCoefs (NPoleu, LowerCol);
}
for (Col = LowerCol + 1; Col <= UpperCol - 1; Col++) {
Cnp = PLib::Bin(RowLength - 1,Col - LowerCol);
Temp = Coefs (NPoleu, Col).XYZ();
Temp.Divide (Cnp);
Poles (NPoleu, Col).SetXYZ (Temp);
if (rat) {
Weights (NPoleu, Col) = WCoefs (NPoleu, Col) / Cnp;
}
}
Poles (NPoleu, UpperCol) = Coefs (NPoleu, UpperCol);
if (rat) {
Weights (NPoleu, UpperCol) = WCoefs (NPoleu, UpperCol);
}
for (I1 = 1; I1 <= RowLength - 1; I1++) {
for (I2 = UpperCol; I2 >= LowerCol + I1; I2--) {
Temp.SetLinearForm
(Poles (NPoleu, I2).XYZ(), Poles (NPoleu, I2-1).XYZ());
Poles (NPoleu, I2).SetXYZ (Temp);
if (rat) Weights(NPoleu, I2) += Weights(NPoleu, I2-1);
}
}
}
for (NPolev = LowerCol; NPolev <= UpperCol; NPolev++){
for (Row = LowerRow + 1; Row <= UpperRow - 1; Row++) {
Cnp = PLib::Bin(ColLength - 1,Row - LowerRow);
Temp = Poles (Row, NPolev).XYZ();
Temp.Divide (Cnp);
Poles (Row, NPolev).SetXYZ (Temp);
if (rat) Weights(Row, NPolev) /= Cnp;
}
for (I1 = 1; I1 <= ColLength - 1; I1++) {
for (I2 = UpperRow; I2 >= LowerRow + I1; I2--) {
Temp.SetLinearForm
(Poles (I2, NPolev).XYZ(), Poles (I2-1, NPolev).XYZ());
Poles (I2, NPolev).SetXYZ (Temp);
if (rat) Weights(I2, NPolev) += Weights(I2-1, NPolev);
}
}
}
if (rat) {
for (Row = LowerRow; Row <= UpperRow; Row++) {
for (Col = LowerCol; Col <= UpperCol; Col++) {
W = Weights (Row, Col);
Temp = Poles(Row, Col).XYZ();
Temp.Divide (W);
Poles(Row, Col).SetXYZ (Temp);
}
}
}
}
//=======================================================================
//function : UTrimming
//purpose :
//=======================================================================
void PLib::UTrimming(const Standard_Real U1,
const Standard_Real U2,
TColgp_Array2OfPnt& Coeffs,
TColStd_Array2OfReal& WCoeffs)
{
Standard_Boolean rat = &WCoeffs != NULL;
Standard_Integer lr = Coeffs.LowerRow();
Standard_Integer ur = Coeffs.UpperRow();
Standard_Integer lc = Coeffs.LowerCol();
Standard_Integer uc = Coeffs.UpperCol();
TColgp_Array1OfPnt Temp (lr,ur);
TColStd_Array1OfReal Temw (lr,ur);
for (Standard_Integer icol = lc; icol <= uc; icol++) {
Standard_Integer irow ;
for ( irow = lr; irow <= ur; irow++) {
Temp (irow) = Coeffs (irow, icol);
if (rat) Temw (irow) = WCoeffs (irow, icol);
}
if (rat) PLib::Trimming (U1, U2, Temp, Temw);
else PLib::Trimming (U1, U2, Temp, PLib::NoWeights());
for (irow = lr; irow <= ur; irow++) {
Coeffs (irow, icol) = Temp (irow);
if (rat) WCoeffs (irow, icol) = Temw (irow);
}
}
}
//=======================================================================
//function : VTrimming
//purpose :
//=======================================================================
void PLib::VTrimming(const Standard_Real V1,
const Standard_Real V2,
TColgp_Array2OfPnt& Coeffs,
TColStd_Array2OfReal& WCoeffs)
{
Standard_Boolean rat = &WCoeffs != NULL;
Standard_Integer lr = Coeffs.LowerRow();
Standard_Integer ur = Coeffs.UpperRow();
Standard_Integer lc = Coeffs.LowerCol();
Standard_Integer uc = Coeffs.UpperCol();
TColgp_Array1OfPnt Temp (lc,uc);
TColStd_Array1OfReal Temw (lc,uc);
for (Standard_Integer irow = lr; irow <= ur; irow++) {
Standard_Integer icol ;
for ( icol = lc; icol <= uc; icol++) {
Temp (icol) = Coeffs (irow, icol);
if (rat) Temw (icol) = WCoeffs (irow, icol);
}
if (rat) PLib::Trimming (V1, V2, Temp, Temw);
else PLib::Trimming (V1, V2, Temp, PLib::NoWeights());
for (icol = lc; icol <= uc; icol++) {
Coeffs (irow, icol) = Temp (icol);
if (rat) WCoeffs (irow, icol) = Temw (icol);
}
}
}
//=======================================================================
//function : HermiteInterpolate
//purpose :
//=======================================================================
Standard_Boolean PLib::HermiteInterpolate
(const Standard_Integer Dimension,
const Standard_Real FirstParameter,
const Standard_Real LastParameter,
const Standard_Integer FirstOrder,
const Standard_Integer LastOrder,
const TColStd_Array2OfReal& FirstConstr,
const TColStd_Array2OfReal& LastConstr,
TColStd_Array1OfReal& Coefficients)
{
Standard_Real Pattern[3][6];
// portage HP : il faut les initialiser 1 par 1
Pattern[0][0] = 1;
Pattern[0][1] = 1;
Pattern[0][2] = 1;
Pattern[0][3] = 1;
Pattern[0][4] = 1;
Pattern[0][5] = 1;
Pattern[1][0] = 0;
Pattern[1][1] = 1;
Pattern[1][2] = 2;
Pattern[1][3] = 3;
Pattern[1][4] = 4;
Pattern[1][5] = 5;
Pattern[2][0] = 0;
Pattern[2][1] = 0;
Pattern[2][2] = 2;
Pattern[2][3] = 6;
Pattern[2][4] = 12;
Pattern[2][5] = 20;
math_Matrix A(0,FirstOrder+LastOrder+1, 0,FirstOrder+LastOrder+1);
// The initialisation of the matrix A
Standard_Integer irow ;
for ( irow=0; irow<=FirstOrder; irow++) {
Standard_Real FirstVal = 1.;
for (Standard_Integer icol=0; icol<=FirstOrder+LastOrder+1; icol++) {
A(irow,icol) = Pattern[irow][icol]*FirstVal;
if (irow <= icol) FirstVal *= FirstParameter;
}
}
for (irow=0; irow<=LastOrder; irow++) {
Standard_Real LastVal = 1.;
for (Standard_Integer icol=0; icol<=FirstOrder+LastOrder+1; icol++) {
A(irow+FirstOrder+1,icol) = Pattern[irow][icol]*LastVal;
if (irow <= icol) LastVal *= LastParameter;
}
}
//
// The filled matrix A for FirstOrder=LastOrder=2 is:
//
// 1 FP FP**2 FP**3 FP**4 FP**5
// 0 1 2*FP 3*FP**2 4*FP**3 5*FP**4 FP - FirstParameter
// 0 0 2 6*FP 12*FP**2 20*FP**3
// 1 LP LP**2 LP**3 LP**4 LP**5
// 0 1 2*LP 3*LP**2 4*LP**3 5*LP**4 LP - LastParameter
// 0 0 2 6*LP 12*LP**2 20*LP**3
//
// If FirstOrder or LastOrder <=2 then some rows and columns are missing.
// For example:
// If FirstOrder=1 then 3th row and 6th column are missing
// If FirstOrder=LastOrder=0 then 2,3,5,6th rows and 3,4,5,6th columns are missing
math_Gauss Equations(A);
// cout << "A=" << A << endl;
for (Standard_Integer idim=1; idim<=Dimension; idim++) {
// cout << "idim=" << idim << endl;
math_Vector B(0,FirstOrder+LastOrder+1);
Standard_Integer icol ;
for ( icol=0; icol<=FirstOrder; icol++)
B(icol) = FirstConstr(idim,icol);
for (icol=0; icol<=LastOrder; icol++)
B(FirstOrder+1+icol) = LastConstr(idim,icol);
// cout << "B=" << B << endl;
// The solving of equations system A * X = B. Then B = X
Equations.Solve(B);
// cout << "After Solving" << endl << "B=" << B << endl;
if (Equations.IsDone()==Standard_False) return Standard_False;
// the filling of the Coefficients
for (icol=0; icol<=FirstOrder+LastOrder+1; icol++)
Coefficients(Dimension*icol+idim-1) = B(icol);
}
return Standard_True;
}
//=======================================================================
//function : JacobiParameters
//purpose :
//=======================================================================
void PLib::JacobiParameters(const GeomAbs_Shape ConstraintOrder,
const Standard_Integer MaxDegree,
const Standard_Integer Code,
Standard_Integer& NbGaussPoints,
Standard_Integer& WorkDegree)
{
// ConstraintOrder: Ordre de contrainte aux extremites :
// C0 = contraintes de passage aux bornes;
// C1 = C0 + contraintes de derivees 1eres;
// C2 = C1 + contraintes de derivees 2ndes.
// MaxDegree: Nombre maxi de coeff de la "courbe" polynomiale
// d' approximation (doit etre superieur ou egal a
// 2*NivConstr+2 et inferieur ou egal a 50).
// Code: Code d' init. des parametres de discretisation.
// (choix de NBPNTS et de NDGJAC de MAPF1C,MAPFXC).
// = -5 Calcul tres rapide mais peu precis (8pts)
// = -4 ' ' ' ' ' ' (10pts)
// = -3 ' ' ' ' ' ' (15pts)
// = -2 ' ' ' ' ' ' (20pts)
// = -1 ' ' ' ' ' ' (25pts)
// = 1 calcul rapide avec precision moyenne (30pts).
// = 2 calcul rapide avec meilleure precision (40pts).
// = 3 calcul un peu plus lent avec bonne precision (50 pts).
// = 4 calcul lent avec la meilleure precision possible
// (61pts).
// The possible values of NbGaussPoints
const Standard_Integer NDEG8=8, NDEG10=10, NDEG15=15, NDEG20=20, NDEG25=25,
NDEG30=30, NDEG40=40, NDEG50=50, NDEG61=61;
Standard_Integer NivConstr=0;
switch (ConstraintOrder) {
case GeomAbs_C0: NivConstr = 0; break;
case GeomAbs_C1: NivConstr = 1; break;
case GeomAbs_C2: NivConstr = 2; break;
default:
Standard_ConstructionError::Raise("Invalid ConstraintOrder");
}
if (MaxDegree < 2*NivConstr+1)
Standard_ConstructionError::Raise("Invalid MaxDegree");
if (Code >= 1)
WorkDegree = MaxDegree + 9;
else
WorkDegree = MaxDegree + 6;
//---> Nbre mini de points necessaires.
Standard_Integer IPMIN=0;
if (WorkDegree < NDEG8)
IPMIN=NDEG8;
else if (WorkDegree < NDEG10)
IPMIN=NDEG10;
else if (WorkDegree < NDEG15)
IPMIN=NDEG15;
else if (WorkDegree < NDEG20)
IPMIN=NDEG20;
else if (WorkDegree < NDEG25)
IPMIN=NDEG25;
else if (WorkDegree < NDEG30)
IPMIN=NDEG30;
else if (WorkDegree < NDEG40)
IPMIN=NDEG40;
else if (WorkDegree < NDEG50)
IPMIN=NDEG50;
else if (WorkDegree < NDEG61)
IPMIN=NDEG61;
else
Standard_ConstructionError::Raise("Invalid MaxDegree");
// ---> Nbre de points voulus.
Standard_Integer IWANT=0;
switch (Code) {
case -5: IWANT=NDEG8; break;
case -4: IWANT=NDEG10; break;
case -3: IWANT=NDEG15; break;
case -2: IWANT=NDEG20; break;
case -1: IWANT=NDEG25; break;
case 1: IWANT=NDEG30; break;
case 2: IWANT=NDEG40; break;
case 3: IWANT=NDEG50; break;
case 4: IWANT=NDEG61; break;
default:
Standard_ConstructionError::Raise("Invalid Code");
}
//--> NbGaussPoints est le nombre de points de discretisation de la fonction,
// il ne peut prendre que les valeurs 8,10,15,20,25,30,40,50 ou 61.
// NbGaussPoints doit etre superieur strictement a WorkDegree.
NbGaussPoints = Max(IPMIN,IWANT);
// NbGaussPoints +=2;
}
//=======================================================================
//function : NivConstr
//purpose : translates from GeomAbs_Shape to Integer
//=======================================================================
Standard_Integer PLib::NivConstr(const GeomAbs_Shape ConstraintOrder)
{
Standard_Integer NivConstr=0;
switch (ConstraintOrder) {
case GeomAbs_C0: NivConstr = 0; break;
case GeomAbs_C1: NivConstr = 1; break;
case GeomAbs_C2: NivConstr = 2; break;
default:
Standard_ConstructionError::Raise("Invalid ConstraintOrder");
}
return NivConstr;
}
//=======================================================================
//function : ConstraintOrder
//purpose : translates from Integer to GeomAbs_Shape
//=======================================================================
GeomAbs_Shape PLib::ConstraintOrder(const Standard_Integer NivConstr)
{
GeomAbs_Shape ConstraintOrder=GeomAbs_C0;
switch (NivConstr) {
case 0: ConstraintOrder = GeomAbs_C0; break;
case 1: ConstraintOrder = GeomAbs_C1; break;
case 2: ConstraintOrder = GeomAbs_C2; break;
default:
Standard_ConstructionError::Raise("Invalid NivConstr");
}
return ConstraintOrder;
}
//=======================================================================
//function : EvalLength
//purpose :
//=======================================================================
void PLib::EvalLength(const Standard_Integer Degree, const Standard_Integer Dimension,
Standard_Real& PolynomialCoeff,
const Standard_Real U1, const Standard_Real U2,
Standard_Real& Length)
{
Standard_Integer i,j,idim, degdim;
Standard_Real C1,C2,Sum,Tran,X1,X2,Der1,Der2,D1,D2,DD;
Standard_Real *PolynomialArray = &PolynomialCoeff ;
Standard_Integer NbGaussPoints = 4 * Min((Degree/4)+1,10);
math_Vector GaussPoints(1,NbGaussPoints);
math::GaussPoints(NbGaussPoints,GaussPoints);
math_Vector GaussWeights(1,NbGaussPoints);
math::GaussWeights(NbGaussPoints,GaussWeights);
C1 = (U2 + U1) / 2.;
C2 = (U2 - U1) / 2.;
//-----------------------------------------------------------
//****** Integration - Boucle sur les intervalles de GAUSS **
//-----------------------------------------------------------
Sum = 0;
for (j=1; j<=NbGaussPoints/2; j++) {
// Integration en tenant compte de la symetrie
Tran = C2 * GaussPoints(j);
X1 = C1 + Tran;
X2 = C1 - Tran;
//****** Derivation sur la dimension de l'espace **
degdim = Degree*Dimension;
Der1 = Der2 = 0.;
for (idim=0; idim<Dimension; idim++) {
D1 = D2 = Degree * PolynomialArray [idim + degdim];
for (i=Degree-1; i>=1; i--) {
DD = i * PolynomialArray [idim + i*Dimension];
D1 = D1 * X1 + DD;
D2 = D2 * X2 + DD;
}
Der1 += D1 * D1;
Der2 += D2 * D2;
}
//****** Integration **
Sum += GaussWeights(j) * C2 * (Sqrt(Der1) + Sqrt(Der2));
//****** Fin de boucle dur les intervalles de GAUSS **
}
Length = Sum;
}
//=======================================================================
//function : EvalLength
//purpose :
//=======================================================================
void PLib::EvalLength(const Standard_Integer Degree, const Standard_Integer Dimension,
Standard_Real& PolynomialCoeff,
const Standard_Real U1, const Standard_Real U2,
const Standard_Real Tol,
Standard_Real& Length, Standard_Real& Error)
{
Standard_Integer i;
Standard_Integer NbSubInt = 1, // Current number of subintervals
MaxNbIter = 13, // Max number of iterations
NbIter = 1; // Current number of iterations
Standard_Real dU,OldLen,LenI;
PLib::EvalLength(Degree,Dimension, PolynomialCoeff, U1,U2, Length);
do {
OldLen = Length;
Length = 0.;
NbSubInt *= 2;
dU = (U2-U1)/NbSubInt;
for (i=1; i<=NbSubInt; i++) {
PLib::EvalLength(Degree,Dimension, PolynomialCoeff, U1+(i-1)*dU,U1+i*dU, LenI);
Length += LenI;
}
NbIter++;
Error = Abs(OldLen-Length);
}
while (Error > Tol && NbIter <= MaxNbIter);
}
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