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0023824: Bad results of sweep operation when a path curve has unpredictable torsion...
[occt.git] / src / GeomFill / GeomFill_CorrectedFrenet.cxx
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b311480e 1// Created on: 1997-12-19
2// Created by: Roman BORISOV /Philippe MANGIN
3// Copyright (c) 1997-1999 Matra Datavision
4// Copyright (c) 1999-2012 OPEN CASCADE SAS
5//
6// The content of this file is subject to the Open CASCADE Technology Public
7// License Version 6.5 (the "License"). You may not use the content of this file
8// except in compliance with the License. Please obtain a copy of the License
9// at http://www.opencascade.org and read it completely before using this file.
10//
11// The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
12// main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
13//
14// The Original Code and all software distributed under the License is
15// distributed on an "AS IS" basis, without warranty of any kind, and the
16// Initial Developer hereby disclaims all such warranties, including without
17// limitation, any warranties of merchantability, fitness for a particular
18// purpose or non-infringement. Please see the License for the specific terms
19// and conditions governing the rights and limitations under the License.
20
7fd59977 21
22#include <stdio.h>
23
24#include <GeomFill_CorrectedFrenet.ixx>
25#include <GeomAbs_CurveType.hxx>
26#include <Adaptor3d_HCurve.hxx>
27#include <gp_Trsf.hxx>
28#include <Precision.hxx>
29#include <TColStd_HArray1OfReal.hxx>
30#include <Law_Interpolate.hxx>
31#include <TColStd_SequenceOfReal.hxx>
32#include <gp_Vec2d.hxx>
33#include <BndLib_Add3dCurve.hxx>
34#include <Bnd_Box.hxx>
35#include <GeomLib.hxx>
36#include <Law_Composite.hxx>
37#include <Law_Constant.hxx>
38#include <Law_BSpFunc.hxx>
39#include <Law_BSpline.hxx>
40#include <GeomFill_SnglrFunc.hxx>
41//Patch
42#include <Geom_Plane.hxx>
43#include <Geom_BezierCurve.hxx>
44#include <Geom_BSplineCurve.hxx>
45#include <TColgp_HArray1OfPnt.hxx>
46
a31abc03 47
7fd59977 48#ifdef DEB
49static Standard_Boolean Affich=0;
50#endif
51
52#ifdef DRAW
53static Standard_Integer CorrNumber = 0;
54#include <Draw_Appli.hxx>
55#include <DrawTrSurf.hxx>
56#include <Draw_Segment2D.hxx>
57//#include <Draw.hxx>
58#include <TColgp_Array1OfPnt.hxx>
59#include <TColStd_Array1OfReal.hxx>
60#include <TColStd_HArray1OfInteger.hxx>
61#endif
62
63#ifdef DRAW
64static void draw(const Handle(Law_Function)& law)
65{
66 Standard_Real Step, u, v, tmin;
67 Standard_Integer NbInt, i, j, jmax;
68 NbInt = law->NbIntervals(GeomAbs_C3);
69 TColStd_Array1OfReal Int(1, NbInt+1);
70 law->Intervals(Int, GeomAbs_C3);
71 gp_Pnt2d old;
72 Handle(Draw_Segment2D) tg2d;
73
74 for(i = 1; i <= NbInt; i++){
75 tmin = Int(i);
76 Step = (Int(i+1)-Int(i))/4;
77 if (i == NbInt) jmax = 4;
78 else jmax = 3;
79 for (j=1; j<=jmax; j++) {
80 u = tmin + (j-1)*Step;
81 v = law->Value(u);
82 gp_Pnt2d point2d(u,v);
83 if ((i>1)||(j>1)) {
84 tg2d = new Draw_Segment2D(old, point2d,Draw_kaki);
85 dout << tg2d;
86 }
87 old = point2d;
88 }
89 }
90 dout.Flush();
91}
92#endif
93
a31abc03 94
95static Standard_Real ComputeTorsion(const Standard_Real Param,
96 const Handle(Adaptor3d_HCurve)& aCurve)
97{
98 Standard_Real Torsion;
99
100 gp_Pnt aPoint;
101 gp_Vec DC1, DC2, DC3;
102 aCurve->D3(Param, aPoint, DC1, DC2, DC3);
103 gp_Vec DC1crossDC2 = DC1 ^ DC2;
104 Standard_Real Norm_DC1crossDC2 = DC1crossDC2.Magnitude();
105
106 Standard_Real DC1DC2DC3 = DC1crossDC2 * DC3 ; //mixed product
107
108 Standard_Real Tol = gp::Resolution();
109 Standard_Real SquareNorm_DC1crossDC2 = Norm_DC1crossDC2 * Norm_DC1crossDC2;
110 if (SquareNorm_DC1crossDC2 <= Tol)
111 Torsion = 0.;
112 else
113 Torsion = DC1DC2DC3 / SquareNorm_DC1crossDC2 ;
114
115 return Torsion;
116}
117
7fd59977 118//===============================================================
119// Function : smoothlaw
120// Purpose : to smooth a law : Reduce the number of knots
121//===============================================================
122static void smoothlaw(Handle(Law_BSpline)& Law,
123 const Handle(TColStd_HArray1OfReal)& Points,
124 const Handle(TColStd_HArray1OfReal)& Param,
125 const Standard_Real Tol)
126{
127 Standard_Real tol, d;
128 Standard_Integer ii, Nbk;
129 Standard_Boolean B, Ok;
130 Handle(Law_BSpline) BS = Law->Copy();
131
132 Nbk = BS->NbKnots();
133 tol = Tol/10;
134 Ok = Standard_False;
135
136 for (ii=Nbk-1; ii>1; ii--) { // Une premiere passe tolerance serres
137 B = BS->RemoveKnot(ii, 0, tol);
138 if (B) Ok = Standard_True;
139 }
140
141 if (Ok) { // controle
142 tol = 0.;
143 for (ii=1; ii<=Param->Length() && Ok; ii++) {
144 d = Abs(BS->Value(Param->Value(ii))-Points->Value(ii));
145 if (d > tol) tol = d;
146 Ok = (tol <= Tol);
147 }
148 if (Ok)
149 tol = (Tol-tol)/2;
150 else {
151#if DEB
152 cout << "smooth law echec" << endl;
153#endif
154 return; // Echec
155 }
156 }
157 else {
158 tol = Tol/2;
159 }
160
161
162 if (Ok) Law = BS;
163
164 Ok = Standard_False; // Une deuxieme passe tolerance desserre
165 Nbk = BS->NbKnots();
166 for (ii=Nbk-1; ii>1; ii--) {
167 B = BS->RemoveKnot(ii, 0, tol);
168 if (B) Ok = Standard_True;
169 }
170
171 if (Ok) { // controle
172 tol = 0.;
173 for (ii=1; ii<=Param->Length() && Ok; ii++) {
174 d = Abs(BS->Value(Param->Value(ii))-Points->Value(ii));
175 if (d > tol) tol = d;
176 Ok = (tol <= Tol);
177 }
178 if (!Ok) {
179#if DEB
180 cout << "smooth law echec" << endl;
181#endif
182 }
183 }
184 if (Ok) Law = BS;
185
186#if DEB
187 if (Affich) {
188 cout << "Knots Law : " << endl;
189 for (ii=1; ii<=BS->NbKnots(); ii++) {
190 cout << ii << " : " << BS->Knot(ii) << endl;
191 }
192 }
193#endif
194}
195
196//===============================================================
197// Function : FindPlane
198// Purpose :
199//===============================================================
200static Standard_Boolean FindPlane ( const Handle(Adaptor3d_HCurve)& c,
201 Handle( Geom_Plane )& P )
202{
203 Standard_Boolean found = Standard_True;
204 Handle(TColgp_HArray1OfPnt) TabP;
205
206 switch (c->GetType()) {
207
208 case GeomAbs_Line:
209 {
210 found = Standard_False;
211 }
212 break;
213
214 case GeomAbs_Circle:
215 P = new Geom_Plane(gp_Ax3(c->Circle().Position()));
216 break;
217
218 case GeomAbs_Ellipse:
219 P = new Geom_Plane(gp_Ax3(c->Ellipse().Position()));
220 break;
221
222 case GeomAbs_Hyperbola:
223 P = new Geom_Plane(gp_Ax3(c->Hyperbola().Position()));
224 break;
225
226 case GeomAbs_Parabola:
227 P = new Geom_Plane(gp_Ax3(c->Parabola().Position()));
228 break;
229
230 case GeomAbs_BezierCurve:
231 {
232 Handle(Geom_BezierCurve) GC = c->Bezier();
233 Standard_Integer nbp = GC->NbPoles();
234 if ( nbp < 2)
235 found = Standard_False;
236 else if ( nbp == 2) {
237 found = Standard_False;
238 }
239 else {
240 TabP = new (TColgp_HArray1OfPnt) (1, nbp);
241 GC->Poles(TabP->ChangeArray1());
242 }
243 }
244 break;
245
246 case GeomAbs_BSplineCurve:
247 {
248 Handle(Geom_BSplineCurve) GC = c->BSpline();
249 Standard_Integer nbp = GC->NbPoles();
250 if ( nbp < 2)
251 found = Standard_False;
252 else if ( nbp == 2) {
253 found = Standard_False;
254 }
255 else {
256 TabP = new (TColgp_HArray1OfPnt) (1, nbp);
257 GC->Poles(TabP->ChangeArray1());
258 }
259 }
260 break;
261
262 default:
263 { // On utilise un echantillonage
264 Standard_Integer nbp = 15 + c->NbIntervals(GeomAbs_C3);
265 Standard_Real f, l, t, inv;
266 Standard_Integer ii;
267 f = c->FirstParameter();
268 l = c->LastParameter();
269 inv = 1./(nbp-1);
270 for (ii=1; ii<=nbp; ii++) {
271 t = ( f*(nbp-ii) + l*(ii-1));
272 t *= inv;
273 TabP->SetValue(ii, c->Value(t));
274 }
275 }
276 }
277
278 if (! TabP.IsNull()) { // Recherche d'un plan moyen et controle
279 Standard_Boolean issingular;
280 gp_Ax2 inertia;
281 GeomLib::AxeOfInertia(TabP->Array1(), inertia, issingular);
282 if (issingular) {
283 found = Standard_False;
284 }
285 else {
286 P = new Geom_Plane(inertia);
287 }
288 if (found)
289 {
290 //control = Controle(TabP->Array1(), P, myTolerance);
291// Standard_Boolean isOnPlane;
292 Standard_Real a,b,c,d, dist;
293 Standard_Integer ii;
294 P->Coefficients(a,b,c,d);
295 for (ii=1; ii<=TabP->Length() && found; ii++) {
296 const gp_XYZ& xyz = TabP->Value(ii).XYZ();
297 dist = a*xyz.X() + b*xyz.Y() + c*xyz.Z() + d;
298 found = (Abs(dist) <= Precision::Confusion());
299 }
300 return found;
301 }
302 }
303
304 return found;
305}
306
307//===============================================================
a31abc03 308// Function : Constructor
7fd59977 309// Purpose :
310//===============================================================
311GeomFill_CorrectedFrenet::GeomFill_CorrectedFrenet()
312 : isFrenet(Standard_False)
313{
314 frenet = new GeomFill_Frenet();
a31abc03 315 myForEvaluation = Standard_False;
316}
317
318//===============================================================
319// Function : Constructor
320// Purpose :
321//===============================================================
322GeomFill_CorrectedFrenet::GeomFill_CorrectedFrenet(const Standard_Boolean ForEvaluation)
323 : isFrenet(Standard_False)
324{
325 frenet = new GeomFill_Frenet();
326 myForEvaluation = ForEvaluation;
7fd59977 327}
328
329Handle(GeomFill_TrihedronLaw) GeomFill_CorrectedFrenet::Copy() const
330{
331 Handle(GeomFill_CorrectedFrenet) copy = new (GeomFill_CorrectedFrenet)();
332 if (!myCurve.IsNull()) copy->SetCurve(myCurve);
333 return copy;
334}
335
336 void GeomFill_CorrectedFrenet::SetCurve(const Handle(Adaptor3d_HCurve)& C)
337{
338
339 GeomFill_TrihedronLaw::SetCurve(C);
340 if (! C.IsNull()) {
341 frenet->SetCurve(C);
342
343 GeomAbs_CurveType type;
344 type = C->GetType();
345 switch (type) {
346 case GeomAbs_Circle:
347 case GeomAbs_Ellipse:
348 case GeomAbs_Hyperbola:
349 case GeomAbs_Parabola:
350 case GeomAbs_Line:
351 {
352 // No probleme isFrenet
353 isFrenet = Standard_True;
a31abc03 354 break;
7fd59977 355 }
356 default :
357 {
358 // We have to search singulaties
359 isFrenet = Standard_True;
360 Init();
361 }
362 }
363 }
364}
365
366
367//===============================================================
368// Function : Init
369// Purpose : Compute angle's law
370//===============================================================
371 void GeomFill_CorrectedFrenet::Init()
372{
373 EvolAroundT = new Law_Composite();
374 Standard_Integer NbI = frenet->NbIntervals(GeomAbs_C0), i;
375 TColStd_Array1OfReal T(1, NbI + 1);
376 frenet->Intervals(T, GeomAbs_C0);
377 Handle(Law_Function) Func;
378 //OCC78
379 TColStd_SequenceOfReal SeqPoles, SeqAngle;
380 TColgp_SequenceOfVec SeqTangent, SeqNormal;
381
382 gp_Vec Tangent, Normal, BN;
383 frenet->D0(myTrimmed->FirstParameter(), Tangent, Normal, BN);
384 Standard_Integer NbStep;
385// Standard_Real StartAng = 0, AvStep, Step, t;
386 Standard_Real StartAng = 0, AvStep, Step;
387
388#if DRAW
389 Standard_Real t;
390
391 if (Affich) { // Display the curve C'^C''(t)
392 GeomFill_SnglrFunc CS(myCurve);
393 NbStep = 99;
394 AvStep = (myTrimmed->LastParameter() -
395 myTrimmed->FirstParameter())/NbStep;
396 TColgp_Array1OfPnt TabP(1, NbStep+1);
397
398 TColStd_Array1OfReal TI(1, NbStep+1);
399 TColStd_Array1OfInteger M(1,NbStep+1);
400 M.Init(1);
401 M(1) = M(NbStep+1) = 2;
402 for (i=1; i<=NbStep+1; i++) {
403 t = (myTrimmed->FirstParameter()+ (i-1)*AvStep);
404 CS.D0(t, TabP(i));
405 TI(i) = t;
406 }
407 char tname[100];
408 Standard_CString name = tname ;
409 sprintf(name,"Binorm_%d", ++CorrNumber);
410 Handle(Geom_BSplineCurve) BS = new
411 (Geom_BSplineCurve) (TabP, TI, M, 1);
412// DrawTrSurf::Set(&name[0], BS);
413 DrawTrSurf::Set(name, BS);
414 }
415#endif
416
417
418 NbStep = 10;
419 AvStep = (myTrimmed->LastParameter() - myTrimmed->FirstParameter())/NbStep;
420 for(i = 1; i <= NbI; i++) {
421 NbStep = Max(Standard_Integer((T(i+1) - T(i))/AvStep), 3);
422 Step = (T(i+1) - T(i))/NbStep;
a31abc03 423 if(!InitInterval(T(i), T(i+1), Step, StartAng, Tangent, Normal, AT, AN, Func,
424 SeqPoles, SeqAngle, SeqTangent, SeqNormal))
425 {
426 if(isFrenet)
427 isFrenet = Standard_False;
428 }
7fd59977 429 Handle(Law_Composite)::DownCast(EvolAroundT)->ChangeLaws().Append(Func);
430 }
431 if(myTrimmed->IsPeriodic())
432 Handle(Law_Composite)::DownCast(EvolAroundT)->SetPeriodic();
433
434 TLaw = EvolAroundT;
435 //OCC78
436 Standard_Integer iEnd = SeqPoles.Length();
437 HArrPoles = new TColStd_HArray1OfReal(1, iEnd);
438 HArrAngle = new TColStd_HArray1OfReal(1, iEnd);
439 HArrTangent = new TColgp_HArray1OfVec(1, iEnd);
440 HArrNormal = new TColgp_HArray1OfVec(1, iEnd);
441 for(i = 1; i <= iEnd; i++){
442 HArrPoles->ChangeValue(i) = SeqPoles(i);
443 HArrAngle->ChangeValue(i) = SeqAngle(i);
444 HArrTangent->ChangeValue(i) = SeqTangent(i);
445 HArrNormal->ChangeValue(i) = SeqNormal(i);
446 };
a31abc03 447
7fd59977 448#if DRAW
449 if (Affich) {
450 draw(EvolAroundT);
451 }
452#endif
453}
454
455//===============================================================
456// Function : InitInterval
457// Purpose : Compute the angle law on a span
458//===============================================================
459 Standard_Boolean GeomFill_CorrectedFrenet::
460 InitInterval(const Standard_Real First, const Standard_Real Last,
461 const Standard_Real Step,
462 Standard_Real& startAng, gp_Vec& prevTangent,
463 gp_Vec& prevNormal, gp_Vec& aT, gp_Vec& aN,
464 Handle(Law_Function)& FuncInt,
465 TColStd_SequenceOfReal& SeqPoles,
466 TColStd_SequenceOfReal& SeqAngle,
467 TColgp_SequenceOfVec& SeqTangent,
468 TColgp_SequenceOfVec& SeqNormal) const
469{
470 Bnd_Box Boite;
471 gp_Vec Tangent, Normal, BN, cross;
472 TColStd_SequenceOfReal parameters;
473 TColStd_SequenceOfReal EvolAT;
474 Standard_Real Param = First, LengthMin, L, norm;
475 Standard_Boolean isZero = Standard_True, isConst = Standard_True;
a31abc03 476 const Standard_Real minnorm = 1.e-16;
7fd59977 477 Standard_Integer i;
478 gp_Pnt PonC;
479 gp_Vec D1;
480
481 frenet->SetInterval(First, Last); //To have the rigth evaluation at bounds
482 GeomFill_SnglrFunc CS(myCurve);
483 BndLib_Add3dCurve::Add(CS, First, Last, 1.e-2, Boite);
484 LengthMin = Boite.GetGap()*1.e-4;
485
486 aT = gp_Vec(0, 0, 0);
487 aN = gp_Vec(0, 0, 0);
488
489 Standard_Real angleAT, currParam, currStep = Step;
490
491 Handle( Geom_Plane ) aPlane;
a31abc03 492 Standard_Boolean isPlanar = Standard_False;
493 if (!myForEvaluation)
494 isPlanar = FindPlane( myCurve, aPlane );
7fd59977 495
496 i = 1;
497 currParam = Param;
498 Standard_Real DLast = Last - Precision::PConfusion();
499
500 while (Param < Last) {
501 if (currParam > DLast) {
502 currStep = DLast - Param;
503 currParam = Last;
504 }
505 if (isPlanar)
506 currParam = Last;
507
508 frenet->D0(currParam, Tangent, Normal, BN);
c6541a0c 509 if (prevTangent.Angle(Tangent) < M_PI/3 || i == 1) {
7fd59977 510 parameters.Append(currParam);
511 //OCC78
512 SeqPoles.Append(Param);
513 SeqAngle.Append(i > 1? EvolAT(i-1) : startAng);
514 SeqTangent.Append(prevTangent);
515 SeqNormal.Append(prevNormal);
516 angleAT = CalcAngleAT(Tangent,Normal,prevTangent,prevNormal);
517
518 if(isConst && i > 1)
519 if(Abs(angleAT) > Precision::PConfusion())
520 isConst = Standard_False;
521
522 angleAT += (i > 1) ? EvolAT(i-1) : startAng;
523 EvolAT.Append(angleAT);
524 prevNormal = Normal;
525
526 if(isZero)
527 if(Abs(angleAT) > Precision::PConfusion())
528 isZero = Standard_False;
529
530 aT += Tangent;
531 cross = Tangent.Crossed(Normal);
532 aN.SetLinearForm(Sin(angleAT), cross,
533 1 - Cos(angleAT), Tangent.Crossed(cross),
534 Normal+aN);
535 prevTangent = Tangent;
536 Param = currParam;
537 i++;
538
539 //Evaluate the Next step
540 CS.D1(Param, PonC, D1);
a31abc03 541
542 L = PonC.XYZ().Modulus()/2;
7fd59977 543 norm = D1.Magnitude();
a31abc03 544 if (norm <= gp::Resolution())
545 {
546 //norm = 2.*gp::Resolution();
547 norm = minnorm;
7fd59977 548 }
549 currStep = L / norm;
a31abc03 550 if (currStep <= gp::Resolution()) //L = 0 => curvature = 0, linear segment
551 currStep = Step;
552 if (currStep < Precision::Confusion()) //too small step
553 currStep = Precision::Confusion();
554 if (currStep > Step) //too big step
555 currStep = Step;//default value
7fd59977 556 }
557 else
558 currStep /= 2; // Step too long !
559
560 currParam = Param + currStep;
561 }
562
563 if (! isPlanar)
564 {
565 aT /= parameters.Length() - 1;
566 aN /= parameters.Length() - 1;
567 }
568 startAng = angleAT;
569
570// Interpolation
571 if (isConst || isPlanar) {
572 FuncInt = new Law_Constant();
573 Handle(Law_Constant)::DownCast(FuncInt)->Set( angleAT, First, Last );
574 }
575
576 else {
577 Standard_Integer Length = parameters.Length();
578 Handle(TColStd_HArray1OfReal) pararr =
579 new TColStd_HArray1OfReal(1, Length);
580 Handle(TColStd_HArray1OfReal) angleATarr =
581 new TColStd_HArray1OfReal(1, Length);
582
583
584 for (i = 1; i <= Length; i++) {
585 pararr->ChangeValue(i) = parameters(i);
586 angleATarr->ChangeValue(i) = EvolAT(i);
587 }
588
589#if DEB
590 if (Affich) {
591 cout<<"NormalEvolution"<<endl;
592 for (i = 1; i <= Length; i++) {
593 cout<<"("<<pararr->Value(i)<<", "<<angleATarr->Value(i)<<")" << endl;
594 }
595 cout<<endl;
596 }
597#endif
598
599 Law_Interpolate lawAT(angleATarr, pararr,
600 Standard_False, Precision::PConfusion());
601 lawAT.Perform();
602 Handle(Law_BSpline) BS = lawAT.Curve();
603 smoothlaw(BS, angleATarr, pararr, 0.1);
604
605 FuncInt = new Law_BSpFunc(BS, First, Last);
606 }
607 return isZero;
608}
609//===============================================================
610// Function : CalcAngleAT (OCC78)
611// Purpose : Calculate angle of rotation of trihedron normal and its derivatives relative
612// at any position on his curve
613//===============================================================
614Standard_Real GeomFill_CorrectedFrenet::CalcAngleAT(const gp_Vec& Tangent, const gp_Vec& Normal,
615 const gp_Vec& prevTangent, const gp_Vec& prevNormal) const
616{
617 Standard_Real angle;
618 gp_Vec Normal_rot, cross;
619 angle = Tangent.Angle(prevTangent);
620 if (Abs(angle) > Precision::Angular()) {
621 cross = Tangent.Crossed(prevTangent).Normalized();
622 Normal_rot = Normal + sin(angle)*cross.Crossed(Normal) +
623 (1 - cos(angle))*cross.Crossed(cross.Crossed(Normal));
624 }
625 else
626 Normal_rot = Normal;
627 Standard_Real angleAT = Normal_rot.Angle(prevNormal);
c6541a0c 628 if(angleAT > Precision::Angular() && M_PI - angleAT > Precision::Angular())
7fd59977 629 if (Normal_rot.Crossed(prevNormal).IsOpposite(prevTangent, Precision::Angular()))
630 angleAT = -angleAT;
631 return angleAT;
632};
633//===============================================================
634// Function : ... (OCC78)
635// Purpose : This family of functions produce conversion of angle utility
636//===============================================================
637static Standard_Real corrPI_2PI(Standard_Real Ang){
c6541a0c 638 return Ang = (Ang >= 0.0? Ang: 2*M_PI+Ang);
7fd59977 639};
640static Standard_Real corr2PI_PI(Standard_Real Ang){
c6541a0c 641 return Ang = (Ang < M_PI? Ang: Ang-2*M_PI);
7fd59977 642};
643static Standard_Real diffAng(Standard_Real A, Standard_Real Ao){
c6541a0c 644 Standard_Real dA = (A-Ao) - Floor((A-Ao)/2.0/M_PI)*2.0*M_PI;
7fd59977 645 return dA = dA >= 0? corr2PI_PI(dA): -corr2PI_PI(-dA);
646};
647//===============================================================
648// Function : CalcAngleAT (OCC78)
649// Purpose : Calculate angle of rotation of trihedron normal and its derivatives relative
650// at any position on his curve
651//===============================================================
652Standard_Real GeomFill_CorrectedFrenet::GetAngleAT(const Standard_Real Param) const{
653 // Search index of low margin from poles of TLaw by bisection method
654 Standard_Integer iB = 1, iE = HArrPoles->Length(), iC = (iE+iB)/2;
655 if(Param == HArrPoles->Value(iB)) return TLaw->Value(Param);
656 if(Param > HArrPoles->Value(iE)) iC = iE;
657 if(iC < iE){
658 while(!(HArrPoles->Value(iC) <= Param && Param <= HArrPoles->Value(iC+1))){
659 if(HArrPoles->Value(iC) < Param) iB = iC; else iE = iC;
660 iC = (iE+iB)/2;
661 };
662 if(HArrPoles->Value(iC) == Param || Param == HArrPoles->Value(iC+1)) return TLaw->Value(Param);
663 };
7fd59977 664 // Calculate differenciation between apporoximated and local values of AngleAT
665 Standard_Real AngP = TLaw->Value(Param), AngPo = HArrAngle->Value(iC), dAng = AngP - AngPo;
666 gp_Vec Tangent, Normal, BN;
667 frenet->D0(Param, Tangent, Normal, BN);
668 Standard_Real DAng = CalcAngleAT(Tangent, Normal, HArrTangent->Value(iC), HArrNormal->Value(iC));
669 Standard_Real DA = diffAng(DAng,dAng);
670 // The correction (there is core of OCC78 bug)
c6541a0c 671 if(Abs(DA) > M_PI/2.0){
7fd59977 672 AngP = AngPo + DAng;
673 };
674 return AngP;
675};
676//===============================================================
677// Function : D0
678// Purpose :
679//===============================================================
680 Standard_Boolean GeomFill_CorrectedFrenet::D0(const Standard_Real Param,
681 gp_Vec& Tangent,
682 gp_Vec& Normal,
683 gp_Vec& BiNormal)
684{
685 frenet->D0(Param, Tangent, Normal, BiNormal);
686 if (isFrenet) return Standard_True;
687
688 Standard_Real angleAT;
689 //angleAT = TLaw->Value(Param);
690 angleAT = GetAngleAT(Param); //OCC78
691
692// rotation around Tangent
693 gp_Vec cross;
694 cross = Tangent.Crossed(Normal);
695 Normal.SetLinearForm(Sin(angleAT), cross,
696 (1 - Cos(angleAT)), Tangent.Crossed(cross),
697 Normal);
698 BiNormal = Tangent.Crossed(Normal);
699
700 return Standard_True;
701}
702
703//===============================================================
704// Function : D1
705// Purpose :
706//===============================================================
707
708 Standard_Boolean GeomFill_CorrectedFrenet::D1(const Standard_Real Param,
709 gp_Vec& Tangent,
710 gp_Vec& DTangent,
711 gp_Vec& Normal,
712 gp_Vec& DNormal,
713 gp_Vec& BiNormal,
714 gp_Vec& DBiNormal)
715{
716 frenet->D1(Param, Tangent, DTangent, Normal, DNormal, BiNormal, DBiNormal);
717 if (isFrenet) return Standard_True;
718
719 Standard_Real angleAT, d_angleAT;
720 Standard_Real sina, cosa;
721
722 TLaw->D1(Param, angleAT, d_angleAT);
723 angleAT = GetAngleAT(Param); //OCC78
724
725 gp_Vec cross, dcross, tcross, dtcross, aux;
726 sina = Sin(angleAT);
727 cosa = Cos(angleAT);
728
729 cross = Tangent.Crossed(Normal);
730 dcross.SetLinearForm(1, DTangent.Crossed(Normal),
731 Tangent.Crossed(DNormal));
732
733 tcross = Tangent.Crossed(cross);
734 dtcross.SetLinearForm(1, DTangent.Crossed(cross),
735 Tangent.Crossed(dcross));
736
737 aux.SetLinearForm(sina, dcross,
738 cosa*d_angleAT, cross);
739 aux.SetLinearForm(1 - cosa, dtcross,
740 sina*d_angleAT, tcross,
741 aux);
742 DNormal+=aux;
743
744 Normal.SetLinearForm( sina, cross,
745 (1 - cosa), tcross,
746 Normal);
747
748 BiNormal = Tangent.Crossed(Normal);
749
750 DBiNormal.SetLinearForm(1, DTangent.Crossed(Normal),
751 Tangent.Crossed(DNormal));
752
753// for test
754/* gp_Vec FDN, Tf, Nf, BNf;
755 Standard_Real h;
756 h = 1.0e-8;
757 if (Param + h > myTrimmed->LastParameter()) h = -h;
758 D0(Param + h, Tf, Nf, BNf);
759 FDN = (Nf - Normal)/h;
760 cout<<"Param = "<<Param<<endl;
761 cout<<"DN = ("<<DNormal.X()<<", "<<DNormal.Y()<<", "<<DNormal.Z()<<")"<<endl;
762 cout<<"FDN = ("<<FDN.X()<<", "<<FDN.Y()<<", "<<FDN.Z()<<")"<<endl;
763*/
764
765 return Standard_True;
766}
767
768//===============================================================
769// Function : D2
770// Purpose :
771//===============================================================
772 Standard_Boolean GeomFill_CorrectedFrenet::D2(const Standard_Real Param,
773 gp_Vec& Tangent,
774 gp_Vec& DTangent,
775 gp_Vec& D2Tangent,
776 gp_Vec& Normal,
777 gp_Vec& DNormal,
778 gp_Vec& D2Normal,
779 gp_Vec& BiNormal,
780 gp_Vec& DBiNormal,
781 gp_Vec& D2BiNormal)
782{
783 frenet->D2(Param, Tangent, DTangent, D2Tangent,
784 Normal, DNormal, D2Normal,
785 BiNormal, DBiNormal, D2BiNormal);
786 if (isFrenet) return Standard_True;
787
788 Standard_Real angleAT, d_angleAT, d2_angleAT;
789 Standard_Real sina, cosa;
790 TLaw->D2(Param, angleAT, d_angleAT, d2_angleAT);
791 angleAT = GetAngleAT(Param); //OCC78
792
793 gp_Vec cross, dcross, d2cross, tcross, dtcross, d2tcross, aux;
794 sina = Sin(angleAT);
795 cosa = Cos(angleAT);
796 cross = Tangent.Crossed(Normal);
797 dcross.SetLinearForm(1, DTangent.Crossed(Normal),
798 Tangent.Crossed(DNormal));
799 d2cross.SetLinearForm(1, D2Tangent.Crossed(Normal),
800 2, DTangent.Crossed(DNormal),
801 Tangent.Crossed(D2Normal));
802
803
804 tcross = Tangent.Crossed(cross);
805 dtcross.SetLinearForm(1, DTangent.Crossed(cross),
806 Tangent.Crossed(dcross));
807 d2tcross.SetLinearForm(1, D2Tangent.Crossed(cross),
808 2, DTangent.Crossed(dcross),
809 Tangent.Crossed(d2cross));
810
811
812 aux.SetLinearForm(sina, d2cross,
813 2*cosa*d_angleAT, dcross,
814 cosa*d2_angleAT - sina*d_angleAT*d_angleAT, cross);
815
816 aux.SetLinearForm(1 - cosa, d2tcross,
817 2*sina*d_angleAT, dtcross,
818 cosa*d_angleAT*d_angleAT + sina*d2_angleAT, tcross,
819 aux);
820 D2Normal += aux;
821
822/* D2Normal += sina*(D2Tangent.Crossed(Normal) + 2*DTangent.Crossed(DNormal) + Tangent.Crossed(D2Normal)) +
823 2*cosa*d_angleAT*(DTangent.Crossed(Normal) + Tangent.Crossed(DNormal)) +
824 (cosa*d2_angleAT - sina*d_angleAT*d_angleAT)*Tangent.Crossed(Normal) +
8252*sina*d_angleAT*(DTangent.Crossed(Tangent.Crossed(Normal)) + Tangent.Crossed(DTangent.Crossed(Normal)) + Tangent.Crossed(Tangent.Crossed(DNormal))) +
826(1 - cosa)*(D2Tangent.Crossed(Tangent.Crossed(Normal)) + Tangent.Crossed(D2Tangent.Crossed(Normal)) + Tangent.Crossed(Tangent.Crossed(D2Normal)) + 2*DTangent.Crossed(DTangent.Crossed(Normal)) + 2*DTangent.Crossed(Tangent.Crossed(DNormal)) + 2*Tangent.Crossed(DTangent.Crossed(DNormal)))
827+
828(cosa*d_angleAT*d_angleAT + sina*d2_angleAT)*Tangent.Crossed(Tangent.Crossed(Normal));*/
829
830
831 aux.SetLinearForm(sina, dcross,
832 cosa*d_angleAT, cross);
833 aux.SetLinearForm(1 - cosa, dtcross,
834 sina*d_angleAT, tcross,
835 aux);
836 DNormal+=aux;
837
838
839 Normal.SetLinearForm( sina, cross,
840 (1 - cosa), tcross,
841 Normal);
842
843 BiNormal = Tangent.Crossed(Normal);
844
845 DBiNormal.SetLinearForm(1, DTangent.Crossed(Normal),
846 Tangent.Crossed(DNormal));
847
848 D2BiNormal.SetLinearForm(1, D2Tangent.Crossed(Normal),
849 2, DTangent.Crossed(DNormal),
850 Tangent.Crossed(D2Normal));
851
852// for test
853/* gp_Vec FD2N, FD2T, FD2BN, Tf, DTf, Nf, DNf, BNf, DBNf;
854 Standard_Real h;
855 h = 1.0e-8;
856 if (Param + h > myTrimmed->LastParameter()) h = -h;
857 D1(Param + h, Tf, DTf, Nf, DNf, BNf, DBNf);
858 FD2N = (DNf - DNormal)/h;
859 FD2T = (DTf - DTangent)/h;
860 FD2BN = (DBNf - DBiNormal)/h;
861 cout<<"Param = "<<Param<<endl;
862 cout<<"D2N = ("<<D2Normal.X()<<", "<<D2Normal.Y()<<", "<<D2Normal.Z()<<")"<<endl;
863 cout<<"FD2N = ("<<FD2N.X()<<", "<<FD2N.Y()<<", "<<FD2N.Z()<<")"<<endl<<endl;
864 cout<<"D2T = ("<<D2Tangent.X()<<", "<<D2Tangent.Y()<<", "<<D2Tangent.Z()<<")"<<endl;
865 cout<<"FD2T = ("<<FD2T.X()<<", "<<FD2T.Y()<<", "<<FD2T.Z()<<")"<<endl<<endl;
866 cout<<"D2BN = ("<<D2BiNormal.X()<<", "<<D2BiNormal.Y()<<", "<<D2BiNormal.Z()<<")"<<endl;
867 cout<<"FD2BN = ("<<FD2BN.X()<<", "<<FD2BN.Y()<<", "<<FD2BN.Z()<<")"<<endl<<endl;
868*/
869//
870 return Standard_True;
871}
872
873//===============================================================
874// Function : NbIntervals
875// Purpose :
876//===============================================================
877 Standard_Integer GeomFill_CorrectedFrenet::NbIntervals(const GeomAbs_Shape S) const
878{
879 Standard_Integer NbFrenet, NbLaw;
880 NbFrenet = frenet->NbIntervals(S);
881 if (isFrenet) return NbFrenet;
882
883 NbLaw = EvolAroundT->NbIntervals(S);
884 if (NbFrenet == 1)
885 return NbLaw;
886
887 TColStd_Array1OfReal FrenetInt(1, NbFrenet + 1);
888 TColStd_Array1OfReal LawInt(1, NbLaw + 1);
889 TColStd_SequenceOfReal Fusion;
890
891 frenet->Intervals(FrenetInt, S);
892 EvolAroundT->Intervals(LawInt, S);
893 GeomLib::FuseIntervals(FrenetInt, LawInt, Fusion);
894
895 return Fusion.Length()-1;
896}
897
898//===============================================================
899// Function : Intervals
900// Purpose :
901//===============================================================
902 void GeomFill_CorrectedFrenet::Intervals(TColStd_Array1OfReal& T,
903 const GeomAbs_Shape S) const
904{
905 Standard_Integer NbFrenet, NbLaw;
906 if (isFrenet) {
907 frenet->Intervals(T, S);
908 return;
909 }
910
911 NbFrenet = frenet->NbIntervals(S);
912 if(NbFrenet==1) {
913 EvolAroundT->Intervals(T, S);
914 }
915
916 NbLaw = EvolAroundT->NbIntervals(S);
917
918 TColStd_Array1OfReal FrenetInt(1, NbFrenet + 1);
919 TColStd_Array1OfReal LawInt(1, NbLaw + 1);
920 TColStd_SequenceOfReal Fusion;
921
922 frenet->Intervals(FrenetInt, S);
923 EvolAroundT->Intervals(LawInt, S);
924 GeomLib::FuseIntervals(FrenetInt, LawInt, Fusion);
925
926 for(Standard_Integer i = 1; i <= Fusion.Length(); i++)
927 T.ChangeValue(i) = Fusion.Value(i);
928}
929
930//===============================================================
931// Function : SetInterval
932// Purpose :
933//===============================================================
934 void GeomFill_CorrectedFrenet::SetInterval(const Standard_Real First,
935 const Standard_Real Last)
936{
937 GeomFill_TrihedronLaw::SetInterval(First, Last);
938 frenet->SetInterval(First, Last);
939 if (!isFrenet) TLaw = EvolAroundT->Trim(First, Last,
940 Precision::PConfusion()/2);
941}
942
943//===============================================================
a31abc03 944// Function : EvaluateBestMode
945// Purpose :
946//===============================================================
947GeomFill_Trihedron GeomFill_CorrectedFrenet::EvaluateBestMode()
948{
949 if (EvolAroundT.IsNull())
950 return GeomFill_IsFrenet; //Frenet
951
952 const Standard_Real MaxAngle = 3.*M_PI/4.;
953 const Standard_Real MaxTorsion = 100.;
954
955 Standard_Real Step, u, v, tmin, tmax;
956 Standard_Integer NbInt, i, j, k = 1;
957 NbInt = EvolAroundT->NbIntervals(GeomAbs_CN);
958 TColStd_Array1OfReal Int(1, NbInt+1);
959 EvolAroundT->Intervals(Int, GeomAbs_CN);
960 gp_Pnt2d old;
961 gp_Vec2d aVec, PrevVec;
962
963 Standard_Integer NbSamples = 10;
964 for(i = 1; i <= NbInt; i++){
965 tmin = Int(i);
966 tmax = Int(i+1);
967 Standard_Real Torsion = ComputeTorsion(tmin, myTrimmed);
968 if (Abs(Torsion) > MaxTorsion)
969 return GeomFill_IsDiscreteTrihedron; //DiscreteTrihedron
970
971 Handle(Law_Function) trimmedlaw = EvolAroundT->Trim(tmin, tmax, Precision::PConfusion()/2);
972 Step = (Int(i+1)-Int(i))/NbSamples;
973 for (j = 0; j <= NbSamples; j++) {
974 u = tmin + j*Step;
975 v = trimmedlaw->Value(u);
976 gp_Pnt2d point2d(u,v);
977 if (j != 0)
978 {
979 aVec.SetXY(point2d.XY() - old.XY());
980 if (k > 2)
981 {
982 Standard_Real theAngle = PrevVec.Angle(aVec);
983 if (Abs(theAngle) > MaxAngle)
984 return GeomFill_IsDiscreteTrihedron; //DiscreteTrihedron
985 }
986 PrevVec = aVec;
987 }
988 old = point2d;
989 k++;
990 }
991 }
992
993 return GeomFill_IsCorrectedFrenet; //CorrectedFrenet
994}
995
996//===============================================================
7fd59977 997// Function : GetAverageLaw
998// Purpose :
999//===============================================================
1000 void GeomFill_CorrectedFrenet::GetAverageLaw(gp_Vec& ATangent,
1001 gp_Vec& ANormal,
1002 gp_Vec& ABiNormal)
1003{
1004 if (isFrenet) frenet->GetAverageLaw(ATangent, ANormal, ABiNormal);
1005 else {
1006 ATangent = AT;
1007 ANormal = AN;
1008 ABiNormal = ATangent;
1009 ABiNormal.Cross(ANormal);
1010 }
1011}
1012
1013//===============================================================
1014// Function : IsConstant
1015// Purpose :
1016//===============================================================
1017 Standard_Boolean GeomFill_CorrectedFrenet::IsConstant() const
1018{
1019 return (myCurve->GetType() == GeomAbs_Line);
1020}
1021
1022//===============================================================
1023// Function : IsOnlyBy3dCurve
1024// Purpose :
1025//===============================================================
1026 Standard_Boolean GeomFill_CorrectedFrenet::IsOnlyBy3dCurve() const
1027{
1028 return Standard_True;
1029}
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