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d5f74e42d6
License statement text corrected; compiler warnings caused by Bison 2.41 disabled for MSVC; a few other compiler warnings on 54-bit Windows eliminated by appropriate type cast Wrong license statements corrected in several files. Copyright and license statements added in XSD and GLSL files. Copyright year updated in some files. Obsolete documentation files removed from DrawResources.
442 lines
11 KiB
C++
442 lines
11 KiB
C++
// Copyright (c) 1997-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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// lpa, le 03/09/91
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// Implementation de la classe resolvant les equations en cosinus-sinus.
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// Equation de la forme a*cos(x)*cos(x)+2*b*cos(x)*sin(x)+c*cos(x)+d*sin(x)+e
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//#ifndef DEB
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#define No_Standard_RangeError
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#define No_Standard_OutOfRange
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#define No_Standard_DimensionError
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//#endif
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#include <math_TrigonometricFunctionRoots.hxx>
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#include <math_DirectPolynomialRoots.hxx>
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#include <Standard_OutOfRange.hxx>
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#include <math_FunctionWithDerivative.hxx>
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#include <math_NewtonFunctionRoot.hxx>
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class MyTrigoFunction: public math_FunctionWithDerivative {
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Standard_Real AA;
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Standard_Real BB;
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Standard_Real CC;
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Standard_Real DD;
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Standard_Real EE;
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public:
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MyTrigoFunction(const Standard_Real A, const Standard_Real B, const Standard_Real C, const Standard_Real D,
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const Standard_Real E);
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Standard_Boolean Value(const Standard_Real X, Standard_Real& F);
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Standard_Boolean Derivative(const Standard_Real X, Standard_Real& D);
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Standard_Boolean Values(const Standard_Real X, Standard_Real& F, Standard_Real& D);
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};
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MyTrigoFunction::MyTrigoFunction(const Standard_Real A, const Standard_Real B, const Standard_Real C,
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const Standard_Real D, const Standard_Real E) {
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AA = A;
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BB = B;
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CC = C;
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DD = D;
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EE = E;
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}
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Standard_Boolean MyTrigoFunction::Value(const Standard_Real X, Standard_Real& F) {
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Standard_Real CN= cos(X), SN = sin(X);
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//-- F= AA*CN*CN+2*BB*CN*SN+CC*CN+DD*SN+EE;
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F=CN*(AA*CN + (BB+BB)*SN + CC) + DD*SN + EE;
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return Standard_True;
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}
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Standard_Boolean MyTrigoFunction::Derivative(const Standard_Real X, Standard_Real& D) {
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Standard_Real CN= Cos(X), SN = Sin(X);
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//-- D = -2*AA*CN*SN+2*BB*(CN*CN-SN*SN)-CC*SN+DD*CN;
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D = -AA*CN*SN + BB*(CN*CN-SN*SN);
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D+=D;
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D-=CC*SN+DD*CN;
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return Standard_True;
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}
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Standard_Boolean MyTrigoFunction::Values(const Standard_Real X, Standard_Real& F, Standard_Real& D) {
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Standard_Real CN= Cos(X), SN = Sin(X);
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//-- F= AA*CN*CN+2*BB*CN*SN+CC*CN+DD*SN+EE;
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//-- D = -2*AA*CN*SN+2*BB*(CN*CN-SN*SN)-CC*SN+DD*CN;
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Standard_Real AACN = AA*CN;
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Standard_Real BBSN = BB*SN;
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F = AACN*CN + BBSN*(CN+CN) + CC*CN + DD*SN + EE;
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D = -AACN*SN + BB*(CN*CN+SN*SN);
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D+=D;
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D+=-CC*SN+DD*CN;
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return Standard_True;
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}
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math_TrigonometricFunctionRoots::math_TrigonometricFunctionRoots(const Standard_Real D,
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const Standard_Real E,
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const Standard_Real InfBound,
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const Standard_Real SupBound): Sol(1, 4) {
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Standard_Real A = 0.0, B = 0.0, C = 0.0;
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Perform(A, B, C, D, E, InfBound, SupBound);
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}
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math_TrigonometricFunctionRoots::math_TrigonometricFunctionRoots(const Standard_Real C,
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const Standard_Real D,
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const Standard_Real E,
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const Standard_Real InfBound,
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const Standard_Real SupBound): Sol(1, 4) {
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Standard_Real A =0.0, B = 0.0;
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Perform(A, B, C, D, E, InfBound, SupBound);
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}
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math_TrigonometricFunctionRoots::math_TrigonometricFunctionRoots(const Standard_Real A,
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const Standard_Real B,
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const Standard_Real C,
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const Standard_Real D,
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const Standard_Real E,
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const Standard_Real InfBound,
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const Standard_Real SupBound): Sol(1, 4) {
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Perform(A, B, C, D, E, InfBound, SupBound);
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}
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void math_TrigonometricFunctionRoots::Perform(const Standard_Real A,
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const Standard_Real B,
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const Standard_Real C,
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const Standard_Real D,
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const Standard_Real E,
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const Standard_Real InfBound,
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const Standard_Real SupBound) {
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Standard_Integer i, j=0, k, l, NZer=0, Nit = 10;
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Standard_Real Depi, Delta, Mod, AA, BB, CC, MyBorneInf;
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Standard_Real Teta, X;
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Standard_Real Eps, Tol1 = 1.e-15;
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TColStd_Array1OfReal ko(1,5), Zer(1,4);
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Standard_Boolean Flag4;
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InfiniteStatus = Standard_False;
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Done = Standard_True;
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Eps = 1.e-12;
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Depi = M_PI+M_PI;
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if (InfBound <= RealFirst() && SupBound >= RealLast()) {
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MyBorneInf = 0.0;
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Delta = Depi;
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Mod = 0.0;
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}
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else if (SupBound >= RealLast()) {
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MyBorneInf = InfBound;
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Delta = Depi;
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Mod = MyBorneInf/Depi;
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}
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else if (InfBound <= RealFirst()) {
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MyBorneInf = SupBound - Depi;
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Delta = Depi;
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Mod = MyBorneInf/Depi;
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}
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else {
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MyBorneInf = InfBound;
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Delta = SupBound-InfBound;
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Mod = InfBound/Depi;
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if ((SupBound-InfBound) > Depi) { Delta = Depi;}
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}
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if ((Abs(A) <= Eps) && (Abs(B) <= Eps)) {
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if (Abs(C) <= Eps) {
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if (Abs(D) <= Eps) {
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if (Abs(E) <= Eps) {
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InfiniteStatus = Standard_True; // infinite de solutions.
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return;
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}
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else {
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NbSol = 0;
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return;
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}
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}
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else {
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// Equation du type d*sin(x) + e = 0
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// =================================
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NbSol = 0;
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AA = -E/D;
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if (Abs(AA) > 1.) {
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return;
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}
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Zer(1) = ASin(AA);
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Zer(2) = M_PI - Zer(1);
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NZer = 2;
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for (i = 1; i <= NZer; i++) {
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if (Zer(i) <= -Eps) {
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Zer(i) = Depi - Abs(Zer(i));
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}
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// On rend les solutions entre InfBound et SupBound:
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// =================================================
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Zer(i) += IntegerPart(Mod)*Depi;
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X = Zer(i)-MyBorneInf;
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if ((X > (-Epsilon(Delta))) && (X < Delta+ Epsilon(Delta))) {
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NbSol++;
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Sol(NbSol) = Zer(i);
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}
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}
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}
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return;
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}
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else if (Abs(D) <= Eps) {
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// Equation du premier degre de la forme c*cos(x) + e = 0
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// ======================================================
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NbSol = 0;
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AA = -E/C;
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if (Abs(AA) >1.) {
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return;
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}
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Zer(1) = ACos(AA);
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Zer(2) = -Zer(1);
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NZer = 2;
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for (i = 1; i <= NZer; i++) {
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if (Zer(i) <= -Eps) {
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Zer(i) = Depi-Abs(Zer(i));
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}
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// On rend les solutions entre InfBound et SupBound:
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// =================================================
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Zer(i) += IntegerPart(Mod)*2.*M_PI;
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X = Zer(i)-MyBorneInf;
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if ((X >= (-Epsilon(Delta))) && (X <= Delta+ Epsilon(Delta))) {
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NbSol++;
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Sol(NbSol) = Zer(i);
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}
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}
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return;
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}
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else {
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// Equation du second degre:
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// =========================
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AA = E - C;
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BB = 2.0*D;
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CC = E + C;
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math_DirectPolynomialRoots Resol(AA, BB, CC);
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if (!Resol.IsDone()) {
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Done = Standard_False;
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return;
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}
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else if(!Resol.InfiniteRoots()) {
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NZer = Resol.NbSolutions();
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for (i = 1; i <= NZer; i++) {
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Zer(i) = Resol.Value(i);
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}
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}
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else if (Resol.InfiniteRoots()) {
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InfiniteStatus = Standard_True;
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return;
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}
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}
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}
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else {
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// Equation du 4 ieme degre
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// ========================
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ko(1) = A-C+E;
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ko(2) = 2.0*D-4.0*B;
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ko(3) = 2.0*E-2.0*A;
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ko(4) = 4.0*B+2.0*D;
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ko(5) = A+C+E;
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Standard_Boolean bko;
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Standard_Integer nbko=0;
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do {
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bko=Standard_False;
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math_DirectPolynomialRoots Resol4(ko(1), ko(2), ko(3), ko(4), ko(5));
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if (!Resol4.IsDone()) {
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Done = Standard_False;
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return;
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}
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else if (!Resol4.InfiniteRoots()) {
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NZer = Resol4.NbSolutions();
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for (i = 1; i <= NZer; i++) {
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Zer(i) = Resol4.Value(i);
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}
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}
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else if (Resol4.InfiniteRoots()) {
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InfiniteStatus = Standard_True;
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return;
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}
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Standard_Boolean triok;
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do {
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triok=Standard_True;
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for(i=1;i<NZer;i++) {
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if(Zer(i)>Zer(i+1)) {
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Standard_Real t=Zer(i);
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Zer(i)=Zer(i+1);
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Zer(i+1)=t;
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triok=Standard_False;
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}
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}
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}
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while(triok==Standard_False);
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for(i=1;i<NZer;i++) {
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if(Abs(Zer(i+1)-Zer(i))<Eps) {
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//-- est ce une racine double ou une erreur numerique ?
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Standard_Real qw=Zer(i+1);
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Standard_Real va=ko(4)+qw*(2.0*ko(3)+qw*(3.0*ko(2)+qw*(4.0*ko(1))));
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//-- cout<<" Val Double ("<<qw<<")=("<<va<<")"<<endl;
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if(Abs(va)>Eps) {
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bko=Standard_True;
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nbko++;
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#ifdef DEB
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//if(nbko==1) {
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// cout<<"Pb ds math_TrigonometricFunctionRoots CC="
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// <<A<<" CS="<<B<<" C="<<C<<" S="<<D<<" Cte="<<E<<endl;
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//}
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#endif
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break;
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}
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}
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}
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if(bko) {
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//-- Si il y a un coeff petit, on divise
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//--
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ko(1)*=0.0001;
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ko(2)*=0.0001;
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ko(3)*=0.0001;
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ko(4)*=0.0001;
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ko(5)*=0.0001;
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}
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}
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while(bko);
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}
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// Verification des solutions par rapport aux bornes:
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// ==================================================
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Standard_Real SupmInfs100 = (SupBound-InfBound)*0.01;
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NbSol = 0;
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for (i = 1; i <= NZer; i++) {
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Teta = atan(Zer(i)); Teta+=Teta;
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if (Zer(i) <= (-Eps)) {
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Teta = Depi-Abs(Teta);
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}
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Teta += IntegerPart(Mod)*Depi;
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if (Teta-MyBorneInf < 0) Teta += Depi;
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X = Teta -MyBorneInf;
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if ((X >= (-Epsilon(Delta))) && (X <= Delta+ Epsilon(Delta))) {
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X = Teta;
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// Appel de Newton:
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//OCC541(apo): Standard_Real TetaNewton=0;
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Standard_Real TetaNewton = Teta;
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MyTrigoFunction MyF(A, B, C, D, E);
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math_NewtonFunctionRoot Resol(MyF, X, Tol1, Eps, Nit);
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if (Resol.IsDone()) {
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TetaNewton = Resol.Root();
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}
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//-- lbr le 7 mars 97 (newton converge tres tres loin de la solution initilale)
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Standard_Real DeltaNewton = TetaNewton-Teta;
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if((DeltaNewton > SupmInfs100) || (DeltaNewton < -SupmInfs100)) {
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//-- cout<<"\n Newton X0="<<Teta<<" -> "<<TetaNewton<<endl;
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}
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else {
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Teta=TetaNewton;
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}
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Flag4 = Standard_False;
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for(k = 1; k <= NbSol; k++) {
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//On met les valeurs par ordre croissant:
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if (Teta < Sol(k)) {
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for (l = k; l <= NbSol; l++) {
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j = NbSol-l+k;
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Sol(j+1) = Sol(j);
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}
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Sol(k) = Teta;
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NbSol++;
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Flag4 = Standard_True;
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break;
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}
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}
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if (!Flag4) {
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NbSol++;
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Sol(NbSol) = Teta;
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}
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}
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}
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// Cas particulier de PI:
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if(NbSol<4) {
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Standard_Integer startIndex = NbSol + 1;
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for( Standard_Integer solIt = startIndex; solIt <= 4; solIt++) {
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Teta = M_PI + IntegerPart(Mod)*2.0*M_PI;;
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X = Teta - MyBorneInf;
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if ((X >= (-Epsilon(Delta))) && (X <= Delta + Epsilon(Delta))) {
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if (Abs(A-C+E) <= Eps) {
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Flag4 = Standard_False;
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for (k = 1; k <= NbSol; k++) {
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j = k;
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if (Teta < Sol(k)) {
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Flag4 = Standard_True;
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break;
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}
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if ((solIt == startIndex) && (Abs(Teta-Sol(k)) <= Eps)) {
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return;
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}
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}
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if (!Flag4) {
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NbSol++;
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Sol(NbSol) = Teta;
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}
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else {
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for (k = j; k <= NbSol; k++) {
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i = NbSol-k+j;
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Sol(i+1) = Sol(i);
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}
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Sol(j) = Teta;
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NbSol++;
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}
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}
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}
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}
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}
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}
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void math_TrigonometricFunctionRoots::Dump(Standard_OStream& o) const
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{
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o << " math_TrigonometricFunctionRoots: \n";
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if (!Done) {
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o << "Not Done \n";
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}
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else if (InfiniteStatus) {
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o << " There is an infinity of roots\n";
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}
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else if (!InfiniteStatus) {
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o << " Number of solutions = " << NbSol <<"\n";
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for (Standard_Integer i = 1; i <= NbSol; i++) {
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o << " Value number " << i << "= " << Sol(i) << "\n";
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}
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}
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}
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