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occt/src/math/math_TrigonometricFunctionRoots.cxx
ifv 18d8e3e794 0029289: Wrong derivatives in math_TrigonometricFunctionRoots.cxx file 
Class MyTrigoFunction is removed from file math_TrigonometricFunctionRoots.cxx.
New class math_TrigonometricEquationFunction with the same functionality is created to provide possibilities
for individual testing.
Expressions for derivatives are corrected.
New Draw command "intconcon" for intersection 2d conic curves is created.
Test command OCC29289 (file QABugs_20.cxx) is created for individual testing math_TrigonometricEquationFunction.
It is used in tests/bugs/modalg_7/bug29289
2017-11-27 11:01:21 +03:00

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// Copyright (c) 1997-1999 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.
// lpa, le 03/09/91
// Implementation de la classe resolvant les equations en cosinus-sinus.
// Equation de la forme a*cos(x)*cos(x)+2*b*cos(x)*sin(x)+c*cos(x)+d*sin(x)+e
//#ifndef OCCT_DEBUG
#define No_Standard_RangeError
#define No_Standard_OutOfRange
#define No_Standard_DimensionError
//#endif
#include <math_TrigonometricFunctionRoots.hxx>
#include <math_TrigonometricEquationFunction.hxx>
#include <math_DirectPolynomialRoots.hxx>
#include <Standard_OutOfRange.hxx>
#include <math_FunctionWithDerivative.hxx>
#include <math_NewtonFunctionRoot.hxx>
#include <Precision.hxx>
math_TrigonometricFunctionRoots::math_TrigonometricFunctionRoots
(const Standard_Real theD,
const Standard_Real theE,
const Standard_Real theInfBound,
const Standard_Real theSupBound)
: NbSol (-1),
Sol (1, 4),
InfiniteStatus(Standard_False),
Done (Standard_False)
{
const Standard_Real A(0.0), B(0.0), C(0.0);
Perform(A, B, C, theD, theE, theInfBound, theSupBound);
}
math_TrigonometricFunctionRoots::math_TrigonometricFunctionRoots
(const Standard_Real theC,
const Standard_Real theD,
const Standard_Real theE,
const Standard_Real theInfBound,
const Standard_Real theSupBound)
: NbSol (-1),
Sol (1, 4),
InfiniteStatus(Standard_False),
Done (Standard_False)
{
const Standard_Real A(0.0), B(0.0);
Perform(A, B, theC, theD, theE, theInfBound, theSupBound);
}
math_TrigonometricFunctionRoots::math_TrigonometricFunctionRoots
(const Standard_Real theA,
const Standard_Real theB,
const Standard_Real theC,
const Standard_Real theD,
const Standard_Real theE,
const Standard_Real theInfBound,
const Standard_Real theSupBound)
: NbSol (-1),
Sol (1, 4),
InfiniteStatus(Standard_False),
Done (Standard_False)
{
Perform(theA, theB, theC, theD, theE, theInfBound, theSupBound);
}
void math_TrigonometricFunctionRoots::Perform(const Standard_Real A,
const Standard_Real B,
const Standard_Real C,
const Standard_Real D,
const Standard_Real E,
const Standard_Real InfBound,
const Standard_Real SupBound) {
Standard_Integer i, j=0, k, l, NZer=0, Nit = 10;
Standard_Real Depi, Delta, Mod, AA, BB, CC, MyBorneInf;
Standard_Real Teta, X;
Standard_Real Eps, Tol1 = 1.e-15;
TColStd_Array1OfReal ko(1,5), Zer(1,4);
Standard_Boolean Flag4;
InfiniteStatus = Standard_False;
Done = Standard_True;
Eps = 1.5e-12;
Depi = M_PI+M_PI;
if (InfBound <= RealFirst() && SupBound >= RealLast()) {
MyBorneInf = 0.0;
Delta = Depi;
Mod = 0.0;
}
else if (SupBound >= RealLast()) {
MyBorneInf = InfBound;
Delta = Depi;
Mod = MyBorneInf/Depi;
}
else if (InfBound <= RealFirst()) {
MyBorneInf = SupBound - Depi;
Delta = Depi;
Mod = MyBorneInf/Depi;
}
else {
MyBorneInf = InfBound;
Delta = SupBound-InfBound;
Mod = InfBound/Depi;
if ((SupBound-InfBound) > Depi) { Delta = Depi;}
}
if ((Abs(A) <= Eps) && (Abs(B) <= Eps)) {
if (Abs(C) <= Eps) {
if (Abs(D) <= Eps) {
if (Abs(E) <= Eps) {
InfiniteStatus = Standard_True; // infinite de solutions.
return;
}
else {
NbSol = 0;
return;
}
}
else {
// Equation du type d*sin(x) + e = 0
// =================================
NbSol = 0;
AA = -E/D;
if (Abs(AA) > 1.) {
return;
}
Zer(1) = ASin(AA);
Zer(2) = M_PI - Zer(1);
NZer = 2;
for (i = 1; i <= NZer; i++) {
if (Zer(i) <= -Eps) {
Zer(i) = Depi - Abs(Zer(i));
}
// On rend les solutions entre InfBound et SupBound:
// =================================================
Zer(i) += IntegerPart(Mod)*Depi;
X = Zer(i)-MyBorneInf;
if ((X > (-Epsilon(Delta))) && (X < Delta+ Epsilon(Delta))) {
NbSol++;
Sol(NbSol) = Zer(i);
}
}
}
return;
}
else if (Abs(D) <= Eps) {
// Equation du premier degre de la forme c*cos(x) + e = 0
// ======================================================
NbSol = 0;
AA = -E/C;
if (Abs(AA) >1.) {
return;
}
Zer(1) = ACos(AA);
Zer(2) = -Zer(1);
NZer = 2;
for (i = 1; i <= NZer; i++) {
if (Zer(i) <= -Eps) {
Zer(i) = Depi - Abs(Zer(i));
}
// On rend les solutions entre InfBound et SupBound:
// =================================================
Zer(i) += IntegerPart(Mod)*2.*M_PI;
X = Zer(i)-MyBorneInf;
if ((X >= (-Epsilon(Delta))) && (X <= Delta+ Epsilon(Delta))) {
NbSol++;
Sol(NbSol) = Zer(i);
}
}
return;
}
else {
// Equation du second degre:
// =========================
AA = E - C;
BB = 2.0*D;
CC = E + C;
math_DirectPolynomialRoots Resol(AA, BB, CC);
if (!Resol.IsDone()) {
Done = Standard_False;
return;
}
else if(!Resol.InfiniteRoots()) {
NZer = Resol.NbSolutions();
for (i = 1; i <= NZer; i++) {
Zer(i) = Resol.Value(i);
}
}
else if (Resol.InfiniteRoots()) {
InfiniteStatus = Standard_True;
return;
}
}
}
else {
// Two additional analytical cases.
if ((Abs(A) <= Eps) &&
(Abs(E) <= Eps))
{
if (Abs(C) <= Eps)
{
// 2 * B * sin * cos + D * sin = 0
NZer = 2;
Zer(1) = 0.0;
Zer(2) = M_PI;
AA = -D/(B * 2);
if (Abs(AA) <= 1.0 + Precision::PConfusion())
{
NZer = 4;
if (AA >= 1.0)
{
Zer(3)= 0.0;
Zer(4)= 0.0;
}
else if (AA <= -1.0)
{
Zer(3)= M_PI;
Zer(4)= M_PI;
}
else
{
Zer(3)= ACos(AA);
Zer(4) = Depi - Zer(3);
}
}
NbSol = 0;
for (i = 1; i <= NZer; i++)
{
if (Zer(i) <= MyBorneInf - Eps)
{
Zer(i) += Depi;
}
// On rend les solutions entre InfBound et SupBound:
// =================================================
Zer(i) += IntegerPart(Mod)*2.*M_PI;
X = Zer(i)-MyBorneInf;
if ((X >= (-Precision::PConfusion())) &&
(X <= Delta + Precision::PConfusion()))
{
if (Zer(i) < InfBound)
Zer(i) = InfBound;
if (Zer(i) > SupBound)
Zer(i) = SupBound;
NbSol++;
Sol(NbSol) = Zer(i);
}
}
return;
}
if (Abs(D) <= Eps)
{
// 2 * B * sin * cos + C * cos = 0
NZer = 2;
Zer(1) = M_PI / 2.0;
Zer(2) = M_PI * 3.0 / 2.0;
AA = -C/(B * 2);
if (Abs(AA) <= 1.0 + Precision::PConfusion())
{
NZer = 4;
if (AA >= 1.0)
{
Zer(3) = M_PI / 2.0;
Zer(4) = M_PI / 2.0;
}
else if (AA <= -1.0)
{
Zer(3) = M_PI * 3.0 / 2.0;
Zer(4) = M_PI * 3.0 / 2.0;
}
else
{
Zer(3)= ASin(AA);
Zer(4) = M_PI - Zer(3);
}
}
NbSol = 0;
for (i = 1; i <= NZer; i++)
{
if (Zer(i) <= MyBorneInf - Eps)
{
Zer(i) += Depi;
}
// On rend les solutions entre InfBound et SupBound:
// =================================================
Zer(i) += IntegerPart(Mod)*2.*M_PI;
X = Zer(i)-MyBorneInf;
if ((X >= (-Precision::PConfusion())) &&
(X <= Delta + Precision::PConfusion()))
{
if (Zer(i) < InfBound)
Zer(i) = InfBound;
if (Zer(i) > SupBound)
Zer(i) = SupBound;
NbSol++;
Sol(NbSol) = Zer(i);
}
}
return;
}
}
// Equation du 4 ieme degre
// ========================
ko(1) = A-C+E;
ko(2) = 2.0*D-4.0*B;
ko(3) = 2.0*E-2.0*A;
ko(4) = 4.0*B+2.0*D;
ko(5) = A+C+E;
Standard_Boolean bko;
Standard_Integer nbko=0;
do {
bko=Standard_False;
math_DirectPolynomialRoots Resol4(ko(1), ko(2), ko(3), ko(4), ko(5));
if (!Resol4.IsDone()) {
Done = Standard_False;
return;
}
else if (!Resol4.InfiniteRoots()) {
NZer = Resol4.NbSolutions();
for (i = 1; i <= NZer; i++) {
Zer(i) = Resol4.Value(i);
}
}
else if (Resol4.InfiniteRoots()) {
InfiniteStatus = Standard_True;
return;
}
Standard_Boolean triok;
do {
triok=Standard_True;
for(i=1;i<NZer;i++) {
if(Zer(i)>Zer(i+1)) {
Standard_Real t=Zer(i);
Zer(i)=Zer(i+1);
Zer(i+1)=t;
triok=Standard_False;
}
}
}
while(triok==Standard_False);
for(i=1;i<NZer;i++) {
if(Abs(Zer(i+1)-Zer(i))<Eps) {
//-- est ce une racine double ou une erreur numerique ?
Standard_Real qw=Zer(i+1);
Standard_Real va=ko(4)+qw*(2.0*ko(3)+qw*(3.0*ko(2)+qw*(4.0*ko(1))));
//-- cout<<" Val Double ("<<qw<<")=("<<va<<")"<<endl;
if(Abs(va)>Eps) {
bko=Standard_True;
nbko++;
#ifdef OCCT_DEBUG
//if(nbko==1) {
// cout<<"Pb ds math_TrigonometricFunctionRoots CC="
// <<A<<" CS="<<B<<" C="<<C<<" S="<<D<<" Cte="<<E<<endl;
//}
#endif
break;
}
}
}
if(bko) {
//-- Si il y a un coeff petit, on divise
//--
ko(1)*=0.0001;
ko(2)*=0.0001;
ko(3)*=0.0001;
ko(4)*=0.0001;
ko(5)*=0.0001;
}
}
while(bko);
}
// Verification des solutions par rapport aux bornes:
// ==================================================
Standard_Real SupmInfs100 = (SupBound-InfBound)*0.01;
NbSol = 0;
for (i = 1; i <= NZer; i++) {
Teta = atan(Zer(i)); Teta+=Teta;
if (Zer(i) <= (-Eps)) {
Teta = Depi-Abs(Teta);
}
Teta += IntegerPart(Mod)*Depi;
if (Teta-MyBorneInf < 0) Teta += Depi;
X = Teta -MyBorneInf;
if ((X >= (-Epsilon(Delta))) && (X <= Delta+ Epsilon(Delta))) {
X = Teta;
// Appel de Newton:
//OCC541(apo): Standard_Real TetaNewton=0;
Standard_Real TetaNewton = Teta;
math_TrigonometricEquationFunction MyF(A, B, C, D, E);
math_NewtonFunctionRoot Resol(MyF, X, Tol1, Eps, Nit);
if (Resol.IsDone()) {
TetaNewton = Resol.Root();
}
//-- lbr le 7 mars 97 (newton converge tres tres loin de la solution initilale)
Standard_Real DeltaNewton = TetaNewton-Teta;
if((DeltaNewton > SupmInfs100) || (DeltaNewton < -SupmInfs100)) {
//-- cout<<"\n Newton X0="<<Teta<<" -> "<<TetaNewton<<endl;
}
else {
Teta=TetaNewton;
}
Flag4 = Standard_False;
for(k = 1; k <= NbSol; k++) {
//On met les valeurs par ordre croissant:
if (Teta < Sol(k)) {
for (l = k; l <= NbSol; l++) {
j = NbSol-l+k;
Sol(j+1) = Sol(j);
}
Sol(k) = Teta;
NbSol++;
Flag4 = Standard_True;
break;
}
}
if (!Flag4) {
NbSol++;
Sol(NbSol) = Teta;
}
}
}
// Cas particulier de PI:
if(NbSol<4) {
Standard_Integer startIndex = NbSol + 1;
for( Standard_Integer solIt = startIndex; solIt <= 4; solIt++) {
Teta = M_PI + IntegerPart(Mod)*2.0*M_PI;;
X = Teta - MyBorneInf;
if ((X >= (-Epsilon(Delta))) && (X <= Delta + Epsilon(Delta))) {
if (Abs(A-C+E) <= Eps) {
Flag4 = Standard_False;
for (k = 1; k <= NbSol; k++) {
j = k;
if (Teta < Sol(k)) {
Flag4 = Standard_True;
break;
}
if ((solIt == startIndex) && (Abs(Teta-Sol(k)) <= Eps)) {
return;
}
}
if (!Flag4) {
NbSol++;
Sol(NbSol) = Teta;
}
else {
for (k = j; k <= NbSol; k++) {
i = NbSol-k+j;
Sol(i+1) = Sol(i);
}
Sol(j) = Teta;
NbSol++;
}
}
}
}
}
}
void math_TrigonometricFunctionRoots::Dump(Standard_OStream& o) const
{
o << " math_TrigonometricFunctionRoots: \n";
if (!Done) {
o << "Not Done \n";
}
else if (InfiniteStatus) {
o << " There is an infinity of roots\n";
}
else if (!InfiniteStatus) {
o << " Number of solutions = " << NbSol <<"\n";
for (Standard_Integer i = 1; i <= NbSol; i++) {
o << " Value number " << i << "= " << Sol(i) << "\n";
}
}
}
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