1 // File: GeomFill_QuasiAngularConvertor.cxx
2 // Created: Wed Aug 6 09:31:38 1997
3 // Author: Philippe MANGIN
7 #include <GeomFill_QuasiAngularConvertor.ixx>
14 #include <Convert_CompPolynomialToPoles.hxx>
16 #include <TColStd_Array1OfReal.hxx>
17 #include <TColStd_HArray2OfReal.hxx>
18 #include <TColStd_HArray1OfInteger.hxx>
19 #include <TColStd_HArray1OfReal.hxx>
21 #define NullAngle 1.e-6
23 // QuasiAngular is rational definition of Cos(theta(t) and sin(theta)
24 // on [-alpha, +alpha] with
27 // cos (theta(t)) = ----------
33 // sin (theta(t)) = ----------
46 // b =--------- + -----------------------
48 // gamma 3*(tang gamma - gamma)
50 // with gamma = alpha / 2
53 GeomFill_QuasiAngularConvertor::GeomFill_QuasiAngularConvertor():
54 myinit(Standard_False),
57 W(1,7), Vx(1, 7), Vy(1, 7), Vw(1,7)
61 Standard_Boolean GeomFill_QuasiAngularConvertor::Initialized() const
66 void GeomFill_QuasiAngularConvertor::Init()
68 if (myinit) return; //On n'initialise qu'une fois
69 Standard_Integer ii, jj, Ordre=7;
71 TColStd_Array1OfReal Coeffs(1, Ordre*Ordre), TrueInter(1,2), Inter(1,2);
72 Handle(TColStd_HArray2OfReal)
73 Poles1d = new (TColStd_HArray2OfReal) (1, Ordre, 1, Ordre);
76 Inter.SetValue(1, -1);
78 TrueInter.SetValue(1, -1);
79 TrueInter.SetValue(2, 1);
82 for (ii=1; ii<=Ordre; ii++) { Coeffs.SetValue(ii+(ii-1)*Ordre, 1); }
85 Convert_CompPolynomialToPoles
86 AConverter(Ordre, Ordre-1, Ordre-1,
90 AConverter.Poles(Poles1d);
92 for (jj=1; jj<=Ordre; jj++) {
93 for (ii=1; ii<=Ordre; ii++) {
94 terme = Poles1d->Value(ii,jj);
95 if (Abs(terme-1) < 1.e-9) terme = 1 ; //petite retouche
96 if (Abs(terme+1) < 1.e-9) terme = -1;
101 // Init des polynomes
108 myinit = Standard_True;
111 void GeomFill_QuasiAngularConvertor::Section(const gp_Pnt& FirstPnt,
112 const gp_Pnt& Center,
114 const Standard_Real Angle,
115 TColgp_Array1OfPnt& Poles,
116 TColStd_Array1OfReal& Weights)
118 Standard_Real b, b2, c, c2,tan_b;
120 Standard_Real beta, beta2, beta3, beta4, beta5, beta6, wi;
123 // Calcul de la transformation
124 gp_Vec V1(Center, FirstPnt), V2;
125 Rot.SetRotation(Dir.XYZ(), Angle/2);
131 gp_Mat M(V1.X(), V2.X(), 0,
135 // Calcul des coeffs -----------
138 beta3 = beta * beta2;
143 if ((M_PI/2 - beta)> NullAngle) {
144 if (Abs(beta) < NullAngle) {
145 Standard_Real cf = 2.0/(3*5*7);
146 b = - (0.2+cf*beta2) / (1+ 0.2*beta2);
152 b += beta / (3*(tan_b - beta));
155 else b = ((Standard_Real) -1)/beta2;
156 c = ((Standard_Real) 1)/ 3 + b;
161 Vx(3) = beta2*(2*b - 1);
162 Vx(5) = beta4*(b2 - 2*c);
167 Vy(4) = beta3*2*(c+b);
171 Vw(3) = beta2*(1 + 2*b);
172 Vw(5) = beta4*(2*c + b2);
182 for (ii=1; ii<=7; ii++) {
184 pnt.SetCoord(Px(ii)/wi, Py(ii)/wi, 0);
187 Poles(ii).ChangeCoord() = pnt;
192 void GeomFill_QuasiAngularConvertor::Section(const gp_Pnt& FirstPnt,
193 const gp_Vec& DFirstPnt,
194 const gp_Pnt& Center,
195 const gp_Vec& DCenter,
198 const Standard_Real Angle,
199 const Standard_Real DAngle,
200 TColgp_Array1OfPnt& Poles,
201 TColgp_Array1OfVec& DPoles,
202 TColStd_Array1OfReal& Weights,
203 TColStd_Array1OfReal& DWeights)
205 Standard_Integer Ordre = 7;
206 math_Vector DVx(1, Ordre), DVy(1, Ordre), DVw(1, Ordre),
207 DPx(1, Ordre), DPy(1, Ordre), DW(1, Ordre);
208 Standard_Real b, b2, c, c2,tan_b;
209 Standard_Real bpr, dtan_b;
211 Standard_Real beta, beta2, beta3, beta4, beta5, beta6, betaprim;
212 gp_Vec V1(Center, FirstPnt), V1Prim, V2;
214 // Calcul des transformations
216 Standard_Real Sina, Cosa;
217 gp_Mat Rot, RotPrim, D, DPrim;
218 // La rotation s'ecrit I + sin(Ang) * D + (1. - cos(Ang)) * D*D
219 // ou D est l'application x -> Dir ^ x
220 Rot.SetRotation(Dir.XYZ(), Angle/2);
221 // La derive s'ecrit donc :
222 // AngPrim * (sin(Ang)*D*D + cos(Ang)*D)
223 // + sin(Ang)*DPrim + (1. - cos(Ang)) *(DPrim*D + D*DPrim)
226 D.SetCross(Dir.XYZ());
227 DPrim.SetCross(DDir.XYZ());
229 RotPrim = (D.Powered(2)).Multiplied(Sina);
230 RotPrim += D.Multiplied(Cosa);
232 RotPrim += DPrim.Multiplied(Sina);
233 RotPrim += ((DPrim.Multiplied(D)).Added(D.Multiplied(DPrim))).Multiplied(1-Cosa);
235 aux = (DFirstPnt - DCenter).XYZ().Multiplied(Rot);
236 aux += V1.XYZ().Multiplied(RotPrim);
242 gp_Mat M (V1.X(), V2.X(), 0,
245 V2 = (DDir.Crossed(V1)).Added(Dir.Crossed(V1Prim));
246 gp_Mat MPrim (V1Prim.X(), V2.X(), 0,
247 V1Prim.Y(), V2.Y(), 0,
248 V1Prim.Z(), V2.Z(), 0);
250 // Calcul des constante -----------
254 beta3 = beta * beta2;
259 if (Abs(beta) < NullAngle) {
260 // On calcul b par D.L
261 Standard_Real cf = 2.0/(3*5*7);
262 Standard_Real Num, Denom;
263 Num = 0.2 + cf*beta2;
266 bpr = -2*beta*betaprim*(cf*Denom - 0.2*Num)/(Denom*Denom);
269 b = ((Standard_Real) -1)/beta2;
270 bpr = (2*betaprim) / beta3;
271 if ((M_PI/2 - beta)> NullAngle) {
273 dtan_b = betaprim * (1 + tan_b*tan_b);
276 bpr += (betaprim*tan_b - beta*dtan_b) / (3*b2*b2);
280 c = ((Standard_Real) 1)/ 3 + b;
286 Vx(3) = beta2*(2*b - 1);
287 Vx(5) = beta4*(b2 - 2*c);
290 DVx(3) = 2*(beta*betaprim*(2*b - 1) + bpr*beta2);
291 DVx(5) = 4*beta3*betaprim*(b2 - 2*c) + 2*beta4*bpr*(b-1);
292 DVx(7) = - 6*beta5*betaprim*c2 - 2*beta6*bpr*c;
296 Vy(4) = beta3*2*(c+b);
300 DVy(4) = 6*beta2*betaprim*(b+c) + 4*beta3*bpr;
301 DVy(6) = 10*beta4*betaprim*b*c + 2*beta5*bpr*(b+c);
304 Vw(3) = beta2*(1 + 2*b);
305 Vw(5) = beta4*(2*c + b2);
308 // DVw(3) = 2*(beta*betaprim*(1 + 2*b) + beta2*bpr);
309 DVw(3) = 2*beta*(betaprim*(1 + 2*b) + beta*bpr);
310 // DVw(5) = 4*beta3*betaprim*(2*c + b2) + 2*beta4*bpr*(b+1);
311 DVw(5) = 2*beta3*(2*betaprim*(2*c + b2) + beta*bpr*(b+1));
312 // DVw(7) = 6*beta5*betaprim*c2 + 2*beta6*bpr*c;
313 DVw(7) = 2*beta5*c*(3*betaprim*c + beta*bpr);
321 DPx.Multiply(B, DVx);
322 DPy.Multiply(B, DVy);
328 for (ii=1; ii<=Ordre; ii++) {
330 P.SetCoord(Px(ii)/wi, Py(ii)/wi, 0);
331 DP.SetCoord(DPx(ii)/wi, DPy(ii)/wi, 0);
334 Poles(ii).ChangeCoord() = M*P + Center.XYZ();
337 aux.SetLinearForm(1, P, 1, DP, DCenter.XYZ());
338 DPoles(ii).SetXYZ(aux);
340 DWeights(ii) = DW(ii);
344 void GeomFill_QuasiAngularConvertor::Section(const gp_Pnt& FirstPnt,
345 const gp_Vec& DFirstPnt,
346 const gp_Vec& D2FirstPnt,
347 const gp_Pnt& Center,
348 const gp_Vec& DCenter,
349 const gp_Vec& D2Center,
353 const Standard_Real Angle,
354 const Standard_Real DAngle,
355 const Standard_Real D2Angle,
356 TColgp_Array1OfPnt& Poles,
357 TColgp_Array1OfVec& DPoles,
358 TColgp_Array1OfVec& D2Poles,
359 TColStd_Array1OfReal& Weights,
360 TColStd_Array1OfReal& DWeights,
361 TColStd_Array1OfReal& D2Weights)
363 Standard_Integer Ordre = 7;
364 math_Vector DVx(1, Ordre), DVy(1, Ordre), DVw(1, Ordre),
365 D2Vx(1, Ordre), D2Vy(1, Ordre), D2Vw(1, Ordre);
366 math_Vector DPx(1, Ordre), DPy(1, Ordre), DW(1, Ordre),
367 D2Px(1, Ordre), D2Py(1, Ordre), D2W(1, Ordre);
370 Standard_Real aux, daux, b, b2, c, c2, bpr, bsc;
371 gp_Vec V1(Center, FirstPnt), V1Prim, V1Secn, V2;
373 // Calcul des transformations
375 Standard_Real Sina, Cosa;
376 gp_Mat Rot, RotPrim, RotSecn, D, DPrim, DSecn, DDP, Maux;
377 // La rotation s'ecrit I + sin(Ang) * D + (1. - cos(Ang)) * D*D
378 // ou D est l'application x -> Dir ^ x
379 Rot.SetRotation(Dir.XYZ(), Angle/2);
380 // La derive s'ecrit donc :
381 // AngPrim * (sin(Ang)*D*D + cos(Ang)*D)
382 // + sin(Ang)*DPrim + (1. - cos(Ang)) *(DPrim*D + D*DPrim)
385 D.SetCross(Dir.XYZ());
386 DPrim.SetCross(DDir.XYZ());
387 DSecn.SetCross(D2Dir.XYZ());
389 DDP = (DPrim.Multiplied(D)).Added(D.Multiplied(DPrim));
390 RotPrim = (D.Powered(2)).Multiplied(Sina);
391 RotPrim += D.Multiplied(Cosa);
393 RotPrim += DPrim.Multiplied(Sina);
394 RotPrim += DDP.Multiplied(1-Cosa);
396 RotSecn = (D.Powered(2)).Multiplied(Sina);
397 RotSecn += D.Multiplied(Cosa);
398 RotSecn *= D2Angle/2;
399 Maux = (D.Powered(2)).Multiplied(Cosa);
400 Maux -= D.Multiplied(Sina);
402 Maux += DDP.Multiplied(2*Sina);
403 Maux += DPrim.Multiplied(2*Cosa);
406 Maux = (DSecn.Multiplied(D)).Added(D.Multiplied(DSecn));
407 Maux += (DPrim.Powered(2)).Multiplied(2);
409 Maux += DSecn.Multiplied(Sina);
412 V1Prim = DFirstPnt - DCenter;
413 auxyz = (D2FirstPnt - D2Center).XYZ().Multiplied(Rot);
414 auxyz += 2*(V1Prim.XYZ().Multiplied(RotPrim));
415 auxyz += V1.XYZ().Multiplied(RotSecn);
416 V1Secn.SetXYZ(auxyz);
417 auxyz = V1Prim.XYZ().Multiplied(Rot);
418 auxyz += V1.XYZ().Multiplied(RotPrim);
419 V1Prim.SetXYZ(auxyz);
425 gp_Mat M (V1.X(), V2.X(), 0,
428 V2 = (DDir.Crossed(V1)).Added(Dir.Crossed(V1Prim));
429 gp_Mat MPrim (V1Prim.X(), V2.X(), 0,
430 V1Prim.Y(), V2.Y(), 0,
431 V1Prim.Z(), V2.Z(), 0);
435 V2 += (D2Dir.Crossed(V1)).Added(Dir.Crossed(V1Secn));
436 gp_Mat MSecn (V1Secn.X(), V2.X(), 0,
437 V1Secn.Y(), V2.Y(), 0,
438 V1Secn.Z(), V2.Z(), 0);
441 // Calcul des coeff -----------
442 Standard_Real tan_b, dtan_b, d2tan_b;
443 Standard_Real beta, beta2, beta3, beta4, beta5, beta6, betaprim, betasecn;
444 Standard_Real betaprim2, bpr2;
447 betasecn = D2Angle/4;
449 beta3 = beta * beta2;
453 betaprim2 = betaprim * betaprim;
455 if (Abs(beta) < NullAngle) {
456 // On calcul b par D.L
457 Standard_Real cf =-2.0/21;
458 Standard_Real Num, Denom, aux;
459 Num = 0.2 + cf*beta2;
461 aux = (cf*Denom - 0.2*Num)/(Denom*Denom);
463 bpr = -2*beta*betaprim*aux;
464 bsc = 2*aux*(betaprim2 + beta*betasecn - 2*beta*betaprim2);
468 b = ((Standard_Real) -1)/beta2;
469 bpr = (2*betaprim) / beta3;
470 bsc = (2*betasecn - 6*betaprim*(betaprim/beta)) / beta3;
471 if ((M_PI/2 - beta)> NullAngle) {
473 dtan_b = betaprim * (1 + tan_b*tan_b);
474 d2tan_b = betasecn * (1 + tan_b*tan_b)
475 + 2*betaprim * tan_b * dtan_b;
478 aux = betaprim*tan_b - beta*dtan_b;
479 bpr += aux / (3*b2*b2);
480 daux = betasecn*tan_b - beta*d2tan_b;
481 bsc += (daux - 2*aux*betaprim*tan_b*tan_b/b2)/(3*b2*b2);
485 c = ((Standard_Real) 1)/ 3 + b;
492 Vx(3) = beta2*(2*b - 1);
493 Vx(5) = beta4*(b2 - 2*c);
496 DVx(3) = 2*(beta*betaprim*(2*b - 1) + bpr*beta2);
497 DVx(5) = 4*beta3*betaprim*(b2 - 2*c) + 2*beta4*bpr*(b-1);
498 DVx(7) = - 6*beta5*betaprim*c2 - 2*beta6*bpr*c;
500 D2Vx(3) = 2*((betaprim2+beta*betasecn)*(2*b - 1)
501 + 8*beta*betaprim*bpr
503 D2Vx(5) = 4*(b2 - 2*c)*(3*beta2*betaprim2 + beta3*betasecn)
504 + 16*beta3*betaprim*bpr*(b-1)
505 + 2*beta4*(bsc*(b-1)+bpr2);
506 D2Vx(7) = - 6 * c2 * (5*beta4*betaprim2+beta5*betasecn)
507 - 24*beta5*betaprim*bpr*c
508 - 2*beta6*(bsc*c + bpr2);
512 Vy(4) = beta3*2*(c+b);
516 DVy(4) = 6*beta2*betaprim*(b+c) + 4*beta3*bpr;
517 DVy(6) = 10*beta4*betaprim*b*c + 2*beta5*bpr*(b+c);
519 D2Vy(2) = 2*betasecn;
520 D2Vy(4) = 6*(b+c)*(2*beta*betaprim2 + beta2*betasecn)
521 + 24*beta2*betaprim*bpr*(b+c)
523 D2Vy(6) = 10*b*c*(4*beta3*betaprim2 + beta4*betasecn)
524 + 40 * beta4*betaprim*bpr*(b+c)
525 + 2*beta5*(bsc*(b+c)+ 2*bpr2);
528 Vw(3) = beta2*(1 + 2*b);
529 Vw(5) = beta4*(2*c + b2);
532 DVw(3) = 2*(beta*betaprim*(1 + 2*b) + beta2*bpr);
533 DVw(5) = 4*beta3*betaprim*(2*c + b2) + 2*beta4*bpr*(b+1);
534 DVw(7) = 6*beta5*betaprim*c2 + 2*beta6*bpr*c;
536 D2Vw(3) = 2*((betaprim2+beta*betasecn)*(2*b + 1)
537 + 8*beta*betaprim*bpr
539 D2Vw(5) = 4*(b2 + 2*c)*(3*beta2*betaprim2 + beta3*betasecn)
540 + 16*beta3*betaprim*bpr*(b+11)
541 + 2*beta4*(bsc*(b+1)+bpr2);
542 D2Vw(7) = 6 * c2 * (5*beta4*betaprim2+beta5*betasecn)
543 + 24*beta5*betaprim*bpr*c
544 + 2*beta6*(bsc*c + bpr2);
556 D2W.Multiply(B, D2Vw);
559 Standard_Real wi, dwi;
560 for (ii=1; ii<=Ordre; ii++) {
563 P.SetCoord(Px(ii)/wi, Py(ii)/wi, 0);
564 DP.SetCoord(DPx(ii)/wi, DPy(ii)/wi, 0);
566 D2P.SetCoord(D2Px(ii)/wi, D2Py(ii)/wi, 0);
567 D2P -= 2*(dwi/wi)*DP;
568 D2P += (2*Pow(dwi/wi, 2) - D2W(ii)/wi)*P;
571 Poles(ii).ChangeCoord() = M*P + Center.XYZ();
572 auxyz.SetLinearForm(1, MPrim*P,
575 DPoles(ii).SetXYZ(auxyz);
579 auxyz.SetLinearForm(1, P,
583 D2Poles(ii).SetXYZ(auxyz);
586 D2Weights(ii) = D2W(ii);