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occt/src/GeomFill/GeomFill_QuasiAngularConvertor.cxx
abv d5f74e42d6 0024624: Lost word in license statement in source files
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C++

// Created on: 1997-08-06
// Created by: Philippe MANGIN
// Copyright (c) 1997-1999 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 <GeomFill_QuasiAngularConvertor.ixx>
#include <PLib.hxx>
#include <gp_Mat.hxx>
#include <gp_Ax1.hxx>
#include <Convert_CompPolynomialToPoles.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_HArray2OfReal.hxx>
#include <TColStd_HArray1OfInteger.hxx>
#include <TColStd_HArray1OfReal.hxx>
#define NullAngle 1.e-6
// QuasiAngular is rational definition of Cos(theta(t) and sin(theta)
// on [-alpha, +alpha] with
// 2 2
// U - V
// cos (theta(t)) = ----------
// 2 2
// U + V
// 2 * U*V
// sin (theta(t)) = ----------
// 2 2
// U + V
// 3
// V(t) = t + c t
// 2
// U(t) = 1 + b t
// 1
// c = --- + b
// 3
// -1 gamma
// b =--------- + -----------------------
// 2
// gamma 3*(tang gamma - gamma)
// with gamma = alpha / 2
GeomFill_QuasiAngularConvertor::GeomFill_QuasiAngularConvertor():
myinit(Standard_False),
B(1, 7, 1, 7),
Px(1, 7), Py(1, 7),
W(1,7), Vx(1, 7), Vy(1, 7), Vw(1,7)
{
}
Standard_Boolean GeomFill_QuasiAngularConvertor::Initialized() const
{
return myinit;
}
void GeomFill_QuasiAngularConvertor::Init()
{
if (myinit) return; //On n'initialise qu'une fois
Standard_Integer ii, jj, Ordre=7;
Standard_Real terme;
TColStd_Array1OfReal Coeffs(1, Ordre*Ordre), TrueInter(1,2), Inter(1,2);
Handle(TColStd_HArray2OfReal)
Poles1d = new (TColStd_HArray2OfReal) (1, Ordre, 1, Ordre);
//Calcul de B
Inter.SetValue(1, -1);
Inter.SetValue(2, 1);
TrueInter.SetValue(1, -1);
TrueInter.SetValue(2, 1);
Coeffs.Init(0);
for (ii=1; ii<=Ordre; ii++) { Coeffs.SetValue(ii+(ii-1)*Ordre, 1); }
//Convertion
Convert_CompPolynomialToPoles
AConverter(Ordre, Ordre-1, Ordre-1,
Coeffs,
Inter,
TrueInter);
AConverter.Poles(Poles1d);
for (jj=1; jj<=Ordre; jj++) {
for (ii=1; ii<=Ordre; ii++) {
terme = Poles1d->Value(ii,jj);
if (Abs(terme-1) < 1.e-9) terme = 1 ; //petite retouche
if (Abs(terme+1) < 1.e-9) terme = -1;
B(ii, jj) = terme;
}
}
// Init des polynomes
Vx.Init(0);
Vx(1) = 1;
Vy.Init(0);
Vy(2) = 2;
Vw.Init(0);
Vw(1) = 1;
myinit = Standard_True;
}
void GeomFill_QuasiAngularConvertor::Section(const gp_Pnt& FirstPnt,
const gp_Pnt& Center,
const gp_Vec& Dir,
const Standard_Real Angle,
TColgp_Array1OfPnt& Poles,
TColStd_Array1OfReal& Weights)
{
Standard_Real b, b2, c, c2,tan_b;
Standard_Integer ii;
Standard_Real beta, beta2, beta3, beta4, beta5, beta6, wi;
gp_XYZ aux;
gp_Mat Rot;
// Calcul de la transformation
gp_Vec V1(Center, FirstPnt), V2;
Rot.SetRotation(Dir.XYZ(), Angle/2);
aux = V1.XYZ();
aux *= Rot;
V1.SetXYZ(aux);
V2 = Dir^V1;
gp_Mat M(V1.X(), V2.X(), 0,
V1.Y(), V2.Y(), 0,
V1.Z(), V2.Z(), 0);
// Calcul des coeffs -----------
beta = Angle/4;
beta2 = beta * beta;
beta3 = beta * beta2;
beta4 = beta2*beta2;
beta5 = beta3*beta2;
beta6 = beta3*beta3;
if ((M_PI/2 - beta)> NullAngle) {
if (Abs(beta) < NullAngle) {
Standard_Real cf = 2.0/(3*5*7);
b = - (0.2+cf*beta2) / (1+ 0.2*beta2);
// b = beta5 / cf;
}
else {
tan_b = Tan(beta);
b = - 1.0e0 / beta2;
b += beta / (3*(tan_b - beta));
}
}
else b = ((Standard_Real) -1)/beta2;
c = ((Standard_Real) 1)/ 3 + b;
b2 = b*b;
c2 = c*c;
// X = U*U - V*V
Vx(3) = beta2*(2*b - 1);
Vx(5) = beta4*(b2 - 2*c);
Vx(7) = -beta6*c2;
//Y = 2*U*V
Vy(2) = 2*beta;
Vy(4) = beta3*2*(c+b);
Vy(6) = 2*beta5*b*c;
// W = U*U + V*V
Vw(3) = beta2*(1 + 2*b);
Vw(5) = beta4*(2*c + b2);
Vw(7) = beta6*c2;
// Calculs des poles
Px.Multiply(B, Vx);
Py.Multiply(B, Vy);
W.Multiply(B, Vw);
// Transfo
gp_XYZ pnt;
for (ii=1; ii<=7; ii++) {
wi = W(ii);
pnt.SetCoord(Px(ii)/wi, Py(ii)/wi, 0);
pnt *= M;
pnt += Center.XYZ();
Poles(ii).ChangeCoord() = pnt;
Weights(ii) = wi;
}
}
void GeomFill_QuasiAngularConvertor::Section(const gp_Pnt& FirstPnt,
const gp_Vec& DFirstPnt,
const gp_Pnt& Center,
const gp_Vec& DCenter,
const gp_Vec& Dir,
const gp_Vec& DDir,
const Standard_Real Angle,
const Standard_Real DAngle,
TColgp_Array1OfPnt& Poles,
TColgp_Array1OfVec& DPoles,
TColStd_Array1OfReal& Weights,
TColStd_Array1OfReal& DWeights)
{
Standard_Integer Ordre = 7;
math_Vector DVx(1, Ordre), DVy(1, Ordre), DVw(1, Ordre),
DPx(1, Ordre), DPy(1, Ordre), DW(1, Ordre);
Standard_Real b, b2, c, c2,tan_b;
Standard_Real bpr, dtan_b;
Standard_Integer ii;
Standard_Real beta, beta2, beta3, beta4, beta5, beta6, betaprim;
gp_Vec V1(Center, FirstPnt), V1Prim, V2;
// Calcul des transformations
gp_XYZ aux;
Standard_Real Sina, Cosa;
gp_Mat Rot, RotPrim, D, DPrim;
// La rotation s'ecrit I + sin(Ang) * D + (1. - cos(Ang)) * D*D
// ou D est l'application x -> Dir ^ x
Rot.SetRotation(Dir.XYZ(), Angle/2);
// La derive s'ecrit donc :
// AngPrim * (sin(Ang)*D*D + cos(Ang)*D)
// + sin(Ang)*DPrim + (1. - cos(Ang)) *(DPrim*D + D*DPrim)
Sina = Sin(Angle/2);
Cosa = Cos(Angle/2);
D.SetCross(Dir.XYZ());
DPrim.SetCross(DDir.XYZ());
RotPrim = (D.Powered(2)).Multiplied(Sina);
RotPrim += D.Multiplied(Cosa);
RotPrim *= DAngle/2;
RotPrim += DPrim.Multiplied(Sina);
RotPrim += ((DPrim.Multiplied(D)).Added(D.Multiplied(DPrim))).Multiplied(1-Cosa);
aux = (DFirstPnt - DCenter).XYZ().Multiplied(Rot);
aux += V1.XYZ().Multiplied(RotPrim);
V1Prim.SetXYZ(aux);
aux = V1.XYZ();
aux.Multiply(Rot);
V1.SetXYZ(aux);
V2 = Dir^V1;
gp_Mat M (V1.X(), V2.X(), 0,
V1.Y(), V2.Y(), 0,
V1.Z(), V2.Z(), 0);
V2 = (DDir.Crossed(V1)).Added(Dir.Crossed(V1Prim));
gp_Mat MPrim (V1Prim.X(), V2.X(), 0,
V1Prim.Y(), V2.Y(), 0,
V1Prim.Z(), V2.Z(), 0);
// Calcul des constante -----------
beta = Angle/4;
betaprim = DAngle/4;
beta2 = beta * beta;
beta3 = beta * beta2;
beta4 = beta2*beta2;
beta5 = beta3*beta2;
beta6 = beta3*beta3;
if (Abs(beta) < NullAngle) {
// On calcul b par D.L
Standard_Real cf = 2.0/(3*5*7);
Standard_Real Num, Denom;
Num = 0.2 + cf*beta2;
Denom = 1+0.2*beta2;
b = - Num/Denom;
bpr = -2*beta*betaprim*(cf*Denom - 0.2*Num)/(Denom*Denom);
}
else {
b = ((Standard_Real) -1)/beta2;
bpr = (2*betaprim) / beta3;
if ((M_PI/2 - beta)> NullAngle) {
tan_b = Tan(beta);
dtan_b = betaprim * (1 + tan_b*tan_b);
b2 = tan_b - beta;
b += beta / (3*b2);
bpr += (betaprim*tan_b - beta*dtan_b) / (3*b2*b2);
}
}
c = ((Standard_Real) 1)/ 3 + b;
b2 = b*b;
c2 = c*c;
// X = U*U - V*V
Vx(3) = beta2*(2*b - 1);
Vx(5) = beta4*(b2 - 2*c);
Vx(7) = -beta6*c2;
DVx.Init(0);
DVx(3) = 2*(beta*betaprim*(2*b - 1) + bpr*beta2);
DVx(5) = 4*beta3*betaprim*(b2 - 2*c) + 2*beta4*bpr*(b-1);
DVx(7) = - 6*beta5*betaprim*c2 - 2*beta6*bpr*c;
//Y = 2*U*V
Vy(2) = 2*beta;
Vy(4) = beta3*2*(c+b);
Vy(6) = 2*beta5*b*c;
DVy.Init(0);
DVy(2) = 2*betaprim;
DVy(4) = 6*beta2*betaprim*(b+c) + 4*beta3*bpr;
DVy(6) = 10*beta4*betaprim*b*c + 2*beta5*bpr*(b+c);
// W = U*U + V*V
Vw(3) = beta2*(1 + 2*b);
Vw(5) = beta4*(2*c + b2);
Vw(7) = beta6*c2;
DVw.Init(0);
// DVw(3) = 2*(beta*betaprim*(1 + 2*b) + beta2*bpr);
DVw(3) = 2*beta*(betaprim*(1 + 2*b) + beta*bpr);
// DVw(5) = 4*beta3*betaprim*(2*c + b2) + 2*beta4*bpr*(b+1);
DVw(5) = 2*beta3*(2*betaprim*(2*c + b2) + beta*bpr*(b+1));
// DVw(7) = 6*beta5*betaprim*c2 + 2*beta6*bpr*c;
DVw(7) = 2*beta5*c*(3*betaprim*c + beta*bpr);
// Calcul des poles
Px.Multiply(B, Vx);
Py.Multiply(B, Vy);
W.Multiply(B, Vw);
DPx.Multiply(B, DVx);
DPy.Multiply(B, DVy);
DW.Multiply(B, DVw);
gp_XYZ P, DP;
Standard_Real wi;
for (ii=1; ii<=Ordre; ii++) {
wi = W(ii);
P.SetCoord(Px(ii)/wi, Py(ii)/wi, 0);
DP.SetCoord(DPx(ii)/wi, DPy(ii)/wi, 0);
DP -= (DW(ii)/wi)*P;
Poles(ii).ChangeCoord() = M*P + Center.XYZ();
P *= MPrim;
DP *= M;
aux.SetLinearForm(1, P, 1, DP, DCenter.XYZ());
DPoles(ii).SetXYZ(aux);
Weights(ii) = wi;
DWeights(ii) = DW(ii);
}
}
void GeomFill_QuasiAngularConvertor::Section(const gp_Pnt& FirstPnt,
const gp_Vec& DFirstPnt,
const gp_Vec& D2FirstPnt,
const gp_Pnt& Center,
const gp_Vec& DCenter,
const gp_Vec& D2Center,
const gp_Vec& Dir,
const gp_Vec& DDir,
const gp_Vec& D2Dir,
const Standard_Real Angle,
const Standard_Real DAngle,
const Standard_Real D2Angle,
TColgp_Array1OfPnt& Poles,
TColgp_Array1OfVec& DPoles,
TColgp_Array1OfVec& D2Poles,
TColStd_Array1OfReal& Weights,
TColStd_Array1OfReal& DWeights,
TColStd_Array1OfReal& D2Weights)
{
Standard_Integer Ordre = 7;
math_Vector DVx(1, Ordre), DVy(1, Ordre), DVw(1, Ordre),
D2Vx(1, Ordre), D2Vy(1, Ordre), D2Vw(1, Ordre);
math_Vector DPx(1, Ordre), DPy(1, Ordre), DW(1, Ordre),
D2Px(1, Ordre), D2Py(1, Ordre), D2W(1, Ordre);
Standard_Integer ii;
Standard_Real aux, daux, b, b2, c, c2, bpr, bsc;
gp_Vec V1(Center, FirstPnt), V1Prim, V1Secn, V2;
// Calcul des transformations
gp_XYZ auxyz;
Standard_Real Sina, Cosa;
gp_Mat Rot, RotPrim, RotSecn, D, DPrim, DSecn, DDP, Maux;
// La rotation s'ecrit I + sin(Ang) * D + (1. - cos(Ang)) * D*D
// ou D est l'application x -> Dir ^ x
Rot.SetRotation(Dir.XYZ(), Angle/2);
// La derive s'ecrit donc :
// AngPrim * (sin(Ang)*D*D + cos(Ang)*D)
// + sin(Ang)*DPrim + (1. - cos(Ang)) *(DPrim*D + D*DPrim)
Sina = Sin(Angle/2);
Cosa = Cos(Angle/2);
D.SetCross(Dir.XYZ());
DPrim.SetCross(DDir.XYZ());
DSecn.SetCross(D2Dir.XYZ());
DDP = (DPrim.Multiplied(D)).Added(D.Multiplied(DPrim));
RotPrim = (D.Powered(2)).Multiplied(Sina);
RotPrim += D.Multiplied(Cosa);
RotPrim *= DAngle/2;
RotPrim += DPrim.Multiplied(Sina);
RotPrim += DDP.Multiplied(1-Cosa);
RotSecn = (D.Powered(2)).Multiplied(Sina);
RotSecn += D.Multiplied(Cosa);
RotSecn *= D2Angle/2;
Maux = (D.Powered(2)).Multiplied(Cosa);
Maux -= D.Multiplied(Sina);
Maux *= DAngle/2;
Maux += DDP.Multiplied(2*Sina);
Maux += DPrim.Multiplied(2*Cosa);
Maux *= DAngle/2;
RotSecn += Maux;
Maux = (DSecn.Multiplied(D)).Added(D.Multiplied(DSecn));
Maux += (DPrim.Powered(2)).Multiplied(2);
Maux *= 1 - Cosa;
Maux += DSecn.Multiplied(Sina);
RotSecn += Maux;
V1Prim = DFirstPnt - DCenter;
auxyz = (D2FirstPnt - D2Center).XYZ().Multiplied(Rot);
auxyz += 2*(V1Prim.XYZ().Multiplied(RotPrim));
auxyz += V1.XYZ().Multiplied(RotSecn);
V1Secn.SetXYZ(auxyz);
auxyz = V1Prim.XYZ().Multiplied(Rot);
auxyz += V1.XYZ().Multiplied(RotPrim);
V1Prim.SetXYZ(auxyz);
auxyz = V1.XYZ();
auxyz.Multiply(Rot);
V1.SetXYZ(auxyz);
V2 = Dir^V1;
gp_Mat M (V1.X(), V2.X(), 0,
V1.Y(), V2.Y(), 0,
V1.Z(), V2.Z(), 0);
V2 = (DDir.Crossed(V1)).Added(Dir.Crossed(V1Prim));
gp_Mat MPrim (V1Prim.X(), V2.X(), 0,
V1Prim.Y(), V2.Y(), 0,
V1Prim.Z(), V2.Z(), 0);
V2 = DDir^V1Prim;
V2 *= 2;
V2 += (D2Dir.Crossed(V1)).Added(Dir.Crossed(V1Secn));
gp_Mat MSecn (V1Secn.X(), V2.X(), 0,
V1Secn.Y(), V2.Y(), 0,
V1Secn.Z(), V2.Z(), 0);
// Calcul des coeff -----------
Standard_Real tan_b, dtan_b, d2tan_b;
Standard_Real beta, beta2, beta3, beta4, beta5, beta6, betaprim, betasecn;
Standard_Real betaprim2, bpr2;
beta = Angle/4;
betaprim = DAngle/4;
betasecn = D2Angle/4;
beta2 = beta * beta;
beta3 = beta * beta2;
beta4 = beta2*beta2;
beta5 = beta3*beta2;
beta6 = beta3*beta3;
betaprim2 = betaprim * betaprim;
if (Abs(beta) < NullAngle) {
// On calcul b par D.L
Standard_Real cf =-2.0/21;
Standard_Real Num, Denom, aux;
Num = 0.2 + cf*beta2;
Denom = 1+0.2*beta2;
aux = (cf*Denom - 0.2*Num)/(Denom*Denom);
b = - Num/Denom;
bpr = -2*beta*betaprim*aux;
bsc = 2*aux*(betaprim2 + beta*betasecn - 2*beta*betaprim2);
}
else {
b = ((Standard_Real) -1)/beta2;
bpr = (2*betaprim) / beta3;
bsc = (2*betasecn - 6*betaprim*(betaprim/beta)) / beta3;
if ((M_PI/2 - beta)> NullAngle) {
tan_b = Tan(beta);
dtan_b = betaprim * (1 + tan_b*tan_b);
d2tan_b = betasecn * (1 + tan_b*tan_b)
+ 2*betaprim * tan_b * dtan_b;
b2 = tan_b - beta;
b += beta / (3*b2);
aux = betaprim*tan_b - beta*dtan_b;
bpr += aux / (3*b2*b2);
daux = betasecn*tan_b - beta*d2tan_b;
bsc += (daux - 2*aux*betaprim*tan_b*tan_b/b2)/(3*b2*b2);
}
}
c = ((Standard_Real) 1)/ 3 + b;
b2 = b*b;
c2 = c*c;
bpr2 = bpr * bpr;
// X = U*U - V*V
Vx(3) = beta2*(2*b - 1);
Vx(5) = beta4*(b2 - 2*c);
Vx(7) = -beta6*c2;
DVx.Init(0);
DVx(3) = 2*(beta*betaprim*(2*b - 1) + bpr*beta2);
DVx(5) = 4*beta3*betaprim*(b2 - 2*c) + 2*beta4*bpr*(b-1);
DVx(7) = - 6*beta5*betaprim*c2 - 2*beta6*bpr*c;
D2Vx.Init(0);
D2Vx(3) = 2*((betaprim2+beta*betasecn)*(2*b - 1)
+ 8*beta*betaprim*bpr
+ bsc*beta2);
D2Vx(5) = 4*(b2 - 2*c)*(3*beta2*betaprim2 + beta3*betasecn)
+ 16*beta3*betaprim*bpr*(b-1)
+ 2*beta4*(bsc*(b-1)+bpr2);
D2Vx(7) = - 6 * c2 * (5*beta4*betaprim2+beta5*betasecn)
- 24*beta5*betaprim*bpr*c
- 2*beta6*(bsc*c + bpr2);
//Y = 2*U*V
Vy(2) = 2*beta;
Vy(4) = beta3*2*(c+b);
Vy(6) = 2*beta5*b*c;
DVy.Init(0);
DVy(2) = 2*betaprim;
DVy(4) = 6*beta2*betaprim*(b+c) + 4*beta3*bpr;
DVy(6) = 10*beta4*betaprim*b*c + 2*beta5*bpr*(b+c);
D2Vy.Init(0);
D2Vy(2) = 2*betasecn;
D2Vy(4) = 6*(b+c)*(2*beta*betaprim2 + beta2*betasecn)
+ 24*beta2*betaprim*bpr*(b+c)
+ 4*beta3*bsc;
D2Vy(6) = 10*b*c*(4*beta3*betaprim2 + beta4*betasecn)
+ 40 * beta4*betaprim*bpr*(b+c)
+ 2*beta5*(bsc*(b+c)+ 2*bpr2);
// W = U*U + V*V
Vw(3) = beta2*(1 + 2*b);
Vw(5) = beta4*(2*c + b2);
Vw(7) = beta6*c2;
DVw.Init(0);
DVw(3) = 2*(beta*betaprim*(1 + 2*b) + beta2*bpr);
DVw(5) = 4*beta3*betaprim*(2*c + b2) + 2*beta4*bpr*(b+1);
DVw(7) = 6*beta5*betaprim*c2 + 2*beta6*bpr*c;
D2Vw.Init(0);
D2Vw(3) = 2*((betaprim2+beta*betasecn)*(2*b + 1)
+ 8*beta*betaprim*bpr
+ bsc*beta2);
D2Vw(5) = 4*(b2 + 2*c)*(3*beta2*betaprim2 + beta3*betasecn)
+ 16*beta3*betaprim*bpr*(b+11)
+ 2*beta4*(bsc*(b+1)+bpr2);
D2Vw(7) = 6 * c2 * (5*beta4*betaprim2+beta5*betasecn)
+ 24*beta5*betaprim*bpr*c
+ 2*beta6*(bsc*c + bpr2);
// Calcul des poles
Px = B * Vx;
Py = B * Vy;
W.Multiply(B, Vw);
DPx = B * DVx;
DPy = B * DVy;
DW.Multiply(B, DVw);
D2Px = B * D2Vx;
D2Py = B * D2Vy;
D2W.Multiply(B, D2Vw);
gp_XYZ P, DP, D2P;
Standard_Real wi, dwi;
for (ii=1; ii<=Ordre; ii++) {
wi = W(ii);
dwi = DW(ii);
P.SetCoord(Px(ii)/wi, Py(ii)/wi, 0);
DP.SetCoord(DPx(ii)/wi, DPy(ii)/wi, 0);
D2P.SetCoord(D2Px(ii)/wi, D2Py(ii)/wi, 0);
D2P -= 2*(dwi/wi)*DP;
D2P += (2*Pow(dwi/wi, 2) - D2W(ii)/wi)*P;
DP -= (DW(ii)/wi)*P;
Poles(ii).ChangeCoord() = M*P + Center.XYZ();
auxyz.SetLinearForm(1, MPrim*P,
1, M*DP,
DCenter.XYZ());
DPoles(ii).SetXYZ(auxyz);
P *= MSecn;
DP *= MPrim;
D2P*= M;
auxyz.SetLinearForm(1, P,
2, DP,
1, D2P,
D2Center.XYZ());
D2Poles(ii).SetXYZ(auxyz);
Weights(ii) = wi;
DWeights(ii) = dwi;
D2Weights(ii) = D2W(ii);
}
}