// Copyright (c) 1995-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.
//-- IntAna_IntLinTorus.cxx
//-- lbr : la methode avec les coefficients est catastrophique.
//-- Mise en place d'une vraie solution.
#include <ElCLib.hxx>
#include <ElSLib.hxx>
#include <gp_Dir.hxx>
#include <gp_Lin.hxx>
#include <gp_Pnt.hxx>
#include <gp_Torus.hxx>
#include <gp_Trsf.hxx>
#include <IntAna_IntLinTorus.hxx>
#include <math_DirectPolynomialRoots.hxx>
#include <Standard_OutOfRange.hxx>
#include <StdFail_NotDone.hxx>
#include <TColStd_Array1OfReal.hxx>
IntAna_IntLinTorus::IntAna_IntLinTorus ()
: done(Standard_False),
nbpt(0)
{
memset (theFi, 0, sizeof (theFi));
memset (theParam, 0, sizeof (theParam));
memset (theTheta, 0, sizeof (theTheta));
}
IntAna_IntLinTorus::IntAna_IntLinTorus (const gp_Lin& L, const gp_Torus& T) {
Perform(L,T);
}
void IntAna_IntLinTorus::Perform (const gp_Lin& L, const gp_Torus& T) {
gp_Pnt PL=L.Location();
gp_Dir DL=L.Direction();
// Reparametrize the line:
// set its location as nearest to the location of torus
gp_Pnt TorLoc = T.Location();
Standard_Real ParamOfNewPL = gp_Vec(PL, TorLoc).Dot(gp_Vec(DL));
gp_Pnt NewPL( PL.XYZ() + ParamOfNewPL * DL.XYZ() );
//--------------------------------------------------------------
//-- Coefficients de la ligne dans le repere du cone
//--
gp_Trsf trsf;
trsf.SetTransformation(T.Position());
NewPL.Transform(trsf);
DL.Transform(trsf);
Standard_Real a,b,c,x1,y1,z1,x0,y0,z0;
Standard_Real a0,a1,a2,a3,a4;
Standard_Real R,r,R2,r2;
x1 = DL.X(); y1 = DL.Y(); z1 = DL.Z();
x0 = NewPL.X(); y0 = NewPL.Y(); z0 = NewPL.Z();
R = T.MajorRadius(); R2 = R*R;
r = T.MinorRadius(); r2 = r*r;
a = x1*x1+y1*y1+z1*z1;
b = 2.0*(x1*x0+y1*y0+z1*z0);
c = x0*x0+y0*y0+z0*z0 - (R2+r2);
a4 = a*a;
a3 = 2.0*a*b;
a2 = 2.0*a*c+4.0*R2*z1*z1+b*b;
a1 = 2.0*b*c+8.0*R2*z1*z0;
a0 = c*c+4.0*R2*(z0*z0-r2);
Standard_Real u,v;
math_DirectPolynomialRoots mdpr(a4,a3,a2,a1,a0);
if(mdpr.IsDone()) {
Standard_Integer nbsolvalid = 0;
Standard_Integer n = mdpr.NbSolutions();
Standard_Integer aNbBadSol = 0;
for(Standard_Integer i = 1; i<=n ; i++) {
Standard_Real t = mdpr.Value(i);
t += ParamOfNewPL;
gp_Pnt PSolL(ElCLib::Value(t,L));
ElSLib::Parameters(T,PSolL,u,v);
gp_Pnt PSolT(ElSLib::Value(u,v,T));
a0 = PSolT.SquareDistance(PSolL);
if(a0>0.0000000001) {
aNbBadSol++;
#if 0
std::cout<<" ------- Erreur : P Ligne < > P Tore "<<std::endl;
std::cout<<"Ligne : X:"<<PSolL.X()<<" Y:"<<PSolL.Y()<<" Z:"<<PSolL.Z()<<" l:"<<t<<std::endl;
std::cout<<"Tore : X:"<<PSolT.X()<<" Y:"<<PSolT.Y()<<" Z:"<<PSolT.Z()<<" u:"<<u<<" v:"<<v<<std::endl;
#endif
}
else {
theParam[nbsolvalid] = t;
theFi[nbsolvalid] = u;
theTheta[nbsolvalid] = v;
thePoint[nbsolvalid] = PSolL;
nbsolvalid++;
}
}
if (n > 0 && nbsolvalid == 0 && aNbBadSol == n)
{
nbpt = 0;
done = Standard_False;
}
else
{
nbpt = nbsolvalid;
done = Standard_True;
}
}
else {
nbpt = 0;
done = Standard_False;
}
}
#if 0
static void MULT_A3_B1(Standard_Real& c4,
Standard_Real& c3,
Standard_Real& c2,
Standard_Real& c1,
Standard_Real& c0,
const Standard_Real a3,
const Standard_Real a2,
const Standard_Real a1,
const Standard_Real a0,
const Standard_Real b1,
const Standard_Real b0) {
c4 = a3 * b1;
c3 = a3 * b0 + a2 * b1;
c2 = a2 * b0 + a1 * b1;
c1 = a1 * b0 + a0 * b1;
c0 = a0 * b0;
}
static void MULT_A2_B2(Standard_Real& c4,
Standard_Real& c3,
Standard_Real& c2,
Standard_Real& c1,
Standard_Real& c0,
const Standard_Real a2,
const Standard_Real a1,
const Standard_Real a0,
const Standard_Real b2,
const Standard_Real b1,
const Standard_Real b0) {
c4 = a2 * b2;
c3 = a2 * b1 + a1 * b2;
c2 = a2 * b0 + a1 * b1 + a0 * b2;
c1 = a1 * b0 + a0 * b1;
c0 = a0 * b0;
}
static void MULT_A2_B1(Standard_Real& c3,
Standard_Real& c2,
Standard_Real& c1,
Standard_Real& c0,
const Standard_Real a2,
const Standard_Real a1,
const Standard_Real a0,
const Standard_Real b1,
const Standard_Real b0) {
c3 = a2 * b1;
c2 = a2 * b0 + a1 * b1;
c1 = a1 * b0 + a0 * b1;
c0 = a0 * b0;
}
void IntAna_IntLinTorus::Perform (const gp_Lin& L, const gp_Torus& T) {
TColStd_Array1OfReal C(1,31);
T.Coefficients(C);
const gp_Pnt& PL=L.Location();
const gp_Dir& DL=L.Direction();
//----------------------------------------------------------------
//-- X = ax1 l + ax0
//-- X2 = ax2 l2 + 2 ax1 ax0 l + bx2
//-- X3 = ax3 l3 + 3 ax2 ax0 l2 + 3 ax1 bx2 l + bx3
//-- X4 = ax4 l4 + 4 ax3 ax0 l3 + 6 ax2 bx2 l2 + 4 ax1 bx3 l + bx4
Standard_Real ax1,ax2,ax3,ax4,ax0,bx2,bx3,bx4;
Standard_Real ay1,ay2,ay3,ay4,ay0,by2,by3,by4;
Standard_Real az1,az2,az3,az4,az0,bz2,bz3,bz4;
Standard_Real c0,c1,c2,c3,c4;
ax1=DL.X(); ax0=PL.X(); ay1=DL.Y(); ay0=PL.Y(); az1=DL.Z(); az0=PL.Z();
ax2=ax1*ax1; ax3=ax2*ax1; ax4=ax3*ax1; bx2=ax0*ax0; bx3=bx2*ax0; bx4=bx3*ax0;
ay2=ay1*ay1; ay3=ay2*ay1; ay4=ay3*ay1; by2=ay0*ay0; by3=by2*ay0; by4=by3*ay0;
az2=az1*az1; az3=az2*az1; az4=az3*az1; bz2=az0*az0; bz3=bz2*az0; bz4=bz3*az0;
//--------------------------------------------------------------------------- Terme X**4
Standard_Real c=C(1);
Standard_Real a4 = c *ax4;
Standard_Real a3 = c *4.0*ax3*ax0;
Standard_Real a2 = c *6.0*ax2*bx2;
Standard_Real a1 = c *4.0*ax1*bx3;
Standard_Real a0 = c *bx4;
//--------------------------------------------------------------------------- Terme Y**4
c = C(2);
a4+= c*ay4;
a3+= c*4.0*ay3*ay0;
a2+= c*6.0*ay2*by2;
a1+= c*4.0*ay1*by3;
a0+= c*by4;
//--------------------------------------------------------------------------- Terme Z**4
c = C(3);
a4+= c*az4 ;
a3+= c*4.0*az3*az0;
a2+= c*6.0*az2*bz2;
a1+= c*4.0*az1*bz3;
a0+= c*bz4;
//--------------------------------------------------------------------------- Terme X**3 Y
c = C(4);
MULT_A3_B1(c4,c3,c2,c1,c0, ax3, 3.0*ax2*ax0, 3.0*ax1*bx2, bx3, ay1,ay0);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme X**3 Z
c = C(5);
MULT_A3_B1(c4,c3,c2,c1,c0, ax3, 3.0*ax2*ax0, 3.0*ax1*bx2, bx3, az1,az0);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Y**3 X
c = C(6);
MULT_A3_B1(c4,c3,c2,c1,c0, ay3, 3.0*ay2*ay0, 3.0*ay1*by2, by3, ax1,ax0);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Y**3 Z
c = C(7);
MULT_A3_B1(c4,c3,c2,c1,c0, ay3, 3.0*ay2*ay0, 3.0*ay1*by2, by3, az1,az0);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Z**3 X
c = C(8);
MULT_A3_B1(c4,c3,c2,c1,c0, az3, 3.0*az2*az0, 3.0*az1*bz2, bz3, ax1,ax0);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Z**3 Y
c = C(9);
MULT_A3_B1(c4,c3,c2,c1,c0, az3, 3.0*az2*az0, 3.0*az1*bz2, bz3, ay1,ay0);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme X**2 Y**2
c = C(10);
MULT_A2_B2(c4,c3,c2,c1,c0, ax2, 2.0*ax1*ax0, bx2, ay2,2.0*ay1*ay0, by2);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme X**2 Z**2
c = C(11);
MULT_A2_B2(c4,c3,c2,c1,c0, ax2, 2.0*ax1*ax0, bx2, az2,2.0*az1*az0, bz2);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Y**2 Z**2
c = C(12);
MULT_A2_B2(c4,c3,c2,c1,c0, ay2, 2.0*ay1*ay0, by2, az2,2.0*az1*az0, bz2);
a4+= c*c4; a3+= c*c3; a2+= c*c2; a1+= c*c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme X**3
c = C(13);
a3+= c*( ax3 );
a2+= c*( 3.0*ax2*ax0 );
a1+= c*( 3.0*ax1*bx2 );
a0+= c*( bx3 );
//--------------------------------------------------------------------------- Terme Y**3
c = C(14);
a3+= c*( ay3 );
a2+= c*( 3.0*ay2*ay0 );
a1+= c*( 3.0*ay1*by2 );
a0+= c*( by3 );
//--------------------------------------------------------------------------- Terme Y**3
c = C(15);
a3+= c*( az3 );
a2+= c*( 3.0*az2*az0 );
a1+= c*( 3.0*az1*bz2 );
a0+= c*( bz3 );
//--------------------------------------------------------------------------- Terme X**2 Y
c = C(16);
MULT_A2_B1(c3,c2,c1,c0, ax2, 2.0*ax1*ax0, bx2, ay1,ay0);
a3+= c*c3; a2+= c* c2; a1+= c* c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme X**2 Z
c = C(17);
MULT_A2_B1(c3,c2,c1,c0, ax2, 2.0*ax1*ax0, bx2, az1,az0);
a3+= c*c3; a2+= c* c2; a1+= c* c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Y**2 X
c = C(18);
MULT_A2_B1(c3,c2,c1,c0, ay2, 2.0*ay1*ay0, by2, ax1,ax0);
a3+= c*c3; a2+= c* c2; a1+= c* c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Y**2 Z
c = C(19);
MULT_A2_B1(c3,c2,c1,c0, ay2, 2.0*ay1*ay0, by2, az1,az0);
a3+= c*c3; a2+= c* c2; a1+= c* c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Z**2 X
c = C(20);
MULT_A2_B1(c3,c2,c1,c0, az2, 2.0*az1*az0, bz2, ax1,ax0);
a3+= c*c3; a2+= c* c2; a1+= c* c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme Z**2 Y
c = C(21);
MULT_A2_B1(c3,c2,c1,c0, az2, 2.0*az1*az0, bz2, ay1,ay0);
a3+= c*c3; a2+= c* c2; a1+= c* c1; a0+= c*c0;
//--------------------------------------------------------------------------- Terme X**2
c = C(22);
a2+= c*ax2;
a1+= c*2.0*ax1*ax0;
a0+= c*bx2;
//--------------------------------------------------------------------------- Terme Y**2
c = C(23);
a2+= c*ay2;
a1+= c*2.0*ay1*ay0;
a0+= c*by2;
//--------------------------------------------------------------------------- Terme Z**2
c = C(24);
a2+= c*az2;
a1+= c*2.0*az1*az0;
a0+= c*bz2;
//--------------------------------------------------------------------------- Terme X Y
c = C(25);
a2+= c*(ax1*ay1);
a1+= c*(ax1*ay0 + ax0*ay1);
a0+= c*(ax0*ay0);
//--------------------------------------------------------------------------- Terme X Z
c = C(26);
a2+= c*(ax1*az1);
a1+= c*(ax1*az0 + ax0*az1);
a0+= c*(ax0*az0);
//--------------------------------------------------------------------------- Terme Y Z
c = C(27);
a2+= c*(ay1*az1);
a1+= c*(ay1*az0 + ay0*az1);
a0+= c*(ay0*az0);
//--------------------------------------------------------------------------- Terme X
c = C(28);
a1+= c*ax1;
a0+= c*ax0;
//--------------------------------------------------------------------------- Terme Y
c = C(29);
a1+= c*ay1;
a0+= c*ay0;
//--------------------------------------------------------------------------- Terme Z
c = C(30);
a1+= c*az1;
a0+= c*az0;
//--------------------------------------------------------------------------- Terme Constant
c = C(31);
a0+=c;
std::cout<<"\n ---------- Coefficients Line - Torus : "<<std::endl;
std::cout<<" a0 : "<<a0<<std::endl;
std::cout<<" a1 : "<<a1<<std::endl;
std::cout<<" a2 : "<<a2<<std::endl;
std::cout<<" a3 : "<<a3<<std::endl;
std::cout<<" a4 : "<<a4<<std::endl;
Standard_Real u,v;
math_DirectPolynomialRoots mdpr(a4,a3,a2,a1,a0);
if(mdpr.IsDone()) {
Standard_Integer nbsolvalid = 0;
Standard_Integer n = mdpr.NbSolutions();
for(Standard_Integer i = 1; i<=n ; i++) {
Standard_Real t = mdpr.Value(i);
gp_Pnt PSolL(ax0+ax1*t, ay0+ay1*t, az0+az1*t);
ElSLib::Parameters(T,PSolL,u,v);
gp_Pnt PSolT(ElSLib::Value(u,v,T));
a0 = PSolT.SquareDistance(PSolL);
if(a0>0.0000000001) {
std::cout<<" ------- Erreur : P Ligne < > P Tore ";
std::cout<<"Ligne : X:"<<PSolL.X()<<" Y:"<<PSolL.Y()<<" Z:"<<PSolL.Z()<<" l:"<<t<<std::endl;
std::cout<<"Tore : X:"<<PSolL.X()<<" Y:"<<PSolL.Y()<<" Z:"<<PSolL.Z()<<" u:"<<u<<" v:"<<v<<std::endl;
}
else {
theParam[nbsolvalid] = t;
theFi[nbsolvalid] = v;
theTheta[nbsolvalid] = u;
thePoint[nbsolvalid] = PSolL;
nbsolvalid++;
}
}
nbpt = nbsolvalid;
done = Standard_True;
}
else {
nbpt = 0;
done = Standard_False;
}
}
#endif