1 // Created on: 1991-08-09
3 // Copyright (c) 1991-1999 Matra Datavision
4 // Copyright (c) 1999-2014 OPEN CASCADE SAS
6 // This file is part of Open CASCADE Technology software library.
8 // This library is free software; you can redistribute it and/or modify it under
9 // the terms of the GNU Lesser General Public License version 2.1 as published
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.
14 // Alternatively, this file may be used under the terms of Open CASCADE
15 // commercial license or contractual agreement.
17 // Modified RLE 9 Sep 1993
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
30 #include <BSplCLib.ixx>
32 #include <NCollection_LocalArray.hxx>
33 #include <Precision.hxx>
34 #include <Standard_NotImplemented.hxx>
38 typedef TColgp_Array1OfPnt Array1OfPnt;
39 typedef TColStd_Array1OfReal Array1OfReal;
40 typedef TColStd_Array1OfInteger Array1OfInteger;
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 //=======================================================================
48 class BSplCLib_LocalMatrix : public math_Matrix
51 BSplCLib_LocalMatrix (Standard_Integer DerivativeRequest, Standard_Integer Order)
52 : math_Matrix (myBuffer, 1, DerivativeRequest + 1, 1, Order)
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");
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];
65 //=======================================================================
68 //=======================================================================
70 void BSplCLib::Hunt (const Array1OfReal& XX,
71 const Standard_Real X,
72 Standard_Integer& Ilc)
74 // replaced by simple dichotomy (RLE)
76 const Standard_Real *px = &XX(Ilc);
83 Standard_Integer Ihi = XX.Upper();
90 while (Ihi - Ilc != 1) {
91 Im = (Ihi + Ilc) >> 1;
92 if (X > px[Im]) Ilc = Im;
97 //=======================================================================
98 //function : FirstUKnotIndex
100 //=======================================================================
102 Standard_Integer BSplCLib::FirstUKnotIndex (const Standard_Integer Degree,
103 const TColStd_Array1OfInteger& Mults)
105 Standard_Integer Index = Mults.Lower();
106 Standard_Integer SigmaMult = Mults(Index);
108 while (SigmaMult <= Degree) {
110 SigmaMult += Mults (Index);
115 //=======================================================================
116 //function : LastUKnotIndex
118 //=======================================================================
120 Standard_Integer BSplCLib::LastUKnotIndex (const Standard_Integer Degree,
121 const Array1OfInteger& Mults)
123 Standard_Integer Index = Mults.Upper();
124 Standard_Integer SigmaMult = Mults(Index);
126 while (SigmaMult <= Degree) {
128 SigmaMult += Mults.Value (Index);
133 //=======================================================================
134 //function : FlatIndex
136 //=======================================================================
138 Standard_Integer BSplCLib::FlatIndex
139 (const Standard_Integer Degree,
140 const Standard_Integer Index,
141 const TColStd_Array1OfInteger& Mults,
142 const Standard_Boolean Periodic)
144 Standard_Integer i, index = Index;
145 const Standard_Integer MLower = Mults.Lower();
146 const Standard_Integer *pmu = &Mults(MLower);
149 for (i = MLower + 1; i <= Index; i++)
154 index += pmu[MLower] - 1;
158 //=======================================================================
159 //function : LocateParameter
160 //purpose : Processing of nodes with multiplicities
161 //pmn 28-01-97 -> compute eventual of the period.
162 //=======================================================================
164 void 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,
175 Standard_Real uf = 0, ul=1;
177 uf = Knots(Knots.Lower());
178 ul = Knots(Knots.Upper());
180 BSplCLib::LocateParameter(Knots,U,IsPeriodic,FromK1,ToK2,
181 KnotIndex,NewU, uf, ul);
184 //=======================================================================
185 //function : LocateParameter
186 //purpose : For plane nodes
187 // pmn 28-01-97 -> There is a need of the degre to calculate
188 // the eventual period
189 //=======================================================================
191 void 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,
202 BSplCLib::LocateParameter(Knots, U, IsPeriodic, FromK1, ToK2,
204 Knots(Knots.Lower() + Degree),
205 Knots(Knots.Upper() - Degree));
207 BSplCLib::LocateParameter(Knots, U, IsPeriodic, FromK1, ToK2,
213 //=======================================================================
214 //function : LocateParameter
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.
218 //=======================================================================
220 void 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,
228 const Standard_Real UFirst,
229 const Standard_Real ULast)
231 Standard_Integer First,Last;
240 Standard_Integer Last1 = Last - 1;
243 Standard_Real Period = ULast - UFirst;
245 while (NewU > ULast )
248 while (NewU < UFirst)
252 BSplCLib::Hunt (Knots, NewU, KnotIndex);
254 Standard_Real Eps = Epsilon(U);
256 if (Eps < 0) Eps = - Eps;
257 Standard_Integer KLower = Knots.Lower();
258 const Standard_Real *knots = &Knots(KLower);
260 if ( KnotIndex < Knots.Upper()) {
261 val = NewU - knots[KnotIndex + 1];
262 if (val < 0) val = - val;
263 // <= to be coherent with Segment where Eps corresponds to a bit of error.
264 if (val <= Eps) KnotIndex++;
266 if (KnotIndex < First) KnotIndex = First;
267 if (KnotIndex > Last1) KnotIndex = Last1;
269 if (KnotIndex != Last1) {
270 Standard_Real K1 = knots[KnotIndex];
271 Standard_Real K2 = knots[KnotIndex + 1];
273 if (val < 0) val = - val;
278 K2 = knots[KnotIndex + 1];
280 if (val < 0) val = - val;
285 //=======================================================================
286 //function : LocateParameter
287 //purpose : the index is recomputed only if out of range
288 //pmn 28-01-97 -> eventual computation of the period.
289 //=======================================================================
291 void 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,
300 Standard_Integer first,last;
303 first = Knots.Lower();
304 last = Knots.Upper();
307 first = FirstUKnotIndex(Degree,Mults);
308 last = LastUKnotIndex (Degree,Mults);
312 first = Knots.Lower() + Degree;
313 last = Knots.Upper() - Degree;
315 if ( KnotIndex < first || KnotIndex > last)
316 BSplCLib::LocateParameter(Knots, U, Periodic, first, last,
317 KnotIndex, NewU, Knots(first), Knots(last));
322 //=======================================================================
323 //function : MaxKnotMult
325 //=======================================================================
327 Standard_Integer BSplCLib::MaxKnotMult
328 (const Array1OfInteger& Mults,
329 const Standard_Integer FromK1,
330 const Standard_Integer ToK2)
332 Standard_Integer MLower = Mults.Lower();
333 const Standard_Integer *pmu = &Mults(MLower);
335 Standard_Integer MaxMult = pmu[FromK1];
337 for (Standard_Integer i = FromK1; i <= ToK2; i++) {
338 if (MaxMult < pmu[i]) MaxMult = pmu[i];
343 //=======================================================================
344 //function : MinKnotMult
346 //=======================================================================
348 Standard_Integer BSplCLib::MinKnotMult
349 (const Array1OfInteger& Mults,
350 const Standard_Integer FromK1,
351 const Standard_Integer ToK2)
353 Standard_Integer MLower = Mults.Lower();
354 const Standard_Integer *pmu = &Mults(MLower);
356 Standard_Integer MinMult = pmu[FromK1];
358 for (Standard_Integer i = FromK1; i <= ToK2; i++) {
359 if (MinMult > pmu[i]) MinMult = pmu[i];
364 //=======================================================================
367 //=======================================================================
369 Standard_Integer BSplCLib::NbPoles(const Standard_Integer Degree,
370 const Standard_Boolean Periodic,
371 const TColStd_Array1OfInteger& Mults)
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);
378 Standard_Integer Mf = pmu[f];
379 Standard_Integer Ml = pmu[l];
380 if (Mf <= 0) return 0;
381 if (Ml <= 0) return 0;
383 if (Mf > Degree) return 0;
384 if (Ml > Degree) return 0;
385 if (Mf != Ml ) return 0;
389 Standard_Integer Deg1 = Degree + 1;
390 if (Mf > Deg1) return 0;
391 if (Ml > Deg1) return 0;
392 sigma = Mf + Ml - Deg1;
395 for (i = f + 1; i < l; i++) {
396 if (pmu[i] <= 0 ) return 0;
397 if (pmu[i] > Degree) return 0;
403 //=======================================================================
404 //function : KnotSequenceLength
406 //=======================================================================
408 Standard_Integer BSplCLib::KnotSequenceLength
409 (const TColStd_Array1OfInteger& Mults,
410 const Standard_Integer Degree,
411 const Standard_Boolean Periodic)
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);
419 for (i = MLower; i <= MUpper; i++)
421 if (Periodic) l += 2 * (Degree + 1 - pmu[MLower]);
425 //=======================================================================
426 //function : KnotSequence
428 //=======================================================================
430 void BSplCLib::KnotSequence
431 (const TColStd_Array1OfReal& Knots,
432 const TColStd_Array1OfInteger& Mults,
433 TColStd_Array1OfReal& KnotSeq)
435 BSplCLib::KnotSequence(Knots,Mults,0,Standard_False,KnotSeq);
438 //=======================================================================
439 //function : KnotSequence
441 //=======================================================================
443 void 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)
451 Standard_Integer Mult;
452 Standard_Integer MLower = Mults.Lower();
453 const Standard_Integer * pmu = &Mults(MLower);
455 Standard_Integer KLower = Knots.Lower();
456 Standard_Integer KUpper = Knots.Upper();
457 const Standard_Real * pkn = &Knots(KLower);
459 Standard_Integer M1 = Degree + 1 - pmu[MLower]; // for periodic
460 Standard_Integer i,j,index = Periodic ? M1 + 1 : 1;
462 for (i = KLower; i <= KUpper; i++) {
466 for (j = 1; j <= Mult; j++) {
472 Standard_Real period = pkn[KUpper] - pkn[KLower];
477 for (i = M1; i >= 1; i--) {
478 KnotSeq(i) = pkn[j] - period;
488 for (i = index; i <= KnotSeq.Upper(); i++) {
489 KnotSeq(i) = pkn[j] + period;
499 //=======================================================================
500 //function : KnotsLength
502 //=======================================================================
503 Standard_Integer BSplCLib::KnotsLength(const TColStd_Array1OfReal& SeqKnots,
504 // const Standard_Boolean Periodic)
505 const Standard_Boolean )
507 Standard_Integer sizeMult = 1;
508 Standard_Real val = SeqKnots(1);
509 for (Standard_Integer jj=2;
510 jj<=SeqKnots.Length();jj++)
512 // test on strict equality on nodes
513 if (SeqKnots(jj)!=val)
522 //=======================================================================
525 //=======================================================================
526 void BSplCLib::Knots(const TColStd_Array1OfReal& SeqKnots,
527 TColStd_Array1OfReal &knots,
528 TColStd_Array1OfInteger &mult,
529 // const Standard_Boolean Periodic)
530 const Standard_Boolean )
532 Standard_Real val = SeqKnots(1);
533 Standard_Integer kk=1;
537 for (Standard_Integer jj=2;jj<=SeqKnots.Length();jj++)
539 // test on strict equality on nodes
540 if (SeqKnots(jj)!=val)
554 //=======================================================================
555 //function : KnotForm
557 //=======================================================================
559 BSplCLib_KnotDistribution BSplCLib::KnotForm
560 (const Array1OfReal& Knots,
561 const Standard_Integer FromK1,
562 const Standard_Integer ToK2)
564 Standard_Real DU0,DU1,Ui,Uj,Eps0,val;
565 BSplCLib_KnotDistribution KForm = BSplCLib_Uniform;
567 Standard_Integer KLower = Knots.Lower();
568 const Standard_Real * pkn = &Knots(KLower);
571 if (Ui < 0) Ui = - Ui;
572 Uj = pkn[FromK1 + 1];
573 if (Uj < 0) Uj = - Uj;
575 if (DU0 < 0) DU0 = - DU0;
576 Eps0 = Epsilon (Ui) + Epsilon (Uj) + Epsilon (DU0);
577 Standard_Integer i = FromK1 + 1;
579 while (KForm != BSplCLib_NonUniform && i < ToK2) {
581 if (Ui < 0) Ui = - Ui;
584 if (Uj < 0) Uj = - Uj;
586 if (DU1 < 0) DU1 = - DU1;
588 if (val < 0) val = -val;
589 if (val > Eps0) KForm = BSplCLib_NonUniform;
591 Eps0 = Epsilon (Ui) + Epsilon (Uj) + Epsilon (DU0);
596 //=======================================================================
597 //function : MultForm
599 //=======================================================================
601 BSplCLib_MultDistribution BSplCLib::MultForm
602 (const Array1OfInteger& Mults,
603 const Standard_Integer FromK1,
604 const Standard_Integer ToK2)
606 Standard_Integer First,Last;
615 Standard_Integer MLower = Mults.Lower();
616 const Standard_Integer *pmu = &Mults(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];
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;
628 else if (i == Last) {
629 if (MForm == BSplCLib_QuasiConstant) {
630 if (FirstMult != pmu[i]) MForm = BSplCLib_NonConstant;
633 if (Mult != pmu[i]) MForm = BSplCLib_NonConstant;
637 if (Mult != pmu[i]) MForm = BSplCLib_NonConstant;
645 //=======================================================================
646 //function : KnotAnalysis
648 //=======================================================================
650 void 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)
657 KnotForm = GeomAbs_NonUniform;
659 BSplCLib_KnotDistribution KSet =
660 BSplCLib::KnotForm (CKnots, 1, CKnots.Length());
663 if (KSet == BSplCLib_Uniform) {
664 BSplCLib_MultDistribution MSet =
665 BSplCLib::MultForm (CMults, 1, CMults.Length());
667 case BSplCLib_NonConstant :
669 case BSplCLib_Constant :
670 if (CKnots.Length() == 2) {
671 KnotForm = GeomAbs_PiecewiseBezier;
674 if (CMults (1) == 1) KnotForm = GeomAbs_Uniform;
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;
687 Standard_Integer FirstKM =
688 Periodic ? CKnots.Lower() : BSplCLib::FirstUKnotIndex (Degree,CMults);
689 Standard_Integer LastKM =
690 Periodic ? CKnots.Upper() : BSplCLib::LastUKnotIndex (Degree,CMults);
692 if (LastKM - FirstKM != 1) {
693 Standard_Integer Multi;
694 for (Standard_Integer i = FirstKM + 1; i < LastKM; i++) {
696 MaxKnotMult = Max (MaxKnotMult, Multi);
701 //=======================================================================
702 //function : Reparametrize
704 //=======================================================================
706 void BSplCLib::Reparametrize
707 (const Standard_Real U1,
708 const Standard_Real U2,
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;
721 for (Standard_Integer i = Lower + 1; i <= Upper; i++) {
722 Knots (i) = Knots (i-1) + DU;
728 Standard_Real K1 = Knots (Lower);
729 Standard_Real Length = Knots (Upper) - Knots (Lower);
730 Knots (Lower) = UFirst;
732 for (Standard_Integer i = Lower + 1; i <= Upper; i++) {
734 Ratio = (K2 - K1) / Length;
735 Knots (i) = Knots (i-1) + (NewLength * Ratio);
738 Standard_Real Eps = Epsilon( Abs(Knots(i-1)) );
739 if (Knots(i) - Knots(i-1) <= Eps)
740 Knots(i) = NextAfter (Knots(i-1) + Eps, RealLast());
747 //=======================================================================
750 //=======================================================================
752 void BSplCLib::Reverse(TColStd_Array1OfReal& Knots)
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;
763 while (first <= last) {
764 tfirst += klast - Knots(last);
765 tlast -= Knots(first) - kfirst;
766 kfirst = Knots(first);
768 Knots(first) = tfirst;
775 //=======================================================================
778 //=======================================================================
780 void BSplCLib::Reverse(TColStd_Array1OfInteger& Mults)
782 Standard_Integer first = Mults.Lower();
783 Standard_Integer last = Mults.Upper();
784 Standard_Integer temp;
786 while (first < last) {
788 Mults(first) = Mults(last);
795 //=======================================================================
798 //=======================================================================
800 void BSplCLib::Reverse(TColStd_Array1OfReal& Weights,
801 const Standard_Integer L)
803 Standard_Integer i, l = L;
804 l = Weights.Lower()+(l-Weights.Lower())%(Weights.Upper()-Weights.Lower()+1);
806 TColStd_Array1OfReal temp(0,Weights.Length()-1);
808 for (i = Weights.Lower(); i <= l; i++)
809 temp(l-i) = Weights(i);
811 for (i = l+1; i <= Weights.Upper(); i++)
812 temp(l-Weights.Lower()+Weights.Upper()-i+1) = Weights(i);
814 for (i = Weights.Lower(); i <= Weights.Upper(); i++)
815 Weights(i) = temp(i-Weights.Lower());
818 //=======================================================================
819 //function : IsRational
821 //=======================================================================
823 Standard_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 )
829 Standard_Integer i, f = Weights.Lower(), l = Weights.Length();
830 Standard_Integer I3 = I2 - f;
831 const Standard_Real * WG = &Weights(f);
834 for (i = I1 - f; i < I3; i++) {
835 if (WG[f + (i % l)] != WG[f + ((i + 1) % l)]) return Standard_True;
837 return Standard_False ;
840 //=======================================================================
842 //purpose : evaluate point and derivatives
843 //=======================================================================
845 void BSplCLib::Eval(const Standard_Real U,
846 const Standard_Integer Degree,
847 Standard_Real& Knots,
848 const Standard_Integer Dimension,
849 Standard_Real& Poles)
851 Standard_Integer step,i,Dms,Dm1,Dpi,Sti;
852 Standard_Real X, Y, *poles, *knots = &Knots;
860 for (step = - 1; step < Dm1; step++) {
866 for (i = 0; i < Dms; i++) {
869 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
871 poles[0] *= X; poles[0] += Y * poles[1];
879 for (step = - 1; step < Dm1; step++) {
885 for (i = 0; i < Dms; i++) {
888 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
890 poles[0] *= X; poles[0] += Y * poles[2];
891 poles[1] *= X; poles[1] += Y * poles[3];
899 for (step = - 1; step < Dm1; step++) {
905 for (i = 0; i < Dms; i++) {
908 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
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];
920 for (step = - 1; step < Dm1; step++) {
926 for (i = 0; i < Dms; i++) {
929 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
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];
943 for (step = - 1; step < Dm1; step++) {
949 for (i = 0; i < Dms; i++) {
952 X = (knots[Dpi] - U) / (knots[Dpi] - knots[Sti]);
955 for (k = 0; k < Dimension; k++) {
957 poles[k] += Y * poles[k + Dimension];
966 //=======================================================================
967 //function : BoorScheme
969 //=======================================================================
971 void 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)
980 // Compute the values
984 // for i = 0 to Depth,
985 // j = 0 to Length - i
987 // The Boor scheme is :
990 // P(i,j) = x * P(i-1,j) + (1-x) * P(i-1,j+1)
992 // where x = (knot(i+j+Degree) - U) / (knot(i+j+Degree) - knot(i+j))
995 // The values are stored in the array Poles
996 // They are alternatively written if the odd and even positions.
998 // The successives contents of the array are
999 // ***** means unitialised, l = Degree + Length
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)
1006 Standard_Integer i,k,step;
1007 Standard_Real *knots = &Knots;
1008 Standard_Real *pole, *firstpole = &Poles - 2 * Dimension;
1009 // the steps of recursion
1011 for (step = 0; step < Depth; step++) {
1012 firstpole += Dimension;
1014 // compute the new row of poles
1016 for (i = step; i < Length; i++) {
1017 pole += 2 * Dimension;
1019 Standard_Real X = (knots[i+Degree-step] - U)
1020 / (knots[i+Degree-step] - knots[i]);
1021 Standard_Real Y = 1. - X;
1023 // P(i,j) = X * P(i-1,j) + (1-X) * P(i-1,j+1)
1025 for (k = 0; k < Dimension; k++)
1026 pole[k] = X * pole[k - Dimension] + Y * pole[k + Dimension];
1031 //=======================================================================
1032 //function : AntiBoorScheme
1034 //=======================================================================
1036 Standard_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)
1045 // do the Boor scheme reverted.
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;
1051 // Test the special case length = 1
1052 // only verification of the central point
1055 X = (knots[Degree] - U) / (knots[Degree] - knots[0]);
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;
1063 return Standard_True;
1067 // the steps of recursion
1069 for (step = Depth-1; step >= 0; step--) {
1070 firstpole -= Dimension;
1073 // first step from left to right
1075 for (i = step; i < Length-1; i++) {
1076 pole += 2 * Dimension;
1078 X = (knots[i+Degree-step] - U) / (knots[i+Degree-step] - knots[i]);
1081 for (k = 0; k < Dimension; k++)
1082 pole[k+Dimension] = (pole[k] - X*pole[k-Dimension]) / Y;
1086 // second step from right to left
1087 pole += 4* Dimension;
1088 half_length = (Length - 1 + step) / 2 ;
1090 // only do half of the way from right to left
1091 // otherwise it start degenerating because of
1095 for (i = Length-1; i > half_length ; i--) {
1096 pole -= 2 * Dimension;
1099 X = (knots[i+Degree-step] - U) / (knots[i+Degree-step] - knots[i]);
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.;
1111 return Standard_True;
1114 //=======================================================================
1115 //function : Derivative
1117 //=======================================================================
1119 void 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)
1126 Standard_Integer i,k,step,span = Degree;
1127 Standard_Real *knot = &Knots;
1129 for (step = 1; step <= Order; step++) {
1130 Standard_Real* pole = &Poles;
1132 for (i = step; i < Length; i++) {
1133 Standard_Real coef = - span / (knot[i+span] - knot[i]);
1135 for (k = 0; k < Dimension; k++) {
1136 pole[k] -= pole[k+Dimension];
1145 //=======================================================================
1148 //=======================================================================
1150 void 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)
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;
1161 if (N < Degree) min = N;
1164 DDmi = (Degree << 1) + 1;
1165 switch (Dimension) {
1167 psDD = psav + Degree;
1168 psDDmDim = psDD - 1;
1170 for (i = 0; i < Degree; i++) {
1176 for (j = Degm1; j >= i; j--) {
1179 *pole = (knot[jDmi] == knot[j]) ? 0.0 : *pole / (knot[jDmi] - knot[j]);
1184 // Second phase, dependant of U
1187 for (i = 0; i < Degree; i++) {
1193 for (j = i; j >= 0; j--) {
1194 *pole += coef * (*tbis);
1199 // multiply by the degrees
1204 for (i = 1; i <= min; i++) {
1205 *pole *= coef; pole++;
1212 psDD = psav + (Degree << 1);
1213 psDDmDim = psDD - 2;
1215 for (i = 0; i < Degree; i++) {
1221 for (j = Degm1; j >= i; j--) {
1223 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. / (knot[jDmi] - knot[j]);
1224 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1225 *pole -= *tbis; *pole *= coef;
1230 // Second phase, dependant of U
1233 for (i = 0; i < Degree; i++) {
1239 for (j = i; j >= 0; j--) {
1240 *pole += coef * (*tbis); pole++; tbis++;
1241 *pole += coef * (*tbis);
1246 // multiply by the degrees
1251 for (i = 1; i <= min; i++) {
1252 *pole *= coef; pole++;
1253 *pole *= coef; pole++;
1260 psDD = psav + (Degree << 1) + Degree;
1261 psDDmDim = psDD - 3;
1263 for (i = 0; i < Degree; i++) {
1269 for (j = Degm1; j >= i; j--) {
1271 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. / (knot[jDmi] - knot[j]);
1272 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1273 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1274 *pole -= *tbis; *pole *= coef;
1279 // Second phase, dependant of U
1282 for (i = 0; i < Degree; i++) {
1288 for (j = i; j >= 0; j--) {
1289 *pole += coef * (*tbis); pole++; tbis++;
1290 *pole += coef * (*tbis); pole++; tbis++;
1291 *pole += coef * (*tbis);
1296 // multiply by the degrees
1301 for (i = 1; i <= min; i++) {
1302 *pole *= coef; pole++;
1303 *pole *= coef; pole++;
1304 *pole *= coef; pole++;
1311 psDD = psav + (Degree << 2);
1312 psDDmDim = psDD - 4;
1314 for (i = 0; i < Degree; i++) {
1320 for (j = Degm1; j >= i; j--) {
1322 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. /(knot[jDmi] - knot[j]) ;
1323 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1324 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1325 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1326 *pole -= *tbis; *pole *= coef;
1331 // Second phase, dependant of U
1334 for (i = 0; i < Degree; i++) {
1340 for (j = i; j >= 0; j--) {
1341 *pole += coef * (*tbis); pole++; tbis++;
1342 *pole += coef * (*tbis); pole++; tbis++;
1343 *pole += coef * (*tbis); pole++; tbis++;
1344 *pole += coef * (*tbis);
1349 // multiply by the degrees
1354 for (i = 1; i <= min; i++) {
1355 *pole *= coef; pole++;
1356 *pole *= coef; pole++;
1357 *pole *= coef; pole++;
1358 *pole *= coef; pole++;
1366 Standard_Integer Dim2 = Dimension << 1;
1367 psDD = psav + Degree * Dimension;
1368 psDDmDim = psDD - Dimension;
1370 for (i = 0; i < Degree; i++) {
1376 for (j = Degm1; j >= i; j--) {
1378 coef = (knot[jDmi] == knot[j]) ? 0.0 : 1. / (knot[jDmi] - knot[j]);
1380 for (k = 0; k < Dimension; k++) {
1381 *pole -= *tbis; *pole *= coef; pole++; tbis++;
1387 // Second phase, dependant of U
1390 for (i = 0; i < Degree; i++) {
1393 tbis = pole + Dimension;
1396 for (j = i; j >= 0; j--) {
1398 for (k = 0; k < Dimension; k++) {
1399 *pole += coef * (*tbis); pole++; tbis++;
1405 // multiply by the degrees
1408 pole = psav + Dimension;
1410 for (i = 1; i <= min; i++) {
1412 for (k = 0; k < Dimension; k++) {
1413 *pole *= coef; pole++;
1422 //=======================================================================
1423 //function : BuildKnots
1425 //=======================================================================
1427 void BSplCLib::BuildKnots(const Standard_Integer Degree,
1428 const Standard_Integer Index,
1429 const Standard_Boolean Periodic,
1430 const TColStd_Array1OfReal& Knots,
1431 const TColStd_Array1OfInteger& Mults,
1434 Standard_Integer KLower = Knots.Lower();
1435 const Standard_Real * pkn = &Knots(KLower);
1437 Standard_Real *knot = &LK;
1438 if (&Mults == NULL) {
1441 Standard_Integer j = Index ;
1442 knot[0] = pkn[j]; j++;
1447 Standard_Integer j = Index - 1;
1448 knot[0] = pkn[j]; j++;
1449 knot[1] = pkn[j]; j++;
1450 knot[2] = pkn[j]; j++;
1455 Standard_Integer j = Index - 2;
1456 knot[0] = pkn[j]; j++;
1457 knot[1] = pkn[j]; j++;
1458 knot[2] = pkn[j]; j++;
1459 knot[3] = pkn[j]; j++;
1460 knot[4] = pkn[j]; j++;
1465 Standard_Integer j = Index - 3;
1466 knot[0] = pkn[j]; j++;
1467 knot[1] = pkn[j]; j++;
1468 knot[2] = pkn[j]; j++;
1469 knot[3] = pkn[j]; j++;
1470 knot[4] = pkn[j]; j++;
1471 knot[5] = pkn[j]; j++;
1472 knot[6] = pkn[j]; j++;
1477 Standard_Integer j = Index - 4;
1478 knot[0] = pkn[j]; j++;
1479 knot[1] = pkn[j]; j++;
1480 knot[2] = pkn[j]; j++;
1481 knot[3] = pkn[j]; j++;
1482 knot[4] = pkn[j]; j++;
1483 knot[5] = pkn[j]; j++;
1484 knot[6] = pkn[j]; j++;
1485 knot[7] = pkn[j]; j++;
1486 knot[8] = pkn[j]; j++;
1491 Standard_Integer j = Index - 5;
1492 knot[ 0] = pkn[j]; j++;
1493 knot[ 1] = pkn[j]; j++;
1494 knot[ 2] = pkn[j]; j++;
1495 knot[ 3] = pkn[j]; j++;
1496 knot[ 4] = pkn[j]; j++;
1497 knot[ 5] = pkn[j]; j++;
1498 knot[ 6] = pkn[j]; j++;
1499 knot[ 7] = pkn[j]; j++;
1500 knot[ 8] = pkn[j]; j++;
1501 knot[ 9] = pkn[j]; j++;
1502 knot[10] = pkn[j]; j++;
1507 Standard_Integer i,j;
1508 Standard_Integer Deg2 = Degree << 1;
1511 for (i = 0; i < Deg2; i++) {
1520 Standard_Integer Deg1 = Degree - 1;
1521 Standard_Integer KUpper = Knots.Upper();
1522 Standard_Integer MLower = Mults.Lower();
1523 Standard_Integer MUpper = Mults.Upper();
1524 const Standard_Integer * pmu = &Mults(MLower);
1526 Standard_Real dknot = 0;
1527 Standard_Integer ilow = Index , mlow = 0;
1528 Standard_Integer iupp = Index + 1, mupp = 0;
1529 Standard_Real loffset = 0., uoffset = 0.;
1530 Standard_Boolean getlow = Standard_True, getupp = Standard_True;
1532 dknot = pkn[KUpper] - pkn[KLower];
1533 if (iupp > MUpper) {
1538 // Find the knots around Index
1540 for (i = 0; i < Degree; i++) {
1543 if (mlow > pmu[ilow]) {
1546 getlow = (ilow >= MLower);
1547 if (Periodic && !getlow) {
1550 getlow = Standard_True;
1554 knot[Deg1 - i] = pkn[ilow] - loffset;
1558 if (mupp > pmu[iupp]) {
1561 getupp = (iupp <= MUpper);
1562 if (Periodic && !getupp) {
1565 getupp = Standard_True;
1569 knot[Degree + i] = pkn[iupp] + uoffset;
1575 //=======================================================================
1576 //function : PoleIndex
1578 //=======================================================================
1580 Standard_Integer BSplCLib::PoleIndex(const Standard_Integer Degree,
1581 const Standard_Integer Index,
1582 const Standard_Boolean Periodic,
1583 const TColStd_Array1OfInteger& Mults)
1585 Standard_Integer i, pindex = 0;
1587 for (i = Mults.Lower(); i <= Index; i++)
1590 pindex -= Mults(Mults.Lower());
1592 pindex -= Degree + 1;
1597 //=======================================================================
1598 //function : BuildBoor
1599 //purpose : builds the local array for boor
1600 //=======================================================================
1602 void BSplCLib::BuildBoor(const Standard_Integer Index,
1603 const Standard_Integer Length,
1604 const Standard_Integer Dimension,
1605 const TColStd_Array1OfReal& Poles,
1608 Standard_Real *poles = &LP;
1609 Standard_Integer i,k, ip = Poles.Lower() + Index * Dimension;
1611 for (i = 0; i < Length+1; i++) {
1613 for (k = 0; k < Dimension; k++) {
1614 poles[k] = Poles(ip);
1616 if (ip > Poles.Upper()) ip = Poles.Lower();
1618 poles += 2 * Dimension;
1622 //=======================================================================
1623 //function : BoorIndex
1625 //=======================================================================
1627 Standard_Integer BSplCLib::BoorIndex(const Standard_Integer Index,
1628 const Standard_Integer Length,
1629 const Standard_Integer Depth)
1631 if (Index <= Depth) return Index;
1632 if (Index <= Length) return 2 * Index - Depth;
1633 return Length + Index - Depth;
1636 //=======================================================================
1637 //function : GetPole
1639 //=======================================================================
1641 void BSplCLib::GetPole(const Standard_Integer Index,
1642 const Standard_Integer Length,
1643 const Standard_Integer Depth,
1644 const Standard_Integer Dimension,
1646 Standard_Integer& Position,
1647 TColStd_Array1OfReal& Pole)
1650 Standard_Real* pole = &LP + BoorIndex(Index,Length,Depth) * Dimension;
1652 for (k = 0; k < Dimension; k++) {
1653 Pole(Position) = pole[k];
1656 if (Position > Pole.Upper()) Position = Pole.Lower();
1659 //=======================================================================
1660 //function : PrepareInsertKnots
1662 //=======================================================================
1664 Standard_Boolean BSplCLib::PrepareInsertKnots
1665 (const Standard_Integer Degree,
1666 const Standard_Boolean Periodic,
1667 const TColStd_Array1OfReal& Knots,
1668 const TColStd_Array1OfInteger& Mults,
1669 const TColStd_Array1OfReal& AddKnots,
1670 const TColStd_Array1OfInteger& AddMults,
1671 Standard_Integer& NbPoles,
1672 Standard_Integer& NbKnots,
1673 const Standard_Real Tolerance,
1674 const Standard_Boolean Add)
1676 Standard_Boolean addflat = &AddMults == NULL;
1678 Standard_Integer first,last;
1680 first = Knots.Lower();
1681 last = Knots.Upper();
1684 first = FirstUKnotIndex(Degree,Mults);
1685 last = LastUKnotIndex(Degree,Mults);
1687 Standard_Real adeltaK1 = Knots(first)-AddKnots(AddKnots.Lower());
1688 Standard_Real adeltaK2 = AddKnots(AddKnots.Upper())-Knots(last);
1689 if (adeltaK1 > Tolerance) return Standard_False;
1690 if (adeltaK2 > Tolerance) return Standard_False;
1692 Standard_Integer sigma = 0, mult, amult;
1694 Standard_Integer k = Knots.Lower() - 1;
1695 Standard_Integer ak = AddKnots.Lower();
1697 if(Periodic && AddKnots.Length() > 1)
1699 //gka for case when segments was produced on full period only one knot
1700 //was added in the end of curve
1701 if(fabs(adeltaK1) <= gp::Resolution() &&
1702 fabs(adeltaK2) <= gp::Resolution())
1706 Standard_Integer aLastKnotMult = Mults (Knots.Upper());
1707 Standard_Real au,oldau = AddKnots(ak),Eps;
1709 while (ak <= AddKnots.Upper()) {
1711 if (au < oldau) return Standard_False;
1714 Eps = Max(Tolerance,Epsilon(au));
1716 while ((k < Knots.Upper()) && (Knots(k+1) - au <= Eps)) {
1722 if (addflat) amult = 1;
1723 else amult = Max(0,AddMults(ak));
1725 while ((ak < AddKnots.Upper()) &&
1726 (Abs(au - AddKnots(ak+1)) <= Eps)) {
1729 if (addflat) amult++;
1730 else amult += Max(0,AddMults(ak));
1735 if (Abs(au - Knots(k)) <= Eps) {
1736 // identic to existing knot
1739 if (mult + amult > Degree)
1740 amult = Max(0,Degree - mult);
1744 else if (amult > mult) {
1745 if (amult > Degree) amult = Degree;
1746 if (k == Knots.Upper () && Periodic)
1748 aLastKnotMult = Max (amult, mult);
1749 sigma += 2 * (aLastKnotMult - mult);
1753 sigma += amult - mult;
1757 // on periodic curves if this is the last knot
1758 // the multiplicity is added twice to account for the first knot
1759 if (k == Knots.Upper() && Periodic) {
1763 sigma += amult - mult;
1768 // not identic to existing knot
1770 if (amult > Degree) amult = Degree;
1779 // count the last knots
1780 while (k < Knots.Upper()) {
1787 //for periodic B-Spline the requirement is that multiplicites of the first
1788 //and last knots must be equal (see Geom_BSplineCurve constructor for
1790 //respectively AddMults() must meet this requirement if AddKnots() contains
1791 //knot(s) coincident with first or last
1792 NbPoles = sigma - aLastKnotMult;
1795 NbPoles = sigma - Degree - 1;
1798 return Standard_True;
1801 //=======================================================================
1803 //purpose : copy reals from an array to an other
1805 // NbValues are copied from OldPoles(OldFirst)
1806 // to NewPoles(NewFirst)
1808 // Periodicity is handled.
1809 // OldFirst and NewFirst are updated
1810 // to the position after the last copied pole.
1812 //=======================================================================
1814 static void Copy(const Standard_Integer NbPoles,
1815 Standard_Integer& OldFirst,
1816 const TColStd_Array1OfReal& OldPoles,
1817 Standard_Integer& NewFirst,
1818 TColStd_Array1OfReal& NewPoles)
1820 // reset the index in the range for periodicity
1822 OldFirst = OldPoles.Lower() +
1823 (OldFirst - OldPoles.Lower()) % (OldPoles.Upper() - OldPoles.Lower() + 1);
1825 NewFirst = NewPoles.Lower() +
1826 (NewFirst - NewPoles.Lower()) % (NewPoles.Upper() - NewPoles.Lower() + 1);
1831 for (i = 1; i <= NbPoles; i++) {
1832 NewPoles(NewFirst) = OldPoles(OldFirst);
1834 if (OldFirst > OldPoles.Upper()) OldFirst = OldPoles.Lower();
1836 if (NewFirst > NewPoles.Upper()) NewFirst = NewPoles.Lower();
1840 //=======================================================================
1841 //function : InsertKnots
1842 //purpose : insert an array of knots and multiplicities
1843 //=======================================================================
1845 void BSplCLib::InsertKnots
1846 (const Standard_Integer Degree,
1847 const Standard_Boolean Periodic,
1848 const Standard_Integer Dimension,
1849 const TColStd_Array1OfReal& Poles,
1850 const TColStd_Array1OfReal& Knots,
1851 const TColStd_Array1OfInteger& Mults,
1852 const TColStd_Array1OfReal& AddKnots,
1853 const TColStd_Array1OfInteger& AddMults,
1854 TColStd_Array1OfReal& NewPoles,
1855 TColStd_Array1OfReal& NewKnots,
1856 TColStd_Array1OfInteger& NewMults,
1857 const Standard_Real Tolerance,
1858 const Standard_Boolean Add)
1860 Standard_Boolean addflat = &AddMults == NULL;
1862 Standard_Integer i,k,mult,firstmult;
1863 Standard_Integer index,kn,curnk,curk;
1864 Standard_Integer p,np, curp, curnp, length, depth;
1866 Standard_Integer need;
1869 // -------------------
1870 // create local arrays
1871 // -------------------
1873 Standard_Real *knots = new Standard_Real[2*Degree];
1874 Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
1876 //----------------------------
1877 // loop on the knots to insert
1878 //----------------------------
1880 curk = Knots.Lower()-1; // current position in Knots
1881 curnk = NewKnots.Lower()-1; // current position in NewKnots
1882 curp = Poles.Lower(); // current position in Poles
1883 curnp = NewPoles.Lower(); // current position in NewPoles
1885 // NewKnots, NewMults, NewPoles contains the current state of the curve
1887 // index is the first pole of the current curve for insertion schema
1889 if (Periodic) index = -Mults(Mults.Lower());
1890 else index = -Degree-1;
1892 // on Periodic curves the first knot and the last knot are inserted later
1893 // (they are the same knot)
1894 firstmult = 0; // multiplicity of the first-last knot for periodic
1897 // kn current knot to insert in AddKnots
1899 for (kn = AddKnots.Lower(); kn <= AddKnots.Upper(); kn++) {
1902 Eps = Max(Tolerance,Epsilon(u));
1904 //-----------------------------------
1905 // find the position in the old knots
1906 // and copy to the new knots
1907 //-----------------------------------
1909 while (curk < Knots.Upper() && Knots(curk+1) - u <= Eps) {
1911 NewKnots(curnk) = Knots(curk);
1912 index += NewMults(curnk) = Mults(curk);
1915 //-----------------------------------
1916 // Slice the knots and the mults
1917 // to the current size of the new curve
1918 //-----------------------------------
1920 i = curnk + Knots.Upper() - curk;
1921 TColStd_Array1OfReal nknots(NewKnots(NewKnots.Lower()),NewKnots.Lower(),i);
1922 TColStd_Array1OfInteger nmults(NewMults(NewMults.Lower()),NewMults.Lower(),i);
1924 //-----------------------------------
1925 // copy enough knots
1926 // to compute the insertion schema
1927 //-----------------------------------
1933 while (mult < Degree && k < Knots.Upper()) {
1935 nknots(i) = Knots(k);
1936 mult += nmults(i) = Mults(k);
1939 // copy knots at the end for periodic curve
1945 while (mult < Degree && i > curnk) {
1946 nknots(i) = Knots(k);
1947 mult += nmults(i) = Mults(k);
1951 nmults(nmults.Upper()) = nmults(nmults.Lower());
1956 //------------------------------------
1957 // do the boor scheme on the new curve
1958 // to insert the new knot
1959 //------------------------------------
1961 Standard_Boolean sameknot = (Abs(u-NewKnots(curnk)) <= Eps);
1963 if (sameknot) length = Max(0,Degree - NewMults(curnk));
1964 else length = Degree;
1966 if (addflat) depth = 1;
1967 else depth = Min(Degree,AddMults(kn));
1971 if ((NewMults(curnk) + depth) > Degree)
1972 depth = Degree - NewMults(curnk);
1975 depth = Max(0,depth-NewMults(curnk));
1979 // on periodic curve the first and last knot are delayed to the end
1980 if (curk == Knots.Lower() || (curk == Knots.Upper())) {
1981 if (firstmult == 0) // do that only once
1987 if (depth <= 0) continue;
1989 BuildKnots(Degree,curnk,Periodic,nknots,nmults,*knots);
1993 need = NewPoles.Lower()+(index+length+1)*Dimension - curnp;
1994 need = Min(need,Poles.Upper() - curp + 1);
1998 Copy(need,p,Poles,np,NewPoles);
2002 // slice the poles to the current number of poles in case of periodic
2003 TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
2005 BuildBoor(index,length,Dimension,npoles,*poles);
2006 BoorScheme(u,Degree,*knots,Dimension,*poles,depth,length);
2008 //-------------------
2009 // copy the new poles
2010 //-------------------
2012 curnp += depth * Dimension; // number of poles is increased by depth
2013 TColStd_Array1OfReal ThePoles(NewPoles(NewPoles.Lower()),NewPoles.Lower(),curnp-1);
2014 np = NewKnots.Lower()+(index+1)*Dimension;
2016 for (i = 1; i <= length + depth; i++)
2017 GetPole(i,length,depth,Dimension,*poles,np,ThePoles);
2019 //-------------------
2021 //-------------------
2025 NewMults(curnk) += depth;
2029 NewKnots(curnk) = u;
2030 NewMults(curnk) = depth;
2034 //------------------------------
2035 // copy the last poles and knots
2036 //------------------------------
2038 Copy(Poles.Upper() - curp + 1,curp,Poles,curnp,NewPoles);
2040 while (curk < Knots.Upper()) {
2042 NewKnots(curnk) = Knots(curk);
2043 NewMults(curnk) = Mults(curk);
2046 //------------------------------
2047 // process the first-last knot
2048 // on periodic curves
2049 //------------------------------
2051 if (firstmult > 0) {
2052 curnk = NewKnots.Lower();
2053 if (NewMults(curnk) + firstmult > Degree) {
2054 firstmult = Degree - NewMults(curnk);
2056 if (firstmult > 0) {
2058 length = Degree - NewMults(curnk);
2061 BuildKnots(Degree,curnk,Periodic,NewKnots,NewMults,*knots);
2062 TColStd_Array1OfReal npoles(NewPoles(NewPoles.Lower()),
2064 NewPoles.Upper()-depth*Dimension);
2065 BuildBoor(0,length,Dimension,npoles,*poles);
2066 BoorScheme(NewKnots(curnk),Degree,*knots,Dimension,*poles,depth,length);
2068 //---------------------------
2069 // copy the new poles
2070 // but rotate them with depth
2071 //---------------------------
2073 np = NewPoles.Lower();
2075 for (i = depth; i < length + depth; i++)
2076 GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
2078 np = NewPoles.Upper() - depth*Dimension + 1;
2080 for (i = 0; i < depth; i++)
2081 GetPole(i,length,depth,Dimension,*poles,np,NewPoles);
2083 NewMults(NewMults.Lower()) += depth;
2084 NewMults(NewMults.Upper()) += depth;
2087 // free local arrays
2092 //=======================================================================
2093 //function : RemoveKnot
2095 //=======================================================================
2097 Standard_Boolean BSplCLib::RemoveKnot
2098 (const Standard_Integer Index,
2099 const Standard_Integer Mult,
2100 const Standard_Integer Degree,
2101 const Standard_Boolean Periodic,
2102 const Standard_Integer Dimension,
2103 const TColStd_Array1OfReal& Poles,
2104 const TColStd_Array1OfReal& Knots,
2105 const TColStd_Array1OfInteger& Mults,
2106 TColStd_Array1OfReal& NewPoles,
2107 TColStd_Array1OfReal& NewKnots,
2108 TColStd_Array1OfInteger& NewMults,
2109 const Standard_Real Tolerance)
2111 Standard_Integer index,i,j,k,p,np;
2113 Standard_Integer TheIndex = Index;
2116 Standard_Integer first,last;
2118 first = Knots.Lower();
2119 last = Knots.Upper();
2122 first = BSplCLib::FirstUKnotIndex(Degree,Mults) + 1;
2123 last = BSplCLib::LastUKnotIndex(Degree,Mults) - 1;
2125 if (Index < first) return Standard_False;
2126 if (Index > last) return Standard_False;
2128 if ( Periodic && (Index == first)) TheIndex = last;
2130 Standard_Integer depth = Mults(TheIndex) - Mult;
2131 Standard_Integer length = Degree - Mult;
2133 // -------------------
2134 // create local arrays
2135 // -------------------
2137 Standard_Real *knots = new Standard_Real[4*Degree];
2138 Standard_Real *poles = new Standard_Real[(2*Degree+1)*Dimension];
2141 // ------------------------------------
2142 // build the knots for anti Boor Scheme
2143 // ------------------------------------
2145 // the new sequence of knots
2146 // is obtained from the knots at Index-1 and Index
2148 BSplCLib::BuildKnots(Degree,TheIndex-1,Periodic,Knots,Mults,*knots);
2149 index = PoleIndex(Degree,TheIndex-1,Periodic,Mults);
2150 BSplCLib::BuildKnots(Degree,TheIndex,Periodic,Knots,Mults,knots[2*Degree]);
2154 for (i = 0; i < Degree - Mult; i++)
2155 knots[i] = knots[i+Mult];
2157 for (i = Degree-Mult; i < 2*Degree; i++)
2158 knots[i] = knots[2*Degree+i];
2161 // ------------------------------------
2162 // build the poles for anti Boor Scheme
2163 // ------------------------------------
2165 p = Poles.Lower()+index * Dimension;
2167 for (i = 0; i <= length + depth; i++) {
2168 j = Dimension * BoorIndex(i,length,depth);
2170 for (k = 0; k < Dimension; k++) {
2171 poles[j+k] = Poles(p+k);
2174 if (p > Poles.Upper()) p = Poles.Lower();
2182 Standard_Boolean result = AntiBoorScheme(Knots(TheIndex),Degree,*knots,
2184 depth,length,Tolerance);
2195 np = NewPoles.Lower();
2197 // unmodified poles before
2198 Copy((index+1)*Dimension,p,Poles,np,NewPoles);
2203 for (i = 1; i <= length; i++)
2204 BSplCLib::GetPole(i,length,0,Dimension,*poles,np,NewPoles);
2205 p += (length + depth) * Dimension ;
2207 // unmodified poles after
2208 if (p != Poles.Lower()) {
2209 i = Poles.Upper() - p + 1;
2210 Copy(i,p,Poles,np,NewPoles);
2218 NewMults(TheIndex) = Mult;
2220 if (TheIndex == first) NewMults(last) = Mult;
2221 if (TheIndex == last) NewMults(first) = Mult;
2225 if (!Periodic || (TheIndex != first && TheIndex != last)) {
2227 for (i = Knots.Lower(); i < TheIndex; i++) {
2228 NewKnots(i) = Knots(i);
2229 NewMults(i) = Mults(i);
2232 for (i = TheIndex+1; i <= Knots.Upper(); i++) {
2233 NewKnots(i-1) = Knots(i);
2234 NewMults(i-1) = Mults(i);
2238 // The interesting case of a Periodic curve
2239 // where the first and last knot is removed.
2241 for (i = first; i < last-1; i++) {
2242 NewKnots(i) = Knots(i+1);
2243 NewMults(i) = Mults(i+1);
2245 NewKnots(last-1) = NewKnots(first) + Knots(last) - Knots(first);
2246 NewMults(last-1) = NewMults(first);
2252 // free local arrays
2259 //=======================================================================
2260 //function : IncreaseDegreeCountKnots
2262 //=======================================================================
2264 Standard_Integer BSplCLib::IncreaseDegreeCountKnots
2265 (const Standard_Integer Degree,
2266 const Standard_Integer NewDegree,
2267 const Standard_Boolean Periodic,
2268 const TColStd_Array1OfInteger& Mults)
2270 if (Periodic) return Mults.Length();
2271 Standard_Integer f = FirstUKnotIndex(Degree,Mults);
2272 Standard_Integer l = LastUKnotIndex(Degree,Mults);
2273 Standard_Integer m,i,removed = 0, step = NewDegree - Degree;
2276 m = Degree + (f - i + 1) * step + 1;
2278 while (m > NewDegree+1) {
2280 m -= Mults(i) + step;
2283 if (m < NewDegree+1) removed--;
2286 m = Degree + (i - l + 1) * step + 1;
2288 while (m > NewDegree+1) {
2290 m -= Mults(i) + step;
2293 if (m < NewDegree+1) removed--;
2295 return Mults.Length() - removed;
2298 //=======================================================================
2299 //function : IncreaseDegree
2301 //=======================================================================
2303 void BSplCLib::IncreaseDegree
2304 (const Standard_Integer Degree,
2305 const Standard_Integer NewDegree,
2306 const Standard_Boolean Periodic,
2307 const Standard_Integer Dimension,
2308 const TColStd_Array1OfReal& Poles,
2309 const TColStd_Array1OfReal& Knots,
2310 const TColStd_Array1OfInteger& Mults,
2311 TColStd_Array1OfReal& NewPoles,
2312 TColStd_Array1OfReal& NewKnots,
2313 TColStd_Array1OfInteger& NewMults)
2315 // Degree elevation of a BSpline Curve
2317 // This algorithms loops on degree incrementation from Degree to NewDegree.
2318 // The variable curDeg is the current degree to increment.
2320 // Before degree incrementations a "working curve" is created.
2321 // It has the same knot, poles and multiplicities.
2323 // If the curve is periodic knots are added on the working curve before
2324 // and after the existing knots to make it a non-periodic curves.
2325 // The poles are also copied.
2327 // The first and last multiplicity of the working curve are set to Degree+1,
2328 // null poles are added if necessary.
2330 // Then the degree is incremented on the working curve.
2331 // The knots are unchanged but all multiplicities will be incremented.
2333 // Each degree incrementation is achieved by averaging curDeg+1 curves.
2335 // See : Degree elevation of B-spline curves
2336 // Hartmut PRAUTZSCH
2340 //-------------------------
2341 // create the working curve
2342 //-------------------------
2344 Standard_Integer i,k,f,l,m,pf,pl,firstknot;
2346 pf = 0; // number of null poles added at beginning
2347 pl = 0; // number of null poles added at end
2349 Standard_Integer nbwknots = Knots.Length();
2350 f = FirstUKnotIndex(Degree,Mults);
2351 l = LastUKnotIndex (Degree,Mults);
2354 // Periodic curves are transformed in non-periodic curves
2356 nbwknots += f - Mults.Lower();
2360 for (i = Mults.Lower(); i <= f; i++)
2363 nbwknots += Mults.Upper() - l;
2367 for (i = l; i <= Mults.Upper(); i++)
2371 // copy the knots and multiplicities
2372 TColStd_Array1OfReal wknots(1,nbwknots);
2373 TColStd_Array1OfInteger wmults(1,nbwknots);
2379 // copy the knots for a periodic curve
2380 Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
2383 for (k = l; k < Knots.Upper(); k++) {
2385 wknots(i) = Knots(k) - period;
2386 wmults(i) = Mults(k);
2389 for (k = Knots.Lower(); k <= Knots.Upper(); k++) {
2391 wknots(i) = Knots(k);
2392 wmults(i) = Mults(k);
2395 for (k = Knots.Lower()+1; k <= f; k++) {
2397 wknots(i) = Knots(k) + period;
2398 wmults(i) = Mults(k);
2402 // set the first and last mults to Degree+1
2403 // and add null poles
2405 pf += Degree + 1 - wmults(1);
2406 wmults(1) = Degree + 1;
2407 pl += Degree + 1 - wmults(nbwknots);
2408 wmults(nbwknots) = Degree + 1;
2410 //---------------------------
2411 // poles of the working curve
2412 //---------------------------
2414 Standard_Integer nbwpoles = 0;
2416 for (i = 1; i <= nbwknots; i++) nbwpoles += wmults(i);
2417 nbwpoles -= Degree + 1;
2419 // we provide space for degree elevation
2420 TColStd_Array1OfReal
2421 wpoles(1,(nbwpoles + (nbwknots-1) * (NewDegree - Degree)) * Dimension);
2423 for (i = 1; i <= pf * Dimension; i++)
2428 for (i = pf * Dimension + 1; i <= (nbwpoles - pl) * Dimension; i++) {
2429 wpoles(i) = Poles(k);
2431 if (k > Poles.Upper()) k = Poles.Lower();
2434 for (i = (nbwpoles-pl)*Dimension+1; i <= nbwpoles*Dimension; i++)
2438 //-----------------------------------------------------------
2439 // Declare the temporary arrays used in degree incrementation
2440 //-----------------------------------------------------------
2442 Standard_Integer nbwp = nbwpoles + (nbwknots-1) * (NewDegree - Degree);
2443 // Arrays for storing the temporary curves
2444 TColStd_Array1OfReal tempc1(1,nbwp * Dimension);
2445 TColStd_Array1OfReal tempc2(1,nbwp * Dimension);
2447 // Array for storing the knots to insert
2448 TColStd_Array1OfReal iknots(1,nbwknots);
2450 // Arrays for receiving the knots after insertion
2451 TColStd_Array1OfReal nknots(1,nbwknots);
2455 //------------------------------
2456 // Loop on degree incrementation
2457 //------------------------------
2459 Standard_Integer step,curDeg;
2460 Standard_Integer nbp = nbwpoles;
2463 for (curDeg = Degree; curDeg < NewDegree; curDeg++) {
2465 nbp = nbwp; // current number of poles
2466 nbwp = nbp + nbwknots - 1; // new number of poles
2468 // For the averaging
2469 TColStd_Array1OfReal nwpoles(1,nbwp * Dimension);
2470 nwpoles.Init(0.0e0) ;
2473 for (step = 0; step <= curDeg; step++) {
2475 // Compute the bspline of rank step.
2477 // if not the first time, decrement the multiplicities back
2479 for (i = 1; i <= nbwknots; i++)
2483 // Poles are the current poles
2484 // but the poles congruent to step are duplicated.
2486 Standard_Integer offset = 0;
2488 for (i = 0; i < nbp; i++) {
2491 for (k = 0; k < Dimension; k++) {
2492 tempc1((offset-1)*Dimension+k+1) =
2493 wpoles(NewPoles.Lower()+i*Dimension+k);
2495 if (i % (curDeg+1) == step) {
2498 for (k = 0; k < Dimension; k++) {
2499 tempc1((offset-1)*Dimension+k+1) =
2500 wpoles(NewPoles.Lower()+i*Dimension+k);
2505 // Knots multiplicities are increased
2506 // For each knot where the sum of multiplicities is congruent to step
2508 Standard_Integer stepmult = step+1;
2509 Standard_Integer nbknots = 0;
2510 Standard_Integer smult = 0;
2512 for (k = 1; k <= nbwknots; k++) {
2514 if (smult >= stepmult) {
2515 // this knot is increased
2516 stepmult += curDeg+1;
2520 // this knot is inserted
2522 iknots(nbknots) = wknots(k);
2526 // the curve is obtained by inserting the knots
2527 // to raise the multiplicities
2529 // we build "slices" of the arrays to set the correct size
2531 TColStd_Array1OfReal aknots(iknots(1),1,nbknots);
2532 TColStd_Array1OfReal curve (tempc1(1),1,offset * Dimension);
2533 TColStd_Array1OfReal ncurve(tempc2(1),1,nbwp * Dimension);
2534 // InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
2535 // aknots,NoMults(),ncurve,nknots,wmults,Epsilon(1.));
2537 InsertKnots(curDeg+1,Standard_False,Dimension,curve,wknots,wmults,
2538 aknots,NoMults(),ncurve,nknots,wmults,0.0);
2540 // add to the average
2542 for (i = 1; i <= nbwp * Dimension; i++)
2543 nwpoles(i) += ncurve(i);
2546 // add to the average
2548 for (i = 1; i <= nbwp * Dimension; i++)
2549 nwpoles(i) += tempc1(i);
2553 // The result is the average
2555 for (i = 1; i <= nbwp * Dimension; i++) {
2556 wpoles(i) = nwpoles(i) / (curDeg+1);
2564 // index in new knots of the first knot of the curve
2566 firstknot = Mults.Upper() - l + 1;
2570 // the new curve starts at index firstknot
2571 // so we must remove knots until the sum of multiplicities
2572 // from the first to the start is NewDegree+1
2574 // m is the current sum of multiplicities
2577 for (k = 1; k <= firstknot; k++)
2580 // compute the new first knot (k), pf will be the index of the first pole
2584 while (m > NewDegree+1) {
2589 if (m < NewDegree+1) {
2591 wmults(k) += m - NewDegree - 1;
2592 pf += m - NewDegree - 1;
2595 // on a periodic curve the knots start with firstknot
2601 for (i = NewKnots.Lower(); i <= NewKnots.Upper(); i++) {
2602 NewKnots(i) = wknots(k);
2603 NewMults(i) = wmults(k);
2610 for (i = NewPoles.Lower(); i <= NewPoles.Upper(); i++) {
2612 NewPoles(i) = wpoles(pf);
2616 //=======================================================================
2617 //function : PrepareUnperiodize
2619 //=======================================================================
2621 void BSplCLib::PrepareUnperiodize
2622 (const Standard_Integer Degree,
2623 const TColStd_Array1OfInteger& Mults,
2624 Standard_Integer& NbKnots,
2625 Standard_Integer& NbPoles)
2628 // initialize NbKnots and NbPoles
2629 NbKnots = Mults.Length();
2630 NbPoles = - Degree - 1;
2632 for (i = Mults.Lower(); i <= Mults.Upper(); i++)
2633 NbPoles += Mults(i);
2635 Standard_Integer sigma, k;
2636 // Add knots at the beginning of the curve to raise Multiplicities
2638 sigma = Mults(Mults.Lower());
2639 k = Mults.Upper() - 1;
2641 while ( sigma < Degree + 1) {
2643 NbPoles += Mults(k);
2647 // We must add exactly until Degree + 1 ->
2648 // Supress the excedent.
2649 if ( sigma > Degree + 1)
2650 NbPoles -= sigma - Degree - 1;
2652 // Add knots at the end of the curve to raise Multiplicities
2654 sigma = Mults(Mults.Upper());
2655 k = Mults.Lower() + 1;
2657 while ( sigma < Degree + 1) {
2659 NbPoles += Mults(k);
2663 // We must add exactly until Degree + 1 ->
2664 // Supress the excedent.
2665 if ( sigma > Degree + 1)
2666 NbPoles -= sigma - Degree - 1;
2669 //=======================================================================
2670 //function : Unperiodize
2672 //=======================================================================
2674 void BSplCLib::Unperiodize
2675 (const Standard_Integer Degree,
2676 const Standard_Integer , // Dimension,
2677 const TColStd_Array1OfInteger& Mults,
2678 const TColStd_Array1OfReal& Knots,
2679 const TColStd_Array1OfReal& Poles,
2680 TColStd_Array1OfInteger& NewMults,
2681 TColStd_Array1OfReal& NewKnots,
2682 TColStd_Array1OfReal& NewPoles)
2684 Standard_Integer sigma, k, index = 0;
2685 // evaluation of index : number of knots to insert before knot(1) to
2686 // raise sum of multiplicities to <Degree + 1>
2687 sigma = Mults(Mults.Lower());
2688 k = Mults.Upper() - 1;
2690 while ( sigma < Degree + 1) {
2696 Standard_Real period = Knots(Knots.Upper()) - Knots(Knots.Lower());
2698 // set the 'interior' knots;
2700 for ( k = 1; k <= Knots.Length(); k++) {
2701 NewKnots ( k + index ) = Knots( k);
2702 NewMults ( k + index ) = Mults( k);
2705 // set the 'starting' knots;
2707 for ( k = 1; k <= index; k++) {
2708 NewKnots( k) = NewKnots( k + Knots.Length() - 1) - period;
2709 NewMults( k) = NewMults( k + Knots.Length() - 1);
2711 NewMults( 1) -= sigma - Degree -1;
2713 // set the 'ending' knots;
2714 sigma = NewMults( index + Knots.Length() );
2716 for ( k = Knots.Length() + index + 1; k <= NewKnots.Length(); k++) {
2717 NewKnots( k) = NewKnots( k - Knots.Length() + 1) + period;
2718 NewMults( k) = NewMults( k - Knots.Length() + 1);
2719 sigma += NewMults( k - Knots.Length() + 1);
2721 NewMults(NewMults.Length()) -= sigma - Degree - 1;
2723 for ( k = 1 ; k <= NewPoles.Length(); k++) {
2724 NewPoles(k ) = Poles( (k-1) % Poles.Length() + 1);
2728 //=======================================================================
2729 //function : PrepareTrimming
2731 //=======================================================================
2733 void BSplCLib::PrepareTrimming(const Standard_Integer Degree,
2734 const Standard_Boolean Periodic,
2735 const TColStd_Array1OfReal& Knots,
2736 const TColStd_Array1OfInteger& Mults,
2737 const Standard_Real U1,
2738 const Standard_Real U2,
2739 Standard_Integer& NbKnots,
2740 Standard_Integer& NbPoles)
2743 Standard_Real NewU1, NewU2;
2744 Standard_Integer index1 = 0, index2 = 0;
2746 // Eval index1, index2 : position of U1 and U2 in the Array Knots
2747 // such as Knots(index1-1) <= U1 < Knots(index1)
2748 // Knots(index2-1) <= U2 < Knots(index2)
2749 LocateParameter( Degree, Knots, Mults, U1, Periodic,
2750 Knots.Lower(), Knots.Upper(), index1, NewU1);
2751 LocateParameter( Degree, Knots, Mults, U2, Periodic,
2752 Knots.Lower(), Knots.Upper(), index2, NewU2);
2754 if ( Abs(Knots(index2) - U2) <= Epsilon( U1))
2758 NbKnots = index2 - index1 + 3;
2761 NbPoles = Degree + 1;
2763 for ( i = index1; i <= index2; i++)
2764 NbPoles += Mults(i);
2767 //=======================================================================
2768 //function : Trimming
2770 //=======================================================================
2772 void BSplCLib::Trimming(const Standard_Integer Degree,
2773 const Standard_Boolean Periodic,
2774 const Standard_Integer Dimension,
2775 const TColStd_Array1OfReal& Knots,
2776 const TColStd_Array1OfInteger& Mults,
2777 const TColStd_Array1OfReal& Poles,
2778 const Standard_Real U1,
2779 const Standard_Real U2,
2780 TColStd_Array1OfReal& NewKnots,
2781 TColStd_Array1OfInteger& NewMults,
2782 TColStd_Array1OfReal& NewPoles)
2784 Standard_Integer i, nbpoles, nbknots;
2785 Standard_Real kk[2];
2786 Standard_Integer mm[2];
2787 TColStd_Array1OfReal K( kk[0], 1, 2 );
2788 TColStd_Array1OfInteger M( mm[0], 1, 2 );
2790 K(1) = U1; K(2) = U2;
2791 mm[0] = mm[1] = Degree;
2792 if (!PrepareInsertKnots( Degree, Periodic, Knots, Mults, K, M,
2793 nbpoles, nbknots, Epsilon( U1), 0))
2794 Standard_OutOfRange::Raise();
2796 TColStd_Array1OfReal TempPoles(1, nbpoles*Dimension);
2797 TColStd_Array1OfReal TempKnots(1, nbknots);
2798 TColStd_Array1OfInteger TempMults(1, nbknots);
2801 // do not allow the multiplicities to Add : they must be less than Degree
2803 InsertKnots(Degree, Periodic, Dimension, Poles, Knots, Mults,
2804 K, M, TempPoles, TempKnots, TempMults, Epsilon(U1),
2807 // find in TempPoles the index of the pole corresponding to U1
2808 Standard_Integer Kindex = 0, Pindex;
2809 Standard_Real NewU1;
2810 LocateParameter( Degree, TempKnots, TempMults, U1, Periodic,
2811 TempKnots.Lower(), TempKnots.Upper(), Kindex, NewU1);
2812 Pindex = PoleIndex ( Degree, Kindex, Periodic, TempMults);
2813 Pindex *= Dimension;
2815 for ( i = 1; i <= NewPoles.Length(); i++) NewPoles(i) = TempPoles(Pindex + i);
2817 for ( i = 1; i <= NewKnots.Length(); i++) {
2818 NewKnots(i) = TempKnots( Kindex+i-1);
2819 NewMults(i) = TempMults( Kindex+i-1);
2821 NewMults(1) = Min(Degree, NewMults(1)) + 1 ;
2822 NewMults(NewMults.Length())= Min(Degree, NewMults(NewMults.Length())) + 1 ;
2825 //=======================================================================
2826 //function : Solves a LU factored Matrix
2828 //=======================================================================
2831 BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
2832 const Standard_Integer UpperBandWidth,
2833 const Standard_Integer LowerBandWidth,
2834 const Standard_Integer ArrayDimension,
2835 Standard_Real& Array)
2837 Standard_Integer ii,
2844 Standard_Real *PolesArray = &Array ;
2845 Standard_Real Inverse ;
2848 if (Matrix.LowerCol() != 1 ||
2849 Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
2854 for (ii = Matrix.LowerRow() + 1; ii <= Matrix.UpperRow() ; ii++) {
2855 MinIndex = (ii - LowerBandWidth >= Matrix.LowerRow() ?
2856 ii - LowerBandWidth : Matrix.LowerRow()) ;
2858 for ( jj = MinIndex ; jj < ii ; jj++) {
2860 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2861 PolesArray[(ii-1) * ArrayDimension + kk] +=
2862 PolesArray[(jj-1) * ArrayDimension + kk] * Matrix(ii, jj - ii + LowerBandWidth + 1) ;
2867 for (ii = Matrix.UpperRow() ; ii >= Matrix.LowerRow() ; ii--) {
2868 MaxIndex = (ii + UpperBandWidth <= Matrix.UpperRow() ?
2869 ii + UpperBandWidth : Matrix.UpperRow()) ;
2871 for (jj = MaxIndex ; jj > ii ; jj--) {
2873 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2874 PolesArray[(ii-1) * ArrayDimension + kk] -=
2875 PolesArray[(jj - 1) * ArrayDimension + kk] *
2876 Matrix(ii, jj - ii + LowerBandWidth + 1) ;
2880 //fixing a bug PRO18577 to avoid divizion by zero
2882 Standard_Real divizor = Matrix(ii,LowerBandWidth + 1) ;
2883 Standard_Real Toler = 1.0e-16;
2884 if ( Abs(divizor) > Toler )
2885 Inverse = 1.0e0 / divizor ;
2888 // cout << " BSplCLib::SolveBandedSystem() : zero determinant " << endl;
2893 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2894 PolesArray[(ii-1) * ArrayDimension + kk] *= Inverse ;
2898 return (ReturnCode) ;
2901 //=======================================================================
2902 //function : Solves a LU factored Matrix
2904 //=======================================================================
2907 BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
2908 const Standard_Integer UpperBandWidth,
2909 const Standard_Integer LowerBandWidth,
2910 const Standard_Boolean HomogeneousFlag,
2911 const Standard_Integer ArrayDimension,
2912 Standard_Real& Poles,
2913 Standard_Real& Weights)
2915 Standard_Integer ii,
2920 Standard_Real Inverse,
2921 *PolesArray = &Poles,
2922 *WeightsArray = &Weights ;
2924 if (Matrix.LowerCol() != 1 ||
2925 Matrix.UpperCol() != UpperBandWidth + LowerBandWidth + 1) {
2929 if (HomogeneousFlag == Standard_False) {
2931 for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1; ii++) {
2933 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2934 PolesArray[ii * ArrayDimension + kk] *=
2940 BSplCLib::SolveBandedSystem(Matrix,
2945 if (ErrorCode != 0) {
2950 BSplCLib::SolveBandedSystem(Matrix,
2955 if (ErrorCode != 0) {
2959 if (HomogeneousFlag == Standard_False) {
2961 for (ii = 0 ; ii < Matrix.UpperRow() - Matrix.LowerRow() + 1 ; ii++) {
2962 Inverse = 1.0e0 / WeightsArray[ii] ;
2964 for (kk = 0 ; kk < ArrayDimension ; kk++) {
2965 PolesArray[ii * ArrayDimension + kk] *= Inverse ;
2969 FINISH : return (ReturnCode) ;
2972 //=======================================================================
2973 //function : BuildSchoenbergPoints
2975 //=======================================================================
2977 void BSplCLib::BuildSchoenbergPoints(const Standard_Integer Degree,
2978 const TColStd_Array1OfReal& FlatKnots,
2979 TColStd_Array1OfReal& Parameters)
2981 Standard_Integer ii,
2983 Standard_Real Inverse ;
2984 Inverse = 1.0e0 / (Standard_Real)Degree ;
2986 for (ii = Parameters.Lower() ; ii <= Parameters.Upper() ; ii++) {
2987 Parameters(ii) = 0.0e0 ;
2989 for (jj = 1 ; jj <= Degree ; jj++) {
2990 Parameters(ii) += FlatKnots(jj + ii) ;
2992 Parameters(ii) *= Inverse ;
2996 //=======================================================================
2997 //function : Interpolate
2999 //=======================================================================
3001 void BSplCLib::Interpolate(const Standard_Integer Degree,
3002 const TColStd_Array1OfReal& FlatKnots,
3003 const TColStd_Array1OfReal& Parameters,
3004 const TColStd_Array1OfInteger& ContactOrderArray,
3005 const Standard_Integer ArrayDimension,
3006 Standard_Real& Poles,
3007 Standard_Integer& InversionProblem)
3009 Standard_Integer ErrorCode,
3012 // Standard_Real *PolesArray = &Poles ;
3013 math_Matrix InterpolationMatrix(1, Parameters.Length(),
3014 1, 2 * Degree + 1) ;
3016 BSplCLib::BuildBSpMatrix(Parameters,
3020 InterpolationMatrix,
3023 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3026 BSplCLib::FactorBandedMatrix(InterpolationMatrix,
3030 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3033 BSplCLib::SolveBandedSystem(InterpolationMatrix,
3039 Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
3042 //=======================================================================
3043 //function : Interpolate
3045 //=======================================================================
3047 void BSplCLib::Interpolate(const Standard_Integer Degree,
3048 const TColStd_Array1OfReal& FlatKnots,
3049 const TColStd_Array1OfReal& Parameters,
3050 const TColStd_Array1OfInteger& ContactOrderArray,
3051 const Standard_Integer ArrayDimension,
3052 Standard_Real& Poles,
3053 Standard_Real& Weights,
3054 Standard_Integer& InversionProblem)
3056 Standard_Integer ErrorCode,
3060 math_Matrix InterpolationMatrix(1, Parameters.Length(),
3061 1, 2 * Degree + 1) ;
3063 BSplCLib::BuildBSpMatrix(Parameters,
3067 InterpolationMatrix,
3070 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3073 BSplCLib::FactorBandedMatrix(InterpolationMatrix,
3077 Standard_OutOfRange_Raise_if (ErrorCode != 0, "BSplCLib::Interpolate") ;
3080 BSplCLib::SolveBandedSystem(InterpolationMatrix,
3088 Standard_OutOfRange_Raise_if (ErrorCode != 0,"BSplCLib::Interpolate") ;
3091 //=======================================================================
3092 //function : Evaluates a Bspline function : uses the ExtrapMode
3093 //purpose : the function is extrapolated using the Taylor expansion
3094 // of degree ExtrapMode[0] to the left and the Taylor
3095 // expansion of degree ExtrapMode[1] to the right
3096 // this evaluates the numerator by multiplying by the weights
3097 // and evaluating it but does not call RationalDerivatives after
3098 //=======================================================================
3101 (const Standard_Real Parameter,
3102 const Standard_Boolean PeriodicFlag,
3103 const Standard_Integer DerivativeRequest,
3104 Standard_Integer& ExtrapMode,
3105 const Standard_Integer Degree,
3106 const TColStd_Array1OfReal& FlatKnots,
3107 const Standard_Integer ArrayDimension,
3108 Standard_Real& Poles,
3109 Standard_Real& Weights,
3110 Standard_Real& PolesResults,
3111 Standard_Real& WeightsResults)
3113 Standard_Integer ii,
3122 ExtrapolatingFlag[2],
3125 FirstNonZeroBsplineIndex,
3126 LocalRequest = DerivativeRequest ;
3127 Standard_Real *PResultArray,
3135 PolesArray = &Poles ;
3136 WeightsArray = &Weights ;
3137 ExtrapModeArray = &ExtrapMode ;
3138 PResultArray = &PolesResults ;
3139 WResultArray = &WeightsResults ;
3140 LocalParameter = Parameter ;
3141 ExtrapolatingFlag[0] =
3142 ExtrapolatingFlag[1] = 0 ;
3144 // check if we are extrapolating to a degree which is smaller than
3145 // the degree of the Bspline
3148 Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
3150 while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
3151 LocalParameter -= Period ;
3154 while (LocalParameter < FlatKnots(2)) {
3155 LocalParameter += Period ;
3158 if (Parameter < FlatKnots(2) &&
3159 LocalRequest < ExtrapModeArray[0] &&
3160 ExtrapModeArray[0] < Degree) {
3161 LocalRequest = ExtrapModeArray[0] ;
3162 LocalParameter = FlatKnots(2) ;
3163 ExtrapolatingFlag[0] = 1 ;
3165 if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
3166 LocalRequest < ExtrapModeArray[1] &&
3167 ExtrapModeArray[1] < Degree) {
3168 LocalRequest = ExtrapModeArray[1] ;
3169 LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
3170 ExtrapolatingFlag[1] = 1 ;
3172 Delta = Parameter - LocalParameter ;
3173 if (LocalRequest >= Order) {
3174 LocalRequest = Degree ;
3177 Modulus = FlatKnots.Length() - Degree -1 ;
3180 Modulus = FlatKnots.Length() - Degree ;
3183 BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
3185 BSplCLib::EvalBsplineBasis(1,
3190 FirstNonZeroBsplineIndex,
3192 if (ErrorCode != 0) {
3195 if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
3199 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3200 Index1 = FirstNonZeroBsplineIndex ;
3202 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3203 PResultArray[Index + kk] = 0.0e0 ;
3205 WResultArray[Index] = 0.0e0 ;
3207 for (jj = 1 ; jj <= Order ; jj++) {
3209 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3210 PResultArray[Index + kk] +=
3211 PolesArray[(Index1-1) * ArrayDimension + kk]
3212 * WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3214 WResultArray[Index2] += WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3216 Index1 = Index1 % Modulus ;
3219 Index += ArrayDimension ;
3225 // store Taylor expansion in LocalRealArray
3227 NewRequest = DerivativeRequest ;
3228 if (NewRequest > Degree) {
3229 NewRequest = Degree ;
3231 NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
3235 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3236 Index1 = FirstNonZeroBsplineIndex ;
3238 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3239 LocalRealArray[Index + kk] = 0.0e0 ;
3242 for (jj = 1 ; jj <= Order ; jj++) {
3244 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3245 LocalRealArray[Index + kk] +=
3246 PolesArray[(Index1-1)*ArrayDimension + kk] *
3247 WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3249 Index1 = Index1 % Modulus ;
3253 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3254 LocalRealArray[Index + kk] *= Inverse ;
3256 Index += ArrayDimension ;
3257 Inverse /= (Standard_Real) ii ;
3259 PLib::EvalPolynomial(Delta,
3268 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3269 Index1 = FirstNonZeroBsplineIndex ;
3270 LocalRealArray[Index] = 0.0e0 ;
3272 for (jj = 1 ; jj <= Order ; jj++) {
3273 LocalRealArray[Index] +=
3274 WeightsArray[Index1-1] * BsplineBasis(ii,jj) ;
3275 Index1 = Index1 % Modulus ;
3278 LocalRealArray[Index + kk] *= Inverse ;
3280 Inverse /= (Standard_Real) ii ;
3282 PLib::EvalPolynomial(Delta,
3292 //=======================================================================
3293 //function : Evaluates a Bspline function : uses the ExtrapMode
3294 //purpose : the function is extrapolated using the Taylor expansion
3295 // of degree ExtrapMode[0] to the left and the Taylor
3296 // expansion of degree ExtrapMode[1] to the right
3297 // WARNING : the array Results is supposed to have at least
3298 // (DerivativeRequest + 1) * ArrayDimension slots and the
3300 //=======================================================================
3303 (const Standard_Real Parameter,
3304 const Standard_Boolean PeriodicFlag,
3305 const Standard_Integer DerivativeRequest,
3306 Standard_Integer& ExtrapMode,
3307 const Standard_Integer Degree,
3308 const TColStd_Array1OfReal& FlatKnots,
3309 const Standard_Integer ArrayDimension,
3310 Standard_Real& Poles,
3311 Standard_Real& Results)
3313 Standard_Integer ii,
3321 ExtrapolatingFlag[2],
3324 FirstNonZeroBsplineIndex,
3325 LocalRequest = DerivativeRequest ;
3327 Standard_Real *ResultArray,
3334 PolesArray = &Poles ;
3335 ExtrapModeArray = &ExtrapMode ;
3336 ResultArray = &Results ;
3337 LocalParameter = Parameter ;
3338 ExtrapolatingFlag[0] =
3339 ExtrapolatingFlag[1] = 0 ;
3341 // check if we are extrapolating to a degree which is smaller than
3342 // the degree of the Bspline
3345 Period = FlatKnots(FlatKnots.Upper() - 1) - FlatKnots(2) ;
3347 while (LocalParameter > FlatKnots(FlatKnots.Upper() - 1)) {
3348 LocalParameter -= Period ;
3351 while (LocalParameter < FlatKnots(2)) {
3352 LocalParameter += Period ;
3355 if (Parameter < FlatKnots(2) &&
3356 LocalRequest < ExtrapModeArray[0] &&
3357 ExtrapModeArray[0] < Degree) {
3358 LocalRequest = ExtrapModeArray[0] ;
3359 LocalParameter = FlatKnots(2) ;
3360 ExtrapolatingFlag[0] = 1 ;
3362 if (Parameter > FlatKnots(FlatKnots.Upper()-1) &&
3363 LocalRequest < ExtrapModeArray[1] &&
3364 ExtrapModeArray[1] < Degree) {
3365 LocalRequest = ExtrapModeArray[1] ;
3366 LocalParameter = FlatKnots(FlatKnots.Upper()-1) ;
3367 ExtrapolatingFlag[1] = 1 ;
3369 Delta = Parameter - LocalParameter ;
3370 if (LocalRequest >= Order) {
3371 LocalRequest = Degree ;
3375 Modulus = FlatKnots.Length() - Degree -1 ;
3378 Modulus = FlatKnots.Length() - Degree ;
3381 BSplCLib_LocalMatrix BsplineBasis (LocalRequest, Order);
3384 BSplCLib::EvalBsplineBasis(1,
3389 FirstNonZeroBsplineIndex,
3391 if (ErrorCode != 0) {
3394 if (ExtrapolatingFlag[0] == 0 && ExtrapolatingFlag[1] == 0) {
3397 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3398 Index1 = FirstNonZeroBsplineIndex ;
3400 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3401 ResultArray[Index + kk] = 0.0e0 ;
3404 for (jj = 1 ; jj <= Order ; jj++) {
3406 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3407 ResultArray[Index + kk] +=
3408 PolesArray[(Index1-1) * ArrayDimension + kk] * BsplineBasis(ii,jj) ;
3410 Index1 = Index1 % Modulus ;
3413 Index += ArrayDimension ;
3418 // store Taylor expansion in LocalRealArray
3420 NewRequest = DerivativeRequest ;
3421 if (NewRequest > Degree) {
3422 NewRequest = Degree ;
3424 NCollection_LocalArray<Standard_Real> LocalRealArray((LocalRequest + 1)*ArrayDimension);
3429 for (ii = 1 ; ii <= LocalRequest + 1 ; ii++) {
3430 Index1 = FirstNonZeroBsplineIndex ;
3432 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3433 LocalRealArray[Index + kk] = 0.0e0 ;
3436 for (jj = 1 ; jj <= Order ; jj++) {
3438 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3439 LocalRealArray[Index + kk] +=
3440 PolesArray[(Index1-1)*ArrayDimension + kk] * BsplineBasis(ii,jj) ;
3442 Index1 = Index1 % Modulus ;
3446 for (kk = 0 ; kk < ArrayDimension ; kk++) {
3447 LocalRealArray[Index + kk] *= Inverse ;
3449 Index += ArrayDimension ;
3450 Inverse /= (Standard_Real) ii ;
3452 PLib::EvalPolynomial(Delta,
3462 //=======================================================================
3463 //function : TangExtendToConstraint
3464 //purpose : Extends a Bspline function using the tangency map
3468 //=======================================================================
3470 void BSplCLib::TangExtendToConstraint
3471 (const TColStd_Array1OfReal& FlatKnots,
3472 const Standard_Real C1Coefficient,
3473 const Standard_Integer NumPoles,
3474 Standard_Real& Poles,
3475 const Standard_Integer CDimension,
3476 const Standard_Integer CDegree,
3477 const TColStd_Array1OfReal& ConstraintPoint,
3478 const Standard_Integer Continuity,
3479 const Standard_Boolean After,
3480 Standard_Integer& NbPolesResult,
3481 Standard_Integer& NbKnotsResult,
3482 Standard_Real& KnotsResult,
3483 Standard_Real& PolesResult)
3486 if (CDegree<Continuity+1) {
3487 cout<<"The BSpline degree must be greater than the order of continuity"<<endl;
3490 Standard_Real * Padr = &Poles ;
3491 Standard_Real * KRadr = &KnotsResult ;
3492 Standard_Real * PRadr = &PolesResult ;
3494 ////////////////////////////////////////////////////////////////////////
3496 // 1. calculation of extension nD
3498 ////////////////////////////////////////////////////////////////////////
3501 Standard_Integer Csize = Continuity + 2;
3502 math_Matrix MatCoefs(1,Csize, 1,Csize);
3504 PLib::HermiteCoefficients(0, 1, // Limits
3505 Continuity, 0, // Orders of constraints
3509 PLib::HermiteCoefficients(0, 1, // Limits
3510 0, Continuity, // Orders of constraints
3515 // position at the node of connection
3516 Standard_Real Tbord ;
3518 Tbord = FlatKnots(FlatKnots.Upper()-CDegree);
3521 Tbord = FlatKnots(FlatKnots.Lower()+CDegree);
3523 Standard_Boolean periodic_flag = Standard_False ;
3524 Standard_Integer ipos, extrap_mode[2], derivative_request = Max(Continuity,1);
3525 extrap_mode[0] = extrap_mode[1] = CDegree;
3526 TColStd_Array1OfReal EvalBS(1, CDimension * (derivative_request+1)) ;
3527 Standard_Real * Eadr = (Standard_Real *) &EvalBS(1) ;
3528 BSplCLib::Eval(Tbord,periodic_flag,derivative_request,extrap_mode[0],
3529 CDegree,FlatKnots,CDimension,Poles,*Eadr);
3531 // norm of the tangent at the node of connection
3532 math_Vector Tgte(1,CDimension);
3534 for (ipos=1;ipos<=CDimension;ipos++) {
3535 Tgte(ipos) = EvalBS(ipos+CDimension);
3537 Standard_Real L1=Tgte.Norm();
3540 // matrix of constraints
3541 math_Matrix Contraintes(1,Csize,1,CDimension);
3544 for (ipos=1;ipos<=CDimension;ipos++) {
3545 Contraintes(1,ipos) = EvalBS(ipos);
3546 Contraintes(2,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
3547 if(Continuity >= 2) Contraintes(3,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
3548 if(Continuity >= 3) Contraintes(4,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
3549 Contraintes(Continuity+2,ipos) = ConstraintPoint(ipos);
3554 for (ipos=1;ipos<=CDimension;ipos++) {
3555 Contraintes(1,ipos) = ConstraintPoint(ipos);
3556 Contraintes(2,ipos) = EvalBS(ipos);
3557 if(Continuity >= 1) Contraintes(3,ipos) = C1Coefficient * EvalBS(ipos+CDimension);
3558 if(Continuity >= 2) Contraintes(4,ipos) = EvalBS(ipos+2*CDimension) * Pow(C1Coefficient,2);
3559 if(Continuity >= 3) Contraintes(5,ipos) = EvalBS(ipos+3*CDimension) * Pow(C1Coefficient,3);
3563 // calculate the coefficients of extension
3564 Standard_Integer ii, jj, kk;
3565 TColStd_Array1OfReal ExtraCoeffs(1,Csize*CDimension);
3566 ExtraCoeffs.Init(0.);
3568 for (ii=1; ii<=Csize; ii++) {
3570 for (jj=1; jj<=Csize; jj++) {
3572 for (kk=1; kk<=CDimension; kk++) {
3573 ExtraCoeffs(kk+(jj-1)*CDimension) += MatCoefs(ii,jj)*Contraintes(ii,kk);
3578 // calculate the poles of extension
3579 TColStd_Array1OfReal ExtrapPoles(1,Csize*CDimension);
3580 Standard_Real * EPadr = &ExtrapPoles(1) ;
3581 PLib::CoefficientsPoles(CDimension,
3582 ExtraCoeffs, PLib::NoWeights(),
3583 ExtrapPoles, PLib::NoWeights());
3585 // calculate the nodes of extension with multiplicities
3586 TColStd_Array1OfReal ExtrapNoeuds(1,2);
3587 ExtrapNoeuds(1) = 0.;
3588 ExtrapNoeuds(2) = 1.;
3589 TColStd_Array1OfInteger ExtrapMults(1,2);
3590 ExtrapMults(1) = Csize;
3591 ExtrapMults(2) = Csize;
3593 // flat nodes of extension
3594 TColStd_Array1OfReal FK2(1, Csize*2);
3595 BSplCLib::KnotSequence(ExtrapNoeuds,ExtrapMults,FK2);
3597 // norm of the tangent at the connection point
3599 BSplCLib::Eval(0.,periodic_flag,1,extrap_mode[0],
3600 Csize-1,FK2,CDimension,*EPadr,*Eadr);
3603 BSplCLib::Eval(1.,periodic_flag,1,extrap_mode[0],
3604 Csize-1,FK2,CDimension,*EPadr,*Eadr);
3607 for (ipos=1;ipos<=CDimension;ipos++) {
3608 Tgte(ipos) = EvalBS(ipos+CDimension);
3610 Standard_Real L2 = Tgte.Norm();
3612 // harmonisation of degrees
3613 TColStd_Array1OfReal NewP2(1, (CDegree+1)*CDimension);
3614 TColStd_Array1OfReal NewK2(1, 2);
3615 TColStd_Array1OfInteger NewM2(1, 2);
3616 if (Csize-1<CDegree) {
3617 BSplCLib::IncreaseDegree(Csize-1,CDegree,Standard_False,CDimension,
3618 ExtrapPoles,ExtrapNoeuds,ExtrapMults,
3622 NewP2 = ExtrapPoles;
3623 NewK2 = ExtrapNoeuds;
3624 NewM2 = ExtrapMults;
3627 // flat nodes of extension after harmonization of degrees
3628 TColStd_Array1OfReal NewFK2(1, (CDegree+1)*2);
3629 BSplCLib::KnotSequence(NewK2,NewM2,NewFK2);
3632 ////////////////////////////////////////////////////////////////////////
3634 // 2. concatenation C0
3636 ////////////////////////////////////////////////////////////////////////
3638 // ratio of reparametrization
3639 Standard_Real Ratio=1, Delta;
3640 if ( (L1 > Precision::Confusion()) && (L2 > Precision::Confusion()) ) {
3643 if ( (Ratio < 1.e-5) || (Ratio > 1.e5) ) Ratio = 1;
3646 // do not touch the first BSpline
3647 Delta = Ratio*NewFK2(NewFK2.Lower()) - FlatKnots(FlatKnots.Upper());
3650 // do not touch the second BSpline
3651 Delta = Ratio*NewFK2(NewFK2.Upper()) - FlatKnots(FlatKnots.Lower());
3654 // result of the concatenation
3655 Standard_Integer NbP1 = NumPoles, NbP2 = CDegree+1;
3656 Standard_Integer NbK1 = FlatKnots.Length(), NbK2 = 2*(CDegree+1);
3657 TColStd_Array1OfReal NewPoles (1, (NbP1+ NbP2-1)*CDimension);
3658 TColStd_Array1OfReal NewFlats (1, NbK1+NbK2-CDegree-2);
3661 Standard_Integer indNP, indP, indEP;
3664 for (ii=1; ii<=NbP1+NbP2-1; ii++) {
3666 for (jj=1; jj<=CDimension; jj++) {
3667 indNP = (ii-1)*CDimension+jj;
3668 indP = (ii-1)*CDimension+jj-1;
3669 indEP = (ii-NbP1)*CDimension+jj;
3670 if (ii<NbP1) NewPoles(indNP) = Padr[indP];
3671 else NewPoles(indNP) = NewP2(indEP);
3677 for (ii=1; ii<=NbP1+NbP2-1; ii++) {
3679 for (jj=1; jj<=CDimension; jj++) {
3680 indNP = (ii-1)*CDimension+jj;
3681 indEP = (ii-1)*CDimension+jj;
3682 indP = (ii-NbP2)*CDimension+jj-1;
3683 if (ii<NbP2) NewPoles(indNP) = NewP2(indEP);
3684 else NewPoles(indNP) = Padr[indP];
3691 // start with the nodes of the initial surface
3693 for (ii=1; ii<NbK1; ii++) {
3694 NewFlats(ii) = FlatKnots(FlatKnots.Lower()+ii-1);
3696 // continue with the reparameterized nodes of the extension
3698 for (ii=1; ii<=NbK2-CDegree-1; ii++) {
3699 NewFlats(NbK1+ii-1) = Ratio*NewFK2(NewFK2.Lower()+ii+CDegree) - Delta;
3703 // start with the reparameterized nodes of the extension
3705 for (ii=1; ii<NbK2-CDegree; ii++) {
3706 NewFlats(ii) = Ratio*NewFK2(NewFK2.Lower()+ii-1) - Delta;
3708 // continue with the nodes of the initial surface
3710 for (ii=2; ii<=NbK1; ii++) {
3711 NewFlats(NbK2+ii-CDegree-2) = FlatKnots(FlatKnots.Lower()+ii-1);
3716 ////////////////////////////////////////////////////////////////////////
3718 // 3. reduction of multiplicite at the node of connection
3720 ////////////////////////////////////////////////////////////////////////
3722 // number of separate nodes
3723 Standard_Integer KLength = 1;
3725 for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
3726 if (NewFlats(ii) != NewFlats(ii-1)) KLength++;
3729 // flat nodes --> nodes + multiplicities
3730 TColStd_Array1OfReal NewKnots (1, KLength);
3731 TColStd_Array1OfInteger NewMults (1, KLength);
3734 NewKnots(jj) = NewFlats(1);
3736 for (ii=2; ii<=NbK1+NbK2-CDegree-2;ii++) {
3737 if (NewFlats(ii) == NewFlats(ii-1)) NewMults(jj)++;
3740 NewKnots(jj) = NewFlats(ii);
3744 // reduction of multiplicity at the second or the last but one node
3745 Standard_Integer Index = 2, M = CDegree;
3746 if (After) Index = KLength-1;
3747 TColStd_Array1OfReal ResultPoles (1, (NbP1+ NbP2-1)*CDimension);
3748 TColStd_Array1OfReal ResultKnots (1, KLength);
3749 TColStd_Array1OfInteger ResultMults (1, KLength);
3750 Standard_Real Tol = 1.e-6;
3751 Standard_Boolean Ok = Standard_True;
3753 while ( (M>CDegree-Continuity) && Ok) {
3754 Ok = RemoveKnot(Index, M-1, CDegree, Standard_False, CDimension,
3755 NewPoles, NewKnots, NewMults,
3756 ResultPoles, ResultKnots, ResultMults, Tol);
3761 // number of poles of the concatenation
3762 NbPolesResult = NbP1 + NbP2 - 1;
3763 // the poles of the concatenation
3764 Standard_Integer PLength = NbPolesResult*CDimension;
3766 for (jj=1; jj<=PLength; jj++) {
3767 PRadr[jj-1] = NewPoles(jj);
3770 // flat nodes of the concatenation
3771 Standard_Integer ideb = 0;
3773 for (jj=0; jj<NewKnots.Length(); jj++) {
3774 for (ii=0; ii<NewMults(jj+1); ii++) {
3775 KRadr[ideb+ii] = NewKnots(jj+1);
3777 ideb += NewMults(jj+1);
3779 NbKnotsResult = ideb;
3783 // number of poles of the result
3784 NbPolesResult = NbP1 + NbP2 - 1 - CDegree + M;
3785 // the poles of the result
3786 Standard_Integer PLength = NbPolesResult*CDimension;
3788 for (jj=0; jj<PLength; jj++) {
3789 PRadr[jj] = ResultPoles(jj+1);
3792 // flat nodes of the result
3793 Standard_Integer ideb = 0;
3795 for (jj=0; jj<ResultKnots.Length(); jj++) {
3796 for (ii=0; ii<ResultMults(jj+1); ii++) {
3797 KRadr[ideb+ii] = ResultKnots(jj+1);
3799 ideb += ResultMults(jj+1);
3801 NbKnotsResult = ideb;
3805 //=======================================================================
3806 //function : Resolution
3809 // Let C(t) = SUM Ci Bi(t) a Bspline curve of degree d
3811 // with nodes tj for j = 1,n+d+1
3815 // Then C (t) = SUM d * --------- Bi (t)
3816 // i = 2,n ti+d - ti
3819 // for the base of BSpline Bi (t) of degree d-1.
3821 // Consequently the upper bound of the norm of the derivative from C is :
3825 // d * Max | --------- |
3826 // i = 2,n | ti+d - ti |
3829 // In the rational case set C(t) = -----
3833 // D(t) = SUM Di Bi(t)
3836 // N(t) = SUM Di * Ci Bi(t)
3839 // N'(t) - D'(t) C(t)
3840 // C'(t) = -----------------------
3844 // N'(t) - D'(t) C(t) =
3846 // Di * (Ci - C(t)) - Di-1 * (Ci-1 - C(t)) d-1
3847 // SUM d * ---------------------------------------- * Bi (t) =
3851 // Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj) d-1
3852 // SUM SUM d * ----------------------------------- * Betaj(t) * Bi (t)
3853 //i=2,n j=1,n ti+d - ti
3858 // Betaj(t) = --------
3861 // Betaj(t) form a partition >= 0 of the entity with support
3862 // tj, tj+d+1. Consequently if Rj = {j-d, ...., j+d+d+1}
3863 // obtain an upper bound of the derivative of C by taking :
3870 // Di * (Ci - Cj) - Di-1 * (Ci-1 - Cj)
3871 // Max Max d * -----------------------------------
3872 // j=1,n i dans Rj ti+d - ti
3874 // --------------------------------------------------------
3880 //=======================================================================
3882 void BSplCLib::Resolution( Standard_Real& Poles,
3883 const Standard_Integer ArrayDimension,
3884 const Standard_Integer NumPoles,
3885 const TColStd_Array1OfReal& Weights,
3886 const TColStd_Array1OfReal& FlatKnots,
3887 const Standard_Integer Degree,
3888 const Standard_Real Tolerance3D,
3889 Standard_Real& UTolerance)
3891 Standard_Integer ii,num_poles,ii_index,jj_index,ii_inDim;
3892 Standard_Integer lower,upper,ii_minus,jj,ii_miDim;
3893 Standard_Integer Deg1 = Degree + 1;
3894 Standard_Integer Deg2 = (Degree << 1) + 1;
3895 Standard_Real value,factor,W,min_weights,inverse;
3896 Standard_Real pa_ii_inDim_0, pa_ii_inDim_1, pa_ii_inDim_2, pa_ii_inDim_3;
3897 Standard_Real pa_ii_miDim_0, pa_ii_miDim_1, pa_ii_miDim_2, pa_ii_miDim_3;
3898 Standard_Real wg_ii_index, wg_ii_minus;
3899 Standard_Real *PA,max_derivative;
3900 const Standard_Real * FK = &FlatKnots(FlatKnots.Lower());
3902 max_derivative = 0.0e0;
3903 num_poles = FlatKnots.Length() - Deg1;
3904 switch (ArrayDimension) {
3906 if (&Weights != NULL) {
3907 const Standard_Real * WG = &Weights(Weights.Lower());
3908 min_weights = WG[0];
3910 for (ii = 1 ; ii < NumPoles ; ii++) {
3912 if (W < min_weights) min_weights = W;
3915 for (ii = 1 ; ii < num_poles ; ii++) {
3916 ii_index = ii % NumPoles;
3917 ii_inDim = ii_index << 1;
3918 ii_minus = (ii - 1) % NumPoles;
3919 ii_miDim = ii_minus << 1;
3920 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
3921 pa_ii_inDim_1 = PA[ii_inDim];
3922 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
3923 pa_ii_miDim_1 = PA[ii_miDim];
3924 wg_ii_index = WG[ii_index];
3925 wg_ii_minus = WG[ii_minus];
3926 inverse = FK[ii + Degree] - FK[ii];
3927 inverse = 1.0e0 / inverse;
3929 if (lower < 0) lower = 0;
3931 if (upper > num_poles) upper = num_poles;
3933 for (jj = lower ; jj < upper ; jj++) {
3934 jj_index = jj % NumPoles;
3935 jj_index = jj_index << 1;
3937 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
3938 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
3939 if (factor < 0) factor = - factor;
3940 value += factor; jj_index++;
3941 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
3942 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
3943 if (factor < 0) factor = - factor;
3946 if (max_derivative < value) max_derivative = value;
3949 max_derivative /= min_weights;
3953 for (ii = 1 ; ii < num_poles ; ii++) {
3954 ii_index = ii % NumPoles;
3955 ii_index = ii_index << 1;
3956 ii_minus = (ii - 1) % NumPoles;
3957 ii_minus = ii_minus << 1;
3958 inverse = FK[ii + Degree] - FK[ii];
3959 inverse = 1.0e0 / inverse;
3961 factor = PA[ii_index] - PA[ii_minus];
3962 if (factor < 0) factor = - factor;
3963 value += factor; ii_index++; ii_minus++;
3964 factor = PA[ii_index] - PA[ii_minus];
3965 if (factor < 0) factor = - factor;
3968 if (max_derivative < value) max_derivative = value;
3974 if (&Weights != NULL) {
3975 const Standard_Real * WG = &Weights(Weights.Lower());
3976 min_weights = WG[0];
3978 for (ii = 1 ; ii < NumPoles ; ii++) {
3980 if (W < min_weights) min_weights = W;
3983 for (ii = 1 ; ii < num_poles ; ii++) {
3984 ii_index = ii % NumPoles;
3985 ii_inDim = (ii_index << 1) + ii_index;
3986 ii_minus = (ii - 1) % NumPoles;
3987 ii_miDim = (ii_minus << 1) + ii_minus;
3988 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
3989 pa_ii_inDim_1 = PA[ii_inDim]; ii_inDim++;
3990 pa_ii_inDim_2 = PA[ii_inDim];
3991 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
3992 pa_ii_miDim_1 = PA[ii_miDim]; ii_miDim++;
3993 pa_ii_miDim_2 = PA[ii_miDim];
3994 wg_ii_index = WG[ii_index];
3995 wg_ii_minus = WG[ii_minus];
3996 inverse = FK[ii + Degree] - FK[ii];
3997 inverse = 1.0e0 / inverse;
3999 if (lower < 0) lower = 0;
4001 if (upper > num_poles) upper = num_poles;
4003 for (jj = lower ; jj < upper ; jj++) {
4004 jj_index = jj % NumPoles;
4005 jj_index = (jj_index << 1) + jj_index;
4007 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
4008 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
4009 if (factor < 0) factor = - factor;
4010 value += factor; jj_index++;
4011 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
4012 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
4013 if (factor < 0) factor = - factor;
4014 value += factor; jj_index++;
4015 factor = (((PA[jj_index] - pa_ii_inDim_2) * wg_ii_index) -
4016 ((PA[jj_index] - pa_ii_miDim_2) * wg_ii_minus));
4017 if (factor < 0) factor = - factor;
4020 if (max_derivative < value) max_derivative = value;
4023 max_derivative /= min_weights;
4027 for (ii = 1 ; ii < num_poles ; ii++) {
4028 ii_index = ii % NumPoles;
4029 ii_index = (ii_index << 1) + ii_index;
4030 ii_minus = (ii - 1) % NumPoles;
4031 ii_minus = (ii_minus << 1) + ii_minus;
4032 inverse = FK[ii + Degree] - FK[ii];
4033 inverse = 1.0e0 / inverse;
4035 factor = PA[ii_index] - PA[ii_minus];
4036 if (factor < 0) factor = - factor;
4037 value += factor; ii_index++; ii_minus++;
4038 factor = PA[ii_index] - PA[ii_minus];
4039 if (factor < 0) factor = - factor;
4040 value += factor; ii_index++; ii_minus++;
4041 factor = PA[ii_index] - PA[ii_minus];
4042 if (factor < 0) factor = - factor;
4045 if (max_derivative < value) max_derivative = value;
4051 if (&Weights != NULL) {
4052 const Standard_Real * WG = &Weights(Weights.Lower());
4053 min_weights = WG[0];
4055 for (ii = 1 ; ii < NumPoles ; ii++) {
4057 if (W < min_weights) min_weights = W;
4060 for (ii = 1 ; ii < num_poles ; ii++) {
4061 ii_index = ii % NumPoles;
4062 ii_inDim = ii_index << 2;
4063 ii_minus = (ii - 1) % NumPoles;
4064 ii_miDim = ii_minus << 2;
4065 pa_ii_inDim_0 = PA[ii_inDim]; ii_inDim++;
4066 pa_ii_inDim_1 = PA[ii_inDim]; ii_inDim++;
4067 pa_ii_inDim_2 = PA[ii_inDim]; ii_inDim++;
4068 pa_ii_inDim_3 = PA[ii_inDim];
4069 pa_ii_miDim_0 = PA[ii_miDim]; ii_miDim++;
4070 pa_ii_miDim_1 = PA[ii_miDim]; ii_miDim++;
4071 pa_ii_miDim_2 = PA[ii_miDim]; ii_miDim++;
4072 pa_ii_miDim_3 = PA[ii_miDim];
4073 wg_ii_index = WG[ii_index];
4074 wg_ii_minus = WG[ii_minus];
4075 inverse = FK[ii + Degree] - FK[ii];
4076 inverse = 1.0e0 / inverse;
4078 if (lower < 0) lower = 0;
4080 if (upper > num_poles) upper = num_poles;
4082 for (jj = lower ; jj < upper ; jj++) {
4083 jj_index = jj % NumPoles;
4084 jj_index = jj_index << 2;
4086 factor = (((PA[jj_index] - pa_ii_inDim_0) * wg_ii_index) -
4087 ((PA[jj_index] - pa_ii_miDim_0) * wg_ii_minus));
4088 if (factor < 0) factor = - factor;
4089 value += factor; jj_index++;
4090 factor = (((PA[jj_index] - pa_ii_inDim_1) * wg_ii_index) -
4091 ((PA[jj_index] - pa_ii_miDim_1) * wg_ii_minus));
4092 if (factor < 0) factor = - factor;
4093 value += factor; jj_index++;
4094 factor = (((PA[jj_index] - pa_ii_inDim_2) * wg_ii_index) -
4095 ((PA[jj_index] - pa_ii_miDim_2) * wg_ii_minus));
4096 if (factor < 0) factor = - factor;
4097 value += factor; jj_index++;
4098 factor = (((PA[jj_index] - pa_ii_inDim_3) * wg_ii_index) -
4099 ((PA[jj_index] - pa_ii_miDim_3) * wg_ii_minus));
4100 if (factor < 0) factor = - factor;
4103 if (max_derivative < value) max_derivative = value;
4106 max_derivative /= min_weights;
4110 for (ii = 1 ; ii < num_poles ; ii++) {
4111 ii_index = ii % NumPoles;
4112 ii_index = ii_index << 2;
4113 ii_minus = (ii - 1) % NumPoles;
4114 ii_minus = ii_minus << 2;
4115 inverse = FK[ii + Degree] - FK[ii];
4116 inverse = 1.0e0 / inverse;
4118 factor = PA[ii_index] - PA[ii_minus];
4119 if (factor < 0) factor = - factor;
4120 value += factor; ii_index++; ii_minus++;
4121 factor = PA[ii_index] - PA[ii_minus];
4122 if (factor < 0) factor = - factor;
4123 value += factor; ii_index++; ii_minus++;
4124 factor = PA[ii_index] - PA[ii_minus];
4125 if (factor < 0) factor = - factor;
4126 value += factor; ii_index++; ii_minus++;
4127 factor = PA[ii_index] - PA[ii_minus];
4128 if (factor < 0) factor = - factor;
4131 if (max_derivative < value) max_derivative = value;
4137 Standard_Integer kk;
4138 if (&Weights != NULL) {
4139 const Standard_Real * WG = &Weights(Weights.Lower());
4140 min_weights = WG[0];
4142 for (ii = 1 ; ii < NumPoles ; ii++) {
4144 if (W < min_weights) min_weights = W;
4147 for (ii = 1 ; ii < num_poles ; ii++) {
4148 ii_index = ii % NumPoles;
4149 ii_inDim = ii_index * ArrayDimension;
4150 ii_minus = (ii - 1) % NumPoles;
4151 ii_miDim = ii_minus * ArrayDimension;
4152 wg_ii_index = WG[ii_index];
4153 wg_ii_minus = WG[ii_minus];
4154 inverse = FK[ii + Degree] - FK[ii];
4155 inverse = 1.0e0 / inverse;
4157 if (lower < 0) lower = 0;
4159 if (upper > num_poles) upper = num_poles;
4161 for (jj = lower ; jj < upper ; jj++) {
4162 jj_index = jj % NumPoles;
4163 jj_index *= ArrayDimension;
4166 for (kk = 0 ; kk < ArrayDimension ; kk++) {
4167 factor = (((PA[jj_index + kk] - PA[ii_inDim + kk]) * wg_ii_index) -
4168 ((PA[jj_index + kk] - PA[ii_miDim + kk]) * wg_ii_minus));
4169 if (factor < 0) factor = - factor;
4173 if (max_derivative < value) max_derivative = value;
4176 max_derivative /= min_weights;
4180 for (ii = 1 ; ii < num_poles ; ii++) {
4181 ii_index = ii % NumPoles;
4182 ii_index *= ArrayDimension;
4183 ii_minus = (ii - 1) % NumPoles;
4184 ii_minus *= ArrayDimension;
4185 inverse = FK[ii + Degree] - FK[ii];
4186 inverse = 1.0e0 / inverse;
4189 for (kk = 0 ; kk < ArrayDimension ; kk++) {
4190 factor = PA[ii_index + kk] - PA[ii_minus + kk];
4191 if (factor < 0) factor = - factor;
4195 if (max_derivative < value) max_derivative = value;
4200 max_derivative *= Degree;
4201 if (max_derivative > RealSmall())
4202 UTolerance = Tolerance3D / max_derivative;
4204 UTolerance = Tolerance3D / RealSmall();
4207 //=======================================================================
4208 // function: FlatBezierKnots
4210 //=======================================================================
4212 // array of flat knots for bezier curve of maximum 25 degree
4213 static const Standard_Real knots[52] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
4214 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
4215 const Standard_Real& BSplCLib::FlatBezierKnots (const Standard_Integer Degree)
4217 Standard_OutOfRange_Raise_if (Degree < 1 || Degree > MaxDegree() || MaxDegree() != 25,
4218 "Bezier curve degree greater than maximal supported");
4220 return knots[25-Degree];