0024510: Remove unused local variables
[occt.git] / src / BSplCLib / BSplCLib.cxx
CommitLineData
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//
973c2be1 8// This library is free software; you can redistribute it and / or modify it
9// under the terms of the GNU Lesser General Public version 2.1 as published
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
645//=======================================================================
06be28a4
RL
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
701//=======================================================================
7fd59977 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--;
1178 *pole -= *tbis; *pole /= (knot[jDmi] - knot[j]);
1179 pole--;
1180 tbis--;
1181 }
1182 }
1183 // Second phase, dependant of U
1184 iDim = - 1;
1185
1186 for (i = 0; i < Degree; i++) {
1187 iDim += 1;
1188 pole = psav + iDim;
1189 tbis = pole + 1;
1190 coef = U - knot[i];
1191
1192 for (j = i; j >= 0; j--) {
1193 *pole += coef * (*tbis);
1194 pole--;
1195 tbis--;
1196 }
1197 }
1198 // multiply by the degrees
1199 coef = Degree;
1200 Dmi = Degree;
1201 pole = psav + 1;
1202
1203 for (i = 1; i <= min; i++) {
1204 *pole *= coef; pole++;
1205 Dmi--;
1206 coef *= Dmi;
1207 }
1208 break;
1209 }
1210 case 2 : {
1211 psDD = psav + (Degree << 1);
1212 psDDmDim = psDD - 2;
1213
1214 for (i = 0; i < Degree; i++) {
1215 DDmi--;
1216 pole = psDD;
1217 tbis = psDDmDim;
1218 jDmi = DDmi;
1219
1220 for (j = Degm1; j >= i; j--) {
1221 jDmi--;
1222 coef = 1. / (knot[jDmi] - knot[j]);
1223 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1224 *pole -= *tbis; *pole *= coef;
1225 pole -= 3;
1226 tbis -= 3;
1227 }
1228 }
1229 // Second phase, dependant of U
1230 iDim = - 2;
1231
1232 for (i = 0; i < Degree; i++) {
1233 iDim += 2;
1234 pole = psav + iDim;
1235 tbis = pole + 2;
1236 coef = U - knot[i];
1237
1238 for (j = i; j >= 0; j--) {
1239 *pole += coef * (*tbis); pole++; tbis++;
1240 *pole += coef * (*tbis);
1241 pole -= 3;
1242 tbis -= 3;
1243 }
1244 }
1245 // multiply by the degrees
1246 coef = Degree;
1247 Dmi = Degree;
1248 pole = psav + 2;
1249
1250 for (i = 1; i <= min; i++) {
1251 *pole *= coef; pole++;
1252 *pole *= coef; pole++;
1253 Dmi--;
1254 coef *= Dmi;
1255 }
1256 break;
1257 }
1258 case 3 : {
1259 psDD = psav + (Degree << 1) + Degree;
1260 psDDmDim = psDD - 3;
1261
1262 for (i = 0; i < Degree; i++) {
1263 DDmi--;
1264 pole = psDD;
1265 tbis = psDDmDim;
1266 jDmi = DDmi;
1267
1268 for (j = Degm1; j >= i; j--) {
1269 jDmi--;
1270 coef = 1. / (knot[jDmi] - knot[j]);
1271 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1272 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1273 *pole -= *tbis; *pole *= coef;
1274 pole -= 5;
1275 tbis -= 5;
1276 }
1277 }
1278 // Second phase, dependant of U
1279 iDim = - 3;
1280
1281 for (i = 0; i < Degree; i++) {
1282 iDim += 3;
1283 pole = psav + iDim;
1284 tbis = pole + 3;
1285 coef = U - knot[i];
1286
1287 for (j = i; j >= 0; j--) {
1288 *pole += coef * (*tbis); pole++; tbis++;
1289 *pole += coef * (*tbis); pole++; tbis++;
1290 *pole += coef * (*tbis);
1291 pole -= 5;
1292 tbis -= 5;
1293 }
1294 }
1295 // multiply by the degrees
1296 coef = Degree;
1297 Dmi = Degree;
1298 pole = psav + 3;
1299
1300 for (i = 1; i <= min; i++) {
1301 *pole *= coef; pole++;
1302 *pole *= coef; pole++;
1303 *pole *= coef; pole++;
1304 Dmi--;
1305 coef *= Dmi;
1306 }
1307 break;
1308 }
1309 case 4 : {
1310 psDD = psav + (Degree << 2);
1311 psDDmDim = psDD - 4;
1312
1313 for (i = 0; i < Degree; i++) {
1314 DDmi--;
1315 pole = psDD;
1316 tbis = psDDmDim;
1317 jDmi = DDmi;
1318
1319 for (j = Degm1; j >= i; j--) {
1320 jDmi--;
1321 coef = 1. / (knot[jDmi] - knot[j]);
1322 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1323 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1324 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1325 *pole -= *tbis; *pole *= coef;
1326 pole -= 7;
1327 tbis -= 7;
1328 }
1329 }
1330 // Second phase, dependant of U
1331 iDim = - 4;
1332
1333 for (i = 0; i < Degree; i++) {
1334 iDim += 4;
1335 pole = psav + iDim;
1336 tbis = pole + 4;
1337 coef = U - knot[i];
1338
1339 for (j = i; j >= 0; j--) {
1340 *pole += coef * (*tbis); pole++; tbis++;
1341 *pole += coef * (*tbis); pole++; tbis++;
1342 *pole += coef * (*tbis); pole++; tbis++;
1343 *pole += coef * (*tbis);
1344 pole -= 7;
1345 tbis -= 7;
1346 }
1347 }
1348 // multiply by the degrees
1349 coef = Degree;
1350 Dmi = Degree;
1351 pole = psav + 4;
1352
1353 for (i = 1; i <= min; i++) {
1354 *pole *= coef; pole++;
1355 *pole *= coef; pole++;
1356 *pole *= coef; pole++;
1357 *pole *= coef; pole++;
1358 Dmi--;
1359 coef *= Dmi;
1360 }
1361 break;
1362 }
1363 default : {
1364 Standard_Integer k;
1365 Standard_Integer Dim2 = Dimension << 1;
1366 psDD = psav + Degree * Dimension;
1367 psDDmDim = psDD - Dimension;
1368
1369 for (i = 0; i < Degree; i++) {
1370 DDmi--;
1371 pole = psDD;
1372 tbis = psDDmDim;
1373 jDmi = DDmi;
1374
1375 for (j = Degm1; j >= i; j--) {
1376 jDmi--;
1377 coef = 1. / (knot[jDmi] - knot[j]);
1378
1379 for (k = 0; k < Dimension; k++) {
1380 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1381 }
1382 pole -= Dim2;
1383 tbis -= Dim2;
1384 }
1385 }
1386 // Second phase, dependant of U
1387 iDim = - Dimension;
1388
1389 for (i = 0; i < Degree; i++) {
1390 iDim += Dimension;
1391 pole = psav + iDim;
1392 tbis = pole + Dimension;
1393 coef = U - knot[i];
1394
1395 for (j = i; j >= 0; j--) {
1396
1397 for (k = 0; k < Dimension; k++) {
1398 *pole += coef * (*tbis); pole++; tbis++;
1399 }
1400 pole -= Dim2;
1401 tbis -= Dim2;
1402 }
1403 }
1404 // multiply by the degrees
1405 coef = Degree;
1406 Dmi = Degree;
1407 pole = psav + Dimension;
1408
1409 for (i = 1; i <= min; i++) {
1410
1411 for (k = 0; k < Dimension; k++) {
1412 *pole *= coef; pole++;
1413 }
1414 Dmi--;
1415 coef *= Dmi;
1416 }
1417 }
1418 }
1419}
1420
1421//=======================================================================
1422//function : BuildKnots
1423//purpose :
1424//=======================================================================
1425
1426void BSplCLib::BuildKnots(const Standard_Integer Degree,
1427 const Standard_Integer Index,
1428 const Standard_Boolean Periodic,
1429 const TColStd_Array1OfReal& Knots,
1430 const TColStd_Array1OfInteger& Mults,
1431 Standard_Real& LK)
1432{
1433 Standard_Integer KLower = Knots.Lower();
1434 const Standard_Real * pkn = &Knots(KLower);
1435 pkn -= KLower;
1436 Standard_Real *knot = &LK;
1437 if (&Mults == NULL) {
1438 switch (Degree) {
1439 case 1 : {
1440 Standard_Integer j = Index ;
1441 knot[0] = pkn[j]; j++;
1442 knot[1] = pkn[j];
1443 break;
1444 }
1445 case 2 : {
1446 Standard_Integer j = Index - 1;
1447 knot[0] = pkn[j]; j++;
1448 knot[1] = pkn[j]; j++;
1449 knot[2] = pkn[j]; j++;
1450 knot[3] = pkn[j];
1451 break;
1452 }
1453 case 3 : {
1454 Standard_Integer j = Index - 2;
1455 knot[0] = pkn[j]; j++;
1456 knot[1] = pkn[j]; j++;
1457 knot[2] = pkn[j]; j++;
1458 knot[3] = pkn[j]; j++;
1459 knot[4] = pkn[j]; j++;
1460 knot[5] = pkn[j];
1461 break;
1462 }
1463 case 4 : {
1464 Standard_Integer j = Index - 3;
1465 knot[0] = pkn[j]; j++;
1466 knot[1] = pkn[j]; j++;
1467 knot[2] = pkn[j]; j++;
1468 knot[3] = pkn[j]; j++;
1469 knot[4] = pkn[j]; j++;
1470 knot[5] = pkn[j]; j++;
1471 knot[6] = pkn[j]; j++;
1472 knot[7] = pkn[j];
1473 break;
1474 }
1475 case 5 : {
1476 Standard_Integer j = Index - 4;
1477 knot[0] = pkn[j]; j++;
1478 knot[1] = pkn[j]; j++;
1479 knot[2] = pkn[j]; j++;
1480 knot[3] = pkn[j]; j++;
1481 knot[4] = pkn[j]; j++;
1482 knot[5] = pkn[j]; j++;
1483 knot[6] = pkn[j]; j++;
1484 knot[7] = pkn[j]; j++;
1485 knot[8] = pkn[j]; j++;
1486 knot[9] = pkn[j];
1487 break;
1488 }
1489 case 6 : {
1490 Standard_Integer j = Index - 5;
1491 knot[ 0] = pkn[j]; j++;
1492 knot[ 1] = pkn[j]; j++;
1493 knot[ 2] = pkn[j]; j++;
1494 knot[ 3] = pkn[j]; j++;
1495 knot[ 4] = pkn[j]; j++;
1496 knot[ 5] = pkn[j]; j++;
1497 knot[ 6] = pkn[j]; j++;
1498 knot[ 7] = pkn[j]; j++;
1499 knot[ 8] = pkn[j]; j++;
1500 knot[ 9] = pkn[j]; j++;
1501 knot[10] = pkn[j]; j++;
1502 knot[11] = pkn[j];
1503 break;
1504 }
1505 default : {
1506 Standard_Integer i,j;
1507 Standard_Integer Deg2 = Degree << 1;
1508 j = Index - Degree;
1509
1510 for (i = 0; i < Deg2; i++) {
1511 j++;
1512 knot[i] = pkn[j];
1513 }
1514 }
1515 }
1516 }
1517 else {
1518 Standard_Integer i;
1519 Standard_Integer Deg1 = Degree - 1;
1520 Standard_Integer KUpper = Knots.Upper();
1521 Standard_Integer MLower = Mults.Lower();
1522 Standard_Integer MUpper = Mults.Upper();
1523 const Standard_Integer * pmu = &Mults(MLower);
1524 pmu -= MLower;
1525 Standard_Real dknot = 0;
1526 Standard_Integer ilow = Index , mlow = 0;
1527 Standard_Integer iupp = Index + 1, mupp = 0;
1528 Standard_Real loffset = 0., uoffset = 0.;
1529 Standard_Boolean getlow = Standard_True, getupp = Standard_True;
1530 if (Periodic) {
1531 dknot = pkn[KUpper] - pkn[KLower];
1532 if (iupp > MUpper) {
1533 iupp = MLower + 1;
1534 uoffset = dknot;
1535 }
1536 }
1537 // Find the knots around Index
1538
1539 for (i = 0; i < Degree; i++) {
1540 if (getlow) {
1541 mlow++;
1542 if (mlow > pmu[ilow]) {
1543 mlow = 1;
1544 ilow--;
1545 getlow = (ilow >= MLower);
1546 if (Periodic && !getlow) {
1547 ilow = MUpper - 1;
1548 loffset = dknot;
1549 getlow = Standard_True;
1550 }
1551 }
1552 if (getlow)
1553 knot[Deg1 - i] = pkn[ilow] - loffset;
1554 }
1555 if (getupp) {
1556 mupp++;
1557 if (mupp > pmu[iupp]) {
1558 mupp = 1;
1559 iupp++;
1560 getupp = (iupp <= MUpper);
1561 if (Periodic && !getupp) {
1562 iupp = MLower + 1;
1563 uoffset = dknot;
1564 getupp = Standard_True;
1565 }
1566 }
1567 if (getupp)
1568 knot[Degree + i] = pkn[iupp] + uoffset;
1569 }
1570 }
1571 }
1572}
1573
1574//=======================================================================
1575//function : PoleIndex
1576//purpose :
1577//=======================================================================
1578
1579Standard_Integer BSplCLib::PoleIndex(const Standard_Integer Degree,
1580 const Standard_Integer Index,
1581 const Standard_Boolean Periodic,
1582 const TColStd_Array1OfInteger& Mults)
1583{
1584 Standard_Integer i, pindex = 0;
1585
1586 for (i = Mults.Lower(); i <= Index; i++)
1587 pindex += Mults(i);
1588 if (Periodic)
1589 pindex -= Mults(Mults.Lower());
1590 else
1591 pindex -= Degree + 1;
1592
1593 return pindex;
1594}
1595
1596//=======================================================================
1597//function : BuildBoor
1598//purpose : builds the local array for boor
1599//=======================================================================
1600
1601void BSplCLib::BuildBoor(const Standard_Integer Index,
1602 const Standard_Integer Length,
1603 const Standard_Integer Dimension,
1604 const TColStd_Array1OfReal& Poles,
1605 Standard_Real& LP)
1606{
1607 Standard_Real *poles = &LP;
1608 Standard_Integer i,k, ip = Poles.Lower() + Index * Dimension;
1609
1610 for (i = 0; i < Length+1; i++) {
1611
1612 for (k = 0; k < Dimension; k++) {
1613 poles[k] = Poles(ip);
1614 ip++;
1615 if (ip > Poles.Upper()) ip = Poles.Lower();
1616 }
1617 poles += 2 * Dimension;
1618 }
1619}
1620
1621//=======================================================================
1622//function : BoorIndex
1623//purpose :
1624//=======================================================================
1625
1626Standard_Integer BSplCLib::BoorIndex(const Standard_Integer Index,
1627 const Standard_Integer Length,
1628 const Standard_Integer Depth)
1629{
1630 if (Index <= Depth) return Index;
1631 if (Index <= Length) return 2 * Index - Depth;
1632 return Length + Index - Depth;
1633}
1634
1635//=======================================================================
1636//function : GetPole
1637//purpose :
1638//=======================================================================
1639
1640void BSplCLib::GetPole(const Standard_Integer Index,
1641 const Standard_Integer Length,
1642 const Standard_Integer Depth,
1643 const Standard_Integer Dimension,
1644 Standard_Real& LP,
1645 Standard_Integer& Position,
1646 TColStd_Array1OfReal& Pole)
1647{
1648 Standard_Integer k;
1649 Standard_Real* pole = &LP + BoorIndex(Index,Length,Depth) * Dimension;
1650
1651 for (k = 0; k < Dimension; k++) {
1652 Pole(Position) = pole[k];
1653 Position++;
1654 }
1655 if (Position > Pole.Upper()) Position = Pole.Lower();
1656}
1657
1658//=======================================================================
1659//function : PrepareInsertKnots
1660//purpose :
1661//=======================================================================
1662
1663Standard_Boolean BSplCLib::PrepareInsertKnots
1664(const Standard_Integer Degree,
1665 const Standard_Boolean Periodic,
1666 const TColStd_Array1OfReal& Knots,
1667 const TColStd_Array1OfInteger& Mults,
1668 const TColStd_Array1OfReal& AddKnots,
1669 const TColStd_Array1OfInteger& AddMults,
1670 Standard_Integer& NbPoles,
1671 Standard_Integer& NbKnots,
1672 const Standard_Real Tolerance,
1673 const Standard_Boolean Add)
1674{
1675 Standard_Boolean addflat = &AddMults == NULL;
1676
1677 Standard_Integer first,last;
1678 if (Periodic) {
1679 first = Knots.Lower();
1680 last = Knots.Upper();
1681 }
1682 else {
1683 first = FirstUKnotIndex(Degree,Mults);
1684 last = LastUKnotIndex(Degree,Mults);
1685 }
1686 Standard_Real adeltaK1 = Knots(first)-AddKnots(AddKnots.Lower());
1687 Standard_Real adeltaK2 = AddKnots(AddKnots.Upper())-Knots(last);
1688 if (adeltaK1 > Tolerance) return Standard_False;
1689 if (adeltaK2 > Tolerance) return Standard_False;
1690
9d091ec1 1691 Standard_Integer sigma = 0, mult, amult;
7fd59977 1692 NbKnots = 0;
1693 Standard_Integer k = Knots.Lower() - 1;
1694 Standard_Integer ak = AddKnots.Lower();
1695
1696 if(Periodic && AddKnots.Length() > 1)
1697 {
1698 //gka for case when segments was produced on full period only one knot
1699 //was added in the end of curve
1700 if(fabs(adeltaK1) <= Precision::PConfusion() &&
1701 fabs(adeltaK2) <= Precision::PConfusion())
1702 ak++;
1703 }
1704
1705 Standard_Real au,oldau = AddKnots(ak),Eps;
1706
1707 while (ak <= AddKnots.Upper()) {
1708 au = AddKnots(ak);
1709 if (au < oldau) return Standard_False;
1710 oldau = au;
1711
1712 Eps = Max(Tolerance,Epsilon(au));
1713
1714 while ((k < Knots.Upper()) && (Knots(k+1) - au <= Eps)) {
1715 k++;
1716 NbKnots++;
1717 sigma += Mults(k);
1718 }
1719
1720 if (addflat) amult = 1;
1721 else amult = Max(0,AddMults(ak));
1722
1723 while ((ak < AddKnots.Upper()) &&
1724 (Abs(au - AddKnots(ak+1)) <= Eps)) {
1725 ak++;
1726 if (Add) {
1727 if (addflat) amult++;
1728 else amult += Max(0,AddMults(ak));
1729 }
1730 }
1731
1732
1733 if (Abs(au - Knots(k)) <= Eps) {
1734 // identic to existing knot
1735 mult = Mults(k);
7fd59977 1736 if (Add) {
1737 if (mult + amult > Degree)
1738 amult = Max(0,Degree - mult);
1739 sigma += amult;
7fd59977 1740
1741 }
1742 else if (amult > mult) {
1743 if (amult > Degree) amult = Degree;
1744 sigma += amult - mult;
7fd59977 1745 }
1746 /*
1747 // on periodic curves if this is the last knot
1748 // the multiplicity is added twice to account for the first knot
1749 if (k == Knots.Upper() && Periodic) {
1750 if (Add)
1751 sigma += amult;
1752 else
1753 sigma += amult - mult;
1754 }
1755 */
1756 }
1757 else {
1758 // not identic to existing knot
1759 if (amult > 0) {
1760 if (amult > Degree) amult = Degree;
1761 NbKnots++;
7fd59977 1762 sigma += amult;
1763 }
1764 }
1765
1766 ak++;
1767 }
1768
1769 // count the last knots
7fd59977 1770 while (k < Knots.Upper()) {
1771 k++;
1772 NbKnots++;
1773 sigma += Mults(k);
1774 }
1775
1776 if (Periodic) {
9d091ec1 1777 //for periodic B-Spline the requirement is that multiplicites of the first
1778 //and last knots must be equal (see Geom_BSplineCurve constructor for
1779 //instance);
1780 //respectively AddMults() must meet this requirement if AddKnots() contains
1781 //knot(s) coincident with first or last
1782 NbPoles = sigma - Mults(Knots.Upper());
7fd59977 1783 }
1784 else {
1785 NbPoles = sigma - Degree - 1;
1786 }
1787
1788 return Standard_True;
1789}
1790
1791//=======================================================================
1792//function : Copy
1793//purpose : copy reals from an array to an other
1794//
1795// NbValues are copied from OldPoles(OldFirst)
1796// to NewPoles(NewFirst)
1797//
1798// Periodicity is handled.
1799// OldFirst and NewFirst are updated
1800// to the position after the last copied pole.
1801//
1802//=======================================================================
1803
1804static void Copy(const Standard_Integer NbPoles,
1805 Standard_Integer& OldFirst,
1806 const TColStd_Array1OfReal& OldPoles,
1807 Standard_Integer& NewFirst,
1808 TColStd_Array1OfReal& NewPoles)
1809{
1810 // reset the index in the range for periodicity
1811
1812 OldFirst = OldPoles.Lower() +
1813 (OldFirst - OldPoles.Lower()) % (OldPoles.Upper() - OldPoles.Lower() + 1);
1814
1815 NewFirst = NewPoles.Lower() +
1816 (NewFirst - NewPoles.Lower()) % (NewPoles.Upper() - NewPoles.Lower() + 1);
1817
1818 // copy
1819 Standard_Integer i;
1820
1821 for (i = 1; i <= NbPoles; i++) {
1822 NewPoles(NewFirst) = OldPoles(OldFirst);
1823 OldFirst++;
1824 if (OldFirst > OldPoles.Upper()) OldFirst = OldPoles.Lower();
1825 NewFirst++;
1826 if (NewFirst > NewPoles.Upper()) NewFirst = NewPoles.Lower();
1827 }
1828}
1829
1830//=======================================================================
1831//function : InsertKnots
1832//purpose : insert an array of knots and multiplicities
1833//=======================================================================
1834
1835void BSplCLib::InsertKnots
1836(const Standard_Integer Degree,
1837 const Standard_Boolean Periodic,
1838 const Standard_Integer Dimension,
1839 const TColStd_Array1OfReal& Poles,
1840 const TColStd_Array1OfReal& Knots,
1841 const TColStd_Array1OfInteger& Mults,
1842 const TColStd_Array1OfReal& AddKnots,
1843 const TColStd_Array1OfInteger& AddMults,
1844 TColStd_Array1OfReal& NewPoles,
1845 TColStd_Array1OfReal& NewKnots,
1846 TColStd_Array1OfInteger& NewMults,
1847 const Standard_Real Tolerance,
1848 const Standard_Boolean Add)
1849{
1850 Standard_Boolean addflat = &AddMults == NULL;
1851
1852 Standard_Integer i,k,mult,firstmult;
1853 Standard_Integer index,kn,curnk,curk;
1854 Standard_Integer p,np, curp, curnp, length, depth;
1855 Standard_Real u;
1856 Standard_Integer need;
1857 Standard_Real Eps;
1858
1859 // -------------------
1860 // create local arrays
1861 // -------------------
1862
1863 Standard_Real *knots = new Standard_Real[2*Degree];
1864 Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
1865
1866 //----------------------------
1867 // loop on the knots to insert
1868 //----------------------------
1869
1870 curk = Knots.Lower()-1; // current position in Knots
1871 curnk = NewKnots.Lower()-1; // current position in NewKnots
1872 curp = Poles.Lower(); // current position in Poles
1873 curnp = NewPoles.Lower(); // current position in NewPoles
1874
1875 // NewKnots, NewMults, NewPoles contains the current state of the curve
1876
1877 // index is the first pole of the current curve for insertion schema
1878
1879 if (Periodic) index = -Mults(Mults.Lower());
1880 else index = -Degree-1;
1881
1882 // on Periodic curves the first knot and the last knot are inserted later
1883 // (they are the same knot)
1884 firstmult = 0; // multiplicity of the first-last knot for periodic
1885
1886
1887 // kn current knot to insert in AddKnots
1888
1889 for (kn = AddKnots.Lower(); kn <= AddKnots.Upper(); kn++) {
1890
1891 u = AddKnots(kn);
1892 Eps = Max(Tolerance,Epsilon(u));
1893
1894 //-----------------------------------
1895 // find the position in the old knots
1896 // and copy to the new knots
1897 //-----------------------------------
1898
1899 while (curk < Knots.Upper() && Knots(curk+1) - u <= Eps) {
1900 curk++; curnk++;
1901 NewKnots(curnk) = Knots(curk);
1902 index += NewMults(curnk) = Mults(curk);
1903 }
1904
1905 //-----------------------------------
1906 // Slice the knots and the mults
1907 // to the current size of the new curve
1908 //-----------------------------------
1909
1910 i = curnk + Knots.Upper() - curk;
1911 TColStd_Array1OfReal nknots(NewKnots(NewKnots.Lower()),NewKnots.Lower(),i);
1912 TColStd_Array1OfInteger nmults(NewMults(NewMults.Lower()),NewMults.Lower(),i);
1913
1914 //-----------------------------------
1915 // copy enough knots
1916 // to compute the insertion schema
1917 //-----------------------------------
1918
1919 k = curk;
1920 i = curnk;
1921 mult = 0;
1922
1923 while (mult < Degree && k < Knots.Upper()) {
1924 k++; i++;
1925 nknots(i) = Knots(k);
1926 mult += nmults(i) = Mults(k);
1927 }
1928
1929 // copy knots at the end for periodic curve
1930 if (Periodic) {
1931 mult = 0;
1932 k = Knots.Upper();
1933 i = nknots.Upper();
1934
1935 while (mult < Degree && i > curnk) {
1936 nknots(i) = Knots(k);
1937 mult += nmults(i) = Mults(k);
1938 k--;
1939 i--;
1940 }
1941 nmults(nmults.Upper()) = nmults(nmults.Lower());
1942 }
1943
1944
1945
1946 //------------------------------------
1947 // do the boor scheme on the new curve
1948 // to insert the new knot
1949 //------------------------------------
1950
1951 Standard_Boolean sameknot = (Abs(u-NewKnots(curnk)) <= Eps);
1952
1953 if (sameknot) length = Max(0,Degree - NewMults(curnk));
1954 else length = Degree;
1955
1956 if (addflat) depth = 1;
1957 else depth = Min(Degree,AddMults(kn));
1958
1959 if (sameknot) {
1960 if (Add) {
1961 if ((NewMults(curnk) + depth) > Degree)
1962 depth = Degree - NewMults(curnk);
1963 }
1964 else {
1965 depth = Max(0,depth-NewMults(curnk));
1966 }
1967
1968 if (Periodic) {
1969 // on periodic curve the first and last knot are delayed to the end
1970 if (curk == Knots.Lower() || (curk == Knots.Upper())) {
1971 firstmult += depth;
1972 depth = 0;
1973 }
1974 }
1975 }
1976 if (depth <= 0) continue;
1977
1978 BuildKnots(Degree,curnk,Periodic,nknots,nmults,*knots);
1979
1980 // copy the poles
1981
1982 need = NewPoles.Lower()+(index+length+1)*Dimension - curnp;
1983 need = Min(need,Poles.Upper() - curp + 1);
1984
1985 p = curp;
1986 np = curnp;
1987 Copy(need,p,Poles,np,NewPoles);
1988 curp += need;
1989 curnp += need;
1990
1991 // slice the poles to the current number of poles in case of periodic
1992 TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
1993
1994 BuildBoor(index,length,Dimension,npoles,*poles);
1995 BoorScheme(u,Degree,*knots,Dimension,*poles,depth,length);
1996
1997 //-------------------
1998 // copy the new poles
1999 //-------------------
2000
2001 curnp += depth * Dimension; // number of poles is increased by depth
2002 TColStd_Array1OfReal ThePoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
2003 np = NewKnots.Lower()+(index+1)*Dimension;
2004
2005 for (i = 1; i <= length + depth; i++)
2006 GetPole(i,length,depth,Dimension,*poles,np,ThePoles);
2007
2008 //-------------------
2009 // insert the knot
2010 //-------------------
2011
2012 index += depth;
2013 if (sameknot) {
2014 NewMults(curnk) += depth;
2015 }
2016 else {
2017 curnk++;
2018 NewKnots(curnk) = u;
2019 NewMults(curnk) = depth;
2020 }
2021 }
2022
2023 //------------------------------
2024 // copy the last poles and knots
2025 //------------------------------
2026
2027 Copy(Poles.Upper() - curp + 1,curp,Poles,curnp,NewPoles);
2028
2029 while (curk < Knots.Upper()) {
2030 curk++; curnk++;
2031 NewKnots(curnk) = Knots(curk);
2032 NewMults(curnk) = Mults(curk);
2033 }
2034
2035 //------------------------------
2036 // process the first-last knot
2037 // on periodic curves
2038 //------------------------------
2039
2040 if (firstmult > 0) {
2041 curnk = NewKnots.Lower();
2042 if (NewMults(curnk) + firstmult > Degree) {
2043 firstmult = Degree - NewMults(curnk);
2044 }
2045 if (firstmult > 0) {
2046
2047 length = Degree - NewMults(curnk);
2048 depth = firstmult;
2049
2050 BuildKnots(Degree,curnk,Periodic,NewKnots,NewMults,*knots);
2051 TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),
2052 NewPoles.Lower(),
2053 NewPoles.Upper()-depth*Dimension);
2054 BuildBoor(0,length,Dimension,npoles,*poles);
2055 BoorScheme(NewKnots(curnk),Degree,*knots,Dimension,*poles,depth,length);
2056
2057 //---------------------------
2058 // copy the new poles
2059 // but rotate them with depth
2060 //---------------------------
2061
2062 np = NewPoles.Lower();
2063
2064 for (i = depth; i < length + depth; i++)
2065 GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
2066
2067 np = NewPoles.Upper() - depth*Dimension + 1;
2068
2069 for (i = 0; i < depth; i++)
2070 GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
2071
2072 NewMults(NewMults.Lower()) += depth;
2073 NewMults(NewMults.Upper()) += depth;
2074 }
2075 }
2076 // free local arrays
2077 delete [] knots;
2078 delete [] poles;
2079}
2080
2081//=======================================================================
2082//function : RemoveKnot
2083//purpose :
2084//=======================================================================
2085
2086Standard_Boolean BSplCLib::RemoveKnot
2087(const Standard_Integer Index,
2088 const Standard_Integer Mult,
2089 const Standard_Integer Degree,
2090 const Standard_Boolean Periodic,
2091 const Standard_Integer Dimension,
2092 const TColStd_Array1OfReal& Poles,
2093 const TColStd_Array1OfReal& Knots,
2094 const TColStd_Array1OfInteger& Mults,
2095 TColStd_Array1OfReal& NewPoles,
2096 TColStd_Array1OfReal& NewKnots,
2097 TColStd_Array1OfInteger& NewMults,
2098 const Standard_Real Tolerance)
2099{
2100 Standard_Integer index,i,j,k,p,np;
2101
2102 Standard_Integer TheIndex = Index;
2103
2104 // protection
2105 Standard_Integer first,last;
2106 if (Periodic) {
2107 first = Knots.Lower();
2108 last = Knots.Upper();
2109 }
2110 else {
2111 first = BSplCLib::FirstUKnotIndex(Degree,Mults) + 1;
2112 last = BSplCLib::LastUKnotIndex(Degree,Mults) - 1;
2113 }
2114 if (Index < first) return Standard_False;
2115 if (Index > last) return Standard_False;
2116
2117 if ( Periodic && (Index == first)) TheIndex = last;
2118
2119 Standard_Integer depth = Mults(TheIndex) - Mult;
2120 Standard_Integer length = Degree - Mult;
2121
2122 // -------------------
2123 // create local arrays
2124 // -------------------
2125
2126 Standard_Real *knots = new Standard_Real[4*Degree];
2127 Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
2128
2129
2130 // ------------------------------------
2131 // build the knots for anti Boor Scheme
2132 // ------------------------------------
2133
2134 // the new sequence of knots
2135 // is obtained from the knots at Index-1 and Index
2136
2137 BSplCLib::BuildKnots(Degree,TheIndex-1,Periodic,Knots,Mults,*knots);
2138 index = PoleIndex(Degree,TheIndex-1,Periodic,Mults);
2139 BSplCLib::BuildKnots(Degree,TheIndex,Periodic,Knots,Mults,knots[2*Degree]);
2140
2141 index += Mult;
2142
2143 for (i = 0; i < Degree - Mult; i++)
2144 knots[i] = knots[i+Mult];
2145
2146 for (i = Degree-Mult; i < 2*Degree; i++)
2147 knots[i] = knots[2*Degree+i];
2148
2149
2150 // ------------------------------------
2151 // build the poles for anti Boor Scheme
2152 // ------------------------------------
2153
2154 p = Poles.Lower()+index * Dimension;
2155
2156 for (i = 0; i <= length + depth; i++) {
2157 j = Dimension * BoorIndex(i,length,depth);
2158
2159 for (k = 0; k < Dimension; k++) {
2160 poles[j+k] = Poles(p+k);
2161 }
2162 p += Dimension;
2163 if (p > Poles.Upper()) p = Poles.Lower();
2164 }
2165
2166
2167 // ----------------
2168 // Anti Boor Scheme
2169 // ----------------
2170
2171 Standard_Boolean result = AntiBoorScheme(Knots(TheIndex),Degree,*knots,
2172 Dimension,*poles,
2173 depth,length,Tolerance);
2174
2175 // ----------------
2176 // copy the results
2177 // ----------------
2178
2179 if (result) {
2180
2181 // poles
2182
2183 p = Poles.Lower();
2184 np = NewPoles.Lower();
2185
2186 // unmodified poles before
2187 Copy((index+1)*Dimension,p,Poles,np,NewPoles);
2188
2189
2190 // modified
2191
2192 for (i = 1; i <= length; i++)
2193 BSplCLib::GetPole(i,length,0,Dimension,*poles,np,NewPoles);
2194 p += (length + depth) * Dimension ;
2195
2196 // unmodified poles after
2197 if (p != Poles.Lower()) {
2198 i = Poles.Upper() - p + 1;
2199 Copy(i,p,Poles,np,NewPoles);
2200 }
2201
2202 // knots and mults
2203
2204 if (Mult > 0) {
2205 NewKnots = Knots;
2206 NewMults = Mults;
2207 NewMults(TheIndex) = Mult;
2208 if (Periodic) {
2209 if (TheIndex == first) NewMults(last) = Mult;
2210 if (TheIndex == last) NewMults(first) = Mult;
2211 }
2212 }
2213 else {
2214 if (!Periodic || (TheIndex != first && TheIndex != last)) {
2215
2216 for (i = Knots.Lower(); i < TheIndex; i++) {
2217 NewKnots(i) = Knots(i);
2218 NewMults(i) = Mults(i);
2219 }
2220
2221 for (i = TheIndex+1; i <= Knots.Upper(); i++) {
2222 NewKnots(i-1) = Knots(i);
2223 NewMults(i-1) = Mults(i);
2224 }
2225 }
2226 else {
2227 // The interesting case of a Periodic curve
2228 // where the first and last knot is removed.
2229
2230 for (i = first; i < last-1; i++) {
2231 NewKnots(i) = Knots(i+1);
2232 NewMults(i) = Mults(i+1);
2233 }
2234 NewKnots(last-1) = NewKnots(first) + Knots(last) - Knots(first);
2235 NewMults(last-1) = NewMults(first);
2236 }
2237 }
2238 }
2239
2240
2241 // free local arrays
2242 delete [] knots;
2243 delete [] poles;
2244
2245 return result;
2246}
2247
2248//=======================================================================
2249//function : IncreaseDegreeCountKnots
2250//purpose :
2251//=======================================================================
2252
2253Standard_Integer BSplCLib::IncreaseDegreeCountKnots
2254(const Standard_Integer Degree,
2255 const Standard_Integer NewDegree,
2256 const Standard_Boolean Periodic,
2257 const TColStd_Array1OfInteger& Mults)
2258{
2259 if (Periodic) return Mults.Length();
2260 Standard_Integer f = FirstUKnotIndex(Degree,Mults);
2261 Standard_Integer l = LastUKnotIndex(Degree,Mults);
2262 Standard_Integer m,i,removed = 0, step = NewDegree - Degree;
2263
2264 i = Mults.Lower();
2265 m = Degree + (f - i + 1) * step + 1;
2266
2267 while (m > NewDegree+1) {
2268 removed++;
2269 m -= Mults(i) + step;
2270 i++;
2271 }
2272 if (m < NewDegree+1) removed--;
2273
2274 i = Mults.Upper();
2275 m = Degree + (i - l + 1) * step + 1;
2276
2277 while (m > NewDegree+1) {
2278 removed++;
2279 m -= Mults(i) + step;
2280 i--;
2281 }
2282 if (m < NewDegree+1) removed--;
2283
2284 return Mults.Length() - removed;
2285}
2286
2287//=======================================================================
2288//function : IncreaseDegree
2289//purpose :
2290//=======================================================================
2291
2292void BSplCLib::IncreaseDegree
2293(const Standard_Integer Degree,
2294 const Standard_Integer NewDegree,
2295 const Standard_Boolean Periodic,
2296 const Standard_Integer Dimension,
2297 const TColStd_Array1OfReal& Poles,
2298 const TColStd_Array1OfReal& Knots,
2299 const TColStd_Array1OfInteger& Mults,
2300 TColStd_Array1OfReal& NewPoles,
2301 TColStd_Array1OfReal& NewKnots,
2302 TColStd_Array1OfInteger& NewMults)
2303{
2304 // Degree elevation of a BSpline Curve
2305
2306 // This algorithms loops on degree incrementation from Degree to NewDegree.
2307 // The variable curDeg is the current degree to increment.
2308
2309 // Before degree incrementations a "working curve" is created.
2310 // It has the same knot, poles and multiplicities.
2311
2312 // If the curve is periodic knots are added on the working curve before
2313 // and after the existing knots to make it a non-periodic curves.
2314 // The poles are also copied.
2315
2316 // The first and last multiplicity of the working curve are set to Degree+1,
2317 // null poles are added if necessary.
2318
2319 // Then the degree is incremented on the working curve.
2320 // The knots are unchanged but all multiplicities will be incremented.
2321
2322 // Each degree incrementation is achieved by averaging curDeg+1 curves.
2323
2324 // See : Degree elevation of B-spline curves
2325 // Hartmut PRAUTZSCH
2326 // CAGD 1 (1984)
2327
2328
2329 //-------------------------
2330 // create the working curve
2331 //-------------------------
2332
2333 Standard_Integer i,k,f,l,m,pf,pl,firstknot;
2334
2335 pf = 0; // number of null poles added at beginning
2336 pl = 0; // number of null poles added at end
2337
2338 Standard_Integer nbwknots = Knots.Length();
2339 f = FirstUKnotIndex(Degree,Mults);
2340 l = LastUKnotIndex (Degree,Mults);
2341
2342 if (Periodic) {
2343 // Periodic curves are transformed in non-periodic curves
2344
2345 nbwknots += f - Mults.Lower();
2346
2347 pf = -Degree - 1;
2348
2349 for (i = Mults.Lower(); i <= f; i++)
2350 pf += Mults(i);
2351
2352 nbwknots += Mults.Upper() - l;
2353
2354 pl = -Degree - 1;
2355
2356 for (i = l; i <= Mults.Upper(); i++)
2357 pl += Mults(i);
2358 }
2359
2360 // copy the knots and multiplicities
2361 TColStd_Array1OfReal wknots(1,nbwknots);
2362 TColStd_Array1OfInteger wmults(1,nbwknots);
2363 if (!Periodic) {
2364 wknots = Knots;
2365 wmults = Mults;
2366 }
2367 else {
2368 // copy the knots for a periodic curve
2369 Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
2370 i = 0;
2371
2372 for (k = l; k < Knots.Upper(); k++) {
2373 i++;
2374 wknots(i) = Knots(k) - period;
2375 wmults(i) = Mults(k);
2376 }
2377
2378 for (k = Knots.Lower(); k <= Knots.Upper(); k++) {
2379 i++;
2380 wknots(i) = Knots(k);
2381 wmults(i) = Mults(k);
2382 }
2383
2384 for (k = Knots.Lower()+1; k <= f; k++) {
2385 i++;
2386 wknots(i) = Knots(k) + period;
2387 wmults(i) = Mults(k);
2388 }
2389 }
2390
2391 // set the first and last mults to Degree+1
2392 // and add null poles
2393
2394 pf += Degree + 1 - wmults(1);
2395 wmults(1) = Degree + 1;
2396 pl += Degree + 1 - wmults(nbwknots);
2397 wmults(nbwknots) = Degree + 1;
2398
2399 //---------------------------
2400 // poles of the working curve
2401 //---------------------------
2402
2403 Standard_Integer nbwpoles = 0;
2404
2405 for (i = 1; i <= nbwknots; i++) nbwpoles += wmults(i);
2406 nbwpoles -= Degree + 1;
2407
2408 // we provide space for degree elevation
2409 TColStd_Array1OfReal
2410 wpoles(1,(nbwpoles + (nbwknots-1) * (NewDegree - Degree)) * Dimension);
2411
2412 for (i = 1; i <= pf * Dimension; i++)
2413 wpoles(i) = 0;
2414
2415 k = Poles.Lower();
2416
2417 for (i = pf * Dimension + 1; i <= (nbwpoles - pl) * Dimension; i++) {
2418 wpoles(i) = Poles(k);
2419 k++;
2420 if (k > Poles.Upper()) k = Poles.Lower();
2421 }
2422
2423 for (i = (nbwpoles-pl)*Dimension+1; i <= nbwpoles*Dimension; i++)
2424 wpoles(i) = 0;
2425
2426
2427 //-----------------------------------------------------------
2428 // Declare the temporary arrays used in degree incrementation
2429 //-----------------------------------------------------------
2430
2431 Standard_Integer nbwp = nbwpoles + (nbwknots-1) * (NewDegree - Degree);
2432 // Arrays for storing the temporary curves
2433 TColStd_Array1OfReal tempc1(1,nbwp * Dimension);
2434 TColStd_Array1OfReal tempc2(1,nbwp * Dimension);
2435
2436 // Array for storing the knots to insert
2437 TColStd_Array1OfReal iknots(1,nbwknots);
2438
2439 // Arrays for receiving the knots after insertion
2440 TColStd_Array1OfReal nknots(1,nbwknots);
2441
2442
2443
2444 //------------------------------
2445 // Loop on degree incrementation
2446 //------------------------------
2447
2448 Standard_Integer step,curDeg;
2449 Standard_Integer nbp = nbwpoles;
2450 nbwp = nbp;
2451
2452 for (curDeg = Degree; curDeg < NewDegree; curDeg++) {
2453
2454 nbp = nbwp; // current number of poles
2455 nbwp = nbp + nbwknots - 1; // new number of poles
2456
2457 // For the averaging
2458 TColStd_Array1OfReal nwpoles(1,nbwp * Dimension);
2459 nwpoles.Init(0.0e0) ;
2460
2461
2462 for (step = 0; step <= curDeg; step++) {
2463
2464 // Compute the bspline of rank step.
2465
2466 // if not the first time, decrement the multiplicities back
2467 if (step != 0) {
2468 for (i = 1; i <= nbwknots; i++)
2469 wmults(i)--;
2470 }
2471
2472 // Poles are the current poles
2473 // but the poles congruent to step are duplicated.
2474
2475 Standard_Integer offset = 0;
2476
2477 for (i = 0; i < nbp; i++) {
2478 offset++;
2479
2480 for (k = 0; k < Dimension; k++) {
2481 tempc1((offset-1)*Dimension+k+1) =
2482 wpoles(NewPoles.Lower()+i*Dimension+k);
2483 }
2484 if (i % (curDeg+1) == step) {
2485 offset++;
2486
2487 for (k = 0; k < Dimension; k++) {
2488 tempc1((offset-1)*Dimension+k+1) =
2489 wpoles(NewPoles.Lower()+i*Dimension+k);
2490 }
2491 }
2492 }
2493
2494 // Knots multiplicities are increased
2495 // For each knot where the sum of multiplicities is congruent to step
2496
2497 Standard_Integer stepmult = step+1;
2498 Standard_Integer nbknots = 0;
2499 Standard_Integer smult = 0;
2500
2501 for (k = 1; k <= nbwknots; k++) {
2502 smult += wmults(k);
2503 if (smult >= stepmult) {
2504 // this knot is increased
2505 stepmult += curDeg+1;
2506 wmults(k)++;
2507 }
2508 else {
2509 // this knot is inserted
2510 nbknots++;
2511 iknots(nbknots) = wknots(k);
2512 }
2513 }
2514
2515 // the curve is obtained by inserting the knots
2516 // to raise the multiplicities
2517
2518 // we build "slices" of the arrays to set the correct size
2519 if (nbknots > 0) {
2520 TColStd_Array1OfReal aknots(iknots(1),1,nbknots);
2521 TColStd_Array1OfReal curve (tempc1(1),1,offset * Dimension);
2522 TColStd_Array1OfReal ncurve(tempc2(1),1,nbwp * Dimension);
2523// InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
2524// aknots,NoMults(),ncurve,nknots,wmults,Epsilon(1.));
2525
2526 InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
2527 aknots,NoMults(),ncurve,nknots,wmults,0.0);
2528
2529 // add to the average
2530
2531 for (i = 1; i <= nbwp * Dimension; i++)
2532 nwpoles(i) += ncurve(i);
2533 }
2534 else {
2535 // add to the average
2536
2537 for (i = 1; i <= nbwp * Dimension; i++)
2538 nwpoles(i) += tempc1(i);
2539 }
2540 }
2541
2542 // The result is the average
2543
2544 for (i = 1; i <= nbwp * Dimension; i++) {
2545 wpoles(i) = nwpoles(i) / (curDeg+1);
2546 }
2547 }
2548
2549 //-----------------
2550 // Copy the results
2551 //-----------------
2552
2553 // index in new knots of the first knot of the curve
2554 if (Periodic)
2555 firstknot = Mults.Upper() - l + 1;
2556 else
2557 firstknot = f;
2558
2559 // the new curve starts at index firstknot
2560 // so we must remove knots until the sum of multiplicities
2561 // from the first to the start is NewDegree+1
2562
2563 // m is the current sum of multiplicities
2564 m = 0;
2565
2566 for (k = 1; k <= firstknot; k++)
2567 m += wmults(k);
2568
2569 // compute the new first knot (k), pf will be the index of the first pole
2570 k = 1;
2571 pf = 0;
2572
2573 while (m > NewDegree+1) {
2574 k++;
2575 m -= wmults(k);
2576 pf += wmults(k);
2577 }
2578 if (m < NewDegree+1) {
2579 k--;
2580 wmults(k) += m - NewDegree - 1;
2581 pf += m - NewDegree - 1;
2582 }
2583
2584 // on a periodic curve the knots start with firstknot
2585 if (Periodic)
2586 k = firstknot;
2587
2588 // copy knots
2589
2590 for (i = NewKnots.Lower(); i <= NewKnots.Upper(); i++) {
2591 NewKnots(i) = wknots(k);
2592 NewMults(i) = wmults(k);
2593 k++;
2594 }
2595
2596 // copy poles
2597 pf *= Dimension;
2598
2599 for (i = NewPoles.Lower(); i <= NewPoles.Upper(); i++) {
2600 pf++;
2601 NewPoles(i) = wpoles(pf);
2602 }
2603}
2604
2605//=======================================================================
2606//function : PrepareUnperiodize
2607//purpose :
2608//=======================================================================
2609
2610void BSplCLib::PrepareUnperiodize
2611(const Standard_Integer Degree,
2612 const TColStd_Array1OfInteger& Mults,
2613 Standard_Integer& NbKnots,
2614 Standard_Integer& NbPoles)
2615{
2616 Standard_Integer i;
2617 // initialize NbKnots and NbPoles
2618 NbKnots = Mults.Length();
2619 NbPoles = - Degree - 1;
2620
2621 for (i = Mults.Lower(); i <= Mults.Upper(); i++)
2622 NbPoles += Mults(i);
2623
2624 Standard_Integer sigma, k;
2625 // Add knots at the beginning of the curve to raise Multiplicities
2626 // to Degre + 1;
2627 sigma = Mults(Mults.Lower());
2628 k = Mults.Upper() - 1;
2629
2630 while ( sigma < Degree + 1) {
2631 sigma += Mults(k);
2632 NbPoles += Mults(k);
2633 k--;
2634 NbKnots++;
2635 }
2636 // We must add exactly until Degree + 1 ->
2637 // Supress the excedent.
2638 if ( sigma > Degree + 1)
2639 NbPoles -= sigma - Degree - 1;
2640
2641 // Add knots at the end of the curve to raise Multiplicities
2642 // to Degre + 1;
2643 sigma = Mults(Mults.Upper());
2644 k = Mults.Lower() + 1;
2645
2646 while ( sigma < Degree + 1) {
2647 sigma += Mults(k);
2648 NbPoles += Mults(k);
2649 k++;
2650 NbKnots++;
2651 }
2652 // We must add exactly until Degree + 1 ->
2653 // Supress the excedent.
2654 if ( sigma > Degree + 1)
2655 NbPoles -= sigma - Degree - 1;
2656}
2657
2658//=======================================================================
2659//function : Unperiodize
2660//purpose :
2661//=======================================================================
2662
2663void BSplCLib::Unperiodize
2664(const Standard_Integer Degree,
2665 const Standard_Integer , // Dimension,
2666 const TColStd_Array1OfInteger& Mults,
2667 const TColStd_Array1OfReal& Knots,
2668 const TColStd_Array1OfReal& Poles,
2669 TColStd_Array1OfInteger& NewMults,
2670 TColStd_Array1OfReal& NewKnots,
2671 TColStd_Array1OfReal& NewPoles)
2672{
2673 Standard_Integer sigma, k, index = 0;
2674 // evaluation of index : number of knots to insert before knot(1) to
2675 // raise sum of multiplicities to <Degree + 1>
2676 sigma = Mults(Mults.Lower());
2677 k = Mults.Upper() - 1;
2678
2679 while ( sigma < Degree + 1) {
2680 sigma += Mults(k);
2681 k--;
2682 index++;
2683 }
2684
2685 Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
2686
2687 // set the 'interior' knots;
2688
2689 for ( k = 1; k <= Knots.Length(); k++) {
2690 NewKnots ( k + index ) = Knots( k);
2691 NewMults ( k + index ) = Mults( k);
2692 }
2693
2694 // set the 'starting' knots;
2695
2696 for ( k = 1; k <= index; k++) {
2697 NewKnots( k) = NewKnots( k + Knots.Length() - 1) - period;
2698 NewMults( k) = NewMults( k + Knots.Length() - 1);
2699 }
2700 NewMults( 1) -= sigma - Degree -1;
2701
2702 // set the 'ending' knots;
2703 sigma = NewMults( index + Knots.Length() );
2704
2705 for ( k = Knots.Length() + index + 1; k <= NewKnots.Length(); k++) {
2706 NewKnots( k) = NewKnots( k - Knots.Length() + 1) + period;
2707 NewMults( k) = NewMults( k - Knots.Length() + 1);
2708 sigma += NewMults( k - Knots.Length() + 1);
2709 }
2710 NewMults(NewMults.Length()) -= sigma - Degree - 1;
2711
2712 for ( k = 1 ; k <= NewPoles.Length(); k++) {
2713 NewPoles(k ) = Poles( (k-1) % Poles.Length() + 1);
2714 }
2715}
2716
2717//=======================================================================
2718//function : PrepareTrimming
2719//purpose :
2720//=======================================================================
2721
2722void BSplCLib::PrepareTrimming(const Standard_Integer Degree,
2723 const Standard_Boolean Periodic,
2724 const TColStd_Array1OfReal& Knots,
2725 const TColStd_Array1OfInteger& Mults,
2726 const Standard_Real U1,
2727 const Standard_Real U2,
2728 Standard_Integer& NbKnots,
2729 Standard_Integer& NbPoles)
2730{
2731 Standard_Integer i;
2732 Standard_Real NewU1, NewU2;
2733 Standard_Integer index1 = 0, index2 = 0;
2734
2735 // Eval index1, index2 : position of U1 and U2 in the Array Knots
2736 // such as Knots(index1-1) <= U1 < Knots(index1)
2737 // Knots(index2-1) <= U2 < Knots(index2)
2738 LocateParameter( Degree, Knots, Mults, U1, Periodic,
2739 Knots.Lower(), Knots.Upper(), index1, NewU1);
2740 LocateParameter( Degree, Knots, Mults, U2, Periodic,
2741 Knots.Lower(), Knots.Upper(), index2, NewU2);
2742 index1++;
2743 if ( Abs(Knots(index2) - U2) <= Epsilon( U1))
2744 index2--;
2745
2746 // eval NbKnots:
2747 NbKnots = index2 - index1 + 3;
2748
2749 // eval NbPoles:
2750 NbPoles = Degree + 1;
2751
2752 for ( i = index1; i <= index2; i++)
2753 NbPoles += Mults(i);
2754}
2755
2756//=======================================================================
2757//function : Trimming
2758//purpose :
2759//=======================================================================
2760
2761void BSplCLib::Trimming(const Standard_Integer Degree,
2762 const Standard_Boolean Periodic,
2763 const Standard_Integer Dimension,
2764 const TColStd_Array1OfReal& Knots,
2765 const TColStd_Array1OfInteger& Mults,
2766 const TColStd_Array1OfReal& Poles,
2767 const Standard_Real U1,
2768 const Standard_Real U2,
2769 TColStd_Array1OfReal& NewKnots,
2770 TColStd_Array1OfInteger& NewMults,
2771 TColStd_Array1OfReal& NewPoles)
2772{
2773 Standard_Integer i, nbpoles, nbknots;
2774 Standard_Real kk[2];
2775 Standard_Integer mm[2];
2776 TColStd_Array1OfReal K( kk[0], 1, 2 );
2777 TColStd_Array1OfInteger M( mm[0], 1, 2 );
2778
2779 K(1) = U1; K(2) = U2;
2780 mm[0] = mm[1] = Degree;
2781 if (!PrepareInsertKnots( Degree, Periodic, Knots, Mults, K, M,
2782 nbpoles, nbknots, Epsilon( U1), 0))
2783 Standard_OutOfRange::Raise();
2784
2785 TColStd_Array1OfReal TempPoles(1, nbpoles*Dimension);
2786 TColStd_Array1OfReal TempKnots(1, nbknots);
2787 TColStd_Array1OfInteger TempMults(1, nbknots);
2788
2789//
2790// do not allow the multiplicities to Add : they must be less than Degree
2791//
2792 InsertKnots(Degree, Periodic, Dimension, Poles, Knots, Mults,
2793 K, M, TempPoles, TempKnots, TempMults, Epsilon(U1),
2794 Standard_False);
2795
2796 // find in TempPoles the index of the pole corresponding to U1
2797 Standard_Integer Kindex = 0, Pindex;
2798 Standard_Real NewU1;
2799 LocateParameter( Degree, TempKnots, TempMults, U1, Periodic,
2800 TempKnots.Lower(), TempKnots.Upper(), Kindex, NewU1);
2801 Pindex = PoleIndex ( Degree, Kindex, Periodic, TempMults);
2802 Pindex *= Dimension;
2803
2804 for ( i = 1; i <= NewPoles.Length(); i++) NewPoles(i) = TempPoles(Pindex + i);
2805
2806 for ( i = 1; i <= NewKnots.Length(); i++) {
2807 NewKnots(i) = TempKnots( Kindex+i-1);
2808 NewMults(i) = TempMults( Kindex+i-1);
2809 }
2810 NewMults(1) = Min(Degree, NewMults(1)) + 1 ;
2811 NewMults(NewMults.Length())= Min(Degree, NewMults(NewMults.Length())) + 1 ;
2812}
2813
2814//=======================================================================
2815//function : Solves a LU factored Matrix
2816//purpose :
2817//=======================================================================
2818
2819Standard_Integer
2820BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
2821 const Standard_Integer UpperBandWidth,
2822 const Standard_Integer LowerBandWidth,
2823 const Standard_Integer ArrayDimension,
2824 Standard_Real& Array)
2825{
2826 Standard_Integer ii,
2827 jj,
2828 kk,
2829 MinIndex,
2830 MaxIndex,
2831 ReturnCode = 0 ;
2832
2833 Standard_Real *PolesArray = &Array ;
2834 Standard_Real Inverse ;
2835
2836
2837 if (Matrix.LowerCol() != 1 ||
2838 Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
2839 ReturnCode = 1 ;
2840 goto FINISH ;
2841 }
2842
2843 for (ii = Matrix.LowerRow() + 1; ii <= Matrix.UpperRow() ; ii++) {
2844 MinIndex = (ii - LowerBandWidth >= Matrix.LowerRow() ?
2845 ii - LowerBandWidth : Matrix.LowerRow()) ;
2846
2847 for ( jj = MinIndex ; jj < ii ; jj++) {
2848
2849 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2850 PolesArray[(ii-1) * ArrayDimension + kk] +=
2851 PolesArray[(jj-1) * ArrayDimension + kk] * Matrix(ii, jj - ii + LowerBandWidth + 1) ;
2852 }
2853 }
2854 }
2855
2856 for (ii = Matrix.UpperRow() ; ii >= Matrix.LowerRow() ; ii--) {
2857 MaxIndex = (ii + UpperBandWidth <= Matrix.UpperRow() ?
2858 ii + UpperBandWidth : Matrix.UpperRow()) ;
2859
2860 for (jj = MaxIndex ; jj > ii ; jj--) {
2861
2862 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2863 PolesArray[(ii-1) * ArrayDimension + kk] -=
2864 PolesArray[(jj - 1) * ArrayDimension + kk] *
2865 Matrix(ii, jj - ii + LowerBandWidth + 1) ;
2866 }
2867 }
2868
2869 //fixing a bug PRO18577 to avoid divizion by zero
2870
2871 Standard_Real divizor = Matrix(ii,LowerBandWidth + 1) ;
2872 Standard_Real Toler = 1.0e-16;
2873 if ( Abs(divizor) > Toler )
2874 Inverse = 1.0e0 / divizor ;
2875 else {
2876 Inverse = 1.0e0;
2877// cout << " BSplCLib::SolveBandedSystem() : zero determinant " << endl;
2878 ReturnCode = 1;
2879 goto FINISH;
2880 }
2881
2882 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2883 PolesArray[(ii-1) * ArrayDimension + kk] *= Inverse ;
2884 }
2885 }
2886 FINISH :
2887 return (ReturnCode) ;
2888}
2889
2890//=======================================================================
2891//function : Solves a LU factored Matrix
2892//purpose :
2893//=======================================================================
2894
2895Standard_Integer
2896BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
2897 const Standard_Integer UpperBandWidth,
2898 const Standard_Integer LowerBandWidth,
2899 const Standard_Boolean HomogeneousFlag,
2900 const Standard_Integer ArrayDimension,
2901 Standard_Real& Poles,
2902 Standard_Real& Weights)
2903{
2904 Standard_Integer ii,
2905 kk,
2906 ErrorCode = 0,
2907 ReturnCode = 0 ;
2908
2909 Standard_Real Inverse,
2910 *PolesArray = &Poles,
2911 *WeightsArray = &Weights ;
2912
2913 if (Matrix.LowerCol() != 1 ||
2914 Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
2915 ReturnCode = 1 ;
2916 goto FINISH ;
2917 }
2918 if (HomogeneousFlag == Standard_False) {
2919
2920 for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1; ii++) {
2921
2922 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2923 PolesArray[ii * ArrayDimension + kk] *=
2924 WeightsArray[ii] ;
2925 }
2926 }
2927 }
2928 ErrorCode =
2929 BSplCLib::SolveBandedSystem(Matrix,
2930 UpperBandWidth,
2931 LowerBandWidth,
2932 ArrayDimension,
2933 Poles) ;
2934 if (ErrorCode != 0) {
2935 ReturnCode = 2 ;
2936 goto FINISH ;
2937 }
2938 ErrorCode =
2939 BSplCLib::SolveBandedSystem(Matrix,
2940 UpperBandWidth,
2941 LowerBandWidth,
2942 1,
2943 Weights) ;
2944 if (ErrorCode != 0) {
2945 ReturnCode = 3 ;
2946 goto FINISH ;
2947 }
2948 if (HomogeneousFlag == Standard_False) {
2949
2950 for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1 ; ii++) {
2951 Inverse = 1.0e0 / WeightsArray[ii] ;
2952
2953 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2954 PolesArray[ii * ArrayDimension + kk] *= Inverse ;
2955 }
2956 }
2957 }
2958 FINISH : return (ReturnCode) ;
2959}
2960
2961//=======================================================================
2962//function : BuildSchoenbergPoints
2963//purpose :
2964//=======================================================================
2965
2966void BSplCLib::BuildSchoenbergPoints(const Standard_Integer Degree,
2967 const TColStd_Array1OfReal& FlatKnots,
2968 TColStd_Array1OfReal& Parameters)
2969{
2970 Standard_Integer ii,
2971 jj ;
2972 Standard_Real Inverse ;
2973 Inverse = 1.0e0 / (Standard_Real)Degree ;
2974
2975 for (ii = Parameters.Lower() ; ii <= Parameters.Upper() ; ii++) {
2976 Parameters(ii) = 0.0e0 ;
2977
2978 for (jj = 1 ; jj <= Degree ; jj++) {
2979 Parameters(ii) += FlatKnots(jj + ii) ;
2980 }
2981 Parameters(ii) *= Inverse ;
2982 }
2983}
2984
2985//=======================================================================
2986//function : Interpolate
2987//purpose :
2988//=======================================================================
2989
2990void BSplCLib::Interpolate(const Standard_Integer Degree,
2991 const TColStd_Array1OfReal& FlatKnots,
2992 const TColStd_Array1OfReal& Parameters,
2993 const TColStd_Array1OfInteger& ContactOrderArray,
2994 const Standard_Integer ArrayDimension,
2995 Standard_Real& Poles,
2996 Standard_Integer& InversionProblem)
2997{
2998 Standard_Integer ErrorCode,
2999 UpperBandWidth,
3000 LowerBandWidth ;
3001// Standard_Real *PolesArray = &Poles ;
3002 math_Matrix InterpolationMatrix(1, Parameters.Length(),
3003 1, 2 * Degree + 1) ;
3004 ErrorCode =
3005 BSplCLib::BuildBSpMatrix(Parameters,
3006 ContactOrderArray,
3007 FlatKnots,
3008 Degree,
3009 InterpolationMatrix,
3010 UpperBandWidth,
3011 LowerBandWidth) ;
3012 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3013
3014 ErrorCode =
3015 BSplCLib::FactorBandedMatrix(InterpolationMatrix,
3016 UpperBandWidth,
3017 LowerBandWidth,
3018 InversionProblem) ;
3019 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3020
3021 ErrorCode =
3022 BSplCLib::SolveBandedSystem(InterpolationMatrix,
3023 UpperBandWidth,
3024 LowerBandWidth,
3025 ArrayDimension,
3026 Poles) ;
3027
3028 Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
3029}
3030
3031//=======================================================================
3032//function : Interpolate
3033//purpose :
3034//=======================================================================
3035
3036void BSplCLib::Interpolate(const Standard_Integer Degree,
3037 const TColStd_Array1OfReal& FlatKnots,
3038 const TColStd_Array1OfReal& Parameters,
3039 const TColStd_Array1OfInteger& ContactOrderArray,
3040 const Standard_Integer ArrayDimension,
3041 Standard_Real& Poles,
3042 Standard_Real& Weights,
3043 Standard_Integer& InversionProblem)
3044{
3045 Standard_Integer ErrorCode,
3046 UpperBandWidth,
3047 LowerBandWidth ;
3048
3049 math_Matrix InterpolationMatrix(1, Parameters.Length(),
3050 1, 2 * Degree + 1) ;
3051 ErrorCode =
3052 BSplCLib::BuildBSpMatrix(Parameters,
3053 ContactOrderArray,
3054 FlatKnots,
3055 Degree,
3056 InterpolationMatrix,
3057 UpperBandWidth,
3058 LowerBandWidth) ;
3059 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3060
3061 ErrorCode =
3062 BSplCLib::FactorBandedMatrix(InterpolationMatrix,
3063 UpperBandWidth,
3064 LowerBandWidth,
3065 InversionProblem) ;
3066 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3067
3068 ErrorCode =
3069 BSplCLib::SolveBandedSystem(InterpolationMatrix,
3070 UpperBandWidth,
3071 LowerBandWidth,
3072 Standard_False,
3073 ArrayDimension,
3074 Poles,
3075 Weights) ;
3076
3077 Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
3078}
3079
3080//=======================================================================
3081//function : Evaluates a Bspline function : uses the ExtrapMode
3082//purpose : the function is extrapolated using the Taylor expansion
3083// of degree ExtrapMode[0] to the left and the Taylor
3084// expansion of degree ExtrapMode[1] to the right
3085// this evaluates the numerator by multiplying by the weights
3086// and evaluating it but does not call RationalDerivatives after
3087//=======================================================================
3088
3089void BSplCLib::Eval
3090(const Standard_Real Parameter,
3091 const Standard_Boolean PeriodicFlag,
3092 const Standard_Integer DerivativeRequest,
3093 Standard_Integer& ExtrapMode,
3094 const Standard_Integer Degree,
3095 const TColStd_Array1OfReal& FlatKnots,
3096 const Standard_Integer ArrayDimension,
3097 Standard_Real& Poles,
3098 Standard_Real& Weights,
3099 Standard_Real& PolesResults,
3100 Standard_Real& WeightsResults)
3101{
3102 Standard_Integer ii,
3103 jj,
3104 kk=0,
3105 Index,
3106 Index1,
3107 Index2,
3108 *ExtrapModeArray,
3109 Modulus,
3110 NewRequest,
3111 ExtrapolatingFlag[2],
3112 ErrorCode,
7fd59977 3113 Order = Degree + 1,
3114 FirstNonZeroBsplineIndex,
3115 LocalRequest = DerivativeRequest ;
3116 Standard_Real *PResultArray,
3117 *WResultArray,
3118 *PolesArray,
3119 *WeightsArray,
3120 LocalParameter,
3121 Period,
3122 Inverse,
3123 Delta ;
3124 PolesArray = &Poles ;
3125 WeightsArray = &Weights ;
3126 ExtrapModeArray = &ExtrapMode ;
3127 PResultArray = &PolesResults ;
3128 WResultArray = &WeightsResults ;
3129 LocalParameter = Parameter ;
3130 ExtrapolatingFlag[0] =
3131 ExtrapolatingFlag[1] = 0 ;
3132 //
3133 // check if we are extrapolating to a degree which is smaller than
3134 // the degree of the Bspline
3135 //
3136 if (PeriodicFlag) {
3137 Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
3138
3139 while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
3140 LocalParameter -= Period ;
3141 }
3142
3143 while (LocalParameter < FlatKnots(2)) {
3144 LocalParameter += Period ;
3145 }
3146 }
3147 if (Parameter < FlatKnots(2) &&
3148 LocalRequest < ExtrapModeArray[0] &&
3149 ExtrapModeArray[0] < Degree) {
3150 LocalRequest = ExtrapModeArray[0] ;
3151 LocalParameter = FlatKnots(2) ;
3152 ExtrapolatingFlag[0] = 1 ;
3153 }
3154 if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
3155 LocalRequest < ExtrapModeArray[1] &&
3156 ExtrapModeArray[1] < Degree) {
3157 LocalRequest = ExtrapModeArray[1] ;
3158 LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
3159 ExtrapolatingFlag[1] = 1 ;
3160 }
3161 Delta = Parameter - LocalParameter ;
3162 if (LocalRequest >= Order) {
3163 LocalRequest = Degree ;
3164 }
3165 if (PeriodicFlag) {
3166 Modulus = FlatKnots.Length() - Degree -1 ;
3167 }
3168 else {
3169 Modulus = FlatKnots.Length() - Degree ;
3170 }
3171
3172 BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
3173 ErrorCode =
3174 BSplCLib::EvalBsplineBasis(1,
3175 LocalRequest,
3176 Order,
3177 FlatKnots,
3178 LocalParameter,
3179 FirstNonZeroBsplineIndex,
3180 BsplineBasis) ;
3181 if (ErrorCode != 0) {
7fd59977 3182 goto FINISH ;
3183 }
3184 if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
3185 Index = 0 ;
3186 Index2 = 0 ;
3187
3188 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3189 Index1 = FirstNonZeroBsplineIndex ;
3190
3191 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3192 PResultArray[Index + kk] = 0.0e0 ;
3193 }
3194 WResultArray[Index] = 0.0e0 ;
3195
3196 for (jj = 1 ; jj <= Order ; jj++) {
3197
3198 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3199 PResultArray[Index + kk] +=
3200 PolesArray[(Index1-1) * ArrayDimension + kk]
3201 * WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3202 }
3203 WResultArray[Index2] += WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3204
3205 Index1 = Index1 % Modulus ;
3206 Index1 += 1 ;
3207 }
3208 Index += ArrayDimension ;
3209 Index2 += 1 ;
3210 }
3211 }
3212 else {
3213 //
3214 // store Taylor expansion in LocalRealArray
3215 //
3216 NewRequest = DerivativeRequest ;
3217 if (NewRequest > Degree) {
3218 NewRequest = Degree ;
3219 }
f7b4312f 3220 NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
7fd59977 3221 Index = 0 ;
3222 Inverse = 1.0e0 ;
3223
3224 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3225 Index1 = FirstNonZeroBsplineIndex ;
3226
3227 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3228 LocalRealArray[Index + kk] = 0.0e0 ;
3229 }
3230
3231 for (jj = 1 ; jj <= Order ; jj++) {
3232
3233 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3234 LocalRealArray[Index + kk] +=
3235 PolesArray[(Index1-1)*ArrayDimension + kk] *
3236 WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3237 }
3238 Index1 = Index1 % Modulus ;
3239 Index1 += 1 ;
3240 }
3241
3242 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3243 LocalRealArray[Index + kk] *= Inverse ;
3244 }
3245 Index += ArrayDimension ;
3246 Inverse /= (Standard_Real) ii ;
3247 }
3248 PLib::EvalPolynomial(Delta,
3249 NewRequest,
3250 Degree,
3251 ArrayDimension,
3252 LocalRealArray[0],
3253 PolesResults) ;
3254 Index = 0 ;
3255 Inverse = 1.0e0 ;
3256
3257 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3258 Index1 = FirstNonZeroBsplineIndex ;
3259 LocalRealArray[Index] = 0.0e0 ;
3260
3261 for (jj = 1 ; jj <= Order ; jj++) {
3262 LocalRealArray[Index] +=
3263 WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3264 Index1 = Index1 % Modulus ;
3265 Index1 += 1 ;
3266 }
3267 LocalRealArray[Index + kk] *= Inverse ;
3268 Index += 1 ;
3269 Inverse /= (Standard_Real) ii ;
3270 }
3271 PLib::EvalPolynomial(Delta,
3272 NewRequest,
3273 Degree,
3274 1,
3275 LocalRealArray[0],
3276 WeightsResults) ;
3277 }
3278 FINISH : ;
3279}
3280
3281//=======================================================================
3282//function : Evaluates a Bspline function : uses the ExtrapMode
3283//purpose : the function is extrapolated using the Taylor expansion
3284// of degree ExtrapMode[0] to the left and the Taylor
3285// expansion of degree ExtrapMode[1] to the right
3286// WARNING : the array Results is supposed to have at least
3287// (DerivativeRequest + 1) * ArrayDimension slots and the
3288//
3289//=======================================================================
3290
3291void BSplCLib::Eval
3292(const Standard_Real Parameter,
3293 const Standard_Boolean PeriodicFlag,
3294 const Standard_Integer DerivativeRequest,
3295 Standard_Integer& ExtrapMode,
3296 const Standard_Integer Degree,
3297 const TColStd_Array1OfReal& FlatKnots,
3298 const Standard_Integer ArrayDimension,
3299 Standard_Real& Poles,
3300 Standard_Real& Results)
3301{
3302 Standard_Integer ii,
3303 jj,
3304 kk,
3305 Index,
3306 Index1,
3307 *ExtrapModeArray,
3308 Modulus,
3309 NewRequest,
3310 ExtrapolatingFlag[2],
3311 ErrorCode,
7fd59977 3312 Order = Degree + 1,
3313 FirstNonZeroBsplineIndex,
3314 LocalRequest = DerivativeRequest ;
3315
3316 Standard_Real *ResultArray,
3317 *PolesArray,
3318 LocalParameter,
3319 Period,
3320 Inverse,
3321 Delta ;
3322
3323 PolesArray = &Poles ;
3324 ExtrapModeArray = &ExtrapMode ;
3325 ResultArray = &Results ;
3326 LocalParameter = Parameter ;
3327 ExtrapolatingFlag[0] =
3328 ExtrapolatingFlag[1] = 0 ;
3329 //
3330 // check if we are extrapolating to a degree which is smaller than
3331 // the degree of the Bspline
3332 //
3333 if (PeriodicFlag) {
3334 Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
3335
3336 while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
3337 LocalParameter -= Period ;
3338 }
3339
3340 while (LocalParameter < FlatKnots(2)) {
3341 LocalParameter += Period ;
3342 }
3343 }
3344 if (Parameter < FlatKnots(2) &&
3345 LocalRequest < ExtrapModeArray[0] &&
3346 ExtrapModeArray[0] < Degree) {
3347 LocalRequest = ExtrapModeArray[0] ;
3348 LocalParameter = FlatKnots(2) ;
3349 ExtrapolatingFlag[0] = 1 ;
3350 }
3351 if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
3352 LocalRequest < ExtrapModeArray[1] &&
3353 ExtrapModeArray[1] < Degree) {
3354 LocalRequest = ExtrapModeArray[1] ;
3355 LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
3356 ExtrapolatingFlag[1] = 1 ;
3357 }
3358 Delta = Parameter - LocalParameter ;
3359 if (LocalRequest >= Order) {
3360 LocalRequest = Degree ;
3361 }
3362
3363 if (PeriodicFlag) {
3364 Modulus = FlatKnots.Length() - Degree -1 ;
3365 }
3366 else {
3367 Modulus = FlatKnots.Length() - Degree ;
3368 }
3369
3370 BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
3371
3372 ErrorCode =
3373 BSplCLib::EvalBsplineBasis(1,
3374 LocalRequest,
3375 Order,
3376 FlatKnots,
3377 LocalParameter,
3378 FirstNonZeroBsplineIndex,
3379 BsplineBasis);
3380 if (ErrorCode != 0) {
7fd59977 3381 goto FINISH ;
3382 }
3383 if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
3384 Index = 0 ;
3385
3386 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3387 Index1 = FirstNonZeroBsplineIndex ;
3388
3389 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3390 ResultArray[Index + kk] = 0.0e0 ;
3391 }
3392
3393 for (jj = 1 ; jj <= Order ; jj++) {
3394
3395 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3396 ResultArray[Index + kk] +=
3397 PolesArray[(Index1-1) * ArrayDimension + kk] * BsplineBasis(ii,jj) ;
3398 }
3399 Index1 = Index1 % Modulus ;
3400 Index1 += 1 ;
3401 }
3402 Index += ArrayDimension ;
3403 }
3404 }
3405 else {
3406 //
3407 // store Taylor expansion in LocalRealArray
3408 //
3409 NewRequest = DerivativeRequest ;
3410 if (NewRequest > Degree) {
3411 NewRequest = Degree ;
3412 }
f7b4312f 3413 NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
7fd59977 3414
3415 Index = 0 ;
3416 Inverse = 1.0e0 ;
3417
3418 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3419 Index1 = FirstNonZeroBsplineIndex ;
3420
3421 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3422 LocalRealArray[Index + kk] = 0.0e0 ;
3423 }
3424
3425 for (jj = 1 ; jj <= Order ; jj++) {
3426
3427 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3428 LocalRealArray[Index + kk] +=
3429 PolesArray[(Index1-1)*ArrayDimension + kk] * BsplineBasis(ii,jj) ;
3430 }
3431 Index1 = Index1 % Modulus ;
3432 Index1 += 1 ;
3433 }
3434
3435 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3436 LocalRealArray[Index + kk] *= Inverse ;
3437 }
3438 Index += ArrayDimension ;
3439 Inverse /= (Standard_Real) ii ;
3440 }
3441 PLib::EvalPolynomial(Delta,
3442 NewRequest,
3443 Degree,
3444 ArrayDimension,
3445 LocalRealArray[0],
3446 Results) ;
3447 }
3448 FINISH : ;
3449}
3450
3451//=======================================================================
3452//function : TangExtendToConstraint
3453//purpose : Extends a Bspline function using the tangency map
3454// WARNING :
3455//
3456//
3457//=======================================================================
3458
3459void BSplCLib::TangExtendToConstraint
3460(const TColStd_Array1OfReal& FlatKnots,
3461 const Standard_Real C1Coefficient,
3462 const Standard_Integer NumPoles,
3463 Standard_Real& Poles,
3464 const Standard_Integer CDimension,
3465 const Standard_Integer CDegree,
3466 const TColStd_Array1OfReal& ConstraintPoint,
3467 const Standard_Integer Continuity,
3468 const Standard_Boolean After,
3469 Standard_Integer& NbPolesResult,
3470 Standard_Integer& NbKnotsResult,
3471 Standard_Real& KnotsResult,
3472 Standard_Real& PolesResult)
3473{
3474#if DEB
3475 if (CDegree<Continuity+1) {
3476 cout<<"The BSpline degree must be greater than the order of continuity"<<endl;
3477 }
3478#endif
3479 Standard_Real * Padr = &Poles ;
3480 Standard_Real * KRadr = &KnotsResult ;
3481 Standard_Real * PRadr = &PolesResult ;
3482
3483////////////////////////////////////////////////////////////////////////
3484//
0d969553 3485// 1. calculation of extension nD
7fd59977 3486//
3487////////////////////////////////////////////////////////////////////////
3488
0d969553 3489// Hermite matrix
7fd59977 3490 Standard_Integer Csize = Continuity + 2;
3491 math_Matrix MatCoefs(1,Csize, 1,Csize);
3492 if (After) {
0d969553
Y
3493 PLib::HermiteCoefficients(0, 1, // Limits
3494 Continuity, 0, // Orders of constraints
7fd59977 3495 MatCoefs);
3496 }
3497 else {
0d969553
Y
3498 PLib::HermiteCoefficients(0, 1, // Limits
3499 0, Continuity, // Orders of constraints
7fd59977 3500 MatCoefs);
3501 }
3502
3503
0d969553 3504// position at the node of connection
7fd59977 3505 Standard_Real Tbord ;
3506 if (After) {
3507 Tbord = FlatKnots(FlatKnots.Upper()-CDegree);
3508 }
3509 else {
3510 Tbord = FlatKnots(FlatKnots.Lower()+CDegree);
3511 }
3512 Standard_Boolean periodic_flag = Standard_False ;
3513 Standard_Integer ipos, extrap_mode[2], derivative_request = Max(Continuity,1);
3514 extrap_mode[0] = extrap_mode[1] = CDegree;
3515 TColStd_Array1OfReal EvalBS(1, CDimension * (derivative_request+1)) ;
3516 Standard_Real * Eadr = (Standard_Real *) &EvalBS(1) ;
3517 BSplCLib::Eval(Tbord,periodic_flag,derivative_request,extrap_mode[0],
3518 CDegree,FlatKnots,CDimension,Poles,*Eadr);
3519
0d969553 3520// norm of the tangent at the node of connection
7fd59977 3521 math_Vector Tgte(1,CDimension);
3522
3523 for (ipos=1;ipos<=CDimension;ipos++) {
3524 Tgte(ipos) = EvalBS(ipos+CDimension);
3525 }
3526 Standard_Real L1=Tgte.Norm();
3527
3528
0d969553 3529// matrix of constraints
7fd59977 3530 math_Matrix Contraintes(1,Csize,1,CDimension);
3531 if (After) {
3532
3533 for (ipos=1;ipos<=CDimension;ipos++) {
3534 Contraintes(1,ipos) = EvalBS(ipos);
3535 Contraintes(2,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
3536 if(Continuity >= 2) Contraintes(3,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
3537 if(Continuity >= 3) Contraintes(4,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
3538 Contraintes(Continuity+2,ipos) = ConstraintPoint(ipos);
3539 }
3540 }
3541 else {
3542
3543 for (ipos=1;ipos<=CDimension;ipos++) {
3544 Contraintes(1,ipos) = ConstraintPoint(ipos);
3545 Contraintes(2,ipos) = EvalBS(ipos);
3546 if(Continuity >= 1) Contraintes(3,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
3547 if(Continuity >= 2) Contraintes(4,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
3548 if(Continuity >= 3) Contraintes(5,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
3549 }
3550 }
3551
0d969553 3552// calculate the coefficients of extension
7fd59977 3553 Standard_Integer ii, jj, kk;
3554 TColStd_Array1OfReal ExtraCoeffs(1,Csize*CDimension);
3555 ExtraCoeffs.Init(0.);
3556
3557 for (ii=1; ii<=Csize; ii++) {
3558
3559 for (jj=1; jj<=Csize; jj++) {
3560
3561 for (kk=1; kk<=CDimension; kk++) {
3562 ExtraCoeffs(kk+(jj-1)*CDimension) += MatCoefs(ii,jj)*Contraintes(ii,kk);
3563 }
3564 }
3565 }
3566
0d969553 3567// calculate the poles of extension
7fd59977 3568 TColStd_Array1OfReal ExtrapPoles(1,Csize*CDimension);
3569 Standard_Real * EPadr = &ExtrapPoles(1) ;
3570 PLib::CoefficientsPoles(CDimension,
3571 ExtraCoeffs, PLib::NoWeights(),
3572 ExtrapPoles, PLib::NoWeights());
3573
0d969553 3574// calculate the nodes of extension with multiplicities
7fd59977 3575 TColStd_Array1OfReal ExtrapNoeuds(1,2);
3576 ExtrapNoeuds(1) = 0.;
3577 ExtrapNoeuds(2) = 1.;
3578 TColStd_Array1OfInteger ExtrapMults(1,2);
3579 ExtrapMults(1) = Csize;
3580 ExtrapMults(2) = Csize;
3581
0d969553 3582// flat nodes of extension
7fd59977 3583 TColStd_Array1OfReal FK2(1, Csize*2);
3584 BSplCLib::KnotSequence(ExtrapNoeuds,ExtrapMults,FK2);
3585
0d969553 3586// norm of the tangent at the connection point
7fd59977 3587 if (After) {
3588 BSplCLib::Eval(0.,periodic_flag,1,extrap_mode[0],
3589 Csize-1,FK2,CDimension,*EPadr,*Eadr);
3590 }
3591 else {
3592 BSplCLib::Eval(1.,periodic_flag,1,extrap_mode[0],
3593 Csize-1,FK2,CDimension,*EPadr,*Eadr);
3594 }
3595
3596 for (ipos=1;ipos<=CDimension;ipos++) {
3597 Tgte(ipos) = EvalBS(ipos+CDimension);
3598 }
3599 Standard_Real L2 = Tgte.Norm();
3600
0d969553 3601// harmonisation of degrees
7fd59977 3602 TColStd_Array1OfReal NewP2(1, (CDegree+1)*CDimension);
3603 TColStd_Array1OfReal NewK2(1, 2);
3604 TColStd_Array1OfInteger NewM2(1, 2);
3605 if (Csize-1<CDegree) {
3606 BSplCLib::IncreaseDegree(Csize-1,CDegree,Standard_False,CDimension,
3607 ExtrapPoles,ExtrapNoeuds,ExtrapMults,
3608 NewP2,NewK2,NewM2);
3609 }
3610 else {
3611 NewP2 = ExtrapPoles;
3612 NewK2 = ExtrapNoeuds;
3613 NewM2 = ExtrapMults;
3614 }
3615
0d969553 3616// flat nodes of extension after harmonization of degrees
7fd59977 3617 TColStd_Array1OfReal NewFK2(1, (CDegree+1)*2);
3618 BSplCLib::KnotSequence(NewK2,NewM2,NewFK2);
3619
3620
3621////////////////////////////////////////////////////////////////////////
3622//
3623// 2. concatenation C0
3624//
3625////////////////////////////////////////////////////////////////////////
3626
0d969553 3627// ratio of reparametrization
7fd59977 3628 Standard_Real Ratio=1, Delta;
3629 if ( (L1 > Precision::Confusion()) && (L2 > Precision::Confusion()) ) {
3630 Ratio = L2 / L1;
3631 }
3632 if ( (Ratio < 1.e-5) || (Ratio > 1.e5) ) Ratio = 1;
3633
3634 if (After) {
0d969553 3635// do not touch the first BSpline
7fd59977 3636 Delta = Ratio*NewFK2(NewFK2.Lower()) - FlatKnots(FlatKnots.Upper());
3637 }
3638 else {
0d969553 3639// do not touch the second BSpline
7fd59977 3640 Delta = Ratio*NewFK2(NewFK2.Upper()) - FlatKnots(FlatKnots.Lower());
3641 }
3642
0d969553 3643// result of the concatenation
7fd59977 3644 Standard_Integer NbP1 = NumPoles, NbP2 = CDegree+1;
3645 Standard_Integer NbK1 = FlatKnots.Length(), NbK2 = 2*(CDegree+1);
3646 TColStd_Array1OfReal NewPoles (1, (NbP1+ NbP2-1)*CDimension);
3647 TColStd_Array1OfReal NewFlats (1, NbK1+NbK2-CDegree-2);
3648
0d969553 3649// poles
7fd59977 3650 Standard_Integer indNP, indP, indEP;
3651 if (After) {
3652
3653 for (ii=1; ii<=NbP1+NbP2-1; ii++) {
3654
3655 for (jj=1; jj<=CDimension; jj++) {
3656 indNP = (ii-1)*CDimension+jj;
3657 indP = (ii-1)*CDimension+jj-1;
3658 indEP = (ii-NbP1)*CDimension+jj;
3659 if (ii<NbP1) NewPoles(indNP) = Padr[indP];
3660 else NewPoles(indNP) = NewP2(indEP);
3661 }
3662 }
3663 }
3664 else {
3665
3666 for (ii=1; ii<=NbP1+NbP2-1; ii++) {
3667
3668 for (jj=1; jj<=CDimension; jj++) {
3669 indNP = (ii-1)*CDimension+jj;
3670 indEP = (ii-1)*CDimension+jj;
3671 indP = (ii-NbP2)*CDimension+jj-1;
3672 if (ii<NbP2) NewPoles(indNP) = NewP2(indEP);
3673 else NewPoles(indNP) = Padr[indP];
3674 }
3675 }
3676 }
3677
0d969553 3678// flat nodes
7fd59977 3679 if (After) {
0d969553 3680// start with the nodes of the initial surface
7fd59977 3681
3682 for (ii=1; ii<NbK1; ii++) {
3683 NewFlats(ii) = FlatKnots(FlatKnots.Lower()+ii-1);
3684 }
0d969553 3685// continue with the reparameterized nodes of the extension
7fd59977 3686
3687 for (ii=1; ii<=NbK2-CDegree-1; ii++) {
3688 NewFlats(NbK1+ii-1) = Ratio*NewFK2(NewFK2.Lower()+ii+CDegree) - Delta;
3689 }
3690 }
3691 else {
0d969553 3692// start with the reparameterized nodes of the extension
7fd59977 3693
3694 for (ii=1; ii<NbK2-CDegree; ii++) {
3695 NewFlats(ii) = Ratio*NewFK2(NewFK2.Lower()+ii-1) - Delta;
3696 }
0d969553 3697// continue with the nodes of the initial surface
7fd59977 3698
3699 for (ii=2; ii<=NbK1; ii++) {
3700 NewFlats(NbK2+ii-CDegree-2) = FlatKnots(FlatKnots.Lower()+ii-1);
3701 }
3702 }
3703
3704
3705////////////////////////////////////////////////////////////////////////
3706//
0d969553 3707// 3. reduction of multiplicite at the node of connection
7fd59977 3708//
3709////////////////////////////////////////////////////////////////////////
3710
0d969553 3711// number of separate nodes
7fd59977 3712 Standard_Integer KLength = 1;
3713
3714 for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
3715 if (NewFlats(ii) != NewFlats(ii-1)) KLength++;
3716 }
3717
0d969553 3718// flat nodes --> nodes + multiplicities
7fd59977 3719 TColStd_Array1OfReal NewKnots (1, KLength);
3720 TColStd_Array1OfInteger NewMults (1, KLength);
3721 NewMults.Init(1);
3722 jj = 1;
3723 NewKnots(jj) = NewFlats(1);
3724
3725 for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
3726 if (NewFlats(ii) == NewFlats(ii-1)) NewMults(jj)++;
3727 else {
3728 jj++;
3729 NewKnots(jj) = NewFlats(ii);
3730 }
3731 }
3732
0d969553 3733// reduction of multiplicity at the second or the last but one node
7fd59977 3734 Standard_Integer Index = 2, M = CDegree;
3735 if (After) Index = KLength-1;
3736 TColStd_Array1OfReal ResultPoles (1, (NbP1+ NbP2-1)*CDimension);
3737 TColStd_Array1OfReal ResultKnots (1, KLength);
3738 TColStd_Array1OfInteger ResultMults (1, KLength);
3739 Standard_Real Tol = 1.e-6;
3740 Standard_Boolean Ok = Standard_True;
3741
3742 while ( (M>CDegree-Continuity) && Ok) {
3743 Ok = RemoveKnot(Index, M-1, CDegree, Standard_False, CDimension,
3744 NewPoles, NewKnots, NewMults,
3745 ResultPoles, ResultKnots, ResultMults, Tol);
3746 if (Ok) M--;
3747 }
3748
3749 if (M == CDegree) {
0d969553 3750// number of poles of the concatenation
7fd59977 3751 NbPolesResult = NbP1 + NbP2 - 1;
0d969553 3752// the poles of the concatenation
7fd59977 3753 Standard_Integer PLength = NbPolesResult*CDimension;
3754
3755 for (jj=1; jj<=PLength; jj++) {
3756 PRadr[jj-1] = NewPoles(jj);
3757 }
3758
0d969553 3759// flat nodes of the concatenation
7fd59977 3760 Standard_Integer ideb = 0;
3761
3762 for (jj=0; jj<NewKnots.Length(); jj++) {
3763 for (ii=0; ii<NewMults(jj+1); ii++) {
3764 KRadr[ideb+ii] = NewKnots(jj+1);
3765 }
3766 ideb += NewMults(jj+1);
3767 }
3768 NbKnotsResult = ideb;
3769 }
3770
3771 else {
0d969553 3772// number of poles of the result
7fd59977 3773 NbPolesResult = NbP1 + NbP2 - 1 - CDegree + M;
0d969553 3774// the poles of the result
7fd59977 3775 Standard_Integer PLength = NbPolesResult*CDimension;
3776
3777 for (jj=0; jj<PLength; jj++) {
3778 PRadr[jj] = ResultPoles(jj+1);
3779 }
3780
0d969553 3781// flat nodes of the result
7fd59977 3782 Standard_Integer ideb = 0;
3783
3784 for (jj=0; jj<ResultKnots.Length(); jj++) {
3785 for (ii=0; ii<ResultMults(jj+1); ii++) {
3786 KRadr[ideb+ii] = ResultKnots(jj+1);
3787 }
3788 ideb += ResultMults(jj+1);
3789 }
3790 NbKnotsResult = ideb;
3791 }
3792}
3793
3794//=======================================================================
3795//function : Resolution
3796//purpose :
3797// d
0d969553 3798// Let C(t) = SUM Ci Bi(t) a Bspline curve of degree d
7fd59977 3799// i = 1,n
0d969553 3800// with nodes tj for j = 1,n+d+1
7fd59977 3801//
3802//
3803// ' C1 - Ci-1 d-1
0d969553 3804// Then C (t) = SUM d * --------- Bi (t)
7fd59977 3805// i = 2,n ti+d - ti
3806//
3807// d-1
0d969553 3808// for the base of BSpline Bi (t) of degree d-1.
7fd59977 3809//
0d969553 3810// Consequently the upper bound of the norm of the derivative from C is :
7fd59977 3811//
3812//
3813// | Ci - Ci-1 |
3814// d * Max | --------- |
3815// i = 2,n | ti+d - ti |
3816//
3817// N(t)
0d969553 3818// In the rational case set C(t) = -----
7fd59977 3819// D(t)
3820//
3821//
3822// D(t) = SUM Di Bi(t)
3823// i=1,n
3824//
3825// N(t) = SUM Di * Ci Bi(t)
3826// i =1,n
3827//
3828// N'(t) - D'(t) C(t)
3829// C'(t) = -----------------------
3830// D(t)
3831//
3832//
3833// N'(t) - D'(t) C(t) =
3834//
3835// Di * (Ci - C(t)) - Di-1 * (Ci-1 - C(t)) d-1
3836// SUM d * ---------------------------------------- * Bi (t) =
3837// i=2,n ti+d - ti
3838//
3839//
3840// Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj) d-1
3841// SUM SUM d * ----------------------------------- * Betaj(t) * Bi (t)
3842//i=2,n j=1,n ti+d - ti
3843//
3844//
3845//
3846// Dj Bj(t)
3847// Betaj(t) = --------
3848// D(t)
3849//
0d969553
Y
3850// Betaj(t) form a partition >= 0 of the entity with support
3851// tj, tj+d+1. Consequently if Rj = {j-d, ...., j+d+d+1}
3852// obtain an upper bound of the derivative of C by taking :
7fd59977 3853//
3854//
3855//
3856//
3857//
3858//
3859// Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj)
3860// Max Max d * -----------------------------------
3861// j=1,n i dans Rj ti+d - ti
3862//
3863// --------------------------------------------------------
3864//
3865// Min Di
3866// i =1,n
3867//
3868//
3869//=======================================================================
3870
3871void BSplCLib::Resolution( Standard_Real& Poles,
3872 const Standard_Integer ArrayDimension,
3873 const Standard_Integer NumPoles,
3874 const TColStd_Array1OfReal& Weights,
3875 const TColStd_Array1OfReal& FlatKnots,
3876 const Standard_Integer Degree,
3877 const Standard_Real Tolerance3D,
3878 Standard_Real& UTolerance)
3879{
3880 Standard_Integer ii,num_poles,ii_index,jj_index,ii_inDim;
3881 Standard_Integer lower,upper,ii_minus,jj,ii_miDim;
3882 Standard_Integer Deg1 = Degree + 1;
3883 Standard_Integer Deg2 = (Degree << 1) + 1;
3884 Standard_Real value,factor,W,min_weights,inverse;
3885 Standard_Real pa_ii_inDim_0, pa_ii_inDim_1, pa_ii_inDim_2, pa_ii_inDim_3;
3886 Standard_Real pa_ii_miDim_0, pa_ii_miDim_1, pa_ii_miDim_2, pa_ii_miDim_3;
3887 Standard_Real wg_ii_index, wg_ii_minus;
3888 Standard_Real *PA,max_derivative;
3889 const Standard_Real * FK = &FlatKnots(FlatKnots.Lower());
3890 PA = &Poles;
3891 max_derivative = 0.0e0;
3892 num_poles = FlatKnots.Length() - Deg1;
3893 switch (ArrayDimension) {
3894 case 2 : {
3895 if (&Weights != NULL) {
3896 const Standard_Real * WG = &Weights(Weights.Lower());
3897 min_weights = WG[0];
3898
3899 for (ii = 1 ; ii < NumPoles ; ii++) {
3900 W = WG[ii];
3901 if (W < min_weights) min_weights = W;
3902 }
3903
3904 for (ii = 1 ; ii < num_poles ; ii++) {
3905 ii_index = ii % NumPoles;
3906 ii_inDim = ii_index << 1;
3907 ii_minus = (ii - 1) % NumPoles;
3908 ii_miDim = ii_minus << 1;
3909 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
3910 pa_ii_inDim_1 = PA[ii_inDim];
3911 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
3912 pa_ii_miDim_1 = PA[ii_miDim];
3913 wg_ii_index = WG[ii_index];
3914 wg_ii_minus = WG[ii_minus];
3915 inverse = FK[ii + Degree] - FK[ii];
3916 inverse = 1.0e0 / inverse;
3917 lower = ii - Deg1;
3918 if (lower < 0) lower = 0;
3919 upper = Deg2 + ii;
3920 if (upper > num_poles) upper = num_poles;
3921
3922 for (jj = lower ; jj < upper ; jj++) {
3923 jj_index = jj % NumPoles;
3924 jj_index = jj_index << 1;
3925 value = 0.0e0;
3926 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
3927 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
3928 if (factor < 0) factor = - factor;
3929 value += factor; jj_index++;
3930 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
3931 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
3932