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//============================================================================
//======================================================= IntAna2d_Outils.cxx
//============================================================================
#include <IntAna2d_Outils.hxx>
#include <math_DirectPolynomialRoots.hxx>
MyDirectPolynomialRoots::MyDirectPolynomialRoots(const Standard_Real A4,
const Standard_Real A3,
const Standard_Real A2,
const Standard_Real A1,
const Standard_Real A0) {
//-- cout<<" IntAna2d : A4..A0 "<<A4<<" "<<A3<<" "<<A2<<" "<<A1<<" "<<A0<<" "<<endl;
nbsol = 0;
same = Standard_False;
// Modified by Sergey KHROMOV - Thu Oct 24 13:10:14 2002 Begin
Standard_Real anAA[5];
anAA[0] = Abs(A0);
anAA[1] = Abs(A1);
anAA[2] = Abs(A2);
anAA[3] = Abs(A3);
anAA[4] = Abs(A4);
// if((Abs(A4)+Abs(A3)+Abs(A2)+Abs(A1)+Abs(A0))<Epsilon(10000.0)) {
if((anAA[0]+anAA[1]+anAA[2]+anAA[3]+anAA[4])<Epsilon(10000.0)) {
// Modified by Sergey KHROMOV - Thu Oct 24 13:10:15 2002 End
same = Standard_True;
return;
}
Standard_Integer i,j,nbp;
for(i=0;i<16;i++) val[i]=RealLast();
Standard_Real tol = Epsilon(100.0);
math_DirectPolynomialRoots MATH_A43210(A4,A3,A2,A1,A0);
Standard_Boolean PbPossible = Standard_False;
Standard_Integer NbsolPolyComplet = 0;
if(MATH_A43210.IsDone()) {
nbp = MATH_A43210.NbSolutions();
NbsolPolyComplet = nbp;
for(i=1;i<=nbp;i++) {
Standard_Real x = MATH_A43210.Value(i);
//-- cout<<" IntAna2d : x Pol Complet :"<<x<<endl;
val[nbsol] = A0 + x*(A1+x*(A2+x*(A3+x*A4)));
sol[nbsol] = x;
if(val[nbsol]> tol || val[nbsol]<-tol) {
PbPossible = Standard_True;
}
nbsol++;
}
if(nbp & 1)
PbPossible = Standard_True;
}
else {
PbPossible = Standard_True;
}
//-- On recherche le plus petit coeff entre A4 et A0
if(PbPossible) {
// Modified by Sergey KHROMOV - Thu Oct 24 12:45:35 2002 Begin
Standard_Real anAMin = RealLast();
Standard_Real anAMax = -1;
Standard_Real anEps = RealEpsilon();
for (i = 0; i < 5; i++) {
anAMin = Min(anAMin, Max(anAA[i], anEps));
anAMax = Max(anAMax, Max(anAA[i], anEps));
}
anEps = Min(1.e-4, Epsilon(1000.*anAMax/anAMin));
// Modified by Sergey KHROMOV - Thu Oct 24 15:46:24 2002 End
math_DirectPolynomialRoots MATH_A4321(A4,A3,A2,A1);
if(MATH_A4321.IsDone()) {
nbp = MATH_A4321.NbSolutions();
//-- On Ajoute les valeurs au tableau
for(i=1;i<=nbp;i++) {
Standard_Real x = MATH_A4321.Value(i);
Standard_Boolean Add = Standard_True;
for(j=0;j<nbsol;j++) {
Standard_Real t = sol[j]-x;
// Modified by Sergey KHROMOV - Thu Oct 24 12:04:26 2002 Begin
// if(Abs(t)<tol) {
if(Abs(t) < anEps) {
// Modified by Sergey KHROMOV - Thu Oct 24 12:04:47 2002 End
Add = Standard_False;
}
}
if(Add) {
val[nbsol] = A0 + x*(A1+x*(A2+x*(A3+x*A4)));
sol[nbsol] = x;
nbsol++;
}
}
}
math_DirectPolynomialRoots MATH_A3210(A3,A2,A1,A0);
if(MATH_A3210.IsDone()) {
nbp = MATH_A3210.NbSolutions();
//-- On Ajoute les valeurs au tableau
for(i=1;i<=nbp;i++) {
Standard_Real x = MATH_A3210.Value(i);
Standard_Boolean Add = Standard_True;
for(j=0;j<nbsol;j++) {
Standard_Real t = sol[j]-x;
// Modified by Sergey KHROMOV - Thu Oct 24 12:06:01 2002 Begin
// if(Abs(t)<tol) {
if(Abs(t) < anEps) {
// Modified by Sergey KHROMOV - Thu Oct 24 12:06:04 2002 End
Add = Standard_False;
}
}
if(Add) {
val[nbsol] = A0 + x*(A1+x*(A2+x*(A3+x*A4)));
sol[nbsol] = x;
nbsol++;
}
}
}
math_DirectPolynomialRoots MATH_A210(A3,A2,A1);
if(MATH_A210.IsDone()) {
nbp = MATH_A210.NbSolutions();
//-- On Ajoute les valeurs au tableau
for(i=1;i<=nbp;i++) {
Standard_Real x = MATH_A210.Value(i);
Standard_Boolean Add = Standard_True;
for(j=0;j<nbsol;j++) {
Standard_Real t = sol[j]-x;
// Modified by Sergey KHROMOV - Thu Oct 24 12:07:04 2002 Begin
// if(Abs(t)<tol) {
if(Abs(t) < anEps) {
// Modified by Sergey KHROMOV - Thu Oct 24 12:07:06 2002 End
Add = Standard_False;
}
}
if(Add) {
val[nbsol] = A0 + x*(A1+x*(A2+x*(A3+x*A4)));
sol[nbsol] = x;
nbsol++;
}
}
}
//------------------------------------------------------------
//-- On trie les valeurs par ordre decroissant de val
//-- for(i=0;i<nbsol;i++) {
//-- cout<<" IntAna2d Sol,Val"<<sol[i]<<" "<<val[i]<<endl;
//-- }
Standard_Boolean TriOK = Standard_False;
do {
TriOK = Standard_True;
for(i=1; i<nbsol;i++) {
if(Abs(val[i])<Abs(val[i-1])) {
Standard_Real t;
t = val[i];
val[i] = val[i-1];
val[i-1] = t;
t = sol[i];
sol[i] = sol[i-1];
sol[i-1] = t;
TriOK = Standard_False;
}
}
}
while(!TriOK);
//-----------------------------------------------------------
//-- On garde les premieres valeurs
//-- Au moins autant que le polynome Complet
//--
for(nbsol=0; nbsol<NbsolPolyComplet || Abs(val[nbsol])<Epsilon(10000.0); nbsol++) ;
//-- cout<<" IntAna2d : nbsol:"<<nbsol<<endl;
}
if(nbsol==0) {
nbsol=-1;
}
if(nbsol>4) {
same=1;
nbsol=0;
}
}
MyDirectPolynomialRoots::MyDirectPolynomialRoots(const Standard_Real A2,
const Standard_Real A1,
const Standard_Real A0) {
//-- cout<<" IntAna2d : A2..A0 "<<A2<<" "<<A1<<" "<<A0<<" "<<endl;
nbsol=0;
if((Abs(A2)+Abs(A1)+Abs(A0))<Epsilon(10000.0)) {
same = Standard_True;
return;
}
math_DirectPolynomialRoots MATH_A210(A2,A1,A0);
same = Standard_False;
if(MATH_A210.IsDone()) {
for(Standard_Integer i=1;i<=MATH_A210.NbSolutions(); i++) {
Standard_Real x = MATH_A210.Value(i);
val[nbsol] = A0 + x*(A1+x*A2);
sol[nbsol] = x;
//-- cout<<" IntAna2d : x Pol Complet :"<<x<<" Val:"<<val[nbsol]<<endl;
nbsol++;
}
}
else {
nbsol = -1;
}
}
Standard_Boolean Points_Confondus(const Standard_Real x1,const Standard_Real y1
,const Standard_Real x2,const Standard_Real y2) {
if(Abs(x1-x2)<Epsilon(x1)) {
if(Abs(y1-y2)<Epsilon(y1)) {
return(Standard_True);
}
}
return(Standard_False);
}
//-----------------------------------------------------------------------------
//--- Les points confondus sont supprimes
//--- Le nombre de points est mis a jour
void Traitement_Points_Confondus(Standard_Integer& nb_pts,
IntAna2d_IntPoint* pts) {
Standard_Integer i,j;
for(i=nb_pts;i>1;i--) {
Standard_Boolean Non_Egalite=Standard_True;
for(j=i-1;(j>0) && Non_Egalite;j--) {
// <--- Deja Teste --->
// | 1 |2 | | J | |I-1| I |I+1| |NPTS|
// | 1 |2 | | J | |I-1|XXX|I+1| |NPTS|
// | 1 |2 | | J | |I-1|I+1|I+2| |NPTS|
if(Points_Confondus(pts[i-1].Value().X(),
pts[i-1].Value().Y(),
pts[j-1].Value().X(),
pts[j-1].Value().Y())) {
Standard_Integer k;
Non_Egalite=Standard_False;
for(k=i;k<nb_pts;k++) {
Standard_Real Xk,Yk,Uk;
Xk=pts[k].Value().X();
Yk=pts[k].Value().Y();
Uk=pts[k].ParamOnFirst();
pts[k-1].SetValue(Xk,Yk,Uk);
}
nb_pts--;
}
}
}
}
//-----------------------------------------------------------------------------
void Coord_Ancien_Repere(Standard_Real& x1,Standard_Real& y1,const gp_Ax2d Dir1) {
Standard_Real t11,t12,t21,t22,t13,t23;
Standard_Real x0,y0;
// x1 et y1 Sont les Coordonnees dans le repere lie a Dir1
// On Renvoie ces Coordonnees dans le repere "absolu"
Dir1.Direction().Coord(t11,t21);
Dir1.Location().Coord(t13,t23);
t22=t11;
t12=-t21;
x0= t11*x1 + t12*y1 + t13;
y0= t21*x1 + t22*y1 + t23;
x1=x0;
y1=y0;
}
#if 0
//-- A Placer dans les ressources de la classe Conic ??
//-----------------------------------------------------------------------------
//--- Calcul des Coefficients A,..F dans le repere lie a Dir1
//--- A Partir des Coefficients dans le repere "Absolu"
void Coeff_Nouveau_Repere(Standard_Real& A,Standard_Real& B,Standard_Real& C
,Standard_Real& D,Standard_Real& E,Standard_Real& F
,const gp_Ax2d Dir1) {
Standard_Real t11,t12,t13; // x = t11 X + t12 Y + t13
Standard_Real t21,t22,t23; // y = t21 X + t22 Y + t23
Standard_Real A1,B1,C1,D1,E1,F1;
// On a P0(x,y)=A x x + B y y + ... + F =0 (x et y ds le repere "Absolu")
// et on cherche P1(X(x,y),Y(x,y))=P0(x,y)
// Avec P1(X,Y)= A1 X X + B1 Y Y + 2 C1 X Y + 2 D1 X + 2 E1 Y + F1
// = A x x + B y y + 2 C x y + 2 D x + 2 E y + f
Dir1.Direction().Coord(t11,t21);
Dir1.Location().Coord(t13,t23);
t22=t11;
t12=-t21;
A1=(t11*(A*t11 + 2*C*t21) + B*t21*t21);
B1=(t12*(A*t12 + 2*C*t22) + B*t22*t22);
C1=(t12*(A*t11 + C*t21) + t22*(C*t11 + B*t21));
D1=(t11*(D + A*t13) + t21*(E + C*t13) + t23*(C*t11 + B*t21));
E1=(t12*(D + A*t13) + t22*(E + C*t13) + t23*(C*t12 + B*t22));
F1=F + t13*(2.0*D + A*t13) + t23*(2.0*E + 2.0*C*t13 + B*t23);
A=A1; B=B1; C=C1; D=D1; E=E1; F=F1;
}
#endif
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