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0023971: Possibility to extract all error messages from test log
[occt.git] / src / BSplCLib / BSplCLib.cxx
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b311480e 1// Created on: 1991-08-09
2// Created by: JCV
3// Copyright (c) 1991-1999 Matra Datavision
973c2be1 4// Copyright (c) 1999-2014 OPEN CASCADE SAS
7fd59977 5//
973c2be1 6// This file is part of Open CASCADE Technology software library.
7fd59977 7//
d5f74e42 8// This library is free software; you can redistribute it and/or modify it under
9// the terms of the GNU Lesser General Public License version 2.1 as published
973c2be1 10// by the Free Software Foundation, with special exception defined in the file
11// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
12// distribution for complete text of the license and disclaimer of any warranty.
b311480e 13//
973c2be1 14// Alternatively, this file may be used under the terms of Open CASCADE
15// commercial license or contractual agreement.
b311480e 16
17// Modified RLE 9 Sep 1993
7fd59977 18// pmn : modified 28-01-97 : fixed a mistake in LocateParameter (PRO6973)
19// pmn : modified 4-11-96 : fixed a mistake in BuildKnots (PRO6124)
20// pmn : modified 28-Jun-96 : fixed a mistake in AntiBoorScheme
21// xab : modified 15-Jun-95 : fixed a mistake in IsRational
22// xab : modified 15-Mar-95 : removed Epsilon comparison in IsRational
23// added RationalDerivatives.
24// xab : 30-Mar-95 : fixed coupling with lti in RationalDerivatives
25// xab : 15-Mar-96 : fixed a typo in Eval with extrapolation
26// jct : 15-Apr-97 : added TangExtendToConstraint
27// jct : 24-Apr-97 : correction on computation of Tbord and NewFlatKnots
28// in TangExtendToConstraint; Continuity can be equal to 0
7fd59977 29
7fd59977 30#include <BSplCLib.ixx>
31#include <PLib.hxx>
f7b4312f 32#include <NCollection_LocalArray.hxx>
7fd59977 33#include <Precision.hxx>
34#include <Standard_NotImplemented.hxx>
35
36typedef gp_Pnt Pnt;
37typedef gp_Vec Vec;
38typedef TColgp_Array1OfPnt Array1OfPnt;
39typedef TColStd_Array1OfReal Array1OfReal;
40typedef TColStd_Array1OfInteger Array1OfInteger;
41
42//=======================================================================
43//class : BSplCLib_LocalMatrix
44//purpose: Auxiliary class optimizing creation of matrix buffer for
45// evaluation of bspline (using stack allocation for main matrix)
46//=======================================================================
47
48class BSplCLib_LocalMatrix : public math_Matrix
49{
41194117 50public:
7fd59977 51 BSplCLib_LocalMatrix (Standard_Integer DerivativeRequest, Standard_Integer Order)
52 : math_Matrix (myBuffer, 1, DerivativeRequest + 1, 1, Order)
53 {
41194117
K		 54 Standard_OutOfRange_Raise_if (DerivativeRequest > BSplCLib::MaxDegree() ||
55 Order > BSplCLib::MaxDegree()+1 || BSplCLib::MaxDegree() > 25,
56 "BSplCLib: bspline degree is greater than maximum supported");
7fd59977 57 }
41194117 58
7fd59977 59 private:
60 // local buffer, to be sufficient for addressing by index [Degree+1][Degree+1]
61 // (see math_Matrix implementation)
62 Standard_Real myBuffer[27*27];
63};
64
7fd59977 65//=======================================================================
66//function : Hunt
67//purpose :
68//=======================================================================
69
70void BSplCLib::Hunt (const Array1OfReal& XX,
71 const Standard_Real X,
72 Standard_Integer& Ilc)
73{
74 // replaced by simple dichotomy (RLE)
75 Ilc = XX.Lower();
76 const Standard_Real *px = &XX(Ilc);
77 px -= Ilc;
78
79 if (X < px[Ilc]) {
80 Ilc--;
81 return;
82 }
83 Standard_Integer Ihi = XX.Upper();
84 if (X > px[Ihi]) {
85 Ilc = Ihi + 1;
86 return;
87 }
88 Standard_Integer Im;
89
90 while (Ihi - Ilc != 1) {
91 Im = (Ihi + Ilc) >> 1;
92 if (X > px[Im]) Ilc = Im;
93 else Ihi = Im;
94 }
95}
96
97//=======================================================================
98//function : FirstUKnotIndex
99//purpose :
100//=======================================================================
101
102Standard_Integer BSplCLib::FirstUKnotIndex (const Standard_Integer Degree,
103 const TColStd_Array1OfInteger& Mults)
104{
105 Standard_Integer Index = Mults.Lower();
106 Standard_Integer SigmaMult = Mults(Index);
107
108 while (SigmaMult <= Degree) {
109 Index++;
110 SigmaMult += Mults (Index);
111 }
112 return Index;
113}
114
115//=======================================================================
116//function : LastUKnotIndex
117//purpose :
118//=======================================================================
119
120Standard_Integer BSplCLib::LastUKnotIndex (const Standard_Integer Degree,
121 const Array1OfInteger& Mults)
122{
123 Standard_Integer Index = Mults.Upper();
124 Standard_Integer SigmaMult = Mults(Index);
125
126 while (SigmaMult <= Degree) {
127 Index--;
128 SigmaMult += Mults.Value (Index);
129 }
130 return Index;
131}
132
133//=======================================================================
134//function : FlatIndex
135//purpose :
136//=======================================================================
137
138Standard_Integer BSplCLib::FlatIndex
139 (const Standard_Integer Degree,
140 const Standard_Integer Index,
141 const TColStd_Array1OfInteger& Mults,
142 const Standard_Boolean Periodic)
143{
144 Standard_Integer i, index = Index;
145 const Standard_Integer MLower = Mults.Lower();
146 const Standard_Integer *pmu = &Mults(MLower);
147 pmu -= MLower;
148
149 for (i = MLower + 1; i <= Index; i++)
150 index += pmu[i] - 1;
151 if ( Periodic)
152 index += Degree;
153 else
154 index += pmu[MLower] - 1;
155 return index;
156}
157
158//=======================================================================
159//function : LocateParameter
0d969553
Y		 160//purpose : Processing of nodes with multiplicities
161//pmn 28-01-97 -> compute eventual of the period.
7fd59977 162//=======================================================================
163
164void BSplCLib::LocateParameter
165(const Standard_Integer , //Degree,
166 const Array1OfReal& Knots,
167 const Array1OfInteger& , //Mults,
168 const Standard_Real U,
169 const Standard_Boolean IsPeriodic,
170 const Standard_Integer FromK1,
171 const Standard_Integer ToK2,
172 Standard_Integer& KnotIndex,
173 Standard_Real& NewU)
174{
175 Standard_Real uf = 0, ul=1;
176 if (IsPeriodic) {
177 uf = Knots(Knots.Lower());
178 ul = Knots(Knots.Upper());
179 }
180 BSplCLib::LocateParameter(Knots,U,IsPeriodic,FromK1,ToK2,
181 KnotIndex,NewU, uf, ul);
182}
183
184//=======================================================================
185//function : LocateParameter
0d969553
Y		 186//purpose : For plane nodes
187// pmn 28-01-97 -> There is a need of the degre to calculate
188// the eventual period
7fd59977 189//=======================================================================
190
191void BSplCLib::LocateParameter
192(const Standard_Integer Degree,
193 const Array1OfReal& Knots,
194 const Standard_Real U,
195 const Standard_Boolean IsPeriodic,
196 const Standard_Integer FromK1,
197 const Standard_Integer ToK2,
198 Standard_Integer& KnotIndex,
199 Standard_Real& NewU)
200{
201 if (IsPeriodic)
202 BSplCLib::LocateParameter(Knots, U, IsPeriodic, FromK1, ToK2,
203 KnotIndex, NewU,
204 Knots(Knots.Lower() + Degree),
205 Knots(Knots.Upper() - Degree));
206 else
207 BSplCLib::LocateParameter(Knots, U, IsPeriodic, FromK1, ToK2,
208 KnotIndex, NewU,
209 0.,
210 1.);
211}
212
213//=======================================================================
214//function : LocateParameter
0d969553
Y		 215//purpose : Effective computation
216// pmn 28-01-97 : Add limits of the period as input argument,
217// as it is imposible to produce them at this level.
7fd59977 218//=======================================================================
219
220void BSplCLib::LocateParameter
221(const TColStd_Array1OfReal& Knots,
222 const Standard_Real U,
223 const Standard_Boolean IsPeriodic,
224 const Standard_Integer FromK1,
225 const Standard_Integer ToK2,
226 Standard_Integer& KnotIndex,
227 Standard_Real& NewU,
228 const Standard_Real UFirst,
229 const Standard_Real ULast)
230{
231 Standard_Integer First,Last;
232 if (FromK1 < ToK2) {
233 First = FromK1;
234 Last = ToK2;
235 }
236 else {
237 First = ToK2;
238 Last = FromK1;
239 }
240 Standard_Integer Last1 = Last - 1;
241 NewU = U;
242 if (IsPeriodic) {
243 Standard_Real Period = ULast - UFirst;
244
245 while (NewU > ULast )
246 NewU -= Period;
247
248 while (NewU < UFirst)
249 NewU += Period;
250 }
251
252 BSplCLib::Hunt (Knots, NewU, KnotIndex);
253
254 Standard_Real Eps = Epsilon(U);
255 Standard_Real val;
256 if (Eps < 0) Eps = - Eps;
257 Standard_Integer KLower = Knots.Lower();
258 const Standard_Real *knots = &Knots(KLower);
259 knots -= KLower;
260 if ( KnotIndex < Knots.Upper()) {
261 val = NewU - knots[KnotIndex + 1];
262 if (val < 0) val = - val;
0d969553 263 // <= to be coherent with Segment where Eps corresponds to a bit of error.
7fd59977 264 if (val <= Eps) KnotIndex++;
265 }
266 if (KnotIndex < First) KnotIndex = First;
267 if (KnotIndex > Last1) KnotIndex = Last1;
268
269 if (KnotIndex != Last1) {
270 Standard_Real K1 = knots[KnotIndex];
271 Standard_Real K2 = knots[KnotIndex + 1];
272 val = K2 - K1;
273 if (val < 0) val = - val;
274
275 while (val <= Eps) {
276 KnotIndex++;
277 K1 = K2;
278 K2 = knots[KnotIndex + 1];
279 val = K2 - K1;
280 if (val < 0) val = - val;
281 }
282 }
283}
284
285//=======================================================================
286//function : LocateParameter
287//purpose : the index is recomputed only if out of range
0d969553 288//pmn 28-01-97 -> eventual computation of the period.
7fd59977 289//=======================================================================
290
291void BSplCLib::LocateParameter
292(const Standard_Integer Degree,
293 const TColStd_Array1OfReal& Knots,
294 const TColStd_Array1OfInteger& Mults,
295 const Standard_Real U,
296 const Standard_Boolean Periodic,
297 Standard_Integer& KnotIndex,
298 Standard_Real& NewU)
299{
300 Standard_Integer first,last;
301 if (&Mults) {
302 if (Periodic) {
303 first = Knots.Lower();
304 last = Knots.Upper();
305 }
306 else {
307 first = FirstUKnotIndex(Degree,Mults);
308 last = LastUKnotIndex (Degree,Mults);
309 }
310 }
311 else {
312 first = Knots.Lower() + Degree;
313 last = Knots.Upper() - Degree;
314 }
315 if ( KnotIndex < first || KnotIndex > last)
316 BSplCLib::LocateParameter(Knots, U, Periodic, first, last,
317 KnotIndex, NewU, Knots(first), Knots(last));
318 else
319 NewU = U;
320}
321
322//=======================================================================
323//function : MaxKnotMult
324//purpose :
325//=======================================================================
326
327Standard_Integer BSplCLib::MaxKnotMult
328(const Array1OfInteger& Mults,
329 const Standard_Integer FromK1,
330 const Standard_Integer ToK2)
331{
332 Standard_Integer MLower = Mults.Lower();
333 const Standard_Integer *pmu = &Mults(MLower);
334 pmu -= MLower;
335 Standard_Integer MaxMult = pmu[FromK1];
336
337 for (Standard_Integer i = FromK1; i <= ToK2; i++) {
338 if (MaxMult < pmu[i]) MaxMult = pmu[i];
339 }
340 return MaxMult;
341}
342
343//=======================================================================
344//function : MinKnotMult
345//purpose :
346//=======================================================================
347
348Standard_Integer BSplCLib::MinKnotMult
349(const Array1OfInteger& Mults,
350 const Standard_Integer FromK1,
351 const Standard_Integer ToK2)
352{
353 Standard_Integer MLower = Mults.Lower();
354 const Standard_Integer *pmu = &Mults(MLower);
355 pmu -= MLower;
356 Standard_Integer MinMult = pmu[FromK1];
357
358 for (Standard_Integer i = FromK1; i <= ToK2; i++) {
359 if (MinMult > pmu[i]) MinMult = pmu[i];
360 }
361 return MinMult;
362}
363
364//=======================================================================
365//function : NbPoles
366//purpose :
367//=======================================================================
368
369Standard_Integer BSplCLib::NbPoles(const Standard_Integer Degree,
370 const Standard_Boolean Periodic,
371 const TColStd_Array1OfInteger& Mults)
372{
373 Standard_Integer i,sigma = 0;
374 Standard_Integer f = Mults.Lower();
375 Standard_Integer l = Mults.Upper();
376 const Standard_Integer * pmu = &Mults(f);
377 pmu -= f;
378 Standard_Integer Mf = pmu[f];
379 Standard_Integer Ml = pmu[l];
380 if (Mf <= 0) return 0;
381 if (Ml <= 0) return 0;
382 if (Periodic) {
383 if (Mf > Degree) return 0;
384 if (Ml > Degree) return 0;
385 if (Mf != Ml ) return 0;
386 sigma = Mf;
387 }
388 else {
389 Standard_Integer Deg1 = Degree + 1;
390 if (Mf > Deg1) return 0;
391 if (Ml > Deg1) return 0;
392 sigma = Mf + Ml - Deg1;
393 }
394
395 for (i = f + 1; i < l; i++) {
396 if (pmu[i] <= 0 ) return 0;
397 if (pmu[i] > Degree) return 0;
398 sigma += pmu[i];
399 }
400 return sigma;
401}
402
403//=======================================================================
404//function : KnotSequenceLength
405//purpose :
406//=======================================================================
407
408Standard_Integer BSplCLib::KnotSequenceLength
409(const TColStd_Array1OfInteger& Mults,
410 const Standard_Integer Degree,
411 const Standard_Boolean Periodic)
412{
413 Standard_Integer i,l = 0;
414 Standard_Integer MLower = Mults.Lower();
415 Standard_Integer MUpper = Mults.Upper();
416 const Standard_Integer * pmu = &Mults(MLower);
417 pmu -= MLower;
418
419 for (i = MLower; i <= MUpper; i++)
420 l += pmu[i];
421 if (Periodic) l += 2 * (Degree + 1 - pmu[MLower]);
422 return l;
423}
424
425//=======================================================================
426//function : KnotSequence
427//purpose :
428//=======================================================================
429
430void BSplCLib::KnotSequence
431(const TColStd_Array1OfReal& Knots,
432 const TColStd_Array1OfInteger& Mults,
433 TColStd_Array1OfReal& KnotSeq)
434{
435 BSplCLib::KnotSequence(Knots,Mults,0,Standard_False,KnotSeq);
436}
437
438//=======================================================================
439//function : KnotSequence
440//purpose :
441//=======================================================================
442
443void BSplCLib::KnotSequence
444(const TColStd_Array1OfReal& Knots,
445 const TColStd_Array1OfInteger& Mults,
446 const Standard_Integer Degree,
447 const Standard_Boolean Periodic,
448 TColStd_Array1OfReal& KnotSeq)
449{
450 Standard_Real K;
451 Standard_Integer Mult;
452 Standard_Integer MLower = Mults.Lower();
453 const Standard_Integer * pmu = &Mults(MLower);
454 pmu -= MLower;
455 Standard_Integer KLower = Knots.Lower();
456 Standard_Integer KUpper = Knots.Upper();
457 const Standard_Real * pkn = &Knots(KLower);
458 pkn -= KLower;
459 Standard_Integer M1 = Degree + 1 - pmu[MLower]; // for periodic
460 Standard_Integer i,j,index = Periodic ? M1 + 1 : 1;
461
462 for (i = KLower; i <= KUpper; i++) {
463 Mult = pmu[i];
464 K = pkn[i];
465
466 for (j = 1; j <= Mult; j++) {
467 KnotSeq (index) = K;
468 index++;
469 }
470 }
471 if (Periodic) {
472 Standard_Real period = pkn[KUpper] - pkn[KLower];
473 Standard_Integer m;
474 m = 1;
475 j = KUpper - 1;
476
477 for (i = M1; i >= 1; i--) {
478 KnotSeq(i) = pkn[j] - period;
479 m++;
480 if (m > pmu[j]) {
481 j--;
482 m = 1;
483 }
484 }
485 m = 1;
486 j = KLower + 1;
487
488 for (i = index; i <= KnotSeq.Upper(); i++) {
489 KnotSeq(i) = pkn[j] + period;
490 m++;
491 if (m > pmu[j]) {
492 j++;
493 m = 1;
494 }
495 }
496 }
497}
498
499//=======================================================================
500//function : KnotsLength
501//purpose :
502//=======================================================================
503 Standard_Integer BSplCLib::KnotsLength(const TColStd_Array1OfReal& SeqKnots,
504// const Standard_Boolean Periodic)
505 const Standard_Boolean )
506{
507 Standard_Integer sizeMult = 1;
508 Standard_Real val = SeqKnots(1);
509 for (Standard_Integer jj=2;
510 jj<=SeqKnots.Length();jj++)
511 {
512 // test on strict equality on nodes
513 if (SeqKnots(jj)!=val)
514 {
515 val = SeqKnots(jj);
516 sizeMult++;
517 }
518 }
519 return sizeMult;
520}
521
522//=======================================================================
523//function : Knots
524//purpose :
525//=======================================================================
526void BSplCLib::Knots(const TColStd_Array1OfReal& SeqKnots,
527 TColStd_Array1OfReal &knots,
528 TColStd_Array1OfInteger &mult,
529// const Standard_Boolean Periodic)
530 const Standard_Boolean )
531{
532 Standard_Real val = SeqKnots(1);
533 Standard_Integer kk=1;
534 knots(kk) = val;
535 mult(kk) = 1;
536
537 for (Standard_Integer jj=2;jj<=SeqKnots.Length();jj++)
538 {
539 // test on strict equality on nodes
540 if (SeqKnots(jj)!=val)
541 {
542 val = SeqKnots(jj);
543 kk++;
544 knots(kk) = val;
545 mult(kk) = 1;
546 }
547 else
548 {
549 mult(kk)++;
550 }
551 }
552}
553
554//=======================================================================
555//function : KnotForm
556//purpose :
557//=======================================================================
558
559BSplCLib_KnotDistribution BSplCLib::KnotForm
560(const Array1OfReal& Knots,
561 const Standard_Integer FromK1,
562 const Standard_Integer ToK2)
563{
564 Standard_Real DU0,DU1,Ui,Uj,Eps0,val;
565 BSplCLib_KnotDistribution KForm = BSplCLib_Uniform;
566
567 Standard_Integer KLower = Knots.Lower();
568 const Standard_Real * pkn = &Knots(KLower);
569 pkn -= KLower;
570 Ui = pkn[FromK1];
571 if (Ui < 0) Ui = - Ui;
572 Uj = pkn[FromK1 + 1];
573 if (Uj < 0) Uj = - Uj;
574 DU0 = Uj - Ui;
575 if (DU0 < 0) DU0 = - DU0;
576 Eps0 = Epsilon (Ui) + Epsilon (Uj) + Epsilon (DU0);
577 Standard_Integer i = FromK1 + 1;
578
579 while (KForm != BSplCLib_NonUniform && i < ToK2) {
580 Ui = pkn[i];
581 if (Ui < 0) Ui = - Ui;
582 i++;
583 Uj = pkn[i];
584 if (Uj < 0) Uj = - Uj;
585 DU1 = Uj - Ui;
586 if (DU1 < 0) DU1 = - DU1;
587 val = DU1 - DU0;
588 if (val < 0) val = -val;
589 if (val > Eps0) KForm = BSplCLib_NonUniform;
590 DU0 = DU1;
591 Eps0 = Epsilon (Ui) + Epsilon (Uj) + Epsilon (DU0);
592 }
593 return KForm;
594}
595
596//=======================================================================
597//function : MultForm
598//purpose :
599//=======================================================================
600
601BSplCLib_MultDistribution BSplCLib::MultForm
602(const Array1OfInteger& Mults,
603 const Standard_Integer FromK1,
604 const Standard_Integer ToK2)
605{
606 Standard_Integer First,Last;
607 if (FromK1 < ToK2) {
608 First = FromK1;
609 Last = ToK2;
610 }
611 else {
612 First = ToK2;
613 Last = FromK1;
614 }
615 Standard_Integer MLower = Mults.Lower();
616 const Standard_Integer *pmu = &Mults(MLower);
617 pmu -= MLower;
618 Standard_Integer FirstMult = pmu[First];
619 BSplCLib_MultDistribution MForm = BSplCLib_Constant;
620 Standard_Integer i = First + 1;
621 Standard_Integer Mult = pmu[i];
622
623// while (MForm != BSplCLib_NonUniform && i <= Last) { ???????????JR????????
624 while (MForm != BSplCLib_NonConstant && i <= Last) {
625 if (i == First + 1) {
626 if (Mult != FirstMult) MForm = BSplCLib_QuasiConstant;
627 }
628 else if (i == Last) {
629 if (MForm == BSplCLib_QuasiConstant) {
630 if (FirstMult != pmu[i]) MForm = BSplCLib_NonConstant;
631 }
632 else {
633 if (Mult != pmu[i]) MForm = BSplCLib_NonConstant;
634 }
635 }
636 else {
637 if (Mult != pmu[i]) MForm = BSplCLib_NonConstant;
638 Mult = pmu[i];
639 }
640 i++;
641 }
642 return MForm;
643}
644
06be28a4
RL		 645//=======================================================================
646//function : KnotAnalysis
647//purpose :
648//=======================================================================
649
650void BSplCLib::KnotAnalysis (const Standard_Integer Degree,
651 const Standard_Boolean Periodic,
652 const TColStd_Array1OfReal& CKnots,
653 const TColStd_Array1OfInteger& CMults,
654 GeomAbs_BSplKnotDistribution& KnotForm,
655 Standard_Integer& MaxKnotMult)
656{
657 KnotForm = GeomAbs_NonUniform;
658
659 BSplCLib_KnotDistribution KSet =
660 BSplCLib::KnotForm (CKnots, 1, CKnots.Length());
661
662
663 if (KSet == BSplCLib_Uniform) {
664 BSplCLib_MultDistribution MSet =
665 BSplCLib::MultForm (CMults, 1, CMults.Length());
666 switch (MSet) {
667 case BSplCLib_NonConstant :
668 break;
669 case BSplCLib_Constant :
670 if (CKnots.Length() == 2) {
671 KnotForm = GeomAbs_PiecewiseBezier;
672 }
673 else {
674 if (CMults (1) == 1) KnotForm = GeomAbs_Uniform;
675 }
676 break;
677 case BSplCLib_QuasiConstant :
678 if (CMults (1) == Degree + 1) {
679 Standard_Real M = CMults (2);
680 if (M == Degree ) KnotForm = GeomAbs_PiecewiseBezier;
681 else if (M == 1) KnotForm = GeomAbs_QuasiUniform;
682 }
683 break;
684 }
685 }
686
687 Standard_Integer FirstKM =
688 Periodic ? CKnots.Lower() : BSplCLib::FirstUKnotIndex (Degree,CMults);
689 Standard_Integer LastKM =
690 Periodic ? CKnots.Upper() : BSplCLib::LastUKnotIndex (Degree,CMults);
691 MaxKnotMult = 0;
692 if (LastKM - FirstKM != 1) {
693 Standard_Integer Multi;
694 for (Standard_Integer i = FirstKM + 1; i < LastKM; i++) {
695 Multi = CMults (i);
696 MaxKnotMult = Max (MaxKnotMult, Multi);
697 }
698 }
699}
700
7fd59977 701//=======================================================================
702//function : Reparametrize
703//purpose :
704//=======================================================================
705
706void BSplCLib::Reparametrize
707(const Standard_Real U1,
708 const Standard_Real U2,
709 Array1OfReal& Knots)
710{
711 Standard_Integer Lower = Knots.Lower();
712 Standard_Integer Upper = Knots.Upper();
713 Standard_Real UFirst = Min (U1, U2);
714 Standard_Real ULast = Max (U1, U2);
715 Standard_Real NewLength = ULast - UFirst;
716 BSplCLib_KnotDistribution KSet = BSplCLib::KnotForm (Knots, Lower, Upper);
717 if (KSet == BSplCLib_Uniform) {
718 Standard_Real DU = NewLength / (Upper - Lower);
719 Knots (Lower) = UFirst;
720
721 for (Standard_Integer i = Lower + 1; i <= Upper; i++) {
722 Knots (i) = Knots (i-1) + DU;
723 }
724 }
725 else {
726 Standard_Real K2;
727 Standard_Real Ratio;
728 Standard_Real K1 = Knots (Lower);
729 Standard_Real Length = Knots (Upper) - Knots (Lower);
730 Knots (Lower) = UFirst;
731
732 for (Standard_Integer i = Lower + 1; i <= Upper; i++) {
733 K2 = Knots (i);
734 Ratio = (K2 - K1) / Length;
735 Knots (i) = Knots (i-1) + (NewLength * Ratio);
736
737 //for CheckCurveData
738 Standard_Real Eps = Epsilon( Abs(Knots(i-1)) );
739 if (Knots(i) - Knots(i-1) <= Eps)
d0ad288a 740 Knots(i) = NextAfter (Knots(i-1) + Eps, RealLast());
7fd59977 741
742 K1 = K2;
743 }
744 }
745}
746
747//=======================================================================
748//function : Reverse
749//purpose :
750//=======================================================================
751
752void BSplCLib::Reverse(TColStd_Array1OfReal& Knots)
753{
754 Standard_Integer first = Knots.Lower();
755 Standard_Integer last = Knots.Upper();
756 Standard_Real kfirst = Knots(first);
757 Standard_Real klast = Knots(last);
758 Standard_Real tfirst = kfirst;
759 Standard_Real tlast = klast;
760 first++;
761 last--;
762
763 while (first <= last) {
764 tfirst += klast - Knots(last);
765 tlast -= Knots(first) - kfirst;
766 kfirst = Knots(first);
767 klast = Knots(last);
768 Knots(first) = tfirst;
769 Knots(last) = tlast;
770 first++;
771 last--;
772 }
773}
774
775//=======================================================================
776//function : Reverse
777//purpose :
778//=======================================================================
779
780void BSplCLib::Reverse(TColStd_Array1OfInteger& Mults)
781{
782 Standard_Integer first = Mults.Lower();
783 Standard_Integer last = Mults.Upper();
784 Standard_Integer temp;
785
786 while (first < last) {
787 temp = Mults(first);
788 Mults(first) = Mults(last);
789 Mults(last) = temp;
790 first++;
791 last--;
792 }
793}
794
795//=======================================================================
796//function : Reverse
797//purpose :
798//=======================================================================
799
800void BSplCLib::Reverse(TColStd_Array1OfReal& Weights,
801 const Standard_Integer L)
802{
803 Standard_Integer i, l = L;
804 l = Weights.Lower()+(l-Weights.Lower())%(Weights.Upper()-Weights.Lower()+1);
805
806 TColStd_Array1OfReal temp(0,Weights.Length()-1);
807
808 for (i = Weights.Lower(); i <= l; i++)
809 temp(l-i) = Weights(i);
810
811 for (i = l+1; i <= Weights.Upper(); i++)
812 temp(l-Weights.Lower()+Weights.Upper()-i+1) = Weights(i);
813
814 for (i = Weights.Lower(); i <= Weights.Upper(); i++)
815 Weights(i) = temp(i-Weights.Lower());
816}
817
818//=======================================================================
819//function : IsRational
820//purpose :
821//=======================================================================
822
823Standard_Boolean BSplCLib::IsRational(const TColStd_Array1OfReal& Weights,
824 const Standard_Integer I1,
825 const Standard_Integer I2,
826// const Standard_Real Epsi)
827 const Standard_Real )
828{
829 Standard_Integer i, f = Weights.Lower(), l = Weights.Length();
830 Standard_Integer I3 = I2 - f;
831 const Standard_Real * WG = &Weights(f);
832 WG -= f;
833
834 for (i = I1 - f; i < I3; i++) {
835 if (WG[f + (i % l)] != WG[f + ((i + 1) % l)]) return Standard_True;
836 }
837 return Standard_False ;
838}
839
840//=======================================================================
841//function : Eval
842//purpose : evaluate point and derivatives
843//=======================================================================
844
845void BSplCLib::Eval(const Standard_Real U,
846 const Standard_Integer Degree,
847 Standard_Real& Knots,
848 const Standard_Integer Dimension,
849 Standard_Real& Poles)
850{
851 Standard_Integer step,i,Dms,Dm1,Dpi,Sti;
852 Standard_Real X, Y, *poles, *knots = &Knots;
853 Dm1 = Dms = Degree;
854 Dm1--;
855 Dms++;
856 switch (Dimension) {
857
858 case 1 : {
859
860 for (step = - 1; step < Dm1; step++) {
861 Dms--;
862 poles = &Poles;
863 Dpi = Dm1;
864 Sti = step;
865
866 for (i = 0; i < Dms; i++) {
867 Dpi++;
868 Sti++;
869 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
870 Y = 1 - X;
871 poles[0] *= X; poles[0] += Y * poles[1];
872 poles += 1;
873 }
874 }
875 break;
876 }
877 case 2 : {
878
879 for (step = - 1; step < Dm1; step++) {
880 Dms--;
881 poles = &Poles;
882 Dpi = Dm1;
883 Sti = step;
884
885 for (i = 0; i < Dms; i++) {
886 Dpi++;
887 Sti++;
888 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
889 Y = 1 - X;
890 poles[0] *= X; poles[0] += Y * poles[2];
891 poles[1] *= X; poles[1] += Y * poles[3];
892 poles += 2;
893 }
894 }
895 break;
896 }
897 case 3 : {
898
899 for (step = - 1; step < Dm1; step++) {
900 Dms--;
901 poles = &Poles;
902 Dpi = Dm1;
903 Sti = step;
904
905 for (i = 0; i < Dms; i++) {
906 Dpi++;
907 Sti++;
908 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
909 Y = 1 - X;
910 poles[0] *= X; poles[0] += Y * poles[3];
911 poles[1] *= X; poles[1] += Y * poles[4];
912 poles[2] *= X; poles[2] += Y * poles[5];
913 poles += 3;
914 }
915 }
916 break;
917 }
918 case 4 : {
919
920 for (step = - 1; step < Dm1; step++) {
921 Dms--;
922 poles = &Poles;
923 Dpi = Dm1;
924 Sti = step;
925
926 for (i = 0; i < Dms; i++) {
927 Dpi++;
928 Sti++;
929 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
930 Y = 1 - X;
931 poles[0] *= X; poles[0] += Y * poles[4];
932 poles[1] *= X; poles[1] += Y * poles[5];
933 poles[2] *= X; poles[2] += Y * poles[6];
934 poles[3] *= X; poles[3] += Y * poles[7];
935 poles += 4;
936 }
937 }
938 break;
939 }
940 default : {
941 Standard_Integer k;
942
943 for (step = - 1; step < Dm1; step++) {
944 Dms--;
945 poles = &Poles;
946 Dpi = Dm1;
947 Sti = step;
948
949 for (i = 0; i < Dms; i++) {
950 Dpi++;
951 Sti++;
952 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
953 Y = 1 - X;
954
955 for (k = 0; k < Dimension; k++) {
956 poles[k] *= X;
957 poles[k] += Y * poles[k + Dimension];
958 }
959 poles += Dimension;
960 }
961 }
962 }
963 }
964}
965
966//=======================================================================
967//function : BoorScheme
968//purpose :
969//=======================================================================
970
971void BSplCLib::BoorScheme(const Standard_Real U,
972 const Standard_Integer Degree,
973 Standard_Real& Knots,
974 const Standard_Integer Dimension,
975 Standard_Real& Poles,
976 const Standard_Integer Depth,
977 const Standard_Integer Length)
978{
979 //
980 // Compute the values
981 //
982 // P(i,j) (U).
983 //
984 // for i = 0 to Depth,
985 // j = 0 to Length - i
986 //
987 // The Boor scheme is :
988 //
989 // P(0,j) = Pole(j)
990 // P(i,j) = x * P(i-1,j) + (1-x) * P(i-1,j+1)
991 //
992 // where x = (knot(i+j+Degree) - U) / (knot(i+j+Degree) - knot(i+j))
993 //
994 //
995 // The values are stored in the array Poles
996 // They are alternatively written if the odd and even positions.
997 //
998 // The successives contents of the array are
999 // ***** means unitialised, l = Degree + Length
1000 //
1001 // P(0,0) ****** P(0,1) ...... P(0,l-1) ******** P(0,l)
1002 // P(0,0) P(1,0) P(0,1) ...... P(0,l-1) P(1,l-1) P(0,l)
1003 // P(0,0) P(1,0) P(2,0) ...... P(2,l-1) P(1,l-1) P(0,l)
1004 //
1005
1006 Standard_Integer i,k,step;
1007 Standard_Real *knots = &Knots;
1008 Standard_Real *pole, *firstpole = &Poles - 2 * Dimension;
1009 // the steps of recursion
1010
1011 for (step = 0; step < Depth; step++) {
1012 firstpole += Dimension;
1013 pole = firstpole;
1014 // compute the new row of poles
1015
1016 for (i = step; i < Length; i++) {
1017 pole += 2 * Dimension;
1018 // coefficient
1019 Standard_Real X = (knots[i+Degree-step] - U)
1020 / (knots[i+Degree-step] - knots[i]);
1021 Standard_Real Y = 1. - X;
1022 // Value
1023 // P(i,j) = X * P(i-1,j) + (1-X) * P(i-1,j+1)
1024
1025 for (k = 0; k < Dimension; k++)
1026 pole[k] = X * pole[k - Dimension] + Y * pole[k + Dimension];
1027 }
1028 }
1029}
1030
1031//=======================================================================
1032//function : AntiBoorScheme
1033//purpose :
1034//=======================================================================
1035
1036Standard_Boolean BSplCLib::AntiBoorScheme(const Standard_Real U,
1037 const Standard_Integer Degree,
1038 Standard_Real& Knots,
1039 const Standard_Integer Dimension,
1040 Standard_Real& Poles,
1041 const Standard_Integer Depth,
1042 const Standard_Integer Length,
1043 const Standard_Real Tolerance)
1044{
1045 // do the Boor scheme reverted.
1046
1047 Standard_Integer i,k,step, half_length;
1048 Standard_Real *knots = &Knots;
1049 Standard_Real z,X,Y,*pole, *firstpole = &Poles + (Depth-1) * Dimension;
1050
1051 // Test the special case length = 1
1052 // only verification of the central point
1053
1054 if (Length == 1) {
1055 X = (knots[Degree] - U) / (knots[Degree] - knots[0]);
1056 Y = 1. - X;
1057
1058 for (k = 0; k < Dimension; k++) {
1059 z = X * firstpole[k] + Y * firstpole[k+2*Dimension];
1060 if (Abs(z - firstpole[k+Dimension]) > Tolerance)
1061 return Standard_False;
1062 }
1063 return Standard_True;
1064 }
1065
1066 // General case
1067 // the steps of recursion
1068
1069 for (step = Depth-1; step >= 0; step--) {
1070 firstpole -= Dimension;
1071 pole = firstpole;
1072
1073 // first step from left to right
1074
1075 for (i = step; i < Length-1; i++) {
1076 pole += 2 * Dimension;
1077
1078 X = (knots[i+Degree-step] - U) / (knots[i+Degree-step] - knots[i]);
1079 Y = 1. - X;
1080
1081 for (k = 0; k < Dimension; k++)
1082 pole[k+Dimension] = (pole[k] - X*pole[k-Dimension]) / Y;
1083
1084 }
1085
1086 // second step from right to left
1087 pole += 4* Dimension;
1088 half_length = (Length - 1 + step) / 2 ;
1089 //
1090 // only do half of the way from right to left
1091 // otherwise it start degenerating because of
1092 // overflows
1093 //
1094
1095 for (i = Length-1; i > half_length ; i--) {
1096 pole -= 2 * Dimension;
1097
1098 // coefficient
1099 X = (knots[i+Degree-step] - U) / (knots[i+Degree-step] - knots[i]);
1100 Y = 1. - X;
1101
1102 for (k = 0; k < Dimension; k++) {
1103 z = (pole[k] - Y * pole[k+Dimension]) / X;
1104 if (Abs(z-pole[k-Dimension]) > Tolerance)
1105 return Standard_False;
1106 pole[k-Dimension] += z;
1107 pole[k-Dimension] /= 2.;
1108 }
1109 }
1110 }
1111 return Standard_True;
1112}
1113
1114//=======================================================================
1115//function : Derivative
1116//purpose :
1117//=======================================================================
1118
1119void BSplCLib::Derivative(const Standard_Integer Degree,
1120 Standard_Real& Knots,
1121 const Standard_Integer Dimension,
1122 const Standard_Integer Length,
1123 const Standard_Integer Order,
1124 Standard_Real& Poles)
1125{
1126 Standard_Integer i,k,step,span = Degree;
1127 Standard_Real *knot = &Knots;
1128
1129 for (step = 1; step <= Order; step++) {
1130 Standard_Real* pole = &Poles;
1131
1132 for (i = step; i < Length; i++) {
1133 Standard_Real coef = - span / (knot[i+span] - knot[i]);
1134
1135 for (k = 0; k < Dimension; k++) {
1136 pole[k] -= pole[k+Dimension];
1137 pole[k] *= coef;
1138 }
1139 pole += Dimension;
1140 }
1141 span--;
1142 }
1143}
1144
1145//=======================================================================
1146//function : Bohm
1147//purpose :
1148//=======================================================================
1149
1150void BSplCLib::Bohm(const Standard_Real U,
1151 const Standard_Integer Degree,
1152 const Standard_Integer N,
1153 Standard_Real& Knots,
1154 const Standard_Integer Dimension,
1155 Standard_Real& Poles)
1156{
1157 // First phase independant of U, compute the poles of the derivatives
1158 Standard_Integer i,j,iDim,min,Dmi,DDmi,jDmi,Degm1;
1159 Standard_Real *knot = &Knots, *pole, coef, *tbis, *psav, *psDD, *psDDmDim;
1160 psav = &Poles;
1161 if (N < Degree) min = N;
1162 else min = Degree;
1163 Degm1 = Degree - 1;
1164 DDmi = (Degree << 1) + 1;
1165 switch (Dimension) {
1166 case 1 : {
1167 psDD = psav + Degree;
1168 psDDmDim = psDD - 1;
1169
1170 for (i = 0; i < Degree; i++) {
1171 DDmi--;
1172 pole = psDD;
1173 tbis = psDDmDim;
1174 jDmi = DDmi;
1175
1176 for (j = Degm1; j >= i; j--) {
1177 jDmi--;
3d58dc49 1178 *pole -= *tbis;
1179 *pole = (knot[jDmi] == knot[j]) ? 0.0 : *pole / (knot[jDmi] - knot[j]);
7fd59977 1180 pole--;
1181 tbis--;
1182 }
1183 }
1184 // Second phase, dependant of U
1185 iDim = - 1;
1186
1187 for (i = 0; i < Degree; i++) {
1188 iDim += 1;
1189 pole = psav + iDim;
1190 tbis = pole + 1;
1191 coef = U - knot[i];
1192
1193 for (j = i; j >= 0; j--) {
1194 *pole += coef * (*tbis);
1195 pole--;
1196 tbis--;
1197 }
1198 }
1199 // multiply by the degrees
1200 coef = Degree;
1201 Dmi = Degree;
1202 pole = psav + 1;
1203
1204 for (i = 1; i <= min; i++) {
1205 *pole *= coef; pole++;
1206 Dmi--;
1207 coef *= Dmi;
1208 }
1209 break;
1210 }
1211 case 2 : {
1212 psDD = psav + (Degree << 1);
1213 psDDmDim = psDD - 2;
1214
1215 for (i = 0; i < Degree; i++) {
1216 DDmi--;
1217 pole = psDD;
1218 tbis = psDDmDim;
1219 jDmi = DDmi;
1220
1221 for (j = Degm1; j >= i; j--) {
1222 jDmi--;
3d58dc49 1223 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. / (knot[jDmi] - knot[j]);
7fd59977 1224 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1225 *pole -= *tbis; *pole *= coef;
1226 pole -= 3;
1227 tbis -= 3;
1228 }
1229 }
1230 // Second phase, dependant of U
1231 iDim = - 2;
1232
1233 for (i = 0; i < Degree; i++) {
1234 iDim += 2;
1235 pole = psav + iDim;
1236 tbis = pole + 2;
1237 coef = U - knot[i];
1238
1239 for (j = i; j >= 0; j--) {
1240 *pole += coef * (*tbis); pole++; tbis++;
1241 *pole += coef * (*tbis);
1242 pole -= 3;
1243 tbis -= 3;
1244 }
1245 }
1246 // multiply by the degrees
1247 coef = Degree;
1248 Dmi = Degree;
1249 pole = psav + 2;
1250
1251 for (i = 1; i <= min; i++) {
1252 *pole *= coef; pole++;
1253 *pole *= coef; pole++;
1254 Dmi--;
1255 coef *= Dmi;
1256 }
1257 break;
1258 }
1259 case 3 : {
1260 psDD = psav + (Degree << 1) + Degree;
1261 psDDmDim = psDD - 3;
1262
1263 for (i = 0; i < Degree; i++) {
1264 DDmi--;
1265 pole = psDD;
1266 tbis = psDDmDim;
1267 jDmi = DDmi;
1268
1269 for (j = Degm1; j >= i; j--) {
1270 jDmi--;
3d58dc49 1271 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. / (knot[jDmi] - knot[j]);
7fd59977 1272 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1273 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1274 *pole -= *tbis; *pole *= coef;
1275 pole -= 5;
1276 tbis -= 5;
1277 }
1278 }
1279 // Second phase, dependant of U
1280 iDim = - 3;
1281
1282 for (i = 0; i < Degree; i++) {
1283 iDim += 3;
1284 pole = psav + iDim;
1285 tbis = pole + 3;
1286 coef = U - knot[i];
1287
1288 for (j = i; j >= 0; j--) {
1289 *pole += coef * (*tbis); pole++; tbis++;
1290 *pole += coef * (*tbis); pole++; tbis++;
1291 *pole += coef * (*tbis);
1292 pole -= 5;
1293 tbis -= 5;
1294 }
1295 }
1296 // multiply by the degrees
1297 coef = Degree;
1298 Dmi = Degree;
1299 pole = psav + 3;
1300
1301 for (i = 1; i <= min; i++) {
1302 *pole *= coef; pole++;
1303 *pole *= coef; pole++;
1304 *pole *= coef; pole++;
1305 Dmi--;
1306 coef *= Dmi;
1307 }
1308 break;
1309 }
1310 case 4 : {
1311 psDD = psav + (Degree << 2);
1312 psDDmDim = psDD - 4;
1313
1314 for (i = 0; i < Degree; i++) {
1315 DDmi--;
1316 pole = psDD;
1317 tbis = psDDmDim;
1318 jDmi = DDmi;
1319
1320 for (j = Degm1; j >= i; j--) {
1321 jDmi--;
3d58dc49 1322 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. /(knot[jDmi] - knot[j]) ;
7fd59977 1323 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1324 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1325 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1326 *pole -= *tbis; *pole *= coef;
1327 pole -= 7;
1328 tbis -= 7;
1329 }
1330 }
1331 // Second phase, dependant of U
1332 iDim = - 4;
1333
1334 for (i = 0; i < Degree; i++) {
1335 iDim += 4;
1336 pole = psav + iDim;
1337 tbis = pole + 4;
1338 coef = U - knot[i];
1339
1340 for (j = i; j >= 0; j--) {
1341 *pole += coef * (*tbis); pole++; tbis++;
1342 *pole += coef * (*tbis); pole++; tbis++;
1343 *pole += coef * (*tbis); pole++; tbis++;
1344 *pole += coef * (*tbis);
1345 pole -= 7;
1346 tbis -= 7;
1347 }
1348 }
1349 // multiply by the degrees
1350 coef = Degree;
1351 Dmi = Degree;
1352 pole = psav + 4;
1353
1354 for (i = 1; i <= min; i++) {
1355 *pole *= coef; pole++;
1356 *pole *= coef; pole++;
1357 *pole *= coef; pole++;
1358 *pole *= coef; pole++;
1359 Dmi--;
1360 coef *= Dmi;
1361 }
1362 break;
1363 }
1364 default : {
1365 Standard_Integer k;
1366 Standard_Integer Dim2 = Dimension << 1;
1367 psDD = psav + Degree * Dimension;
1368 psDDmDim = psDD - Dimension;
1369
1370 for (i = 0; i < Degree; i++) {
1371 DDmi--;
1372 pole = psDD;
1373 tbis = psDDmDim;
1374 jDmi = DDmi;
1375
1376 for (j = Degm1; j >= i; j--) {
1377 jDmi--;
3d58dc49 1378 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. / (knot[jDmi] - knot[j]);
7fd59977 1379
1380 for (k = 0; k < Dimension; k++) {
1381 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1382 }
1383 pole -= Dim2;
1384 tbis -= Dim2;
1385 }
1386 }
1387 // Second phase, dependant of U
1388 iDim = - Dimension;
1389
1390 for (i = 0; i < Degree; i++) {
1391 iDim += Dimension;
1392 pole = psav + iDim;
1393 tbis = pole + Dimension;
1394 coef = U - knot[i];
1395
1396 for (j = i; j >= 0; j--) {
1397
1398 for (k = 0; k < Dimension; k++) {
1399 *pole += coef * (*tbis); pole++; tbis++;
1400 }
1401 pole -= Dim2;
1402 tbis -= Dim2;
1403 }
1404 }
1405 // multiply by the degrees
1406 coef = Degree;
1407 Dmi = Degree;
1408 pole = psav + Dimension;
1409
1410 for (i = 1; i <= min; i++) {
1411
1412 for (k = 0; k < Dimension; k++) {
1413 *pole *= coef; pole++;
1414 }
1415 Dmi--;
1416 coef *= Dmi;
1417 }
1418 }
1419 }
1420}
1421
1422//=======================================================================
1423//function : BuildKnots
1424//purpose :
1425//=======================================================================
1426
1427void BSplCLib::BuildKnots(const Standard_Integer Degree,
1428 const Standard_Integer Index,
1429 const Standard_Boolean Periodic,
1430 const TColStd_Array1OfReal& Knots,
1431 const TColStd_Array1OfInteger& Mults,
1432 Standard_Real& LK)
1433{
1434 Standard_Integer KLower = Knots.Lower();
1435 const Standard_Real * pkn = &Knots(KLower);
1436 pkn -= KLower;
1437 Standard_Real *knot = &LK;
1438 if (&Mults == NULL) {
1439 switch (Degree) {
1440 case 1 : {
1441 Standard_Integer j = Index ;
1442 knot[0] = pkn[j]; j++;
1443 knot[1] = pkn[j];
1444 break;
1445 }
1446 case 2 : {
1447 Standard_Integer j = Index - 1;
1448 knot[0] = pkn[j]; j++;
1449 knot[1] = pkn[j]; j++;
1450 knot[2] = pkn[j]; j++;
1451 knot[3] = pkn[j];
1452 break;
1453 }
1454 case 3 : {
1455 Standard_Integer j = Index - 2;
1456 knot[0] = pkn[j]; j++;
1457 knot[1] = pkn[j]; j++;
1458 knot[2] = pkn[j]; j++;
1459 knot[3] = pkn[j]; j++;
1460 knot[4] = pkn[j]; j++;
1461 knot[5] = pkn[j];
1462 break;
1463 }
1464 case 4 : {
1465 Standard_Integer j = Index - 3;
1466 knot[0] = pkn[j]; j++;
1467 knot[1] = pkn[j]; j++;
1468 knot[2] = pkn[j]; j++;
1469 knot[3] = pkn[j]; j++;
1470 knot[4] = pkn[j]; j++;
1471 knot[5] = pkn[j]; j++;
1472 knot[6] = pkn[j]; j++;
1473 knot[7] = pkn[j];
1474 break;
1475 }
1476 case 5 : {
1477 Standard_Integer j = Index - 4;
1478 knot[0] = pkn[j]; j++;
1479 knot[1] = pkn[j]; j++;
1480 knot[2] = pkn[j]; j++;
1481 knot[3] = pkn[j]; j++;
1482 knot[4] = pkn[j]; j++;
1483 knot[5] = pkn[j]; j++;
1484 knot[6] = pkn[j]; j++;
1485 knot[7] = pkn[j]; j++;
1486 knot[8] = pkn[j]; j++;
1487 knot[9] = pkn[j];
1488 break;
1489 }
1490 case 6 : {
1491 Standard_Integer j = Index - 5;
1492 knot[ 0] = pkn[j]; j++;
1493 knot[ 1] = pkn[j]; j++;
1494 knot[ 2] = pkn[j]; j++;
1495 knot[ 3] = pkn[j]; j++;
1496 knot[ 4] = pkn[j]; j++;
1497 knot[ 5] = pkn[j]; j++;
1498 knot[ 6] = pkn[j]; j++;
1499 knot[ 7] = pkn[j]; j++;
1500 knot[ 8] = pkn[j]; j++;
1501 knot[ 9] = pkn[j]; j++;
1502 knot[10] = pkn[j]; j++;
1503 knot[11] = pkn[j];
1504 break;
1505 }
1506 default : {
1507 Standard_Integer i,j;
1508 Standard_Integer Deg2 = Degree << 1;
1509 j = Index - Degree;
1510
1511 for (i = 0; i < Deg2; i++) {
1512 j++;
1513 knot[i] = pkn[j];
1514 }
1515 }
1516 }
1517 }
1518 else {
1519 Standard_Integer i;
1520 Standard_Integer Deg1 = Degree - 1;
1521 Standard_Integer KUpper = Knots.Upper();
1522 Standard_Integer MLower = Mults.Lower();
1523 Standard_Integer MUpper = Mults.Upper();
1524 const Standard_Integer * pmu = &Mults(MLower);
1525 pmu -= MLower;
1526 Standard_Real dknot = 0;
1527 Standard_Integer ilow = Index , mlow = 0;
1528 Standard_Integer iupp = Index + 1, mupp = 0;
1529 Standard_Real loffset = 0., uoffset = 0.;
1530 Standard_Boolean getlow = Standard_True, getupp = Standard_True;
1531 if (Periodic) {
1532 dknot = pkn[KUpper] - pkn[KLower];
1533 if (iupp > MUpper) {
1534 iupp = MLower + 1;
1535 uoffset = dknot;
1536 }
1537 }
1538 // Find the knots around Index
1539
1540 for (i = 0; i < Degree; i++) {
1541 if (getlow) {
1542 mlow++;
1543 if (mlow > pmu[ilow]) {
1544 mlow = 1;
1545 ilow--;
1546 getlow = (ilow >= MLower);
1547 if (Periodic && !getlow) {
1548 ilow = MUpper - 1;
1549 loffset = dknot;
1550 getlow = Standard_True;
1551 }
1552 }
1553 if (getlow)
1554 knot[Deg1 - i] = pkn[ilow] - loffset;
1555 }
1556 if (getupp) {
1557 mupp++;
1558 if (mupp > pmu[iupp]) {
1559 mupp = 1;
1560 iupp++;
1561 getupp = (iupp <= MUpper);
1562 if (Periodic && !getupp) {
1563 iupp = MLower + 1;
1564 uoffset = dknot;
1565 getupp = Standard_True;
1566 }
1567 }
1568 if (getupp)
1569 knot[Degree + i] = pkn[iupp] + uoffset;
1570 }
1571 }
1572 }
1573}
1574
1575//=======================================================================
1576//function : PoleIndex
1577//purpose :
1578//=======================================================================
1579
1580Standard_Integer BSplCLib::PoleIndex(const Standard_Integer Degree,
1581 const Standard_Integer Index,
1582 const Standard_Boolean Periodic,
1583 const TColStd_Array1OfInteger& Mults)
1584{
1585 Standard_Integer i, pindex = 0;
1586
1587 for (i = Mults.Lower(); i <= Index; i++)
1588 pindex += Mults(i);
1589 if (Periodic)
1590 pindex -= Mults(Mults.Lower());
1591 else
1592 pindex -= Degree + 1;
1593
1594 return pindex;
1595}
1596
1597//=======================================================================
1598//function : BuildBoor
1599//purpose : builds the local array for boor
1600//=======================================================================
1601
1602void BSplCLib::BuildBoor(const Standard_Integer Index,
1603 const Standard_Integer Length,
1604 const Standard_Integer Dimension,
1605 const TColStd_Array1OfReal& Poles,
1606 Standard_Real& LP)
1607{
1608 Standard_Real *poles = &LP;
1609 Standard_Integer i,k, ip = Poles.Lower() + Index * Dimension;
1610
1611 for (i = 0; i < Length+1; i++) {
1612
1613 for (k = 0; k < Dimension; k++) {
1614 poles[k] = Poles(ip);
1615 ip++;
1616 if (ip > Poles.Upper()) ip = Poles.Lower();
1617 }
1618 poles += 2 * Dimension;
1619 }
1620}
1621
1622//=======================================================================
1623//function : BoorIndex
1624//purpose :
1625//=======================================================================
1626
1627Standard_Integer BSplCLib::BoorIndex(const Standard_Integer Index,
1628 const Standard_Integer Length,
1629 const Standard_Integer Depth)
1630{
1631 if (Index <= Depth) return Index;
1632 if (Index <= Length) return 2 * Index - Depth;
1633 return Length + Index - Depth;
1634}
1635
1636//=======================================================================
1637//function : GetPole
1638//purpose :
1639//=======================================================================
1640
1641void BSplCLib::GetPole(const Standard_Integer Index,
1642 const Standard_Integer Length,
1643 const Standard_Integer Depth,
1644 const Standard_Integer Dimension,
1645 Standard_Real& LP,
1646 Standard_Integer& Position,
1647 TColStd_Array1OfReal& Pole)
1648{
1649 Standard_Integer k;
1650 Standard_Real* pole = &LP + BoorIndex(Index,Length,Depth) * Dimension;
1651
1652 for (k = 0; k < Dimension; k++) {
1653 Pole(Position) = pole[k];
1654 Position++;
1655 }
1656 if (Position > Pole.Upper()) Position = Pole.Lower();
1657}
1658
1659//=======================================================================
1660//function : PrepareInsertKnots
1661//purpose :
1662//=======================================================================
1663
1664Standard_Boolean BSplCLib::PrepareInsertKnots
1665(const Standard_Integer Degree,
1666 const Standard_Boolean Periodic,
1667 const TColStd_Array1OfReal& Knots,
1668 const TColStd_Array1OfInteger& Mults,
1669 const TColStd_Array1OfReal& AddKnots,
1670 const TColStd_Array1OfInteger& AddMults,
1671 Standard_Integer& NbPoles,
1672 Standard_Integer& NbKnots,
1673 const Standard_Real Tolerance,
1674 const Standard_Boolean Add)
1675{
1676 Standard_Boolean addflat = &AddMults == NULL;
1677
1678 Standard_Integer first,last;
1679 if (Periodic) {
1680 first = Knots.Lower();
1681 last = Knots.Upper();
1682 }
1683 else {
1684 first = FirstUKnotIndex(Degree,Mults);
1685 last = LastUKnotIndex(Degree,Mults);
1686 }
1687 Standard_Real adeltaK1 = Knots(first)-AddKnots(AddKnots.Lower());
1688 Standard_Real adeltaK2 = AddKnots(AddKnots.Upper())-Knots(last);
1689 if (adeltaK1 > Tolerance) return Standard_False;
1690 if (adeltaK2 > Tolerance) return Standard_False;
1691
9d091ec1 1692 Standard_Integer sigma = 0, mult, amult;
7fd59977 1693 NbKnots = 0;
1694 Standard_Integer k = Knots.Lower() - 1;
1695 Standard_Integer ak = AddKnots.Lower();
1696
1697 if(Periodic && AddKnots.Length() > 1)
1698 {
1699 //gka for case when segments was produced on full period only one knot
1700 //was added in the end of curve
70d08ce5 1701 if(fabs(adeltaK1) <= gp::Resolution() &&
1702 fabs(adeltaK2) <= gp::Resolution())
7fd59977 1703 ak++;
1704 }
1705
c1c03615 1706 Standard_Integer aLastKnotMult = Mults (Knots.Upper());
7fd59977 1707 Standard_Real au,oldau = AddKnots(ak),Eps;
1708
1709 while (ak <= AddKnots.Upper()) {
1710 au = AddKnots(ak);
1711 if (au < oldau) return Standard_False;
1712 oldau = au;
1713
1714 Eps = Max(Tolerance,Epsilon(au));
1715
1716 while ((k < Knots.Upper()) && (Knots(k+1) - au <= Eps)) {
1717 k++;
1718 NbKnots++;
1719 sigma += Mults(k);
1720 }
1721
1722 if (addflat) amult = 1;
1723 else amult = Max(0,AddMults(ak));
1724
1725 while ((ak < AddKnots.Upper()) &&
1726 (Abs(au - AddKnots(ak+1)) <= Eps)) {
1727 ak++;
1728 if (Add) {
1729 if (addflat) amult++;
1730 else amult += Max(0,AddMults(ak));
1731 }
1732 }
1733
1734
1735 if (Abs(au - Knots(k)) <= Eps) {
1736 // identic to existing knot
1737 mult = Mults(k);
7fd59977 1738 if (Add) {
1739 if (mult + amult > Degree)
1740 amult = Max(0,Degree - mult);
1741 sigma += amult;
7fd59977 1742
1743 }
1744 else if (amult > mult) {
1745 if (amult > Degree) amult = Degree;
c1c03615 1746 if (k == Knots.Upper () && Periodic)
1747 {
1748 aLastKnotMult = Max (amult, mult);
1749 sigma += 2 * (aLastKnotMult - mult);
1750 }
1751 else
1752 {
1753 sigma += amult - mult;
1754 }
7fd59977 1755 }
1756 /*
1757 // on periodic curves if this is the last knot
1758 // the multiplicity is added twice to account for the first knot
1759 if (k == Knots.Upper() && Periodic) {
1760 if (Add)
1761 sigma += amult;
1762 else
1763 sigma += amult - mult;
1764 }
1765 */
1766 }
1767 else {
1768 // not identic to existing knot
1769 if (amult > 0) {
1770 if (amult > Degree) amult = Degree;
1771 NbKnots++;
7fd59977 1772 sigma += amult;
1773 }
1774 }
1775
1776 ak++;
1777 }
1778
1779 // count the last knots
7fd59977 1780 while (k < Knots.Upper()) {
1781 k++;
1782 NbKnots++;
1783 sigma += Mults(k);
1784 }
1785
1786 if (Periodic) {
9d091ec1 1787 //for periodic B-Spline the requirement is that multiplicites of the first
1788 //and last knots must be equal (see Geom_BSplineCurve constructor for
1789 //instance);
1790 //respectively AddMults() must meet this requirement if AddKnots() contains
1791 //knot(s) coincident with first or last
c1c03615 1792 NbPoles = sigma - aLastKnotMult;
7fd59977 1793 }
1794 else {
1795 NbPoles = sigma - Degree - 1;
1796 }
1797
1798 return Standard_True;
1799}
1800
1801//=======================================================================
1802//function : Copy
1803//purpose : copy reals from an array to an other
1804//
1805// NbValues are copied from OldPoles(OldFirst)
1806// to NewPoles(NewFirst)
1807//
1808// Periodicity is handled.
1809// OldFirst and NewFirst are updated
1810// to the position after the last copied pole.
1811//
1812//=======================================================================
1813
1814static void Copy(const Standard_Integer NbPoles,
1815 Standard_Integer& OldFirst,
1816 const TColStd_Array1OfReal& OldPoles,
1817 Standard_Integer& NewFirst,
1818 TColStd_Array1OfReal& NewPoles)
1819{
1820 // reset the index in the range for periodicity
1821
1822 OldFirst = OldPoles.Lower() +
1823 (OldFirst - OldPoles.Lower()) % (OldPoles.Upper() - OldPoles.Lower() + 1);
1824
1825 NewFirst = NewPoles.Lower() +
1826 (NewFirst - NewPoles.Lower()) % (NewPoles.Upper() - NewPoles.Lower() + 1);
1827
1828 // copy
1829 Standard_Integer i;
1830
1831 for (i = 1; i <= NbPoles; i++) {
1832 NewPoles(NewFirst) = OldPoles(OldFirst);
1833 OldFirst++;
1834 if (OldFirst > OldPoles.Upper()) OldFirst = OldPoles.Lower();
1835 NewFirst++;
1836 if (NewFirst > NewPoles.Upper()) NewFirst = NewPoles.Lower();
1837 }
1838}
1839
1840//=======================================================================
1841//function : InsertKnots
1842//purpose : insert an array of knots and multiplicities
1843//=======================================================================
1844
1845void BSplCLib::InsertKnots
1846(const Standard_Integer Degree,
1847 const Standard_Boolean Periodic,
1848 const Standard_Integer Dimension,
1849 const TColStd_Array1OfReal& Poles,
1850 const TColStd_Array1OfReal& Knots,
1851 const TColStd_Array1OfInteger& Mults,
1852 const TColStd_Array1OfReal& AddKnots,
1853 const TColStd_Array1OfInteger& AddMults,
1854 TColStd_Array1OfReal& NewPoles,
1855 TColStd_Array1OfReal& NewKnots,
1856 TColStd_Array1OfInteger& NewMults,
1857 const Standard_Real Tolerance,
1858 const Standard_Boolean Add)
1859{
1860 Standard_Boolean addflat = &AddMults == NULL;
1861
1862 Standard_Integer i,k,mult,firstmult;
1863 Standard_Integer index,kn,curnk,curk;
1864 Standard_Integer p,np, curp, curnp, length, depth;
1865 Standard_Real u;
1866 Standard_Integer need;
1867 Standard_Real Eps;
1868
1869 // -------------------
1870 // create local arrays
1871 // -------------------
1872
1873 Standard_Real *knots = new Standard_Real[2*Degree];
1874 Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
1875
1876 //----------------------------
1877 // loop on the knots to insert
1878 //----------------------------
1879
1880 curk = Knots.Lower()-1; // current position in Knots
1881 curnk = NewKnots.Lower()-1; // current position in NewKnots
1882 curp = Poles.Lower(); // current position in Poles
1883 curnp = NewPoles.Lower(); // current position in NewPoles
1884
1885 // NewKnots, NewMults, NewPoles contains the current state of the curve
1886
1887 // index is the first pole of the current curve for insertion schema
1888
1889 if (Periodic) index = -Mults(Mults.Lower());
1890 else index = -Degree-1;
1891
1892 // on Periodic curves the first knot and the last knot are inserted later
1893 // (they are the same knot)
1894 firstmult = 0; // multiplicity of the first-last knot for periodic
1895
1896
1897 // kn current knot to insert in AddKnots
1898
1899 for (kn = AddKnots.Lower(); kn <= AddKnots.Upper(); kn++) {
1900
1901 u = AddKnots(kn);
1902 Eps = Max(Tolerance,Epsilon(u));
1903
1904 //-----------------------------------
1905 // find the position in the old knots
1906 // and copy to the new knots
1907 //-----------------------------------
1908
1909 while (curk < Knots.Upper() && Knots(curk+1) - u <= Eps) {
1910 curk++; curnk++;
1911 NewKnots(curnk) = Knots(curk);
1912 index += NewMults(curnk) = Mults(curk);
1913 }
1914
1915 //-----------------------------------
1916 // Slice the knots and the mults
1917 // to the current size of the new curve
1918 //-----------------------------------
1919
1920 i = curnk + Knots.Upper() - curk;
1921 TColStd_Array1OfReal nknots(NewKnots(NewKnots.Lower()),NewKnots.Lower(),i);
1922 TColStd_Array1OfInteger nmults(NewMults(NewMults.Lower()),NewMults.Lower(),i);
1923
1924 //-----------------------------------
1925 // copy enough knots
1926 // to compute the insertion schema
1927 //-----------------------------------
1928
1929 k = curk;
1930 i = curnk;
1931 mult = 0;
1932
1933 while (mult < Degree && k < Knots.Upper()) {
1934 k++; i++;
1935 nknots(i) = Knots(k);
1936 mult += nmults(i) = Mults(k);
1937 }
1938
1939 // copy knots at the end for periodic curve
1940 if (Periodic) {
1941 mult = 0;
1942 k = Knots.Upper();
1943 i = nknots.Upper();
1944
1945 while (mult < Degree && i > curnk) {
1946 nknots(i) = Knots(k);
1947 mult += nmults(i) = Mults(k);
1948 k--;
1949 i--;
1950 }
1951 nmults(nmults.Upper()) = nmults(nmults.Lower());
1952 }
1953
1954
1955
1956 //------------------------------------
1957 // do the boor scheme on the new curve
1958 // to insert the new knot
1959 //------------------------------------
1960
1961 Standard_Boolean sameknot = (Abs(u-NewKnots(curnk)) <= Eps);
1962
1963 if (sameknot) length = Max(0,Degree - NewMults(curnk));
1964 else length = Degree;
1965
1966 if (addflat) depth = 1;
1967 else depth = Min(Degree,AddMults(kn));
1968
1969 if (sameknot) {
1970 if (Add) {
1971 if ((NewMults(curnk) + depth) > Degree)
1972 depth = Degree - NewMults(curnk);
1973 }
1974 else {
1975 depth = Max(0,depth-NewMults(curnk));
1976 }
1977
1978 if (Periodic) {
1979 // on periodic curve the first and last knot are delayed to the end
1980 if (curk == Knots.Lower() || (curk == Knots.Upper())) {
c1c03615 1981 if (firstmult == 0) // do that only once
1982 firstmult += depth;
7fd59977 1983 depth = 0;
1984 }
1985 }
1986 }
1987 if (depth <= 0) continue;
1988
1989 BuildKnots(Degree,curnk,Periodic,nknots,nmults,*knots);
1990
1991 // copy the poles
1992
1993 need = NewPoles.Lower()+(index+length+1)*Dimension - curnp;
1994 need = Min(need,Poles.Upper() - curp + 1);
1995
1996 p = curp;
1997 np = curnp;
1998 Copy(need,p,Poles,np,NewPoles);
1999 curp += need;
2000 curnp += need;
2001
2002 // slice the poles to the current number of poles in case of periodic
2003 TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
2004
2005 BuildBoor(index,length,Dimension,npoles,*poles);
2006 BoorScheme(u,Degree,*knots,Dimension,*poles,depth,length);
2007
2008 //-------------------
2009 // copy the new poles
2010 //-------------------
2011
2012 curnp += depth * Dimension; // number of poles is increased by depth
2013 TColStd_Array1OfReal ThePoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
2014 np = NewKnots.Lower()+(index+1)*Dimension;
2015
2016 for (i = 1; i <= length + depth; i++)
2017 GetPole(i,length,depth,Dimension,*poles,np,ThePoles);
2018
2019 //-------------------
2020 // insert the knot
2021 //-------------------
2022
2023 index += depth;
2024 if (sameknot) {
2025 NewMults(curnk) += depth;
2026 }
2027 else {
2028 curnk++;
2029 NewKnots(curnk) = u;
2030 NewMults(curnk) = depth;
2031 }
2032 }
2033
2034 //------------------------------
2035 // copy the last poles and knots
2036 //------------------------------
2037
2038 Copy(Poles.Upper() - curp + 1,curp,Poles,curnp,NewPoles);
2039
2040 while (curk < Knots.Upper()) {
2041 curk++; curnk++;
2042 NewKnots(curnk) = Knots(curk);
2043 NewMults(curnk) = Mults(curk);
2044 }
2045
2046 //------------------------------
2047 // process the first-last knot
2048 // on periodic curves
2049 //------------------------------
2050
2051 if (firstmult > 0) {
2052 curnk = NewKnots.Lower();
2053 if (NewMults(curnk) + firstmult > Degree) {
2054 firstmult = Degree - NewMults(curnk);
2055 }
2056 if (firstmult > 0) {
2057
2058 length = Degree - NewMults(curnk);
2059 depth = firstmult;
2060
2061 BuildKnots(Degree,curnk,Periodic,NewKnots,NewMults,*knots);
2062 TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),
2063 NewPoles.Lower(),
2064 NewPoles.Upper()-depth*Dimension);
2065 BuildBoor(0,length,Dimension,npoles,*poles);
2066 BoorScheme(NewKnots(curnk),Degree,*knots,Dimension,*poles,depth,length);
2067
2068 //---------------------------
2069 // copy the new poles
2070 // but rotate them with depth
2071 //---------------------------
2072
2073 np = NewPoles.Lower();
2074
2075 for (i = depth; i < length + depth; i++)
2076 GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
2077
2078 np = NewPoles.Upper() - depth*Dimension + 1;
2079
2080 for (i = 0; i < depth; i++)
2081 GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
2082
2083 NewMults(NewMults.Lower()) += depth;
2084 NewMults(NewMults.Upper()) += depth;
2085 }
2086 }
2087 // free local arrays
2088 delete [] knots;
2089 delete [] poles;
2090}
2091
2092//=======================================================================
2093//function : RemoveKnot
2094//purpose :
2095//=======================================================================
2096
2097Standard_Boolean BSplCLib::RemoveKnot
2098(const Standard_Integer Index,
2099 const Standard_Integer Mult,
2100 const Standard_Integer Degree,
2101 const Standard_Boolean Periodic,
2102 const Standard_Integer Dimension,
2103 const TColStd_Array1OfReal& Poles,
2104 const TColStd_Array1OfReal& Knots,
2105 const TColStd_Array1OfInteger& Mults,
2106 TColStd_Array1OfReal& NewPoles,
2107 TColStd_Array1OfReal& NewKnots,
2108 TColStd_Array1OfInteger& NewMults,
2109 const Standard_Real Tolerance)
2110{
2111 Standard_Integer index,i,j,k,p,np;
2112
2113 Standard_Integer TheIndex = Index;
2114
2115 // protection
2116 Standard_Integer first,last;
2117 if (Periodic) {
2118 first = Knots.Lower();
2119 last = Knots.Upper();
2120 }
2121 else {
2122 first = BSplCLib::FirstUKnotIndex(Degree,Mults) + 1;
2123 last = BSplCLib::LastUKnotIndex(Degree,Mults) - 1;
2124 }
2125 if (Index < first) return Standard_False;
2126 if (Index > last) return Standard_False;
2127
2128 if ( Periodic && (Index == first)) TheIndex = last;
2129
2130 Standard_Integer depth = Mults(TheIndex) - Mult;
2131 Standard_Integer length = Degree - Mult;
2132
2133 // -------------------
2134 // create local arrays
2135 // -------------------
2136
2137 Standard_Real *knots = new Standard_Real[4*Degree];
2138 Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
2139
2140
2141 // ------------------------------------
2142 // build the knots for anti Boor Scheme
2143 // ------------------------------------
2144
2145 // the new sequence of knots
2146 // is obtained from the knots at Index-1 and Index
2147
2148 BSplCLib::BuildKnots(Degree,TheIndex-1,Periodic,Knots,Mults,*knots);
2149 index = PoleIndex(Degree,TheIndex-1,Periodic,Mults);
2150 BSplCLib::BuildKnots(Degree,TheIndex,Periodic,Knots,Mults,knots[2*Degree]);
2151
2152 index += Mult;
2153
2154 for (i = 0; i < Degree - Mult; i++)
2155 knots[i] = knots[i+Mult];
2156
2157 for (i = Degree-Mult; i < 2*Degree; i++)
2158 knots[i] = knots[2*Degree+i];
2159
2160
2161 // ------------------------------------
2162 // build the poles for anti Boor Scheme
2163 // ------------------------------------
2164
2165 p = Poles.Lower()+index * Dimension;
2166
2167 for (i = 0; i <= length + depth; i++) {
2168 j = Dimension * BoorIndex(i,length,depth);
2169
2170 for (k = 0; k < Dimension; k++) {
2171 poles[j+k] = Poles(p+k);
2172 }
2173 p += Dimension;
2174 if (p > Poles.Upper()) p = Poles.Lower();
2175 }
2176
2177
2178 // ----------------
2179 // Anti Boor Scheme
2180 // ----------------
2181
2182 Standard_Boolean result = AntiBoorScheme(Knots(TheIndex),Degree,*knots,
2183 Dimension,*poles,
2184 depth,length,Tolerance);
2185
2186 // ----------------
2187 // copy the results
2188 // ----------------
2189
2190 if (result) {
2191
2192 // poles
2193
2194 p = Poles.Lower();
2195 np = NewPoles.Lower();
2196
2197 // unmodified poles before
2198 Copy((index+1)*Dimension,p,Poles,np,NewPoles);
2199
2200
2201 // modified
2202
2203 for (i = 1; i <= length; i++)
2204 BSplCLib::GetPole(i,length,0,Dimension,*poles,np,NewPoles);
2205 p += (length + depth) * Dimension ;
2206
2207 // unmodified poles after
2208 if (p != Poles.Lower()) {
2209 i = Poles.Upper() - p + 1;
2210 Copy(i,p,Poles,np,NewPoles);
2211 }
2212
2213 // knots and mults
2214
2215 if (Mult > 0) {
2216 NewKnots = Knots;
2217 NewMults = Mults;
2218 NewMults(TheIndex) = Mult;
2219 if (Periodic) {
2220 if (TheIndex == first) NewMults(last) = Mult;
2221 if (TheIndex == last) NewMults(first) = Mult;
2222 }
2223 }
2224 else {
2225 if (!Periodic || (TheIndex != first && TheIndex != last)) {
2226
2227 for (i = Knots.Lower(); i < TheIndex; i++) {
2228 NewKnots(i) = Knots(i);
2229 NewMults(i) = Mults(i);
2230 }
2231
2232 for (i = TheIndex+1; i <= Knots.Upper(); i++) {
2233 NewKnots(i-1) = Knots(i);
2234 NewMults(i-1) = Mults(i);
2235 }
2236 }
2237 else {
2238 // The interesting case of a Periodic curve
2239 // where the first and last knot is removed.
2240
2241 for (i = first; i < last-1; i++) {
2242 NewKnots(i) = Knots(i+1);
2243 NewMults(i) = Mults(i+1);
2244 }
2245 NewKnots(last-1) = NewKnots(first) + Knots(last) - Knots(first);
2246 NewMults(last-1) = NewMults(first);
2247 }
2248 }
2249 }
2250
2251
2252 // free local arrays
2253 delete [] knots;
2254 delete [] poles;
2255
2256 return result;
2257}
2258
2259//=======================================================================
2260//function : IncreaseDegreeCountKnots
2261//purpose :
2262//=======================================================================
2263
2264Standard_Integer BSplCLib::IncreaseDegreeCountKnots
2265(const Standard_Integer Degree,
2266 const Standard_Integer NewDegree,
2267 const Standard_Boolean Periodic,
2268 const TColStd_Array1OfInteger& Mults)
2269{
2270 if (Periodic) return Mults.Length();
2271 Standard_Integer f = FirstUKnotIndex(Degree,Mults);
2272 Standard_Integer l = LastUKnotIndex(Degree,Mults);
2273 Standard_Integer m,i,removed = 0, step = NewDegree - Degree;
2274
2275 i = Mults.Lower();
2276 m = Degree + (f - i + 1) * step + 1;
2277
2278 while (m > NewDegree+1) {
2279 removed++;
2280 m -= Mults(i) + step;
2281 i++;
2282 }
2283 if (m < NewDegree+1) removed--;
2284
2285 i = Mults.Upper();
2286 m = Degree + (i - l + 1) * step + 1;
2287
2288 while (m > NewDegree+1) {
2289 removed++;
2290 m -= Mults(i) + step;
2291 i--;
2292 }
2293 if (m < NewDegree+1) removed--;
2294
2295 return Mults.Length() - removed;
2296}
2297
2298//=======================================================================
2299//function : IncreaseDegree
2300//purpose :
2301//=======================================================================
2302
2303void BSplCLib::IncreaseDegree
2304(const Standard_Integer Degree,
2305 const Standard_Integer NewDegree,
2306 const Standard_Boolean Periodic,
2307 const Standard_Integer Dimension,
2308 const TColStd_Array1OfReal& Poles,
2309 const TColStd_Array1OfReal& Knots,
2310 const TColStd_Array1OfInteger& Mults,
2311 TColStd_Array1OfReal& NewPoles,
2312 TColStd_Array1OfReal& NewKnots,
2313 TColStd_Array1OfInteger& NewMults)
2314{
2315 // Degree elevation of a BSpline Curve
2316
2317 // This algorithms loops on degree incrementation from Degree to NewDegree.
2318 // The variable curDeg is the current degree to increment.
2319
2320 // Before degree incrementations a "working curve" is created.
2321 // It has the same knot, poles and multiplicities.
2322
2323 // If the curve is periodic knots are added on the working curve before
2324 // and after the existing knots to make it a non-periodic curves.
2325 // The poles are also copied.
2326
2327 // The first and last multiplicity of the working curve are set to Degree+1,
2328 // null poles are added if necessary.
2329
2330 // Then the degree is incremented on the working curve.
2331 // The knots are unchanged but all multiplicities will be incremented.
2332
2333 // Each degree incrementation is achieved by averaging curDeg+1 curves.
2334
2335 // See : Degree elevation of B-spline curves
2336 // Hartmut PRAUTZSCH
2337 // CAGD 1 (1984)
2338
2339
2340 //-------------------------
2341 // create the working curve
2342 //-------------------------
2343
2344 Standard_Integer i,k,f,l,m,pf,pl,firstknot;
2345
2346 pf = 0; // number of null poles added at beginning
2347 pl = 0; // number of null poles added at end
2348
2349 Standard_Integer nbwknots = Knots.Length();
2350 f = FirstUKnotIndex(Degree,Mults);
2351 l = LastUKnotIndex (Degree,Mults);
2352
2353 if (Periodic) {
2354 // Periodic curves are transformed in non-periodic curves
2355
2356 nbwknots += f - Mults.Lower();
2357
2358 pf = -Degree - 1;
2359
2360 for (i = Mults.Lower(); i <= f; i++)
2361 pf += Mults(i);
2362
2363 nbwknots += Mults.Upper() - l;
2364
2365 pl = -Degree - 1;
2366
2367 for (i = l; i <= Mults.Upper(); i++)
2368 pl += Mults(i);
2369 }
2370
2371 // copy the knots and multiplicities
2372 TColStd_Array1OfReal wknots(1,nbwknots);
2373 TColStd_Array1OfInteger wmults(1,nbwknots);
2374 if (!Periodic) {
2375 wknots = Knots;
2376 wmults = Mults;
2377 }
2378 else {
2379 // copy the knots for a periodic curve
2380 Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
2381 i = 0;
2382
2383 for (k = l; k < Knots.Upper(); k++) {
2384 i++;
2385 wknots(i) = Knots(k) - period;
2386 wmults(i) = Mults(k);
2387 }
2388
2389 for (k = Knots.Lower(); k <= Knots.Upper(); k++) {
2390 i++;
2391 wknots(i) = Knots(k);
2392 wmults(i) = Mults(k);
2393 }
2394
2395 for (k = Knots.Lower()+1; k <= f; k++) {
2396 i++;
2397 wknots(i) = Knots(k) + period;
2398 wmults(i) = Mults(k);
2399 }
2400 }
2401
2402 // set the first and last mults to Degree+1
2403 // and add null poles
2404
2405 pf += Degree + 1 - wmults(1);
2406 wmults(1) = Degree + 1;
2407 pl += Degree + 1 - wmults(nbwknots);
2408 wmults(nbwknots) = Degree + 1;
2409
2410 //---------------------------
2411 // poles of the working curve
2412 //---------------------------
2413
2414 Standard_Integer nbwpoles = 0;
2415
2416 for (i = 1; i <= nbwknots; i++) nbwpoles += wmults(i);
2417 nbwpoles -= Degree + 1;
2418
2419 // we provide space for degree elevation
2420 TColStd_Array1OfReal
2421 wpoles(1,(nbwpoles + (nbwknots-1) * (NewDegree - Degree)) * Dimension);
2422
2423 for (i = 1; i <= pf * Dimension; i++)
2424 wpoles(i) = 0;
2425
2426 k = Poles.Lower();
2427
2428 for (i = pf * Dimension + 1; i <= (nbwpoles - pl) * Dimension; i++) {
2429 wpoles(i) = Poles(k);
2430 k++;
2431 if (k > Poles.Upper()) k = Poles.Lower();
2432 }
2433
2434 for (i = (nbwpoles-pl)*Dimension+1; i <= nbwpoles*Dimension; i++)
2435 wpoles(i) = 0;
2436
2437
2438 //-----------------------------------------------------------
2439 // Declare the temporary arrays used in degree incrementation
2440 //-----------------------------------------------------------
2441
2442 Standard_Integer nbwp = nbwpoles + (nbwknots-1) * (NewDegree - Degree);
2443 // Arrays for storing the temporary curves
2444 TColStd_Array1OfReal tempc1(1,nbwp * Dimension);
2445 TColStd_Array1OfReal tempc2(1,nbwp * Dimension);
2446
2447 // Array for storing the knots to insert
2448 TColStd_Array1OfReal iknots(1,nbwknots);
2449
2450 // Arrays for receiving the knots after insertion
2451 TColStd_Array1OfReal nknots(1,nbwknots);
2452
2453
2454
2455 //------------------------------
2456 // Loop on degree incrementation
2457 //------------------------------
2458
2459 Standard_Integer step,curDeg;
2460 Standard_Integer nbp = nbwpoles;
2461 nbwp = nbp;
2462
2463 for (curDeg = Degree; curDeg < NewDegree; curDeg++) {
2464
2465 nbp = nbwp; // current number of poles
2466 nbwp = nbp + nbwknots - 1; // new number of poles
2467
2468 // For the averaging
2469 TColStd_Array1OfReal nwpoles(1,nbwp * Dimension);
2470 nwpoles.Init(0.0e0) ;
2471
2472
2473 for (step = 0; step <= curDeg; step++) {
2474
2475 // Compute the bspline of rank step.
2476
2477 // if not the first time, decrement the multiplicities back
2478 if (step != 0) {
2479 for (i = 1; i <= nbwknots; i++)
2480 wmults(i)--;
2481 }
2482
2483 // Poles are the current poles
2484 // but the poles congruent to step are duplicated.
2485
2486 Standard_Integer offset = 0;
2487
2488 for (i = 0; i < nbp; i++) {
2489 offset++;
2490
2491 for (k = 0; k < Dimension; k++) {
2492 tempc1((offset-1)*Dimension+k+1) =
2493 wpoles(NewPoles.Lower()+i*Dimension+k);
2494 }
2495 if (i % (curDeg+1) == step) {
2496 offset++;
2497
2498 for (k = 0; k < Dimension; k++) {
2499 tempc1((offset-1)*Dimension+k+1) =
2500 wpoles(NewPoles.Lower()+i*Dimension+k);
2501 }
2502 }
2503 }
2504
2505 // Knots multiplicities are increased
2506 // For each knot where the sum of multiplicities is congruent to step
2507
2508 Standard_Integer stepmult = step+1;
2509 Standard_Integer nbknots = 0;
2510 Standard_Integer smult = 0;
2511
2512 for (k = 1; k <= nbwknots; k++) {
2513 smult += wmults(k);
2514 if (smult >= stepmult) {
2515 // this knot is increased
2516 stepmult += curDeg+1;
2517 wmults(k)++;
2518 }
2519 else {
2520 // this knot is inserted
2521 nbknots++;
2522 iknots(nbknots) = wknots(k);
2523 }
2524 }
2525
2526 // the curve is obtained by inserting the knots
2527 // to raise the multiplicities
2528
2529 // we build "slices" of the arrays to set the correct size
2530 if (nbknots > 0) {
2531 TColStd_Array1OfReal aknots(iknots(1),1,nbknots);
2532 TColStd_Array1OfReal curve (tempc1(1),1,offset * Dimension);
2533 TColStd_Array1OfReal ncurve(tempc2(1),1,nbwp * Dimension);
2534// InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
2535// aknots,NoMults(),ncurve,nknots,wmults,Epsilon(1.));
2536
2537 InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
2538 aknots,NoMults(),ncurve,nknots,wmults,0.0);
2539
2540 // add to the average
2541
2542 for (i = 1; i <= nbwp * Dimension; i++)
2543 nwpoles(i) += ncurve(i);
2544 }
2545 else {
2546 // add to the average
2547
2548 for (i = 1; i <= nbwp * Dimension; i++)
2549 nwpoles(i) += tempc1(i);
2550 }
2551 }
2552
2553 // The result is the average
2554
2555 for (i = 1; i <= nbwp * Dimension; i++) {
2556 wpoles(i) = nwpoles(i) / (curDeg+1);
2557 }
2558 }
2559
2560 //-----------------
2561 // Copy the results
2562 //-----------------
2563
2564 // index in new knots of the first knot of the curve
2565 if (Periodic)
2566 firstknot = Mults.Upper() - l + 1;
2567 else
2568 firstknot = f;
2569
2570 // the new curve starts at index firstknot
2571 // so we must remove knots until the sum of multiplicities
2572 // from the first to the start is NewDegree+1
2573
2574 // m is the current sum of multiplicities
2575 m = 0;
2576
2577 for (k = 1; k <= firstknot; k++)
2578 m += wmults(k);
2579
2580 // compute the new first knot (k), pf will be the index of the first pole
2581 k = 1;
2582 pf = 0;
2583
2584 while (m > NewDegree+1) {
2585 k++;
2586 m -= wmults(k);
2587 pf += wmults(k);
2588 }
2589 if (m < NewDegree+1) {
2590 k--;
2591 wmults(k) += m - NewDegree - 1;
2592 pf += m - NewDegree - 1;
2593 }
2594
2595 // on a periodic curve the knots start with firstknot
2596 if (Periodic)
2597 k = firstknot;
2598
2599 // copy knots
2600
2601 for (i = NewKnots.Lower(); i <= NewKnots.Upper(); i++) {
2602 NewKnots(i) = wknots(k);
2603 NewMults(i) = wmults(k);
2604 k++;
2605 }
2606
2607 // copy poles
2608 pf *= Dimension;
2609
2610 for (i = NewPoles.Lower(); i <= NewPoles.Upper(); i++) {
2611 pf++;
2612 NewPoles(i) = wpoles(pf);
2613 }
2614}
2615
2616//=======================================================================
2617//function : PrepareUnperiodize
2618//purpose :
2619//=======================================================================
2620
2621void BSplCLib::PrepareUnperiodize
2622(const Standard_Integer Degree,
2623 const TColStd_Array1OfInteger& Mults,
2624 Standard_Integer& NbKnots,
2625 Standard_Integer& NbPoles)
2626{
2627 Standard_Integer i;
2628 // initialize NbKnots and NbPoles
2629 NbKnots = Mults.Length();
2630 NbPoles = - Degree - 1;
2631
2632 for (i = Mults.Lower(); i <= Mults.Upper(); i++)
2633 NbPoles += Mults(i);
2634
2635 Standard_Integer sigma, k;
2636 // Add knots at the beginning of the curve to raise Multiplicities
2637 // to Degre + 1;
2638 sigma = Mults(Mults.Lower());
2639 k = Mults.Upper() - 1;
2640
2641 while ( sigma < Degree + 1) {
2642 sigma += Mults(k);
2643 NbPoles += Mults(k);
2644 k--;
2645 NbKnots++;
2646 }
2647 // We must add exactly until Degree + 1 ->
2648 // Supress the excedent.
2649 if ( sigma > Degree + 1)
2650 NbPoles -= sigma - Degree - 1;
2651
2652 // Add knots at the end of the curve to raise Multiplicities
2653 // to Degre + 1;
2654 sigma = Mults(Mults.Upper());
2655 k = Mults.Lower() + 1;
2656
2657 while ( sigma < Degree + 1) {
2658 sigma += Mults(k);
2659 NbPoles += Mults(k);
2660 k++;
2661 NbKnots++;
2662 }
2663 // We must add exactly until Degree + 1 ->
2664 // Supress the excedent.
2665 if ( sigma > Degree + 1)
2666 NbPoles -= sigma - Degree - 1;
2667}
2668
2669//=======================================================================
2670//function : Unperiodize
2671//purpose :
2672//=======================================================================
2673
2674void BSplCLib::Unperiodize
2675(const Standard_Integer Degree,
2676 const Standard_Integer , // Dimension,
2677 const TColStd_Array1OfInteger& Mults,
2678 const TColStd_Array1OfReal& Knots,
2679 const TColStd_Array1OfReal& Poles,
2680 TColStd_Array1OfInteger& NewMults,
2681 TColStd_Array1OfReal& NewKnots,
2682 TColStd_Array1OfReal& NewPoles)
2683{
2684 Standard_Integer sigma, k, index = 0;
2685 // evaluation of index : number of knots to insert before knot(1) to
2686 // raise sum of multiplicities to <Degree + 1>
2687 sigma = Mults(Mults.Lower());
2688 k = Mults.Upper() - 1;
2689
2690 while ( sigma < Degree + 1) {
2691 sigma += Mults(k);
2692 k--;
2693 index++;
2694 }
2695
2696 Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
2697
2698 // set the 'interior' knots;
2699
2700 for ( k = 1; k <= Knots.Length(); k++) {
2701 NewKnots ( k + index ) = Knots( k);
2702 NewMults ( k + index ) = Mults( k);
2703 }
2704
2705 // set the 'starting' knots;
2706
2707 for ( k = 1; k <= index; k++) {
2708 NewKnots( k) = NewKnots( k + Knots.Length() - 1) - period;
2709 NewMults( k) = NewMults( k + Knots.Length() - 1);
2710 }
2711 NewMults( 1) -= sigma - Degree -1;
2712
2713 // set the 'ending' knots;
2714 sigma = NewMults( index + Knots.Length() );
2715
2716 for ( k = Knots.Length() + index + 1; k <= NewKnots.Length(); k++) {
2717 NewKnots( k) = NewKnots( k - Knots.Length() + 1) + period;
2718 NewMults( k) = NewMults( k - Knots.Length() + 1);
2719 sigma += NewMults( k - Knots.Length() + 1);
2720 }
2721 NewMults(NewMults.Length()) -= sigma - Degree - 1;
2722
2723 for ( k = 1 ; k <= NewPoles.Length(); k++) {
2724 NewPoles(k ) = Poles( (k-1) % Poles.Length() + 1);
2725 }
2726}
2727
2728//=======================================================================
2729//function : PrepareTrimming
2730//purpose :
2731//=======================================================================
2732
2733void BSplCLib::PrepareTrimming(const Standard_Integer Degree,
2734 const Standard_Boolean Periodic,
2735 const TColStd_Array1OfReal& Knots,
2736 const TColStd_Array1OfInteger& Mults,
2737 const Standard_Real U1,
2738 const Standard_Real U2,
2739 Standard_Integer& NbKnots,
2740 Standard_Integer& NbPoles)
2741{
2742 Standard_Integer i;
2743 Standard_Real NewU1, NewU2;
2744 Standard_Integer index1 = 0, index2 = 0;
2745
2746 // Eval index1, index2 : position of U1 and U2 in the Array Knots
2747 // such as Knots(index1-1) <= U1 < Knots(index1)
2748 // Knots(index2-1) <= U2 < Knots(index2)
2749 LocateParameter( Degree, Knots, Mults, U1, Periodic,
2750 Knots.Lower(), Knots.Upper(), index1, NewU1);
2751 LocateParameter( Degree, Knots, Mults, U2, Periodic,
2752 Knots.Lower(), Knots.Upper(), index2, NewU2);
2753 index1++;
2754 if ( Abs(Knots(index2) - U2) <= Epsilon( U1))
2755 index2--;
2756
2757 // eval NbKnots:
2758 NbKnots = index2 - index1 + 3;
2759
2760 // eval NbPoles:
2761 NbPoles = Degree + 1;
2762
2763 for ( i = index1; i <= index2; i++)
2764 NbPoles += Mults(i);
2765}
2766
2767//=======================================================================
2768//function : Trimming
2769//purpose :
2770//=======================================================================
2771
2772void BSplCLib::Trimming(const Standard_Integer Degree,
2773 const Standard_Boolean Periodic,
2774 const Standard_Integer Dimension,
2775 const TColStd_Array1OfReal& Knots,
2776 const TColStd_Array1OfInteger& Mults,
2777 const TColStd_Array1OfReal& Poles,
2778 const Standard_Real U1,
2779 const Standard_Real U2,
2780 TColStd_Array1OfReal& NewKnots,
2781 TColStd_Array1OfInteger& NewMults,
2782 TColStd_Array1OfReal& NewPoles)
2783{
2784 Standard_Integer i, nbpoles, nbknots;
2785 Standard_Real kk[2];
2786 Standard_Integer mm[2];
2787 TColStd_Array1OfReal K( kk[0], 1, 2 );
2788 TColStd_Array1OfInteger M( mm[0], 1, 2 );
2789
2790 K(1) = U1; K(2) = U2;
2791 mm[0] = mm[1] = Degree;
2792 if (!PrepareInsertKnots( Degree, Periodic, Knots, Mults, K, M,
2793 nbpoles, nbknots, Epsilon( U1), 0))
2794 Standard_OutOfRange::Raise();
2795
2796 TColStd_Array1OfReal TempPoles(1, nbpoles*Dimension);
2797 TColStd_Array1OfReal TempKnots(1, nbknots);
2798 TColStd_Array1OfInteger TempMults(1, nbknots);
2799
2800//
2801// do not allow the multiplicities to Add : they must be less than Degree
2802//
2803 InsertKnots(Degree, Periodic, Dimension, Poles, Knots, Mults,
2804 K, M, TempPoles, TempKnots, TempMults, Epsilon(U1),
2805 Standard_False);
2806
2807 // find in TempPoles the index of the pole corresponding to U1
2808 Standard_Integer Kindex = 0, Pindex;
2809 Standard_Real NewU1;
2810 LocateParameter( Degree, TempKnots, TempMults, U1, Periodic,
2811 TempKnots.Lower(), TempKnots.Upper(), Kindex, NewU1);
2812 Pindex = PoleIndex ( Degree, Kindex, Periodic, TempMults);
2813 Pindex *= Dimension;
2814
2815 for ( i = 1; i <= NewPoles.Length(); i++) NewPoles(i) = TempPoles(Pindex + i);
2816
2817 for ( i = 1; i <= NewKnots.Length(); i++) {
2818 NewKnots(i) = TempKnots( Kindex+i-1);
2819 NewMults(i) = TempMults( Kindex+i-1);
2820 }
2821 NewMults(1) = Min(Degree, NewMults(1)) + 1 ;
2822 NewMults(NewMults.Length())= Min(Degree, NewMults(NewMults.Length())) + 1 ;
2823}
2824
2825//=======================================================================
2826//function : Solves a LU factored Matrix
2827//purpose :
2828//=======================================================================
2829
2830Standard_Integer
2831BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
2832 const Standard_Integer UpperBandWidth,
2833 const Standard_Integer LowerBandWidth,
2834 const Standard_Integer ArrayDimension,
2835 Standard_Real& Array)
2836{
2837 Standard_Integer ii,
2838 jj,
2839 kk,
2840 MinIndex,
2841 MaxIndex,
2842 ReturnCode = 0 ;
2843
2844 Standard_Real *PolesArray = &Array ;
2845 Standard_Real Inverse ;
2846
2847
2848 if (Matrix.LowerCol() != 1 ||
2849 Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
2850 ReturnCode = 1 ;
2851 goto FINISH ;
2852 }
2853
2854 for (ii = Matrix.LowerRow() + 1; ii <= Matrix.UpperRow() ; ii++) {
2855 MinIndex = (ii - LowerBandWidth >= Matrix.LowerRow() ?
2856 ii - LowerBandWidth : Matrix.LowerRow()) ;
2857
2858 for ( jj = MinIndex ; jj < ii ; jj++) {
2859
2860 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2861 PolesArray[(ii-1) * ArrayDimension + kk] +=
2862 PolesArray[(jj-1) * ArrayDimension + kk] * Matrix(ii, jj - ii + LowerBandWidth + 1) ;
2863 }
2864 }
2865 }
2866
2867 for (ii = Matrix.UpperRow() ; ii >= Matrix.LowerRow() ; ii--) {
2868 MaxIndex = (ii + UpperBandWidth <= Matrix.UpperRow() ?
2869 ii + UpperBandWidth : Matrix.UpperRow()) ;
2870
2871 for (jj = MaxIndex ; jj > ii ; jj--) {
2872
2873 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2874 PolesArray[(ii-1) * ArrayDimension + kk] -=
2875 PolesArray[(jj - 1) * ArrayDimension + kk] *
2876 Matrix(ii, jj - ii + LowerBandWidth + 1) ;
2877 }
2878 }
2879
2880 //fixing a bug PRO18577 to avoid divizion by zero
2881
2882 Standard_Real divizor = Matrix(ii,LowerBandWidth + 1) ;
2883 Standard_Real Toler = 1.0e-16;
2884 if ( Abs(divizor) > Toler )
2885 Inverse = 1.0e0 / divizor ;
2886 else {
2887 Inverse = 1.0e0;
2888// cout << " BSplCLib::SolveBandedSystem() : zero determinant " << endl;
2889 ReturnCode = 1;
2890 goto FINISH;
2891 }
2892
2893 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2894 PolesArray[(ii-1) * ArrayDimension + kk] *= Inverse ;
2895 }
2896 }
2897 FINISH :
2898 return (ReturnCode) ;
2899}
2900
2901//=======================================================================
2902//function : Solves a LU factored Matrix
2903//purpose :
2904//=======================================================================
2905
2906Standard_Integer
2907BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
2908 const Standard_Integer UpperBandWidth,
2909 const Standard_Integer LowerBandWidth,
2910 const Standard_Boolean HomogeneousFlag,
2911 const Standard_Integer ArrayDimension,
2912 Standard_Real& Poles,
2913 Standard_Real& Weights)
2914{
2915 Standard_Integer ii,
2916 kk,
2917 ErrorCode = 0,
2918 ReturnCode = 0 ;
2919
2920 Standard_Real Inverse,
2921 *PolesArray = &Poles,
2922 *WeightsArray = &Weights ;
2923
2924 if (Matrix.LowerCol() != 1 ||
2925 Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
2926 ReturnCode = 1 ;
2927 goto FINISH ;
2928 }
2929 if (HomogeneousFlag == Standard_False) {
2930
2931 for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1; ii++) {
2932
2933 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2934 PolesArray[ii * ArrayDimension + kk] *=
2935 WeightsArray[ii] ;
2936 }
2937 }
2938 }
2939 ErrorCode =
2940 BSplCLib::SolveBandedSystem(Matrix,
2941 UpperBandWidth,
2942 LowerBandWidth,
2943 ArrayDimension,
2944 Poles) ;
2945 if (ErrorCode != 0) {
2946 ReturnCode = 2 ;
2947 goto FINISH ;
2948 }
2949 ErrorCode =
2950 BSplCLib::SolveBandedSystem(Matrix,
2951 UpperBandWidth,
2952 LowerBandWidth,
2953 1,
2954 Weights) ;
2955 if (ErrorCode != 0) {
2956 ReturnCode = 3 ;
2957 goto FINISH ;
2958 }
2959 if (HomogeneousFlag == Standard_False) {
2960
2961 for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1 ; ii++) {
2962 Inverse = 1.0e0 / WeightsArray[ii] ;
2963
2964 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2965 PolesArray[ii * ArrayDimension + kk] *= Inverse ;
2966 }
2967 }
2968 }
2969 FINISH : return (ReturnCode) ;
2970}
2971
2972//=======================================================================
2973//function : BuildSchoenbergPoints
2974//purpose :
2975//=======================================================================
2976
2977void BSplCLib::BuildSchoenbergPoints(const Standard_Integer Degree,
2978 const TColStd_Array1OfReal& FlatKnots,
2979 TColStd_Array1OfReal& Parameters)
2980{
2981 Standard_Integer ii,
2982 jj ;
2983 Standard_Real Inverse ;
2984 Inverse = 1.0e0 / (Standard_Real)Degree ;
2985
2986 for (ii = Parameters.Lower() ; ii <= Parameters.Upper() ; ii++) {
2987 Parameters(ii) = 0.0e0 ;
2988
2989 for (jj = 1 ; jj <= Degree ; jj++) {
2990 Parameters(ii) += FlatKnots(jj + ii) ;
2991 }
2992 Parameters(ii) *= Inverse ;
2993 }
2994}
2995
2996//=======================================================================
2997//function : Interpolate
2998//purpose :
2999//=======================================================================
3000
3001void BSplCLib::Interpolate(const Standard_Integer Degree,
3002 const TColStd_Array1OfReal& FlatKnots,
3003 const TColStd_Array1OfReal& Parameters,
3004 const TColStd_Array1OfInteger& ContactOrderArray,
3005 const Standard_Integer ArrayDimension,
3006 Standard_Real& Poles,
3007 Standard_Integer& InversionProblem)
3008{
3009 Standard_Integer ErrorCode,
3010 UpperBandWidth,
3011 LowerBandWidth ;
3012// Standard_Real *PolesArray = &Poles ;
3013 math_Matrix InterpolationMatrix(1, Parameters.Length(),
3014 1, 2 * Degree + 1) ;
3015 ErrorCode =
3016 BSplCLib::BuildBSpMatrix(Parameters,
3017 ContactOrderArray,
3018 FlatKnots,
3019 Degree,
3020 InterpolationMatrix,
3021 UpperBandWidth,
3022 LowerBandWidth) ;
3023 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3024
3025 ErrorCode =
3026 BSplCLib::FactorBandedMatrix(InterpolationMatrix,
3027 UpperBandWidth,
3028 LowerBandWidth,
3029 InversionProblem) ;
3030 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3031
3032 ErrorCode =
3033 BSplCLib::SolveBandedSystem(InterpolationMatrix,
3034 UpperBandWidth,
3035 LowerBandWidth,
3036 ArrayDimension,
3037 Poles) ;
3038
3039 Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
3040}
3041
3042//=======================================================================
3043//function : Interpolate
3044//purpose :
3045//=======================================================================
3046
3047void BSplCLib::Interpolate(const Standard_Integer Degree,
3048 const TColStd_Array1OfReal& FlatKnots,
3049 const TColStd_Array1OfReal& Parameters,
3050 const TColStd_Array1OfInteger& ContactOrderArray,
3051 const Standard_Integer ArrayDimension,
3052 Standard_Real& Poles,
3053 Standard_Real& Weights,
3054 Standard_Integer& InversionProblem)
3055{
3056 Standard_Integer ErrorCode,
3057 UpperBandWidth,
3058 LowerBandWidth ;
3059
3060 math_Matrix InterpolationMatrix(1, Parameters.Length(),
3061 1, 2 * Degree + 1) ;
3062 ErrorCode =
3063 BSplCLib::BuildBSpMatrix(Parameters,
3064 ContactOrderArray,
3065 FlatKnots,
3066 Degree,
3067 InterpolationMatrix,
3068 UpperBandWidth,
3069 LowerBandWidth) ;
3070 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3071
3072 ErrorCode =
3073 BSplCLib::FactorBandedMatrix(InterpolationMatrix,
3074 UpperBandWidth,
3075 LowerBandWidth,
3076 InversionProblem) ;
3077 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3078
3079 ErrorCode =
3080 BSplCLib::SolveBandedSystem(InterpolationMatrix,
3081 UpperBandWidth,
3082 LowerBandWidth,
3083 Standard_False,
3084 ArrayDimension,
3085 Poles,
3086 Weights) ;
3087
3088 Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
3089}
3090
3091//=======================================================================
3092//function : Evaluates a Bspline function : uses the ExtrapMode
3093//purpose : the function is extrapolated using the Taylor expansion
3094// of degree ExtrapMode[0] to the left and the Taylor
3095// expansion of degree ExtrapMode[1] to the right
3096// this evaluates the numerator by multiplying by the weights
3097// and evaluating it but does not call RationalDerivatives after
3098//=======================================================================
3099
3100void BSplCLib::Eval
3101(const Standard_Real Parameter,
3102 const Standard_Boolean PeriodicFlag,
3103 const Standard_Integer DerivativeRequest,
3104 Standard_Integer& ExtrapMode,
3105 const Standard_Integer Degree,
3106 const TColStd_Array1OfReal& FlatKnots,
3107 const Standard_Integer ArrayDimension,
3108 Standard_Real& Poles,
3109 Standard_Real& Weights,
3110 Standard_Real& PolesResults,
3111 Standard_Real& WeightsResults)
3112{
3113 Standard_Integer ii,
3114 jj,
3115 kk=0,
3116 Index,
3117 Index1,
3118 Index2,
3119 *ExtrapModeArray,
3120 Modulus,
3121 NewRequest,
3122 ExtrapolatingFlag[2],
3123 ErrorCode,
7fd59977 3124 Order = Degree + 1,
3125 FirstNonZeroBsplineIndex,
3126 LocalRequest = DerivativeRequest ;
3127 Standard_Real *PResultArray,
3128 *WResultArray,
3129 *PolesArray,
3130 *WeightsArray,
3131 LocalParameter,
3132 Period,
3133 Inverse,
3134 Delta ;
3135 PolesArray = &Poles ;
3136 WeightsArray = &Weights ;
3137 ExtrapModeArray = &ExtrapMode ;
3138 PResultArray = &PolesResults ;
3139 WResultArray = &WeightsResults ;
3140 LocalParameter = Parameter ;
3141 ExtrapolatingFlag[0] =
3142 ExtrapolatingFlag[1] = 0 ;
3143 //
3144 // check if we are extrapolating to a degree which is smaller than
3145 // the degree of the Bspline
3146 //
3147 if (PeriodicFlag) {
3148 Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
3149
3150 while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
3151 LocalParameter -= Period ;
3152 }
3153
3154 while (LocalParameter < FlatKnots(2)) {
3155 LocalParameter += Period ;
3156 }
3157 }
3158 if (Parameter < FlatKnots(2) &&
3159 LocalRequest < ExtrapModeArray[0] &&
3160 ExtrapModeArray[0] < Degree) {
3161 LocalRequest = ExtrapModeArray[0] ;
3162 LocalParameter = FlatKnots(2) ;
3163 ExtrapolatingFlag[0] = 1 ;
3164 }
3165 if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
3166 LocalRequest < ExtrapModeArray[1] &&
3167 ExtrapModeArray[1] < Degree) {
3168 LocalRequest = ExtrapModeArray[1] ;
3169 LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
3170 ExtrapolatingFlag[1] = 1 ;
3171 }
3172 Delta = Parameter - LocalParameter ;
3173 if (LocalRequest >= Order) {
3174 LocalRequest = Degree ;
3175 }
3176 if (PeriodicFlag) {
3177 Modulus = FlatKnots.Length() - Degree -1 ;
3178 }
3179 else {
3180 Modulus = FlatKnots.Length() - Degree ;
3181 }
3182
3183 BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
3184 ErrorCode =
3185 BSplCLib::EvalBsplineBasis(1,
3186 LocalRequest,
3187 Order,
3188 FlatKnots,
3189 LocalParameter,
3190 FirstNonZeroBsplineIndex,
3191 BsplineBasis) ;
3192 if (ErrorCode != 0) {
7fd59977 3193 goto FINISH ;
3194 }
3195 if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
3196 Index = 0 ;
3197 Index2 = 0 ;
3198
3199 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3200 Index1 = FirstNonZeroBsplineIndex ;
3201
3202 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3203 PResultArray[Index + kk] = 0.0e0 ;
3204 }
3205 WResultArray[Index] = 0.0e0 ;
3206
3207 for (jj = 1 ; jj <= Order ; jj++) {
3208
3209 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3210 PResultArray[Index + kk] +=
3211 PolesArray[(Index1-1) * ArrayDimension + kk]
3212 * WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3213 }
3214 WResultArray[Index2] += WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3215
3216 Index1 = Index1 % Modulus ;
3217 Index1 += 1 ;
3218 }
3219 Index += ArrayDimension ;
3220 Index2 += 1 ;
3221 }
3222 }
3223 else {
3224 //
3225 // store Taylor expansion in LocalRealArray
3226 //
3227 NewRequest = DerivativeRequest ;
3228 if (NewRequest > Degree) {
3229 NewRequest = Degree ;
3230 }
f7b4312f 3231 NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
7fd59977 3232 Index = 0 ;
3233 Inverse = 1.0e0 ;
3234
3235 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3236 Index1 = FirstNonZeroBsplineIndex ;
3237
3238 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3239 LocalRealArray[Index + kk] = 0.0e0 ;
3240 }
3241
3242 for (jj = 1 ; jj <= Order ; jj++) {
3243
3244 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3245 LocalRealArray[Index + kk] +=
3246 PolesArray[(Index1-1)*ArrayDimension + kk] *
3247 WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3248 }
3249 Index1 = Index1 % Modulus ;
3250 Index1 += 1 ;
3251 }
3252
3253 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3254 LocalRealArray[Index + kk] *= Inverse ;
3255 }
3256 Index += ArrayDimension ;
3257 Inverse /= (Standard_Real) ii ;
3258 }
3259 PLib::EvalPolynomial(Delta,
3260 NewRequest,
3261 Degree,
3262 ArrayDimension,
3263 LocalRealArray[0],
3264 PolesResults) ;
3265 Index = 0 ;
3266 Inverse = 1.0e0 ;
3267
3268 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3269 Index1 = FirstNonZeroBsplineIndex ;
3270 LocalRealArray[Index] = 0.0e0 ;
3271
3272 for (jj = 1 ; jj <= Order ; jj++) {
3273 LocalRealArray[Index] +=
3274 WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3275 Index1 = Index1 % Modulus ;
3276 Index1 += 1 ;
3277 }
3278 LocalRealArray[Index + kk] *= Inverse ;
3279 Index += 1 ;
3280 Inverse /= (Standard_Real) ii ;
3281 }
3282 PLib::EvalPolynomial(Delta,
3283 NewRequest,
3284 Degree,
3285 1,
3286 LocalRealArray[0],
3287 WeightsResults) ;
3288 }
3289 FINISH : ;
3290}
3291
3292//=======================================================================
3293//function : Evaluates a Bspline function : uses the ExtrapMode
3294//purpose : the function is extrapolated using the Taylor expansion
3295// of degree ExtrapMode[0] to the left and the Taylor
3296// expansion of degree ExtrapMode[1] to the right
3297// WARNING : the array Results is supposed to have at least
3298// (DerivativeRequest + 1) * ArrayDimension slots and the
3299//
3300//=======================================================================
3301
3302void BSplCLib::Eval
3303(const Standard_Real Parameter,
3304 const Standard_Boolean PeriodicFlag,
3305 const Standard_Integer DerivativeRequest,
3306 Standard_Integer& ExtrapMode,
3307 const Standard_Integer Degree,
3308 const TColStd_Array1OfReal& FlatKnots,
3309 const Standard_Integer ArrayDimension,
3310 Standard_Real& Poles,
3311 Standard_Real& Results)
3312{
3313 Standard_Integer ii,
3314 jj,
3315 kk,
3316 Index,
3317 Index1,
3318 *ExtrapModeArray,
3319 Modulus,
3320 NewRequest,
3321 ExtrapolatingFlag[2],
3322 ErrorCode,
7fd59977 3323 Order = Degree + 1,
3324 FirstNonZeroBsplineIndex,
3325 LocalRequest = DerivativeRequest ;
3326
3327 Standard_Real *ResultArray,
3328 *PolesArray,
3329 LocalParameter,
3330 Period,
3331 Inverse,
3332 Delta ;
3333
3334 PolesArray = &Poles ;
3335 ExtrapModeArray = &ExtrapMode ;
3336 ResultArray = &Results ;
3337 LocalParameter = Parameter ;
3338 ExtrapolatingFlag[0] =
3339 ExtrapolatingFlag[1] = 0 ;
3340 //
3341 // check if we are extrapolating to a degree which is smaller than
3342 // the degree of the Bspline
3343 //
3344 if (PeriodicFlag) {
3345 Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
3346
3347 while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
3348 LocalParameter -= Period ;
3349 }
3350
3351 while (LocalParameter < FlatKnots(2)) {
3352 LocalParameter += Period ;
3353 }
3354 }
3355 if (Parameter < FlatKnots(2) &&
3356 LocalRequest < ExtrapModeArray[0] &&
3357 ExtrapModeArray[0] < Degree) {
3358 LocalRequest = ExtrapModeArray[0] ;
3359 LocalParameter = FlatKnots(2) ;
3360 ExtrapolatingFlag[0] = 1 ;
3361 }
3362 if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
3363 LocalRequest < ExtrapModeArray[1] &&
3364 ExtrapModeArray[1] < Degree) {
3365 LocalRequest = ExtrapModeArray[1] ;
3366 LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
3367 ExtrapolatingFlag[1] = 1 ;
3368 }
3369 Delta = Parameter - LocalParameter ;
3370 if (LocalRequest >= Order) {
3371 LocalRequest = Degree ;
3372 }
3373
3374 if (PeriodicFlag) {
3375 Modulus = FlatKnots.Length() - Degree -1 ;
3376 }
3377 else {
3378 Modulus = FlatKnots.Length() - Degree ;
3379 }
3380
3381 BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
3382
3383 ErrorCode =
3384 BSplCLib::EvalBsplineBasis(1,
3385 LocalRequest,
3386 Order,
3387 FlatKnots,
3388 LocalParameter,
3389 FirstNonZeroBsplineIndex,
3390 BsplineBasis);
3391 if (ErrorCode != 0) {
7fd59977 3392 goto FINISH ;
3393 }
3394 if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
3395 Index = 0 ;
3396
3397 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3398 Index1 = FirstNonZeroBsplineIndex ;
3399
3400 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3401 ResultArray[Index + kk] = 0.0e0 ;
3402 }
3403
3404 for (jj = 1 ; jj <= Order ; jj++) {
3405
3406 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3407 ResultArray[Index + kk] +=
3408 PolesArray[(Index1-1) * ArrayDimension + kk] * BsplineBasis(ii,jj) ;
3409 }
3410 Index1 = Index1 % Modulus ;
3411 Index1 += 1 ;
3412 }
3413 Index += ArrayDimension ;
3414 }
3415 }
3416 else {
3417 //
3418 // store Taylor expansion in LocalRealArray
3419 //
3420 NewRequest = DerivativeRequest ;
3421 if (NewRequest > Degree) {
3422 NewRequest = Degree ;
3423 }
f7b4312f 3424 NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
7fd59977 3425
3426 Index = 0 ;
3427 Inverse = 1.0e0 ;
3428
3429 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3430 Index1 = FirstNonZeroBsplineIndex ;
3431
3432 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3433 LocalRealArray[Index + kk] = 0.0e0 ;
3434 }
3435
3436 for (jj = 1 ; jj <= Order ; jj++) {
3437
3438 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3439 LocalRealArray[Index + kk] +=
3440 PolesArray[(Index1-1)*ArrayDimension + kk] * BsplineBasis(ii,jj) ;
3441 }
3442 Index1 = Index1 % Modulus ;
3443 Index1 += 1 ;
3444 }
3445
3446 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3447 LocalRealArray[Index + kk] *= Inverse ;
3448 }
3449 Index += ArrayDimension ;
3450 Inverse /= (Standard_Real) ii ;
3451 }
3452 PLib::EvalPolynomial(Delta,
3453 NewRequest,
3454 Degree,
3455 ArrayDimension,
3456 LocalRealArray[0],
3457 Results) ;
3458 }
3459 FINISH : ;
3460}
3461
3462//=======================================================================
3463//function : TangExtendToConstraint
3464//purpose : Extends a Bspline function using the tangency map
3465// WARNING :
3466//
3467//
3468//=======================================================================
3469
3470void BSplCLib::TangExtendToConstraint
3471(const TColStd_Array1OfReal& FlatKnots,
3472 const Standard_Real C1Coefficient,
3473 const Standard_Integer NumPoles,
3474 Standard_Real& Poles,
3475 const Standard_Integer CDimension,
3476 const Standard_Integer CDegree,
3477 const TColStd_Array1OfReal& ConstraintPoint,
3478 const Standard_Integer Continuity,
3479 const Standard_Boolean After,
3480 Standard_Integer& NbPolesResult,
3481 Standard_Integer& NbKnotsResult,
3482 Standard_Real& KnotsResult,
3483 Standard_Real& PolesResult)
3484{
0797d9d3 3485#ifdef OCCT_DEBUG
7fd59977 3486 if (CDegree<Continuity+1) {
3487 cout<<"The BSpline degree must be greater than the order of continuity"<<endl;
3488 }
3489#endif
3490 Standard_Real * Padr = &Poles ;
3491 Standard_Real * KRadr = &KnotsResult ;
3492 Standard_Real * PRadr = &PolesResult ;
3493
3494////////////////////////////////////////////////////////////////////////
3495//
0d969553 3496// 1. calculation of extension nD
7fd59977 3497//
3498////////////////////////////////////////////////////////////////////////
3499
0d969553 3500// Hermite matrix
7fd59977 3501 Standard_Integer Csize = Continuity + 2;
3502 math_Matrix MatCoefs(1,Csize, 1,Csize);
3503 if (After) {
0d969553
Y		 3504 PLib::HermiteCoefficients(0, 1, // Limits
3505 Continuity, 0, // Orders of constraints
7fd59977 3506 MatCoefs);
3507 }
3508 else {
0d969553
Y		 3509 PLib::HermiteCoefficients(0, 1, // Limits
3510 0, Continuity, // Orders of constraints
7fd59977 3511 MatCoefs);
3512 }
3513
3514
0d969553 3515// position at the node of connection
7fd59977 3516 Standard_Real Tbord ;
3517 if (After) {
3518 Tbord = FlatKnots(FlatKnots.Upper()-CDegree);
3519 }
3520 else {
3521 Tbord = FlatKnots(FlatKnots.Lower()+CDegree);
3522 }
3523 Standard_Boolean periodic_flag = Standard_False ;
3524 Standard_Integer ipos, extrap_mode[2], derivative_request = Max(Continuity,1);
3525 extrap_mode[0] = extrap_mode[1] = CDegree;
3526 TColStd_Array1OfReal EvalBS(1, CDimension * (derivative_request+1)) ;
3527 Standard_Real * Eadr = (Standard_Real *) &EvalBS(1) ;
3528 BSplCLib::Eval(Tbord,periodic_flag,derivative_request,extrap_mode[0],
3529 CDegree,FlatKnots,CDimension,Poles,*Eadr);
3530
0d969553 3531// norm of the tangent at the node of connection
7fd59977 3532 math_Vector Tgte(1,CDimension);
3533
3534 for (ipos=1;ipos<=CDimension;ipos++) {
3535 Tgte(ipos) = EvalBS(ipos+CDimension);
3536 }
3537 Standard_Real L1=Tgte.Norm();
3538
3539
0d969553 3540// matrix of constraints
7fd59977 3541 math_Matrix Contraintes(1,Csize,1,CDimension);
3542 if (After) {
3543
3544 for (ipos=1;ipos<=CDimension;ipos++) {
3545 Contraintes(1,ipos) = EvalBS(ipos);
3546 Contraintes(2,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
3547 if(Continuity >= 2) Contraintes(3,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
3548 if(Continuity >= 3) Contraintes(4,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
3549 Contraintes(Continuity+2,ipos) = ConstraintPoint(ipos);
3550 }
3551 }
3552 else {
3553
3554 for (ipos=1;ipos<=CDimension;ipos++) {
3555 Contraintes(1,ipos) = ConstraintPoint(ipos);
3556 Contraintes(2,ipos) = EvalBS(ipos);
3557 if(Continuity >= 1) Contraintes(3,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
3558 if(Continuity >= 2) Contraintes(4,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
3559 if(Continuity >= 3) Contraintes(5,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
3560 }
3561 }
3562
0d969553 3563// calculate the coefficients of extension
7fd59977 3564 Standard_Integer ii, jj, kk;
3565 TColStd_Array1OfReal ExtraCoeffs(1,Csize*CDimension);
3566 ExtraCoeffs.Init(0.);
3567
3568 for (ii=1; ii<=Csize; ii++) {
3569
3570 for (jj=1; jj<=Csize; jj++) {
3571
3572 for (kk=1; kk<=CDimension; kk++) {
3573 ExtraCoeffs(kk+(jj-1)*CDimension) += MatCoefs(ii,jj)*Contraintes(ii,kk);
3574 }
3575 }
3576 }
3577
0d969553 3578// calculate the poles of extension
7fd59977 3579 TColStd_Array1OfReal ExtrapPoles(1,Csize*CDimension);
3580 Standard_Real * EPadr = &ExtrapPoles(1) ;
3581 PLib::CoefficientsPoles(CDimension,
3582 ExtraCoeffs, PLib::NoWeights(),
3583 ExtrapPoles, PLib::NoWeights());
3584
0d969553 3585// calculate the nodes of extension with multiplicities
7fd59977 3586 TColStd_Array1OfReal ExtrapNoeuds(1,2);
3587 ExtrapNoeuds(1) = 0.;
3588 ExtrapNoeuds(2) = 1.;
3589 TColStd_Array1OfInteger ExtrapMults(1,2);
3590 ExtrapMults(1) = Csize;
3591 ExtrapMults(2) = Csize;
3592
0d969553 3593// flat nodes of extension
7fd59977 3594 TColStd_Array1OfReal FK2(1, Csize*2);
3595 BSplCLib::KnotSequence(ExtrapNoeuds,ExtrapMults,FK2);
3596
0d969553 3597// norm of the tangent at the connection point
7fd59977 3598 if (After) {
3599 BSplCLib::Eval(0.,periodic_flag,1,extrap_mode[0],
3600 Csize-1,FK2,CDimension,*EPadr,*Eadr);
3601 }
3602 else {
3603 BSplCLib::Eval(1.,periodic_flag,1,extrap_mode[0],
3604 Csize-1,FK2,CDimension,*EPadr,*Eadr);
3605 }
3606
3607 for (ipos=1;ipos<=CDimension;ipos++) {
3608 Tgte(ipos) = EvalBS(ipos+CDimension);
3609 }
3610 Standard_Real L2 = Tgte.Norm();
3611
0d969553 3612// harmonisation of degrees
7fd59977 3613 TColStd_Array1OfReal NewP2(1, (CDegree+1)*CDimension);
3614 TColStd_Array1OfReal NewK2(1, 2);
3615 TColStd_Array1OfInteger NewM2(1, 2);
3616 if (Csize-1<CDegree) {
3617 BSplCLib::IncreaseDegree(Csize-1,CDegree,Standard_False,CDimension,
3618 ExtrapPoles,ExtrapNoeuds,ExtrapMults,
3619 NewP2,NewK2,NewM2);
3620 }
3621 else {
3622 NewP2 = ExtrapPoles;
3623 NewK2 = ExtrapNoeuds;
3624 NewM2 = ExtrapMults;
3625 }
3626
0d969553 3627// flat nodes of extension after harmonization of degrees
7fd59977 3628 TColStd_Array1OfReal NewFK2(1, (CDegree+1)*2);
3629 BSplCLib::KnotSequence(NewK2,NewM2,NewFK2);
3630
3631
3632////////////////////////////////////////////////////////////////////////
3633//
3634// 2. concatenation C0
3635//
3636////////////////////////////////////////////////////////////////////////
3637
0d969553 3638// ratio of reparametrization
7fd59977 3639 Standard_Real Ratio=1, Delta;
3640 if ( (L1 > Precision::Confusion()) && (L2 > Precision::Confusion()) ) {
3641 Ratio = L2 / L1;
3642 }
3643 if ( (Ratio < 1.e-5) || (Ratio > 1.e5) ) Ratio = 1;
3644
3645 if (After) {
0d969553 3646// do not touch the first BSpline
7fd59977 3647 Delta = Ratio*NewFK2(NewFK2.Lower()) - FlatKnots(FlatKnots.Upper());
3648 }
3649 else {
0d969553 3650// do not touch the second BSpline
7fd59977 3651 Delta = Ratio*NewFK2(NewFK2.Upper()) - FlatKnots(FlatKnots.Lower());
3652 }
3653
0d969553 3654// result of the concatenation
7fd59977 3655 Standard_Integer NbP1 = NumPoles, NbP2 = CDegree+1;
3656 Standard_Integer NbK1 = FlatKnots.Length(), NbK2 = 2*(CDegree+1);
3657 TColStd_Array1OfReal NewPoles (1, (NbP1+ NbP2-1)*CDimension);
3658 TColStd_Array1OfReal NewFlats (1, NbK1+NbK2-CDegree-2);
3659
0d969553 3660// poles
7fd59977 3661 Standard_Integer indNP, indP, indEP;
3662 if (After) {
3663
3664 for (ii=1; ii<=NbP1+NbP2-1; ii++) {
3665
3666 for (jj=1; jj<=CDimension; jj++) {
3667 indNP = (ii-1)*CDimension+jj;
3668 indP = (ii-1)*CDimension+jj-1;
3669 indEP = (ii-NbP1)*CDimension+jj;
3670 if (ii<NbP1) NewPoles(indNP) = Padr[indP];
3671 else NewPoles(indNP) = NewP2(indEP);
3672 }
3673 }
3674 }
3675 else {
3676
3677 for (ii=1; ii<=NbP1+NbP2-1; ii++) {
3678
3679 for (jj=1; jj<=CDimension; jj++) {
3680 indNP = (ii-1)*CDimension+jj;
3681 indEP = (ii-1)*CDimension+jj;
3682 indP = (ii-NbP2)*CDimension+jj-1;
3683 if (ii<NbP2) NewPoles(indNP) = NewP2(indEP);
3684 else NewPoles(indNP) = Padr[indP];
3685 }
3686 }
3687 }
3688
0d969553 3689// flat nodes
7fd59977 3690 if (After) {
0d969553 3691// start with the nodes of the initial surface
7fd59977 3692
3693 for (ii=1; ii<NbK1; ii++) {
3694 NewFlats(ii) = FlatKnots(FlatKnots.Lower()+ii-1);
3695 }
0d969553 3696// continue with the reparameterized nodes of the extension
7fd59977 3697
3698 for (ii=1; ii<=NbK2-CDegree-1; ii++) {
3699 NewFlats(NbK1+ii-1) = Ratio*NewFK2(NewFK2.Lower()+ii+CDegree) - Delta;
3700 }
3701 }
3702 else {
0d969553 3703// start with the reparameterized nodes of the extension
7fd59977 3704
3705 for (ii=1; ii<NbK2-CDegree; ii++) {
3706 NewFlats(ii) = Ratio*NewFK2(NewFK2.Lower()+ii-1) - Delta;
3707 }
0d969553 3708// continue with the nodes of the initial surface
7fd59977 3709
3710 for (ii=2; ii<=NbK1; ii++) {
3711 NewFlats(NbK2+ii-CDegree-2) = FlatKnots(FlatKnots.Lower()+ii-1);
3712 }
3713 }
3714
3715
3716////////////////////////////////////////////////////////////////////////
3717//
0d969553 3718// 3. reduction of multiplicite at the node of connection
7fd59977 3719//
3720////////////////////////////////////////////////////////////////////////
3721
0d969553 3722// number of separate nodes
7fd59977 3723 Standard_Integer KLength = 1;
3724
3725 for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
3726 if (NewFlats(ii) != NewFlats(ii-1)) KLength++;
3727 }
3728
0d969553 3729// flat nodes --> nodes + multiplicities
7fd59977 3730 TColStd_Array1OfReal NewKnots (1, KLength);
3731 TColStd_Array1OfInteger NewMults (1, KLength);
3732 NewMults.Init(1);
3733 jj = 1;
3734 NewKnots(jj) = NewFlats(1);
3735
3736 for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
3737 if (NewFlats(ii) == NewFlats(ii-1)) NewMults(jj)++;
3738 else {
3739 jj++;
3740 NewKnots(jj) = NewFlats(ii);
3741 }
3742 }
3743
0d969553 3744// reduction of multiplicity at the second or the last but one node
7fd59977 3745 Standard_Integer Index = 2, M = CDegree;
3746 if (After) Index = KLength-1;
3747 TColStd_Array1OfReal ResultPoles (1, (NbP1+ NbP2-1)*CDimension);
3748 TColStd_Array1OfReal ResultKnots (1, KLength);
3749 TColStd_Array1OfInteger ResultMults (1, KLength);
3750 Standard_Real Tol = 1.e-6;
3751 Standard_Boolean Ok = Standard_True;
3752
3753 while ( (M>CDegree-Continuity) && Ok) {
3754 Ok = RemoveKnot(Index, M-1, CDegree, Standard_False, CDimension,
3755 NewPoles, NewKnots, NewMults,
3756 ResultPoles, ResultKnots, ResultMults, Tol);
3757 if (Ok) M--;
3758 }
3759
3760 if (M == CDegree) {
0d969553 3761// number of poles of the concatenation
7fd59977 3762 NbPolesResult = NbP1 + NbP2 - 1;
0d969553 3763// the poles of the concatenation
7fd59977 3764 Standard_Integer PLength = NbPolesResult*CDimension;
3765
3766 for (jj=1; jj<=PLength; jj++) {
3767 PRadr[jj-1] = NewPoles(jj);
3768 }
3769
0d969553 3770// flat nodes of the concatenation
7fd59977 3771 Standard_Integer ideb = 0;
3772
3773 for (jj=0; jj<NewKnots.Length(); jj++) {
3774 for (ii=0; ii<NewMults(jj+1); ii++) {
3775 KRadr[ideb+ii] = NewKnots(jj+1);
3776 }
3777 ideb += NewMults(jj+1);
3778 }
3779 NbKnotsResult = ideb;
3780 }
3781
3782 else {
0d969553 3783// number of poles of the result
7fd59977 3784 NbPolesResult = NbP1 + NbP2 - 1 - CDegree + M;
0d969553 3785// the poles of the result
7fd59977 3786 Standard_Integer PLength = NbPolesResult*CDimension;
3787
3788 for (jj=0; jj<PLength; jj++) {
3789 PRadr[jj] = ResultPoles(jj+1);
3790 }
3791
0d969553 3792// flat nodes of the result
7fd59977 3793 Standard_Integer ideb = 0;
3794
3795 for (jj=0; jj<ResultKnots.Length(); jj++) {
3796 for (ii=0; ii<ResultMults(jj+1); ii++) {
3797 KRadr[ideb+ii] = ResultKnots(jj+1);
3798 }
3799 ideb += ResultMults(jj+1);
3800 }
3801 NbKnotsResult = ideb;
3802 }
3803}
3804
3805//=======================================================================
3806//function : Resolution
3807//purpose :
3808// d
0d969553 3809// Let C(t) = SUM Ci Bi(t) a Bspline curve of degree d
7fd59977 3810// i = 1,n
0d969553 3811// with nodes tj for j = 1,n+d+1
7fd59977 3812//
3813//
3814// ' C1 - Ci-1 d-1
0d969553 3815// Then C (t) = SUM d * --------- Bi (t)
7fd59977 3816// i = 2,n ti+d - ti
3817//
3818// d-1
0d969553 3819// for the base of BSpline Bi (t) of degree d-1.
7fd59977 3820//
0d969553 3821// Consequently the upper bound of the norm of the derivative from C is :
7fd59977 3822//
3823//
3824// | Ci - Ci-1 |
3825// d * Max | --------- |
3826// i = 2,n | ti+d - ti |
3827//
3828// N(t)
0d969553 3829// In the rational case set C(t) = -----
7fd59977 3830// D(t)
3831//
3832//
3833// D(t) = SUM Di Bi(t)
3834// i=1,n
3835//
3836// N(t) = SUM Di * Ci Bi(t)
3837// i =1,n
3838//
3839// N'(t) - D'(t) C(t)
3840// C'(t) = -----------------------
3841// D(t)
3842//
3843//
3844// N'(t) - D'(t) C(t) =
3845//
3846// Di * (Ci - C(t)) - Di-1 * (Ci-1 - C(t)) d-1
3847// SUM d * ---------------------------------------- * Bi (t) =
3848// i=2,n ti+d - ti
3849//
3850//
3851// Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj) d-1
3852// SUM SUM d * ----------------------------------- * Betaj(t) * Bi (t)
3853//i=2,n j=1,n ti+d - ti
3854//
3855//
3856//
3857// Dj Bj(t)
3858// Betaj(t) = --------
3859// D(t)
3860//
0d969553
Y		 3861// Betaj(t) form a partition >= 0 of the entity with support
3862// tj, tj+d+1. Consequently if Rj = {j-d, ...., j+d+d+1}
3863// obtain an upper bound of the derivative of C by taking :
7fd59977 3864//
3865//
3866//
3867//
3868//
3869//
3870// Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj)
3871// Max Max d * -----------------------------------
3872// j=1,n i dans Rj ti+d - ti
3873//
3874// --------------------------------------------------------
3875//
3876// Min Di
3877// i =1,n
3878//
3879//
3880//=======================================================================
3881
3882void BSplCLib::Resolution( Standard_Real& Poles,
3883 const Standard_Integer ArrayDimension,
3884 const Standard_Integer NumPoles,
3885 const TColStd_Array1OfReal& Weights,
3886 const TColStd_Array1OfReal& FlatKnots,
3887 const Standard_Integer Degree,
3888 const Standard_Real Tolerance3D,
3889 Standard_Real& UTolerance)
3890{
3891 Standard_Integer ii,num_poles,ii_index,jj_index,ii_inDim;
3892 Standard_Integer lower,upper,ii_minus,jj,ii_miDim;
3893 Standard_Integer Deg1 = Degree + 1;
3894 Standard_Integer Deg2 = (Degree << 1) + 1;
3895 Standard_Real value,factor,W,min_weights,inverse;
3896 Standard_Real pa_ii_inDim_0, pa_ii_inDim_1, pa_ii_inDim_2, pa_ii_inDim_3;
3897 Standard_Real pa_ii_miDim_0, pa_ii_miDim_1, pa_ii_miDim_2, pa_ii_miDim_3;
3898 Standard_Real wg_ii_index, wg_ii_minus;
3899 Standard_Real *PA,max_derivative;
3900 const Standard_Real * FK = &FlatKnots(FlatKnots.Lower());
3901 PA = &Poles;
3902 max_derivative = 0.0e0;
3903 num_poles = FlatKnots.Length() - Deg1;
3904 switch (ArrayDimension) {
3905 case 2 : {
3906 if (&Weights != NULL) {
3907 const Standard_Real * WG = &Weights(Weights.Lower());
3908 min_weights = WG[0];
3909
3910 for (ii = 1 ; ii < NumPoles ; ii++) {
3911 W = WG[ii];
3912 if (W < min_weights) min_weights = W;
3913 }
3914
3915 for (ii = 1 ; ii < num_poles ; ii++) {
3916 ii_index = ii % NumPoles;
3917 ii_inDim = ii_index << 1;
3918 ii_minus = (ii - 1) % NumPoles;
3919 ii_miDim = ii_minus << 1;
3920 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
3921 pa_ii_inDim_1 = PA[ii_inDim];
3922 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
3923 pa_ii_miDim_1 = PA[ii_miDim];
3924 wg_ii_index = WG[ii_index];
3925 wg_ii_minus = WG[ii_minus];
3926 inverse = FK[ii + Degree] - FK[ii];
3927 inverse = 1.0e0 / inverse;
3928 lower = ii - Deg1;
3929 if (lower < 0) lower = 0;
3930 upper = Deg2 + ii;
3931 if (upper > num_poles) upper = num_poles;
3932
3933 for (jj = lower ; jj < upper ; jj++) {
3934 jj_index = jj % NumPoles;
3935 jj_index = jj_index << 1;
3936 value = 0.0e0;
3937 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
3938 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
3939 if (factor < 0) factor = - factor;
3940 value += factor; jj_index++;
3941 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
3942 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
3943 if (factor < 0) factor = - factor;
3944 value += factor;
3945 value *= inverse;
3946 if (max_derivative < value) max_derivative = value;
3947 }
3948 }
3949 max_derivative /= min_weights;
3950 }
3951 else {
3952
3953 for (ii = 1 ; ii < num_poles ; ii++) {
3954 ii_index = ii % NumPoles;
3955 ii_index = ii_index << 1;
3956 ii_minus = (ii - 1) % NumPoles;
3957 ii_minus = ii_minus << 1;
3958 inverse = FK[ii + Degree] - FK[ii];
3959 inverse = 1.0e0 / inverse;
3960 value = 0.0e0;
3961 factor = PA[ii_index] - PA[ii_minus];
3962 if (factor < 0) factor = - factor;
3963 value += factor; ii_index++; ii_minus++;
3964 factor = PA[ii_index] - PA[ii_minus];
3965 if (factor < 0) factor = - factor;
3966 value += factor;
3967 value *= inverse;
3968 if (max_derivative < value) max_derivative = value;
3969 }
3970 }
3971 break;
3972 }
3973 case 3 : {
3974 if (&Weights != NULL) {
3975 const Standard_Real * WG = &Weights(Weights.Lower());
3976 min_weights = WG[0];
3977
3978 for (ii = 1 ; ii < NumPoles ; ii++) {
3979 W = WG[ii];
3980 if (W < min_weights) min_weights = W;
3981 }
3982
3983 for (ii = 1 ; ii < num_poles ; ii++) {
3984 ii_index = ii % NumPoles;
3985 ii_inDim = (ii_index << 1) + ii_index;
3986 ii_minus = (ii - 1) % NumPoles;
3987 ii_miDim = (ii_minus << 1) + ii_minus;
3988 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
3989 pa_ii_inDim_1 = PA[ii_inDim]; ii_inDim++;
3990 pa_ii_inDim_2 = PA[ii_inDim];
3991 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
3992 pa_ii_miDim_1 = PA[ii_miDim]; ii_miDim++;
3993 pa_ii_miDim_2 = PA[ii_miDim];
3994 wg_ii_index = WG[ii_index];
3995 wg_ii_minus = WG[ii_minus];
3996 inverse = FK[ii + Degree] - FK[ii];
3997 inverse = 1.0e0 / inverse;
3998 lower = ii - Deg1;
3999 if (lower < 0) lower = 0;
4000 upper = Deg2 + ii;
4001 if (upper > num_poles) upper = num_poles;
4002
4003 for (jj = lower ; jj < upper ; jj++) {
4004 jj_index = jj % NumPoles;
4005 jj_index = (jj_index << 1) + jj_index;
4006 value = 0.0e0;
4007 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
4008 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
4009 if (factor < 0) factor = - factor;
4010 value += factor; jj_index++;
4011 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
4012 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
4013 if (factor < 0) factor = - factor;
4014 value += factor; jj_index++;
4015 factor = (((PA[jj_index] - pa_ii_inDim_2) * wg_ii_index) -
4016 ((PA[jj_index] - pa_ii_miDim_2) * wg_ii_minus));
4017 if (factor < 0) factor = - factor;
4018 value += factor;
4019 value *= inverse;
4020 if (max_derivative < value) max_derivative = value;
4021 }
4022 }
4023 max_derivative /= min_weights;
4024 }
4025 else {
4026
4027 for (ii = 1 ; ii < num_poles ; ii++) {
4028 ii_index = ii % NumPoles;
4029 ii_index = (ii_index << 1) + ii_index;
4030 ii_minus = (ii - 1) % NumPoles;
4031 ii_minus = (ii_minus << 1) + ii_minus;
4032 inverse = FK[ii + Degree] - FK[ii];
4033 inverse = 1.0e0 / inverse;
4034 value = 0.0e0;
4035 factor = PA[ii_index] - PA[ii_minus];
4036 if (factor < 0) factor = - factor;
4037 value += factor; ii_index++; ii_minus++;
4038 factor = PA[ii_index] - PA[ii_minus];
4039 if (factor < 0) factor = - factor;
4040 value += factor; ii_index++; ii_minus++;
4041 factor = PA[ii_index] - PA[ii_minus];
4042 if (factor < 0) factor = - factor;
4043 value += factor;
4044 value *= inverse;
4045 if (max_derivative < value) max_derivative = value;
4046 }
4047 }
4048 break;
4049 }
4050 case 4 : {
4051 if (&Weights != NULL) {
4052 const Standard_Real * WG = &Weights(Weights.Lower());
4053 min_weights = WG[0];
4054
4055 for (ii = 1 ; ii < NumPoles ; ii++) {
4056 W = WG[ii];
4057 if (W < min_weights) min_weights = W;
4058 }
4059
4060 for (ii = 1 ; ii < num_poles ; ii++) {
4061 ii_index = ii % NumPoles;
4062 ii_inDim = ii_index << 2;
4063 ii_minus = (ii - 1) % NumPoles;
4064 ii_miDim = ii_minus << 2;
4065 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
4066 pa_ii_inDim_1 = PA[ii_inDim]; ii_inDim++;
4067 pa_ii_inDim_2 = PA[ii_inDim]; ii_inDim++;
4068 pa_ii_inDim_3 = PA[ii_inDim];
4069 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
4070 pa_ii_miDim_1 = PA[ii_miDim]; ii_miDim++;
4071 pa_ii_miDim_2 = PA[ii_miDim]; ii_miDim++;
4072 pa_ii_miDim_3 = PA[ii_miDim];
4073 wg_ii_index = WG[ii_index];
4074 wg_ii_minus = WG[ii_minus];
4075 inverse = FK[ii + Degree] - FK[ii];
4076 inverse = 1.0e0 / inverse;
4077 lower = ii - Deg1;
4078 if (lower < 0) lower = 0;
4079 upper = Deg2 + ii;
4080 if (upper > num_poles) upper = num_poles;
4081
4082 for (jj = lower ; jj < upper ; jj++) {
4083 jj_index = jj % NumPoles;
4084 jj_index = jj_index << 2;
4085 value = 0.0e0;
4086 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
4087 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
4088 if (factor < 0) factor = - factor;
4089 value += factor; jj_index++;
4090 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
4091 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
4092 if (factor < 0) factor = - factor;
4093 value += factor; jj_index++;
4094 factor = (((PA[jj_index] - pa_ii_inDim_2) * wg_ii_index) -
4095 ((PA[jj_index] - pa_ii_miDim_2) * wg_ii_minus));
4096 if (factor < 0) factor = - factor;
4097 value += factor; jj_index++;
4098 factor = (((PA[jj_index] - pa_ii_inDim_3) * wg_ii_index) -
4099 ((PA[jj_index] - pa_ii_miDim_3) * wg_ii_minus));
4100 if (factor < 0) factor = - factor;
4101 value += factor;
4102 value *= inverse;
4103 if (max_derivative < value) max_derivative = value;
4104 }
4105 }
4106 max_derivative /= min_weights;
4107 }
4108 else {
4109
4110 for (ii = 1 ; ii < num_poles ; ii++) {
4111 ii_index = ii % NumPoles;
4112 ii_index = ii_index << 2;
4113 ii_minus = (ii - 1) % NumPoles;
4114 ii_minus = ii_minus << 2;
4115 inverse = FK[ii + Degree] - FK[ii];
4116 inverse = 1.0e0 / inverse;
4117 value = 0.0e0;
4118 factor = PA[ii_index] - PA[ii_minus];
4119 if (factor < 0) factor = - factor;
4120 value += factor; ii_index++; ii_minus++;
4121 factor = PA[ii_index] - PA[ii_minus];
4122 if (factor < 0) factor = - factor;
4123 value += factor; ii_index++; ii_minus++;
4124 factor = PA[ii_index] - PA[ii_minus];
4125 if (factor < 0) factor = - factor;
4126 value += factor; ii_index++; ii_minus++;
4127 factor = PA[ii_index] - PA[ii_minus];
4128 if (factor < 0) factor = - factor;
4129 value += factor;
4130 value *= inverse;
4131 if (max_derivative < value) max_derivative = value;
4132 }
4133 }
4134 break;
4135 }
4136 default : {
4137 Standard_Integer kk;
4138 if (&Weights != NULL) {
4139 const Standard_Real * WG = &Weights(Weights.Lower());
4140 min_weights = WG[0];
4141
4142 for (ii = 1 ; ii < NumPoles ; ii++) {
4143 W = WG[ii];
4144 if (W < min_weights) min_weights = W;
4145 }
4146
4147 for (ii = 1 ; ii < num_poles ; ii++) {
4148 ii_index = ii % NumPoles;
4149 ii_inDim = ii_index * ArrayDimension;
4150 ii_minus = (ii - 1) % NumPoles;
4151 ii_miDim = ii_minus * ArrayDimension;
4152 wg_ii_index = WG[ii_index];
4153 wg_ii_minus = WG[ii_minus];
4154 inverse = FK[ii + Degree] - FK[ii];
4155 inverse = 1.0e0 / inverse;
4156 lower = ii - Deg1;
4157 if (lower < 0) lower = 0;
4158 upper = Deg2 + ii;
4159 if (upper > num_poles) upper = num_poles;
4160
4161 for (jj = lower ; jj < upper ; jj++) {
4162 jj_index = jj % NumPoles;
4163 jj_index *= ArrayDimension;
4164 value = 0.0e0;
4165
4166 for (kk = 0 ; kk < ArrayDimension ; kk++) {
4167 factor = (((PA[jj_index + kk] - PA[ii_inDim + kk]) * wg_ii_index) -
4168 ((PA[jj_index + kk] - PA[ii_miDim + kk]) * wg_ii_minus));
4169 if (factor < 0) factor = - factor;
4170 value += factor;
4171 }
4172 value *= inverse;
4173 if (max_derivative < value) max_derivative = value;
4174 }
4175 }
4176 max_derivative /= min_weights;
4177 }
4178 else {
4179
4180 for (ii = 1 ; ii < num_poles ; ii++) {
4181 ii_index = ii % NumPoles;
4182 ii_index *= ArrayDimension;
4183 ii_minus = (ii - 1) % NumPoles;
4184 ii_minus *= ArrayDimension;
4185 inverse = FK[ii + Degree] - FK[ii];
4186 inverse = 1.0e0 / inverse;
4187 value = 0.0e0;
4188
4189 for (kk = 0 ; kk < ArrayDimension ; kk++) {
4190 factor = PA[ii_index + kk] - PA[ii_minus + kk];
4191 if (factor < 0) factor = - factor;
4192 value += factor;
4193 }
4194 value *= inverse;
4195 if (max_derivative < value) max_derivative = value;
4196 }
4197 }
4198 }
4199 }
4200 max_derivative *= Degree;
4201 if (max_derivative > RealSmall())
4202 UTolerance = Tolerance3D / max_derivative;
4203 else
4204 UTolerance = Tolerance3D / RealSmall();
4205}
4206
4207//=======================================================================
4208// function: FlatBezierKnots
4209// purpose :
4210//=======================================================================
4211
41194117
K		 4212// array of flat knots for bezier curve of maximum 25 degree
4213static const Standard_Real knots[52] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
4214 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
7fd59977 4215const Standard_Real& BSplCLib::FlatBezierKnots (const Standard_Integer Degree)
4216{
41194117
K		 4217 Standard_OutOfRange_Raise_if (Degree < 1 || Degree > MaxDegree() || MaxDegree() != 25,
4218 "Bezier curve degree greater than maximal supported");
4219
7fd59977 4220 return knots[25-Degree];
4221}
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