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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.
1086 lines
32 KiB
C++
1086 lines
32 KiB
C++
// Copyright (c) 1995-1999 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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#include <stdio.h>
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#include <Extrema_ExtElC.ixx>
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#include <StdFail_InfiniteSolutions.hxx>
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#include <StdFail_NotDone.hxx>
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#include <ElCLib.hxx>
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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 <Standard_NotImplemented.hxx>
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#include <Precision.hxx>
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#include <Extrema_ExtPElC.hxx>
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#include <IntAna_QuadQuadGeo.hxx>
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#include <Extrema_ExtPElC.hxx>
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#include <gp_Pln.hxx>
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#include <gp_Ax3.hxx>
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#include <gp_Ax2.hxx>
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#include <gp_Pnt.hxx>
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#include <gp_Dir.hxx>
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#include <gp_Ax1.hxx>
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static
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void RefineDir(gp_Dir& aDir);
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//=======================================================================
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//class : ExtremaExtElC_TrigonometricRoots
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//purpose :
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//== Classe Interne (Donne des racines classees d un polynome trigo)
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//== Code duplique avec IntAna_IntQuadQuad.cxx (lbr le 26 mars 98)
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//== Solution fiable aux problemes de coefficients proches de 0
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//== avec essai de rattrapage si coeff<1.e-10 (jct le 27 avril 98)
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//=======================================================================
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class ExtremaExtElC_TrigonometricRoots {
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private:
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Standard_Real Roots[4];
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Standard_Boolean done;
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Standard_Integer NbRoots;
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Standard_Boolean infinite_roots;
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public:
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ExtremaExtElC_TrigonometricRoots(const Standard_Real CC,
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const Standard_Real SC,
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const Standard_Real C,
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const Standard_Real S,
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const Standard_Real Cte,
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const Standard_Real Binf,
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const Standard_Real Bsup);
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//
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Standard_Boolean IsDone() {
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return done;
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}
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//
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Standard_Boolean IsARoot(Standard_Real u) {
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Standard_Real PIpPI, aEps;
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//
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aEps=RealEpsilon();
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PIpPI = M_PI + M_PI;
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for(Standard_Integer i=0 ; i<NbRoots; i++) {
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if(Abs(u - Roots[i])<=aEps) {
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return Standard_True ;
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}
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if(Abs(u - Roots[i]-PIpPI)<=aEps) {
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return Standard_True;
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}
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}
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return Standard_False;
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}
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//
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Standard_Integer NbSolutions() {
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if(!done) {
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StdFail_NotDone::Raise();
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}
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return NbRoots;
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}
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//
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Standard_Boolean InfiniteRoots() {
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if(!done) {
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StdFail_NotDone::Raise();
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}
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return infinite_roots;
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}
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//
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Standard_Real Value(const Standard_Integer& n) {
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if((!done)||(n>NbRoots)) {
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StdFail_NotDone::Raise();
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}
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return Roots[n-1];
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}
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};
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//=======================================================================
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//function : ExtremaExtElC_TrigonometricRoots
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//purpose :
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//=======================================================================
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ExtremaExtElC_TrigonometricRoots::
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ExtremaExtElC_TrigonometricRoots(const Standard_Real CC,
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const Standard_Real SC,
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const Standard_Real C,
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const Standard_Real S,
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const Standard_Real Cte,
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const Standard_Real Binf,
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const Standard_Real Bsup)
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{
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Standard_Integer i, nbessai;
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Standard_Real cc ,sc, c, s, cte;
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//
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nbessai = 1;
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cc = CC;
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sc = SC;
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c = C;
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s = S;
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cte = Cte;
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done=Standard_False;
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while (nbessai<=2 && !done) {
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//-- F= AA*CN*CN+2*BB*CN*SN+CC*CN+DD*SN+EE;
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math_TrigonometricFunctionRoots MTFR(cc,sc,c,s,cte,Binf,Bsup);
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//
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if(MTFR.IsDone()) {
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done=Standard_True;
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if(MTFR.InfiniteRoots()) {
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infinite_roots=Standard_True;
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}
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else { //else #1
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Standard_Boolean Triee;
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Standard_Integer j, SvNbRoots;
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Standard_Real aTwoPI, aMaxCoef, aPrecision;
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//
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aTwoPI=M_PI+M_PI;
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NbRoots=MTFR.NbSolutions();
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for(i=0;i<NbRoots;++i) {
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Roots[i]=MTFR.Value(i+1);
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if(Roots[i]<0.) {
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Roots[i]=Roots[i]+aTwoPI;
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}
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if(Roots[i]>aTwoPI) {
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Roots[i]=Roots[i]-aTwoPI;
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}
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}
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//
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//-- La recherche directe donne n importe quoi.
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aMaxCoef = Max(CC,SC);
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aMaxCoef = Max(aMaxCoef,C);
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aMaxCoef = Max(aMaxCoef,S);
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aMaxCoef = Max(aMaxCoef,Cte);
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aPrecision = Max(1.e-8, 1.e-12*aMaxCoef);
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SvNbRoots=NbRoots;
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for(i=0; i<SvNbRoots; ++i) {
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Standard_Real y;
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Standard_Real co=cos(Roots[i]);
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Standard_Real si=sin(Roots[i]);
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y=co*(CC*co + (SC+SC)*si + C) + S*si + Cte;
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// modified by OCC Tue Oct 3 18:43:00 2006
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if(Abs(y)>aPrecision) {
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NbRoots--;
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Roots[i]=1000.0;
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}
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}
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//
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do {
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Standard_Real t;
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//
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Triee=Standard_True;
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for(i=1, j=0; i<SvNbRoots; ++i, ++j) {
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if(Roots[i]<Roots[j]) {
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Triee=Standard_False;
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t=Roots[i];
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Roots[i]=Roots[j];
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Roots[j]=t;
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}
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}
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}
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while(!Triee);
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//
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infinite_roots=Standard_False;
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if(NbRoots==0) { //--!!!!! Detect case Pol = Cte ( 1e-50 ) !!!!
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if((Abs(CC) + Abs(SC) + Abs(C) + Abs(S)) < 1e-10) {
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if(Abs(Cte) < 1e-10) {
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infinite_roots=Standard_True;
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}
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}
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}
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} // else #1
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} // if(MTFR.IsDone()) {
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else {
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// try to set very small coefficients to ZERO
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if (Abs(CC)<1e-10) {
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cc = 0.0;
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}
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if (Abs(SC)<1e-10) {
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sc = 0.0;
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}
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if (Abs(C)<1e-10) {
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c = 0.0;
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}
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if (Abs(S)<1e-10){
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s = 0.0;
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}
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if (Abs(Cte)<1e-10){
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cte = 0.0;
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}
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nbessai++;
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}
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} // while (nbessai<=2 && !done) {
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}
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//=======================================================================
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//function : Extrema_ExtElC
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//purpose :
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//=======================================================================
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Extrema_ExtElC::Extrema_ExtElC ()
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{
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myDone = Standard_False;
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}
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//=======================================================================
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//function : Extrema_ExtElC
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//purpose :
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//=======================================================================
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Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
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const gp_Lin& C2,
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const Standard_Real)
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// Function:
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// Find min distance between 2 straight lines.
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// Method:
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// Let D1 and D2, be 2 directions of straight lines C1 and C2.
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// 2 cases are considered:
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// 1- if Angle(D1,D2) < AngTol, straight lines are parallel.
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// The distance is the distance between a point of C1 and the straight line C2.
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// 2- if Angle(D1,D2) > AngTol:
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// Let P1=C1(u1) and P2=C2(u2) be 2 solution points:
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// Then, ( P1P2.D1 = 0. (1)
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// ( P1P2.D2 = 0. (2)
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// Let O1 and O2 be the origins of C1 and C2;
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// THen, (1) <=> (O1P2-u1*D1).D1 = 0. as O1P1 = u1*D1
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// <=> u1 = O1P2.D1 as D1.D1 = 1.
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// (2) <=> (P1O2+u2*D2).D2 = 0. as O2P2 = u2*D2
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// <=> u2 = O2P1.D2 as D2.D2 = 1.
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// <=> u2 = (O2O1+O1P1).D2
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// <=> u2 = O2O1.D2+((O1P2.T1)T1).T2) as O1P1 = u1*T1 = (O1P2.T1)T1
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// <=> u2 = O2O1.D2+(((O1O2+O2P2).D1)D1).D2)
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// <=> u2 = O2O1.D2+((O1O2.D1)D1).D2)+(O2P2.D1)(D1.D2)
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// <=> u2 = ((O1O2.D1)D1-O1O2).D2 + u2*(D2.D1)(D1.D2)
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// <=> u2 = (((O1O2.D1)D1-O1O2).D2) / 1.-(D1.D2)**2
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{
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myDone = Standard_False;
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myNbExt = 0;
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gp_Dir D1 = C1.Position().Direction();
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gp_Dir D2 = C2.Position().Direction();
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// MSV 16/01/2000: avoid "divide by zero"
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Standard_Real D1DotD2 = D1.Dot(D2);
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Standard_Real aSin = 1.-D1DotD2*D1DotD2;
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if (aSin < gp::Resolution() ||
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D1.IsParallel(D2, Precision::Angular())) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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myIsPar = Standard_False;
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gp_Pnt O1 = C1.Location();
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gp_Pnt O2 = C2.Location();
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gp_Vec O1O2 (O1,O2);
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Standard_Real U2 = (D1.XYZ()*(O1O2.Dot(D1))-(O1O2.XYZ())).Dot(D2.XYZ());
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if( Precision::IsInfinite(U2) ) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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U2 /= aSin;
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if( Precision::IsInfinite(U2) ) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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gp_Pnt P2(ElCLib::Value(U2,C2));
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Standard_Real U1 = (gp_Vec(O1,P2)).Dot(D1);
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if( Precision::IsInfinite(U1) ) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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gp_Pnt P1(ElCLib::Value(U1,C1));
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mySqDist[myNbExt] = P1.SquareDistance(P2);
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myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
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myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
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myNbExt = 1;
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}
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}
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}
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}
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myDone = Standard_True;
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}
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//=======================================================================
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//function : Extrema_ExtElC
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//purpose :
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// Find extreme distances between straight line C1 and circle C2.
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//
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//Method:
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// Let P1=C1(u1) and P2=C2(u2) be two solution points
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// D the direction of straight line C1
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// T tangent at point P2;
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// Then, ( P1P2.D = 0. (1)
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// ( P1P2.T = 0. (2)
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// Let O1 and O2 be the origins of C1 and C2;
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// Then, (1) <=> (O1P2-u1*D).D = 0. as O1P1 = u1*D
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// <=> u1 = O1P2.D as D.D = 1.
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// (2) <=> P1O2.T = 0. as O2P2.T = 0.
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// <=> ((P2O1.D)D+O1O2).T = 0. as P1O1 = -u1*D = (P2O1.D)D
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// <=> (((P2O2+O2O1).D)D+O1O2).T = 0.
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// <=> ((P2O2.D)(D.T)+((O2O1.D)D-O2O1).T = 0.
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// We are in the reference of the circle; let:
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// Cos = Cos(u2) and Sin = Sin(u2),
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// P2 (R*Cos,R*Sin,0.),
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// T (-R*Sin,R*Cos,0.),
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// D (Dx,Dy,Dz),
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// V (Vx,Vy,Vz) = (O2O1.D)D-O2O1;
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// Then, the equation by Cos and Sin is as follows:
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// -(2*R*R*Dx*Dy) * Cos**2 + A1
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// R*R*(Dx**2-Dy**2) * Cos*Sin + 2* A2
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// R*Vy * Cos + A3
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// -R*Vx * Sin + A4
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// R*R*Dx*Dy = 0. A5
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//Use the algorithm math_TrigonometricFunctionRoots to solve this equation.
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//=======================================================================
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Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
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const gp_Circ& C2,
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const Standard_Real)
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{
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Standard_Real Dx,Dy,Dz,aRO2O1, aTolRO2O1;
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Standard_Real R, A1, A2, A3, A4, A5, aTol;
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gp_Dir x2, y2, z2, D, D1;
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//
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myIsPar = Standard_False;
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myDone = Standard_False;
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myNbExt = 0;
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// Calculate T1 in the reference of the circle ...
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D = C1.Direction();
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D1 = D;
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x2 = C2.XAxis().Direction();
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y2 = C2.YAxis().Direction();
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z2 = C2.Axis().Direction();
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Dx = D.Dot(x2);
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Dy = D.Dot(y2);
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Dz = D.Dot(z2);
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//
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D.SetCoord(Dx, Dy, Dz);
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RefineDir(D);
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D.Coord(Dx, Dy, Dz);
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//
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// Calcul de V dans le repere du cercle:
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gp_Pnt O1 = C1.Location();
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gp_Pnt O2 = C2.Location();
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gp_Vec O2O1 (O2,O1);
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//
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aTolRO2O1=gp::Resolution();
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aRO2O1=O2O1.Magnitude();
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if (aRO2O1 > aTolRO2O1) {
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gp_Dir aDO2O1;
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//
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O2O1.Multiply(1./aRO2O1);
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aDO2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
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RefineDir(aDO2O1);
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O2O1.SetXYZ(aRO2O1*aDO2O1.XYZ());
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}
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else {
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O2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
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}
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//
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gp_XYZ Vxyz = (D.XYZ()*(O2O1.Dot(D)))-O2O1.XYZ();
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//
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//modified by NIZNHY-PKV Tue Mar 20 10:36:38 2012
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/*
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R = C2.Radius();
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A5 = R*R*Dx*Dy;
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A1 = -2.*A5;
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A2 = R*R*(Dx*Dx-Dy*Dy)/2.;
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A3 = R*Vxyz.Y();
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A4 = -R*Vxyz.X();
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//
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aTol=1.e-12;
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//
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if(fabs(A5) <= aTol) {
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A5 = 0.;
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}
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if(fabs(A1) <= aTol) {
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A1 = 0.;
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}
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if(fabs(A2) <= aTol) {
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A2 = 0.;
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}
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if(fabs(A3) <= aTol) {
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A3 = 0.;
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}
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if(fabs(A4) <= aTol) {
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A4 = 0.;
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}
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*/
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//
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aTol=1.e-12;
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// Calculate the coefficients of the equation by Cos and Sin ...
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// [divided by R]
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R = C2.Radius();
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A5 = R*Dx*Dy;
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A1 = -2.*A5;
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A2 = 0.5*R*(Dx*Dx-Dy*Dy);// /2.;
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A3 = Vxyz.Y();
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A4 = -Vxyz.X();
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//
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if (A1>=-aTol && A1<=aTol) {
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A1 = 0.;
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}
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if (A2>=-aTol && A2<=aTol) {
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A2 = 0.;
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}
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if (A3>=-aTol && A3<=aTol) {
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A3 = 0.;
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}
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if (A4>=-aTol && A4<=aTol) {
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A4 = 0.;
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}
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if (A5>=-aTol && A5<=aTol) {
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A5 = 0.;
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}
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//modified by NIZNHY-PKV Tue Mar 20 10:36:40 2012t
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//
|
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ExtremaExtElC_TrigonometricRoots Sol(A1, A2, A3, A4, A5, 0., M_PI+M_PI);
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if (!Sol.IsDone()) {
|
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return;
|
|
}
|
|
if (Sol.InfiniteRoots()) {
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myIsPar = Standard_True;
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mySqDist[0] = R*R;
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myDone = Standard_True;
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return;
|
|
}
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// Storage of solutions ...
|
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Standard_Integer NoSol, NbSol;
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Standard_Real U1,U2;
|
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gp_Pnt P1,P2;
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//
|
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NbSol = Sol.NbSolutions();
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for (NoSol=1; NoSol<=NbSol; ++NoSol) {
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U2 = Sol.Value(NoSol);
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P2 = ElCLib::Value(U2,C2);
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U1 = (gp_Vec(O1,P2)).Dot(D1);
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P1 = ElCLib::Value(U1,C1);
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mySqDist[myNbExt] = P1.SquareDistance(P2);
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//modified by NIZNHY-PKV Wed Mar 21 08:11:33 2012f
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//myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
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//myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
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myPoint[myNbExt][0].SetValues(U1,P1);
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myPoint[myNbExt][1].SetValues(U2,P2);
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//modified by NIZNHY-PKV Wed Mar 21 08:11:36 2012t
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myNbExt++;
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}
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myDone = Standard_True;
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}
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//=======================================================================
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//function : Extrema_ExtElC
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//purpose :
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//=======================================================================
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Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
|
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const gp_Elips& C2)
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{
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/*-----------------------------------------------------------------------------
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Function:
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Find extreme distances between straight line C1 and ellipse C2.
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|
|
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Method:
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Let P1=C1(u1) and P2=C2(u2) two solution points
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D the direction of straight line C1
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T the tangent to point P2;
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Then, ( P1P2.D = 0. (1)
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( P1P2.T = 0. (2)
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Let O1 and O2 be the origins of C1 and C2;
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Then, (1) <=> (O1P2-u1*D).D = 0. as O1P1 = u1*D
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<=> u1 = O1P2.D as D.D = 1.
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(2) <=> P1O2.T = 0. as O2P2.T = 0.
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<=> ((P2O1.D)D+O1O2).T = 0. as P1O1 = -u1*D = (P2O1.D)D
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<=> (((P2O2+O2O1).D)D+O1O2).T = 0.
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<=> ((P2O2.D)(D.T)+((O2O1.D)D-O2O1).T = 0.
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We are in the reference of the ellipse; let:
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Cos = Cos(u2) and Sin = Sin(u2),
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P2 (MajR*Cos,MinR*Sin,0.),
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T (-MajR*Sin,MinR*Cos,0.),
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D (Dx,Dy,Dz),
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V (Vx,Vy,Vz) = (O2O1.D)D-O2O1;
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Then, get the following equation by Cos and Sin:
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-(2*MajR*MinR*Dx*Dy) * Cos**2 +
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(MajR*MajR*Dx**2-MinR*MinR*Dy**2) * Cos*Sin +
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MinR*Vy * Cos +
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- MajR*Vx * Sin +
|
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MinR*MajR*Dx*Dy = 0.
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Use algorithm math_TrigonometricFunctionRoots to solve this equation.
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-----------------------------------------------------------------------------*/
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myIsPar = Standard_False;
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myDone = Standard_False;
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myNbExt = 0;
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// Calculate T1 the reference of the ellipse ...
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gp_Dir D = C1.Direction();
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gp_Dir D1 = D;
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gp_Dir x2, y2, z2;
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x2 = C2.XAxis().Direction();
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y2 = C2.YAxis().Direction();
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z2 = C2.Axis().Direction();
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Standard_Real Dx = D.Dot(x2);
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Standard_Real Dy = D.Dot(y2);
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Standard_Real Dz = D.Dot(z2);
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D.SetCoord(Dx,Dy,Dz);
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// Calculate V ...
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gp_Pnt O1 = C1.Location();
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gp_Pnt O2 = C2.Location();
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gp_Vec O2O1 (O2,O1);
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O2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
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gp_XYZ Vxyz = (D.XYZ()*(O2O1.Dot(D)))-O2O1.XYZ();
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// Calculate the coefficients of the equation by Cos and Sin ...
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Standard_Real MajR = C2.MajorRadius();
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Standard_Real MinR = C2.MinorRadius();
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Standard_Real A5 = MajR*MinR*Dx*Dy;
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Standard_Real A1 = -2.*A5;
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Standard_Real R2 = MajR*MajR;
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Standard_Real r2 = MinR*MinR;
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Standard_Real A2 =(R2*Dx*Dx -r2*Dy*Dy -R2 +r2)/2.0;
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Standard_Real A3 = MinR*Vxyz.Y();
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Standard_Real A4 = -MajR*Vxyz.X();
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|
//
|
|
Standard_Real aEps=1.e-12;
|
|
//
|
|
if(fabs(A5) <= aEps) A5 = 0.;
|
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if(fabs(A1) <= aEps) A1 = 0.;
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if(fabs(A2) <= aEps) A2 = 0.;
|
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if(fabs(A3) <= aEps) A3 = 0.;
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if(fabs(A4) <= aEps) A4 = 0.;
|
|
//
|
|
ExtremaExtElC_TrigonometricRoots Sol(A1,A2,A3,A4,A5,0.,M_PI+M_PI);
|
|
if (!Sol.IsDone()) { return; }
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|
|
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// Storage of solutions ...
|
|
gp_Pnt P1,P2;
|
|
Standard_Real U1,U2;
|
|
Standard_Integer NbSol = Sol.NbSolutions();
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|
for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
|
|
U2 = Sol.Value(NoSol);
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P2 = ElCLib::Value(U2,C2);
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U1 = (gp_Vec(O1,P2)).Dot(D1);
|
|
P1 = ElCLib::Value(U1,C1);
|
|
mySqDist[myNbExt] = P1.SquareDistance(P2);
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myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
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myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
|
|
myNbExt++;
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|
}
|
|
myDone = Standard_True;
|
|
}
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|
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
|
|
const gp_Hypr& C2)
|
|
{
|
|
/*-----------------------------------------------------------------------------
|
|
Function:
|
|
Find extrema between straight line C1 and hyperbola C2.
|
|
|
|
Method:
|
|
Let P1=C1(u1) and P2=C2(u2) be two solution points
|
|
D the direction of straight line C1
|
|
T the tangent at point P2;
|
|
Then, ( P1P2.D = 0. (1)
|
|
( P1P2.T = 0. (2)
|
|
Let O1 and O2 be the origins of C1 and C2;
|
|
Then, (1) <=> (O1P2-u1*D).D = 0. as O1P1 = u1*D
|
|
<=> u1 = O1P2.D as D.D = 1.
|
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(2) <=> (P1O2 + O2P2).T= 0.
|
|
<=> ((P2O1.D)D+O1O2 + O2P2).T = 0. as P1O1 = -u1*D = (P2O1.D)D
|
|
<=> (((P2O2+O2O1).D)D+O1O2 + O2P2).T = 0.
|
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<=> (P2O2.D)(D.T)+((O2O1.D)D-O2O1).T + O2P2.T= 0.
|
|
We are in the reference of the hyperbola; let:
|
|
by writing P (R* Chu, r* Shu, 0.0)
|
|
and Chu = (v**2 + 1)/(2*v) ,
|
|
Shu = (V**2 - 1)/(2*v)
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|
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T(R*Shu, r*Chu)
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D (Dx,Dy,Dz),
|
|
V (Vx,Vy,Vz) = (O2O1.D)D-O2O1;
|
|
|
|
Then we obtain the following equation by v:
|
|
(-2*R*r*Dx*Dy - R*R*Dx*Dx-r*r*Dy*Dy + R*R + r*r) * v**4 +
|
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(2*R*Vx + 2*r*Vy) * v**3 +
|
|
(-2*R*Vx + 2*r*Vy) * v +
|
|
(-2*R*r*Dx*Dy - (R*R*Dx*Dx-r*r*Dy*Dy + R*R + r*r)) = 0
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|
|
|
|
|
Use the algorithm math_DirectPolynomialRoots to solve this equation.
|
|
-----------------------------------------------------------------------------*/
|
|
myIsPar = Standard_False;
|
|
myDone = Standard_False;
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|
myNbExt = 0;
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|
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// Calculate T1 in the reference of the hyperbola...
|
|
gp_Dir D = C1.Direction();
|
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gp_Dir D1 = D;
|
|
gp_Dir x2, y2, z2;
|
|
x2 = C2.XAxis().Direction();
|
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y2 = C2.YAxis().Direction();
|
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z2 = C2.Axis().Direction();
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Standard_Real Dx = D.Dot(x2);
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Standard_Real Dy = D.Dot(y2);
|
|
Standard_Real Dz = D.Dot(z2);
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D.SetCoord(Dx,Dy,Dz);
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|
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// Calculate V ...
|
|
gp_Pnt O1 = C1.Location();
|
|
gp_Pnt O2 = C2.Location();
|
|
gp_Vec O2O1 (O2,O1);
|
|
O2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
|
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gp_XYZ Vxyz = (D.XYZ()*(O2O1.Dot(D)))-O2O1.XYZ();
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Standard_Real Vx = Vxyz.X();
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Standard_Real Vy = Vxyz.Y();
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|
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// Calculate coefficients of the equation by v
|
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Standard_Real R = C2.MajorRadius();
|
|
Standard_Real r = C2.MinorRadius();
|
|
Standard_Real a = -2*R*r*Dx*Dy;
|
|
Standard_Real b = -R*R*Dx*Dx - r*r*Dy*Dy + R*R + r*r;
|
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Standard_Real A1 = a + b;
|
|
Standard_Real A2 = 2*R*Vx + 2*r*Vy;
|
|
Standard_Real A4 = -2*R*Vx + 2*r*Vy;
|
|
Standard_Real A5 = a - b;
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|
|
math_DirectPolynomialRoots Sol(A1,A2,0.0,A4, A5);
|
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if (!Sol.IsDone()) { return; }
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|
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// Store solutions ...
|
|
gp_Pnt P1,P2;
|
|
Standard_Real U1,U2, v;
|
|
Standard_Integer NbSol = Sol.NbSolutions();
|
|
for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
|
|
v = Sol.Value(NoSol);
|
|
if (v > 0.0) {
|
|
U2 = Log(v);
|
|
P2 = ElCLib::Value(U2,C2);
|
|
U1 = (gp_Vec(O1,P2)).Dot(D1);
|
|
P1 = ElCLib::Value(U1,C1);
|
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mySqDist[myNbExt] = P1.SquareDistance(P2);
|
|
myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
|
|
myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
|
|
myNbExt++;
|
|
}
|
|
}
|
|
myDone = Standard_True;
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
|
|
const gp_Parab& C2)
|
|
{
|
|
/*-----------------------------------------------------------------------------
|
|
Function:
|
|
Find extreme distances between straight line C1 and parabole C2.
|
|
|
|
Method:
|
|
Let P1=C1(u1) and P2=C2(u2) be two solution points
|
|
D the direction of straight line C1
|
|
T the tangent to point P2;
|
|
Then, ( P1P2.D = 0. (1)
|
|
( P1P2.T = 0. (2)
|
|
Let O1 and O2 be the origins of C1 and C2;
|
|
Then, (1) <=> (O1P2-u1*D).D = 0. as O1P1 = u1*D
|
|
<=> u1 = O1P2.D as D.D = 1.
|
|
(2) <=> (P1O2 + O2P2).T= 0.
|
|
<=> ((P2O1.D)D+O1O2 + O2P2).T = 0. as P1O1 = -u1*D = (P2O1.D)D
|
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<=> (((P2O2+O2O1).D)D+O1O2 + O2P2).T = 0.
|
|
<=> (P2O2.D)(D.T)+((O2O1.D)D-O2O1).T + O2P2.T = 0.
|
|
We are in the reference of the parabola; let:
|
|
P2 (y*y/(2*p), y, 0)
|
|
T (y/p, 1, 0)
|
|
D (Dx,Dy,Dz),
|
|
V (Vx,Vy,Vz) = (O2O1.D)D-O2O1;
|
|
|
|
Then, get the following equation by y:
|
|
((1-Dx*Dx)/(2*p*p)) * y*y*y + A1
|
|
(-3*Dx*Dy/(2*p)) * y*y + A2
|
|
(1-Dy*Dy + Vx/p) * y + A3
|
|
Vy = 0. A4
|
|
|
|
Use the algorithm math_DirectPolynomialRoots to solve this equation.
|
|
-----------------------------------------------------------------------------*/
|
|
myIsPar = Standard_False;
|
|
myDone = Standard_False;
|
|
myNbExt = 0;
|
|
|
|
// Calculate T1 in the reference of the parabola...
|
|
gp_Dir D = C1.Direction();
|
|
gp_Dir D1 = D;
|
|
gp_Dir x2, y2, z2;
|
|
x2 = C2.XAxis().Direction();
|
|
y2 = C2.YAxis().Direction();
|
|
z2 = C2.Axis().Direction();
|
|
Standard_Real Dx = D.Dot(x2);
|
|
Standard_Real Dy = D.Dot(y2);
|
|
Standard_Real Dz = D.Dot(z2);
|
|
D.SetCoord(Dx,Dy,Dz);
|
|
|
|
// Calculate V ...
|
|
gp_Pnt O1 = C1.Location();
|
|
gp_Pnt O2 = C2.Location();
|
|
gp_Vec O2O1 (O2,O1);
|
|
O2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
|
|
gp_XYZ Vxyz = (D.XYZ()*(O2O1.Dot(D)))-O2O1.XYZ();
|
|
|
|
// Calculate coefficients of the equation by y
|
|
Standard_Real P = C2.Parameter();
|
|
Standard_Real A1 = (1-Dx*Dx)/(2.0*P*P);
|
|
Standard_Real A2 = (-3.0*Dx*Dy/(2.0*P));
|
|
Standard_Real A3 = (1 - Dy*Dy + Vxyz.X()/P);
|
|
Standard_Real A4 = Vxyz.Y();
|
|
|
|
math_DirectPolynomialRoots Sol(A1,A2,A3,A4);
|
|
if (!Sol.IsDone()) { return; }
|
|
|
|
// Storage of solutions ...
|
|
gp_Pnt P1,P2;
|
|
Standard_Real U1,U2;
|
|
Standard_Integer NbSol = Sol.NbSolutions();
|
|
for (Standard_Integer NoSol = 1; NoSol <= NbSol; NoSol++) {
|
|
U2 = Sol.Value(NoSol);
|
|
P2 = ElCLib::Value(U2,C2);
|
|
U1 = (gp_Vec(O1,P2)).Dot(D1);
|
|
P1 = ElCLib::Value(U1,C1);
|
|
mySqDist[myNbExt] = P1.SquareDistance(P2);
|
|
myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
|
|
myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
|
|
myNbExt++;
|
|
}
|
|
myDone = Standard_True;
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Circ& C1,
|
|
const gp_Circ& C2)
|
|
{
|
|
Standard_Boolean bIsSamePlane, bIsSameAxe;
|
|
Standard_Real aTolD, aTolD2, aTolA, aD2, aDC2;
|
|
gp_Pnt aPc1, aPc2;
|
|
gp_Dir aDc1, aDc2;
|
|
//
|
|
myIsPar = Standard_False;
|
|
myDone = Standard_False;
|
|
myNbExt = 0;
|
|
//
|
|
aTolA=Precision::Angular();
|
|
aTolD=Precision::Confusion();
|
|
aTolD2=aTolD*aTolD;
|
|
//
|
|
aPc1=C1.Location();
|
|
aDc1=C1.Axis().Direction();
|
|
|
|
aPc2=C2.Location();
|
|
aDc2=C2.Axis().Direction();
|
|
gp_Pln aPlc1(aPc1, aDc1);
|
|
//
|
|
aD2=aPlc1.SquareDistance(aPc2);
|
|
bIsSamePlane=aDc1.IsParallel(aDc2, aTolA) && aD2<aTolD2;
|
|
if (!bIsSamePlane) {
|
|
return;
|
|
}
|
|
//
|
|
aDC2=aPc1.SquareDistance(aPc2);
|
|
bIsSameAxe=aDC2<aTolD2;
|
|
//
|
|
if(bIsSameAxe) {
|
|
myIsPar = Standard_True;
|
|
Standard_Real dR = C1.Radius() - C2.Radius();
|
|
Standard_Real dC = C1.Location().Distance(C2.Location());
|
|
mySqDist[0] = dR*dR + dC*dC;
|
|
dR = C1.Radius() + C2.Radius();
|
|
mySqDist[1] = dR*dR + dC*dC;
|
|
myDone = Standard_True;
|
|
}
|
|
else {
|
|
Standard_Boolean bIn, bOut;
|
|
Standard_Integer j1, j2;
|
|
Standard_Real aR1, aR2, aD12, aT11, aT12, aT21, aT22;
|
|
gp_Circ aC1, aC2;
|
|
gp_Pnt aP11, aP12, aP21, aP22;
|
|
//
|
|
myDone = Standard_True;
|
|
//
|
|
aR1=C1.Radius();
|
|
aR2=C2.Radius();
|
|
//
|
|
j1=0;
|
|
j2=1;
|
|
aC1=C1;
|
|
aC2=C2;
|
|
if (aR2>aR1) {
|
|
j1=1;
|
|
j2=0;
|
|
aC1=C2;
|
|
aC2=C1;
|
|
}
|
|
//
|
|
aR1=aC1.Radius(); // max radius
|
|
aR2=aC2.Radius(); // min radius
|
|
//
|
|
aPc1=aC1.Location();
|
|
aPc2=aC2.Location();
|
|
//
|
|
aD12=aPc1.Distance(aPc2);
|
|
gp_Vec aVec12(aPc1, aPc2);
|
|
gp_Dir aDir12(aVec12);
|
|
//
|
|
// 1. Four common solutions
|
|
myNbExt=4;
|
|
//
|
|
aP11.SetXYZ(aPc1.XYZ()-aR1*aDir12.XYZ());
|
|
aP12.SetXYZ(aPc1.XYZ()+aR1*aDir12.XYZ());
|
|
aP21.SetXYZ(aPc2.XYZ()-aR2*aDir12.XYZ());
|
|
aP22.SetXYZ(aPc2.XYZ()+aR2*aDir12.XYZ());
|
|
//
|
|
aT11=ElCLib::Parameter(aC1, aP11);
|
|
aT12=ElCLib::Parameter(aC1, aP12);
|
|
aT21=ElCLib::Parameter(aC2, aP21);
|
|
aT22=ElCLib::Parameter(aC2, aP22);
|
|
//
|
|
// P11, P21
|
|
myPoint[0][j1].SetValues(aT11, aP11);
|
|
myPoint[0][j2].SetValues(aT21, aP21);
|
|
mySqDist[0]=aP11.SquareDistance(aP21);
|
|
// P11, P22
|
|
myPoint[1][j1].SetValues(aT11, aP11);
|
|
myPoint[1][j2].SetValues(aT22, aP22);
|
|
mySqDist[1]=aP11.SquareDistance(aP22);
|
|
//
|
|
// P12, P21
|
|
myPoint[2][j1].SetValues(aT12, aP12);
|
|
myPoint[2][j2].SetValues(aT21, aP21);
|
|
mySqDist[2]=aP12.SquareDistance(aP21);
|
|
//
|
|
// P12, P22
|
|
myPoint[3][j1].SetValues(aT12, aP12);
|
|
myPoint[3][j2].SetValues(aT22, aP22);
|
|
mySqDist[3]=aP12.SquareDistance(aP22);
|
|
//
|
|
// 2. Check for intersections
|
|
bOut=aD12>(aR1+aR2+aTolD);
|
|
bIn =aD12<(aR1-aR2-aTolD);
|
|
if (!bOut && !bIn) {
|
|
Standard_Boolean bNbExt6;
|
|
Standard_Real aAlpha, aBeta, aT[2], aVal, aDist2;
|
|
gp_Pnt aPt, aPL1, aPL2;
|
|
gp_Dir aDLt;
|
|
//
|
|
aAlpha=0.5*(aR1*aR1-aR2*aR2+aD12*aD12)/aD12;
|
|
aVal=aR1*aR1-aAlpha*aAlpha;
|
|
if (aVal<0.) {// see pkv/900/L4 for details
|
|
aVal=-aVal;
|
|
}
|
|
aBeta=Sqrt(aVal);
|
|
//aBeta=Sqrt(aR1*aR1-aAlpha*aAlpha);
|
|
//--
|
|
aPt.SetXYZ(aPc1.XYZ()+aAlpha*aDir12.XYZ());
|
|
//
|
|
aDLt=aDc1^aDir12;
|
|
aPL1.SetXYZ(aPt.XYZ()+aBeta*aDLt.XYZ());
|
|
aPL2.SetXYZ(aPt.XYZ()-aBeta*aDLt.XYZ());
|
|
//
|
|
aDist2=aPL1.SquareDistance(aPL2);
|
|
bNbExt6=aDist2>aTolD2;
|
|
//
|
|
myNbExt=5;// just in case. see pkv/900/L4 for details
|
|
aT[j1]=ElCLib::Parameter(aC1, aPL1);
|
|
aT[j2]=ElCLib::Parameter(aC2, aPL1);
|
|
myPoint[4][j1].SetValues(aT[j1], aPL1);
|
|
myPoint[4][j2].SetValues(aT[j2], aPL1);
|
|
mySqDist[4]=0.;
|
|
//
|
|
if (bNbExt6) {
|
|
myNbExt=6;
|
|
aT[j1]=ElCLib::Parameter(aC1, aPL2);
|
|
aT[j2]=ElCLib::Parameter(aC2, aPL2);
|
|
myPoint[5][j1].SetValues(aT[j1], aPL2);
|
|
myPoint[5][j2].SetValues(aT[j2], aPL2);
|
|
mySqDist[5]=0.;
|
|
}
|
|
//
|
|
}// if (!bOut || !bIn) {
|
|
}// else
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Circ&, const gp_Elips&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Circ&, const gp_Hypr&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Circ&, const gp_Parab&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Elips&, const gp_Elips&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Elips&, const gp_Hypr&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Elips&, const gp_Parab&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Hypr&, const gp_Hypr&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Hypr&, const gp_Parab&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : Extrema_ExtElC
|
|
//purpose :
|
|
//=======================================================================
|
|
Extrema_ExtElC::Extrema_ExtElC (const gp_Parab&, const gp_Parab&)
|
|
{
|
|
Standard_NotImplemented::Raise();
|
|
}
|
|
//=======================================================================
|
|
//function : IsDone
|
|
//purpose :
|
|
//=======================================================================
|
|
Standard_Boolean Extrema_ExtElC::IsDone () const {
|
|
return myDone;
|
|
}
|
|
//=======================================================================
|
|
//function : IsParallel
|
|
//purpose :
|
|
//=======================================================================
|
|
Standard_Boolean Extrema_ExtElC::IsParallel () const
|
|
{
|
|
if (!IsDone()) {
|
|
StdFail_NotDone::Raise();
|
|
}
|
|
return myIsPar;
|
|
}
|
|
//=======================================================================
|
|
//function : NbExt
|
|
//purpose :
|
|
//=======================================================================
|
|
Standard_Integer Extrema_ExtElC::NbExt () const
|
|
{
|
|
if (IsParallel()) {
|
|
StdFail_InfiniteSolutions::Raise();
|
|
}
|
|
return myNbExt;
|
|
}
|
|
//=======================================================================
|
|
//function : SquareDistance
|
|
//purpose :
|
|
//=======================================================================
|
|
Standard_Real Extrema_ExtElC::SquareDistance (const Standard_Integer N) const
|
|
{
|
|
if (!myDone) {
|
|
StdFail_NotDone::Raise();
|
|
}
|
|
if (myIsPar) {
|
|
if (N < 1 || N > 2) {
|
|
Standard_OutOfRange::Raise();
|
|
}
|
|
}
|
|
else {
|
|
if (N < 1 || N > NbExt()) {
|
|
Standard_OutOfRange::Raise();
|
|
}
|
|
}
|
|
return mySqDist[N-1];
|
|
}
|
|
//=======================================================================
|
|
//function : Points
|
|
//purpose :
|
|
//=======================================================================
|
|
void Extrema_ExtElC::Points (const Standard_Integer N,
|
|
Extrema_POnCurv& P1,
|
|
Extrema_POnCurv& P2) const
|
|
{
|
|
if (N < 1 || N > NbExt()) {
|
|
Standard_OutOfRange::Raise();
|
|
}
|
|
P1 = myPoint[N-1][0];
|
|
P2 = myPoint[N-1][1];
|
|
}
|
|
|
|
|
|
//=======================================================================
|
|
//function : RefineDir
|
|
//purpose :
|
|
//=======================================================================
|
|
void RefineDir(gp_Dir& aDir)
|
|
{
|
|
Standard_Integer i, j, k, iK;
|
|
Standard_Real aCx[3], aEps, aX1, aX2, aOne;
|
|
//
|
|
iK=3;
|
|
aEps=RealEpsilon();
|
|
aDir.Coord(aCx[0], aCx[1], aCx[2]);
|
|
//
|
|
for (i=0; i<iK; ++i) {
|
|
aOne=(aCx[i]>0.) ? 1. : -1.;
|
|
aX1=aOne-aEps;
|
|
aX2=aOne+aEps;
|
|
//
|
|
if (aCx[i]>aX1 && aCx[i]<aX2) {
|
|
j=(i+1)%iK;
|
|
k=(i+2)%iK;
|
|
aCx[i]=aOne;
|
|
aCx[j]=0.;
|
|
aCx[k]=0.;
|
|
aDir.SetCoord(aCx[0], aCx[1], aCx[2]);
|
|
return;
|
|
}
|
|
}
|
|
}
|