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// File: GccIter_FunctionTanCuCu.gxx
// Created: Mon Jan 20 16:35:40 1992
// Author: Remi GILET
// <reg@phobox>
#include <gp_Vec2d.hxx>
#include <gp_Pnt2d.hxx>
#include <ElCLib.hxx>
void GccIter_FunctionTanCuCu::
InitDerivative(const math_Vector& X ,
gp_Pnt2d& Point1,
gp_Pnt2d& Point2,
gp_Vec2d& Tan1 ,
gp_Vec2d& Tan2 ,
gp_Vec2d& D21 ,
gp_Vec2d& D22 ) {
switch (TheType) {
case GccIter_CuCu:
{
TheCurveTool::D2(TheCurve1,X(1),Point1,Tan1,D21);
TheCurveTool::D2(TheCurve2,X(2),Point2,Tan2,D22);
}
break;
case GccIter_CiCu:
{
ElCLib::D2(X(1),TheCirc1,Point1,Tan1,D21);
TheCurveTool::D2(TheCurve2,X(2),Point2,Tan2,D22);
}
break;
default:
{
}
}
}
GccIter_FunctionTanCuCu::
GccIter_FunctionTanCuCu(const TheCurve& C1 ,
const TheCurve& C2 ) {
TheCurve1 = C1;
TheCurve2 = C2;
TheType = GccIter_CuCu;
}
GccIter_FunctionTanCuCu::
GccIter_FunctionTanCuCu(const gp_Circ2d& C1 ,
const TheCurve& C2 ) {
TheCirc1 = C1;
TheCurve2 = C2;
TheType = GccIter_CiCu;
}
//=========================================================================
// soit P1 le point sur la courbe TheCurve1 d abscisse u1. +
// soit P2 le point sur la courbe TheCurve2 d abscisse u2. +
// soit T1 la tangente a la courbe TheCurve1 en P1. +
// soit T2 la tangente a la courbe TheCurve2 en P2. +
// Nous voulons P1 et P2 tels que : +
// ---> --> +
// * P1P2 /\ T1 = 0 +
// +
// --> --> +
// * T1 /\ T2 = 0 +
// +
// Nous cherchons donc les zeros des fonctions suivantes: +
// ---> --> +
// * P1P2 /\ T1 +
// --------------- = F1(u) +
// ---> --> +
// ||P1P2||*||T1|| +
// +
// --> --> +
// * T1 /\ T2 +
// --------------- = F2(u) +
// --> --> +
// ||T2||*||T1|| +
// +
// Les derivees de ces fonctions sont : +
// 2 2 +
// dF1 P1P2/\N1 (P1P2/\T1)*[T1*(-T1).P1P2+P1P2*(T1.N1)] +
// ----- = --------------- - ----------------------------------------- +
// du1 3 3 +
// ||P1P2||*||T1|| ||P1P2|| * ||T1|| +
// +
// 2 +
// dF1 T2/\T1 (P1P2/\T1)*[T1*(T2.P1P2) +
// ----- = --------------- - ----------------------------------------- +
// du2 3 3 +
// ||P1P2||*||T1|| ||P1P2|| * ||T1|| +
// +
// 2 +
// dF2 N1/\T2 T1/\T2*(N1.T1)T2 +
// ----- = ---------------- - ----------------------------- +
// du1 3 3 +
// ||T1||*||T2|| ||T1|| * ||T2|| +
// +
// 2 +
// dF2 T1/\N2 T1/\T2*(N2.T2)T1 +
// ----- = ---------------- - ----------------------------- +
// du2 3 3 +
// ||T1||*||T2|| ||T1|| * ||T2|| +
// +
//=========================================================================
Standard_Integer GccIter_FunctionTanCuCu::
NbVariables() const { return 2; }
Standard_Integer GccIter_FunctionTanCuCu::
NbEquations() const { return 2; }
Standard_Boolean GccIter_FunctionTanCuCu::
Value (const math_Vector& X ,
math_Vector& Fval ) {
gp_Pnt2d Point1;
gp_Pnt2d Point2;
gp_Vec2d Vect11;
gp_Vec2d Vect21;
gp_Vec2d Vect12;
gp_Vec2d Vect22;
InitDerivative(X,Point1,Point2,Vect11,Vect21,Vect12,Vect22);
Standard_Real NormeD11 = Vect11.Magnitude();
Standard_Real NormeD21 = Vect21.Magnitude();
gp_Vec2d TheDirection(Point1,Point2);
Standard_Real squaredir = TheDirection.Dot(TheDirection);
Fval(1) = TheDirection.Crossed(Vect11)/(NormeD11*squaredir);
Fval(2) = Vect11.Crossed(Vect21)/(NormeD11*NormeD21);
return Standard_True;
}
Standard_Boolean GccIter_FunctionTanCuCu::
Derivatives (const math_Vector& X ,
math_Matrix& Deriv ) {
gp_Pnt2d Point1;
gp_Pnt2d Point2;
gp_Vec2d Vect11;
gp_Vec2d Vect21;
gp_Vec2d Vect12;
gp_Vec2d Vect22;
InitDerivative(X,Point1,Point2,Vect11,Vect21,Vect12,Vect22);
Standard_Real NormeD11 = Vect11.Magnitude();
Standard_Real NormeD21 = Vect21.Magnitude();
#ifdef DEB
gp_Vec2d V2V1(Vect11.XY(),Vect21.XY());
#else
Vect11.XY();
Vect21.XY();
#endif
gp_Vec2d TheDirection(Point1,Point2);
Standard_Real squaredir = TheDirection.Dot(TheDirection);
Deriv(1,1) = TheDirection.Crossed(Vect12)/(NormeD11*squaredir)+
(TheDirection.Crossed(Vect11)*NormeD11*NormeD11*Vect11.Dot(TheDirection))/
(NormeD11*NormeD11*NormeD11*squaredir*squaredir*squaredir);
Deriv(1,2) = Vect21.Crossed(Vect11)/(NormeD11*squaredir)-
(TheDirection.Crossed(Vect11)*NormeD11*NormeD11*Vect21.Dot(TheDirection))/
(NormeD11*NormeD11*NormeD11*squaredir*squaredir*squaredir);
Deriv(2,1)=(Vect12.Crossed(Vect21))/(NormeD11*NormeD21)-
(Vect11.Crossed(Vect21))*(Vect12.Dot(Vect11))*NormeD21*NormeD21/
(NormeD11*NormeD11*NormeD11*NormeD21*NormeD21*NormeD21);
Deriv(2,2)=(Vect11.Crossed(Vect22))/(NormeD11*NormeD21)-
(Vect11.Crossed(Vect21))*(Vect22.Dot(Vect21))*NormeD11*NormeD11/
(NormeD11*NormeD11*NormeD11*NormeD21*NormeD21*NormeD21);
return Standard_True;
}
Standard_Boolean GccIter_FunctionTanCuCu::
Values (const math_Vector& X ,
math_Vector& Fval ,
math_Matrix& Deriv ) {
gp_Pnt2d Point1;
gp_Pnt2d Point2;
gp_Vec2d Vect11;
gp_Vec2d Vect21;
gp_Vec2d Vect12;
gp_Vec2d Vect22;
InitDerivative(X,Point1,Point2,Vect11,Vect21,Vect12,Vect22);
Standard_Real NormeD11 = Vect11.Magnitude();
Standard_Real NormeD21 = Vect21.Magnitude();
#ifdef DEB
gp_Vec2d V2V1(Vect11.XY(),Vect21.XY());
#else
Vect11.XY();
Vect21.XY();
#endif
gp_Vec2d TheDirection(Point1,Point2);
Standard_Real squaredir = TheDirection.Dot(TheDirection);
Fval(1) = TheDirection.Crossed(Vect11)/(NormeD11*squaredir);
Fval(2) = Vect11.Crossed(Vect21)/(NormeD11*NormeD21);
Deriv(1,1) = TheDirection.Crossed(Vect12)/(NormeD11*squaredir)+
(TheDirection.Crossed(Vect11)*NormeD11*NormeD11*Vect11.Dot(TheDirection))/
(NormeD11*NormeD11*NormeD11*squaredir*squaredir*squaredir);
Deriv(1,2) = Vect21.Crossed(Vect11)/(NormeD11*squaredir)-
(TheDirection.Crossed(Vect11)*NormeD11*NormeD11*Vect21.Dot(TheDirection))/
(NormeD11*NormeD11*NormeD11*squaredir*squaredir*squaredir);
Deriv(2,1)=(Vect12.Crossed(Vect21))/(NormeD11*NormeD21)-
(Vect11.Crossed(Vect21))*(Vect12.Dot(Vect11))*NormeD21*NormeD21/
(NormeD11*NormeD11*NormeD11*NormeD21*NormeD21*NormeD21);
Deriv(2,2)=(Vect11.Crossed(Vect22))/(NormeD11*NormeD21)-
(Vect11.Crossed(Vect21))*(Vect22.Dot(Vect21))*NormeD11*NormeD11/
(NormeD11*NormeD11*NormeD11*NormeD21*NormeD21*NormeD21);
return Standard_True;
}
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