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occt/src/Extrema/Extrema_ExtElC.cxx

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// 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.
#include <ElCLib.hxx>
#include <Extrema_ExtElC.hxx>
#include <Extrema_ExtElC2d.hxx>
#include <Extrema_POnCurv.hxx>
#include <gp_Ax1.hxx>
#include <gp_Ax2.hxx>
#include <gp_Circ.hxx>
#include <gp_Circ2d.hxx>
#include <gp_Dir.hxx>
#include <gp_Elips.hxx>
#include <gp_Hypr.hxx>
#include <gp_Lin.hxx>
#include <gp_Lin2d.hxx>
#include <gp_Parab.hxx>
#include <gp_Pln.hxx>
#include <gp_Pnt.hxx>
#include <IntAna2d_AnaIntersection.hxx>
#include <math_DirectPolynomialRoots.hxx>
#include <math_TrigonometricFunctionRoots.hxx>
#include <Precision.hxx>
#include <Standard_OutOfRange.hxx>
#include <StdFail_NotDone.hxx>
static
void RefineDir(gp_Dir& aDir);
//=======================================================================
//class : ExtremaExtElC_TrigonometricRoots
//purpose :
//== Classe Interne (Donne des racines classees d un polynome trigo)
//== Code duplique avec IntAna_IntQuadQuad.cxx (lbr le 26 mars 98)
//== Solution fiable aux problemes de coefficients proches de 0
//== avec essai de rattrapage si coeff<1.e-10 (jct le 27 avril 98)
//=======================================================================
class ExtremaExtElC_TrigonometricRoots {
private:
Standard_Real Roots[4];
Standard_Boolean done;
Standard_Integer NbRoots;
Standard_Boolean infinite_roots;
public:
ExtremaExtElC_TrigonometricRoots(const Standard_Real CC,
const Standard_Real SC,
const Standard_Real C,
const Standard_Real S,
const Standard_Real Cte,
const Standard_Real Binf,
const Standard_Real Bsup);
//
Standard_Boolean IsDone() {
return done;
}
//
Standard_Boolean IsARoot(Standard_Real u) {
Standard_Real PIpPI, aEps;
//
aEps=RealEpsilon();
PIpPI = M_PI + M_PI;
for(Standard_Integer i=0 ; i<NbRoots; i++) {
if(Abs(u - Roots[i])<=aEps) {
return Standard_True ;
}
if(Abs(u - Roots[i]-PIpPI)<=aEps) {
return Standard_True;
}
}
return Standard_False;
}
//
Standard_Integer NbSolutions() {
if(!done) {
throw StdFail_NotDone();
}
return NbRoots;
}
//
Standard_Boolean InfiniteRoots() {
if(!done) {
throw StdFail_NotDone();
}
return infinite_roots;
}
//
Standard_Real Value(const Standard_Integer& n) {
if((!done)||(n>NbRoots)) {
throw StdFail_NotDone();
}
return Roots[n-1];
}
};
//=======================================================================
//function : ExtremaExtElC_TrigonometricRoots
//purpose :
//=======================================================================
ExtremaExtElC_TrigonometricRoots::
ExtremaExtElC_TrigonometricRoots(const Standard_Real CC,
const Standard_Real SC,
const Standard_Real C,
const Standard_Real S,
const Standard_Real Cte,
const Standard_Real Binf,
const Standard_Real Bsup)
: NbRoots(0),
infinite_roots(Standard_False)
{
Standard_Integer i, nbessai;
Standard_Real cc ,sc, c, s, cte;
//
nbessai = 1;
cc = CC;
sc = SC;
c = C;
s = S;
cte = Cte;
done=Standard_False;
while (nbessai<=2 && !done) {
//-- F= AA*CN*CN+2*BB*CN*SN+CC*CN+DD*SN+EE;
math_TrigonometricFunctionRoots MTFR(cc,sc,c,s,cte,Binf,Bsup);
//
if(MTFR.IsDone()) {
done=Standard_True;
if(MTFR.InfiniteRoots()) {
infinite_roots=Standard_True;
}
else { //else #1
Standard_Boolean Triee;
Standard_Integer j, SvNbRoots;
Standard_Real aTwoPI, aMaxCoef, aPrecision;
//
aTwoPI=M_PI+M_PI;
NbRoots=MTFR.NbSolutions();
for(i=0;i<NbRoots;++i) {
Roots[i]=MTFR.Value(i+1);
if(Roots[i]<0.) {
Roots[i]=Roots[i]+aTwoPI;
}
if(Roots[i]>aTwoPI) {
Roots[i]=Roots[i]-aTwoPI;
}
}
//
//-- La recherche directe donne n importe quoi.
aMaxCoef = Max(CC,SC);
aMaxCoef = Max(aMaxCoef,C);
aMaxCoef = Max(aMaxCoef,S);
aMaxCoef = Max(aMaxCoef,Cte);
aPrecision = Max(1.e-8, 1.e-12*aMaxCoef);
SvNbRoots=NbRoots;
for(i=0; i<SvNbRoots; ++i) {
Standard_Real y;
Standard_Real co=cos(Roots[i]);
Standard_Real si=sin(Roots[i]);
y=co*(CC*co + (SC+SC)*si + C) + S*si + Cte;
// modified by OCC Tue Oct 3 18:43:00 2006
if(Abs(y)>aPrecision) {
NbRoots--;
Roots[i]=1000.0;
}
}
//
do {
Standard_Real t;
//
Triee=Standard_True;
for(i=1, j=0; i<SvNbRoots; ++i, ++j) {
if(Roots[i]<Roots[j]) {
Triee=Standard_False;
t=Roots[i];
Roots[i]=Roots[j];
Roots[j]=t;
}
}
}
while(!Triee);
//
infinite_roots=Standard_False;
if(NbRoots==0) { //--!!!!! Detect case Pol = Cte ( 1e-50 ) !!!!
if((Abs(CC) + Abs(SC) + Abs(C) + Abs(S)) < 1e-10) {
if(Abs(Cte) < 1e-10) {
infinite_roots=Standard_True;
}
}
}
} // else #1
} // if(MTFR.IsDone()) {
else {
// try to set very small coefficients to ZERO
if (Abs(CC)<1e-10) {
cc = 0.0;
}
if (Abs(SC)<1e-10) {
sc = 0.0;
}
if (Abs(C)<1e-10) {
c = 0.0;
}
if (Abs(S)<1e-10){
s = 0.0;
}
if (Abs(Cte)<1e-10){
cte = 0.0;
}
nbessai++;
}
} // while (nbessai<=2 && !done) {
}
//=======================================================================
//function : Extrema_ExtElC
//purpose :
//=======================================================================
Extrema_ExtElC::Extrema_ExtElC ()
{
myDone = Standard_False;
myIsPar = Standard_False;
myNbExt = 0;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
}
//=======================================================================
//function : Extrema_ExtElC
//purpose :
//=======================================================================
Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& theC1,
const gp_Lin& theC2,
const Standard_Real)
// Function:
// Find min distance between 2 straight lines.
// Method:
// Let D1 and D2, be 2 directions of straight lines C1 and C2.
// 2 cases are considered:
// 1- if Angle(D1,D2) < AngTol, straight lines are parallel.
// The distance is the distance between a point of C1 and the straight line C2.
// 2- if Angle(D1,D2) > AngTol:
// Let P1=C1(u1) and P2=C2(u2).
// Then we must find u1 and u2 such as the distance P1P2 is minimal.
// Target function is:
// F(u1, u2) = ((L1x+D1x*u1)-(L2x+D2x*u2))^2 +
// ((L1y+D1y*u1)-(L2y+D2y*u2))^2 +
// ((L1z+D1z*u1)-(L2z+D2z*u2))^2 --> min,
// where L1 and L2 are lines locations, D1 and D2 are lines directions.
// Let simplify the function F
// F(u1, u2) = (D1x*u1-D2x*u2-Lx)^2 + (D1y*u1-D2y*u2-Ly)^2 + (D1z*u1-D2z*u2-Lz)^2,
// where L is a vector L1L2.
// In point of minimum, the condition
// {dF/du1 = 0
// {dF/du2 = 0
// must be satisfied.
// dF/du1 = 2*D1x*(D1x*u1-D2x*u2-Lx) +
// 2*D1y*(D1y*u1-D2y*u2-Ly) +
// 2*D1z*(D1z*u1-D2z*u2-Lz) =
// = 2*((D1^2)*u1-(D1.D2)*u2-L.D1) =
// = 2*(u1-(D1.D2)*u2-L.D1)
// dF/du2 = -2*D2x*(D1x*u1-D2x*u2-Lx) -
// 2*D2y*(D1y*u1-D2y*u2-Ly) -
// 2*D2z*(D1z*u1-D2z*u2-Lz)=
// = -2*((D2.D1)*u1-(D2^2)*u2-(D2.L)) =
// = -2*((D2.D1)*u1-u2-(D2.L))
// Consequently, we have two-equation system with two variables:
// {u1 - (D1.D2)*u2 = L.D1
// {(D1.D2)*u1 - u2 = L.D2
// This system has one solution if (D1.D2)^2 != 1
// (if straight lines are not parallel).
{
myDone = Standard_False;
myNbExt = 0;
myIsPar = Standard_False;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
const gp_Dir &aD1 = theC1.Position().Direction(),
&aD2 = theC2.Position().Direction();
const Standard_Real aCosA = aD1.Dot(aD2);
const Standard_Real aSqSinA = 1.0 - aCosA * aCosA;
Standard_Real aU1 = 0.0, aU2 = 0.0;
if (aSqSinA < gp::Resolution() || aD1.IsParallel(aD2, Precision::Angular()))
{
myIsPar = Standard_True;
}
else
{
const gp_XYZ aL1L2 = theC2.Location().XYZ() - theC1.Location().XYZ();
const Standard_Real aD1L = aD1.XYZ().Dot(aL1L2),
aD2L = aD2.XYZ().Dot(aL1L2);
aU1 = (aD1L - aCosA * aD2L) / aSqSinA;
aU2 = (aCosA * aD1L - aD2L) / aSqSinA;
myIsPar = Precision::IsInfinite(aU1) || Precision::IsInfinite(aU2);
}
if (myIsPar)
{
mySqDist[0] = theC2.SquareDistance(theC1.Location());
myNbExt = 1;
myDone = Standard_True;
return;
}
// Here myIsPar == Standard_False;
const gp_Pnt aP1(ElCLib::Value(aU1, theC1)),
aP2(ElCLib::Value(aU2, theC2));
mySqDist[myNbExt] = aP1.SquareDistance(aP2);
myPoint[myNbExt][0] = Extrema_POnCurv(aU1, aP1);
myPoint[myNbExt][1] = Extrema_POnCurv(aU2, aP2);
myNbExt = 1;
myDone = Standard_True;
}
//=======================================================================
//function : PlanarLineCircleExtrema
//purpose :
//=======================================================================
Standard_Boolean Extrema_ExtElC::PlanarLineCircleExtrema(const gp_Lin& theLin,
const gp_Circ& theCirc)
{
const gp_Dir &aDirC = theCirc.Axis().Direction(),
&aDirL = theLin.Direction();
if (Abs(aDirC.Dot(aDirL)) > Precision::Angular())
return Standard_False;
//The line is in the circle-plane completely
//(or parallel to the circle-plane).
//Therefore, we are looking for extremas and
//intersections in 2D-space.
const gp_XYZ &aCLoc = theCirc.Location().XYZ();
const gp_XYZ &aDCx = theCirc.Position().XDirection().XYZ(),
&aDCy = theCirc.Position().YDirection().XYZ();
const gp_XYZ &aLLoc = theLin.Location().XYZ();
const gp_XYZ &aLDir = theLin.Direction().XYZ();
const gp_XYZ aVecCL(aLLoc - aCLoc);
//Center of 2D-circle
const gp_Pnt2d aPC(0.0, 0.0);
gp_Ax22d aCircAxis(aPC, gp_Dir2d(1.0, 0.0), gp_Dir2d(0.0, 1.0));
gp_Circ2d aCirc2d(aCircAxis, theCirc.Radius());
gp_Pnt2d aPL(aVecCL.Dot(aDCx), aVecCL.Dot(aDCy));
gp_Dir2d aDL(aLDir.Dot(aDCx), aLDir.Dot(aDCy));
gp_Lin2d aLin2d(aPL, aDL);
// Extremas
Extrema_ExtElC2d anExt2d(aLin2d, aCirc2d, Precision::Confusion());
//Intersections
IntAna2d_AnaIntersection anInters(aLin2d, aCirc2d);
myDone = anExt2d.IsDone() || anInters.IsDone();
if (!myDone)
return Standard_True;
const Standard_Integer aNbExtr = anExt2d.NbExt();
const Standard_Integer aNbSol = anInters.NbPoints();
const Standard_Integer aNbSum = aNbExtr + aNbSol;
for (Standard_Integer anExtrID = 1; anExtrID <= aNbSum; anExtrID++)
{
const Standard_Integer aDelta = anExtrID - aNbExtr;
Standard_Real aLinPar = 0.0, aCircPar = 0.0;
if (aDelta < 1)
{
Extrema_POnCurv2d aPLin2d, aPCirc2d;
anExt2d.Points(anExtrID, aPLin2d, aPCirc2d);
aLinPar = aPLin2d.Parameter();
aCircPar = aPCirc2d.Parameter();
}
else
{
aLinPar = anInters.Point(aDelta).ParamOnFirst();
aCircPar = anInters.Point(aDelta).ParamOnSecond();
}
const gp_Pnt aPOnL(ElCLib::LineValue(aLinPar, theLin.Position())),
aPOnC(ElCLib::CircleValue(aCircPar,
theCirc.Position(), theCirc.Radius()));
mySqDist[myNbExt] = aPOnL.SquareDistance(aPOnC);
myPoint[myNbExt][0].SetValues(aLinPar, aPOnL);
myPoint[myNbExt][1].SetValues(aCircPar, aPOnC);
myNbExt++;
}
return Standard_True;
}
//=======================================================================
//function : Extrema_ExtElC
//purpose :
// Find extreme distances between straight line C1 and circle C2.
//
//Method:
// Let P1=C1(u1) and P2=C2(u2) be two solution points
// D the direction of straight line C1
// T 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.
// (2) <=> P1O2.T = 0. as O2P2.T = 0.
// <=> ((P2O1.D)D+O1O2).T = 0. as P1O1 = -u1*D = (P2O1.D)D
// <=> (((P2O2+O2O1).D)D+O1O2).T = 0.
// <=> ((P2O2.D)(D.T)+((O2O1.D)D-O2O1).T = 0.
// We are in the reference of the circle; let:
// Cos = Cos(u2) and Sin = Sin(u2),
// P2 (R*Cos,R*Sin,0.),
// T (-R*Sin,R*Cos,0.),
// D (Dx,Dy,Dz),
// V (Vx,Vy,Vz) = (O2O1.D)D-O2O1;
// Then, the equation by Cos and Sin is as follows:
// -(2*R*R*Dx*Dy) * Cos**2 + A1
// R*R*(Dx**2-Dy**2) * Cos*Sin + 2* A2
// R*Vy * Cos + A3
// -R*Vx * Sin + A4
// R*R*Dx*Dy = 0. A5
//Use the algorithm math_TrigonometricFunctionRoots to solve this equation.
//=======================================================================
Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
const gp_Circ& C2,
const Standard_Real)
{
Standard_Real Dx,Dy,Dz,aRO2O1, aTolRO2O1;
Standard_Real R, A1, A2, A3, A4, A5, aTol;
gp_Dir x2, y2, z2, D, D1;
//
myIsPar = Standard_False;
myDone = Standard_False;
myNbExt = 0;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
if (PlanarLineCircleExtrema(C1, C2))
{
return;
}
// Calculate T1 in the reference of the circle ...
D = C1.Direction();
D1 = D;
x2 = C2.XAxis().Direction();
y2 = C2.YAxis().Direction();
z2 = C2.Axis().Direction();
Dx = D.Dot(x2);
Dy = D.Dot(y2);
Dz = D.Dot(z2);
//
D.SetCoord(Dx, Dy, Dz);
RefineDir(D);
D.Coord(Dx, Dy, Dz);
//
// Calcul de V dans le repere du cercle:
gp_Pnt O1 = C1.Location();
gp_Pnt O2 = C2.Location();
gp_Vec O2O1 (O2,O1);
//
aTolRO2O1=gp::Resolution();
aRO2O1=O2O1.Magnitude();
if (aRO2O1 > aTolRO2O1) {
gp_Dir aDO2O1;
//
O2O1.Multiply(1./aRO2O1);
aDO2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
RefineDir(aDO2O1);
O2O1.SetXYZ(aRO2O1*aDO2O1.XYZ());
}
else {
O2O1.SetCoord(O2O1.Dot(x2), O2O1.Dot(y2), O2O1.Dot(z2));
}
//
gp_XYZ Vxyz = (D.XYZ()*(O2O1.Dot(D)))-O2O1.XYZ();
//
//modified by NIZNHY-PKV Tue Mar 20 10:36:38 2012
/*
R = C2.Radius();
A5 = R*R*Dx*Dy;
A1 = -2.*A5;
A2 = R*R*(Dx*Dx-Dy*Dy)/2.;
A3 = R*Vxyz.Y();
A4 = -R*Vxyz.X();
//
aTol=1.e-12;
//
if(fabs(A5) <= aTol) {
A5 = 0.;
}
if(fabs(A1) <= aTol) {
A1 = 0.;
}
if(fabs(A2) <= aTol) {
A2 = 0.;
}
if(fabs(A3) <= aTol) {
A3 = 0.;
}
if(fabs(A4) <= aTol) {
A4 = 0.;
}
*/
//
aTol=1.e-12;
// Calculate the coefficients of the equation by Cos and Sin ...
// [divided by R]
R = C2.Radius();
A5 = R*Dx*Dy;
A1 = -2.*A5;
A2 = 0.5*R*(Dx*Dx-Dy*Dy);// /2.;
A3 = Vxyz.Y();
A4 = -Vxyz.X();
//
if (A1>=-aTol && A1<=aTol) {
A1 = 0.;
}
if (A2>=-aTol && A2<=aTol) {
A2 = 0.;
}
if (A3>=-aTol && A3<=aTol) {
A3 = 0.;
}
if (A4>=-aTol && A4<=aTol) {
A4 = 0.;
}
if (A5>=-aTol && A5<=aTol) {
A5 = 0.;
}
//modified by NIZNHY-PKV Tue Mar 20 10:36:40 2012t
//
ExtremaExtElC_TrigonometricRoots Sol(A1, A2, A3, A4, A5, 0., M_PI+M_PI);
if (!Sol.IsDone()) {
return;
}
if (Sol.InfiniteRoots()) {
myIsPar = Standard_True;
mySqDist[0] = R*R;
myNbExt = 1;
myDone = Standard_True;
return;
}
// Storage of solutions ...
Standard_Integer NoSol, NbSol;
Standard_Real U1,U2;
gp_Pnt P1,P2;
//
NbSol = Sol.NbSolutions();
for (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);
//modified by NIZNHY-PKV Wed Mar 21 08:11:33 2012f
//myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
//myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
myPoint[myNbExt][0].SetValues(U1,P1);
myPoint[myNbExt][1].SetValues(U2,P2);
//modified by NIZNHY-PKV Wed Mar 21 08:11:36 2012t
myNbExt++;
}
myDone = Standard_True;
}
//=======================================================================
//function : Extrema_ExtElC
//purpose :
//=======================================================================
Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
const gp_Elips& C2)
{
/*-----------------------------------------------------------------------------
Function:
Find extreme distances between straight line C1 and ellipse C2.
Method:
Let P1=C1(u1) and P2=C2(u2) 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.T = 0. as O2P2.T = 0.
<=> ((P2O1.D)D+O1O2).T = 0. as P1O1 = -u1*D = (P2O1.D)D
<=> (((P2O2+O2O1).D)D+O1O2).T = 0.
<=> ((P2O2.D)(D.T)+((O2O1.D)D-O2O1).T = 0.
We are in the reference of the ellipse; let:
Cos = Cos(u2) and Sin = Sin(u2),
P2 (MajR*Cos,MinR*Sin,0.),
T (-MajR*Sin,MinR*Cos,0.),
D (Dx,Dy,Dz),
V (Vx,Vy,Vz) = (O2O1.D)D-O2O1;
Then, get the following equation by Cos and Sin:
-(2*MajR*MinR*Dx*Dy) * Cos**2 +
(MajR*MajR*Dx**2-MinR*MinR*Dy**2) * Cos*Sin +
MinR*Vy * Cos +
- MajR*Vx * Sin +
MinR*MajR*Dx*Dy = 0.
Use algorithm math_TrigonometricFunctionRoots to solve this equation.
-----------------------------------------------------------------------------*/
myIsPar = Standard_False;
myDone = Standard_False;
myNbExt = 0;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
// Calculate T1 the reference of the ellipse ...
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 the coefficients of the equation by Cos and Sin ...
Standard_Real MajR = C2.MajorRadius();
Standard_Real MinR = C2.MinorRadius();
Standard_Real A5 = MajR*MinR*Dx*Dy;
Standard_Real A1 = -2.*A5;
Standard_Real R2 = MajR*MajR;
Standard_Real r2 = MinR*MinR;
Standard_Real A2 =(R2*Dx*Dx -r2*Dy*Dy -R2 +r2)/2.0;
Standard_Real A3 = MinR*Vxyz.Y();
Standard_Real A4 = -MajR*Vxyz.X();
//
Standard_Real aEps=1.e-12;
//
if(fabs(A5) <= aEps) A5 = 0.;
if(fabs(A1) <= aEps) A1 = 0.;
if(fabs(A2) <= aEps) A2 = 0.;
if(fabs(A3) <= aEps) A3 = 0.;
if(fabs(A4) <= aEps) A4 = 0.;
//
ExtremaExtElC_TrigonometricRoots Sol(A1,A2,A3,A4,A5,0.,M_PI+M_PI);
if (!Sol.IsDone()) { return; }
//
if (Sol.InfiniteRoots()) {
myIsPar = Standard_True;
gp_Pnt aP = ElCLib::EllipseValue(0., C2.Position(), C2.MajorRadius(), C2.MinorRadius());
mySqDist[0] = C1.SquareDistance(aP);
myNbExt = 1;
myDone = Standard_True;
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_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.
(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.
<=> (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)
T(R*Shu, r*Chu)
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 +
(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
Use the algorithm math_DirectPolynomialRoots to solve this equation.
-----------------------------------------------------------------------------*/
myIsPar = Standard_False;
myDone = Standard_False;
myNbExt = 0;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
// Calculate T1 in the reference of the hyperbola...
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();
Standard_Real Vx = Vxyz.X();
Standard_Real Vy = Vxyz.Y();
// Calculate coefficients of the equation by v
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;
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;
math_DirectPolynomialRoots Sol(A1,A2,0.0,A4, A5);
if (!Sol.IsDone()) { return; }
// 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);
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
<=> (((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;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
// 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;
for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++)
{
mySqDist[anIdx] = RealLast();
}
//
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;
}
// Here, both circles are in the same plane.
//
aDC2=aPc1.SquareDistance(aPc2);
bIsSameAxe=aDC2<aTolD2;
//
if(bIsSameAxe)
{
myIsPar = Standard_True;
myNbExt = 1;
myDone = Standard_True;
const Standard_Real aDR = C1.Radius() - C2.Radius();
mySqDist[0] = aDR*aDR;
return;
}
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) {
}
//=======================================================================
//function : IsDone
//purpose :
//=======================================================================
Standard_Boolean Extrema_ExtElC::IsDone () const {
return myDone;
}
//=======================================================================
//function : IsParallel
//purpose :
//=======================================================================
Standard_Boolean Extrema_ExtElC::IsParallel () const
{
if (!IsDone()) {
throw StdFail_NotDone();
}
return myIsPar;
}
//=======================================================================
//function : NbExt
//purpose :
//=======================================================================
Standard_Integer Extrema_ExtElC::NbExt () const
{
if (!IsDone())
{
throw StdFail_NotDone();
}
return myNbExt;
}
//=======================================================================
//function : SquareDistance
//purpose :
//=======================================================================
Standard_Real Extrema_ExtElC::SquareDistance (const Standard_Integer N) const
{
if (N < 1 || N > NbExt())
{
throw Standard_OutOfRange();
}
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())
{
throw Standard_OutOfRange();
}
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;
}
}
}
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