1 // Created on: 1994-08-18
2 // Created by: Laurent PAINNOT
3 // Copyright (c) 1994-1999 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 // 8-Aug-95 : xab : interpolation uses BSplCLib::Interpolate
19 #include <BSplCLib.hxx>
20 #include <Geom2d_BSplineCurve.hxx>
21 #include <Geom2dAPI_Interpolate.hxx>
22 #include <gp_Vec2d.hxx>
24 #include <Standard_ConstructionError.hxx>
25 #include <StdFail_NotDone.hxx>
26 #include <TColgp_Array1OfPnt2d.hxx>
27 #include <TColStd_Array1OfBoolean.hxx>
28 #include <TColStd_Array1OfInteger.hxx>
29 #include <TColStd_HArray1OfBoolean.hxx>
30 #include <TColStd_HArray1OfReal.hxx>
32 //=======================================================================
33 //function : CheckPoints
35 //=======================================================================
36 static Standard_Boolean CheckPoints(const TColgp_Array1OfPnt2d& PointArray,
37 const Standard_Real Tolerance)
40 Standard_Real tolerance_squared = Tolerance * Tolerance,
42 Standard_Boolean result = Standard_True ;
43 for (ii = PointArray.Lower() ; result && ii < PointArray.Upper() ; ii++) {
45 PointArray.Value(ii).SquareDistance(PointArray.Value(ii+1)) ;
46 result = (distance_squared >= tolerance_squared) ;
51 //=======================================================================
52 //function : CheckTangents
54 //=======================================================================
55 static Standard_Boolean CheckTangents(
56 const TColgp_Array1OfVec2d& Tangents,
57 const TColStd_Array1OfBoolean& TangentFlags,
58 const Standard_Real Tolerance)
62 Standard_Real tolerance_squared = Tolerance * Tolerance,
64 Standard_Boolean result = Standard_True ;
65 index = TangentFlags.Lower() ;
66 for (ii = Tangents.Lower(); result && ii <= Tangents.Upper() ; ii++) {
67 if(TangentFlags.Value(index)) {
69 Tangents.Value(ii).SquareMagnitude() ;
70 result = (distance_squared >= tolerance_squared) ;
77 //=======================================================================
78 //function : CheckParameters
80 //=======================================================================
81 static Standard_Boolean CheckParameters(const
82 TColStd_Array1OfReal& Parameters)
85 Standard_Real distance ;
86 Standard_Boolean result = Standard_True ;
87 for (ii = Parameters.Lower() ; result && ii < Parameters.Upper() ; ii++) {
89 Parameters.Value(ii+1) - Parameters.Value(ii) ;
90 result = (distance >= RealSmall()) ;
94 //=======================================================================
95 //function : BuildParameters
97 //=======================================================================
98 static void BuildParameters(const Standard_Boolean PeriodicFlag,
99 const TColgp_Array1OfPnt2d& PointsArray,
100 Handle(TColStd_HArray1OfReal)& ParametersPtr)
104 Standard_Real distance ;
106 num_parameters = PointsArray.Length() ;
108 num_parameters += 1 ;
111 new TColStd_HArray1OfReal(1,
113 ParametersPtr->SetValue(1,0.0e0) ;
115 for (ii = PointsArray.Lower() ; ii < PointsArray.Upper() ; ii++) {
117 PointsArray.Value(ii).Distance(PointsArray.Value(ii+1)) ;
118 ParametersPtr->SetValue(index,
119 ParametersPtr->Value(ii) + distance) ;
124 PointsArray.Value(PointsArray.Upper()).
125 Distance(PointsArray.Value(PointsArray.Lower())) ;
126 ParametersPtr->SetValue(index,
127 ParametersPtr->Value(ii) + distance) ;
130 //=======================================================================
131 //function : BuildPeriodicTangents
133 //=======================================================================
135 static void BuildPeriodicTangent(
136 const TColgp_Array1OfPnt2d& PointsArray,
137 TColgp_Array1OfVec2d& TangentsArray,
138 TColStd_Array1OfBoolean& TangentFlags,
139 const TColStd_Array1OfReal& ParametersArray)
144 Standard_Real *point_array,
150 if (PointsArray.Length() < 3) {
151 throw Standard_ConstructionError();
154 if (!TangentFlags.Value(1)) {
156 if (PointsArray.Length() == 3) {
159 point_array = (Standard_Real *) &PointsArray.Value(PointsArray.Lower()) ;
161 (Standard_Real *) &ParametersArray.Value(1) ;
162 TangentFlags.SetValue(1,Standard_True) ;
163 PLib::EvalLagrange(ParametersArray.Value(1),
170 for (ii = 1 ; ii <= 2 ; ii++) {
171 a_vector.SetCoord(ii,eval_result[1][ii-1]) ;
173 TangentsArray.SetValue(1,a_vector) ;
176 //=======================================================================
177 //function : BuildTangents
179 //=======================================================================
181 static void BuildTangents(const TColgp_Array1OfPnt2d& PointsArray,
182 TColgp_Array1OfVec2d& TangentsArray,
183 TColStd_Array1OfBoolean& TangentFlags,
184 const TColStd_Array1OfReal& ParametersArray)
188 Standard_Real *point_array,
196 if ( PointsArray.Length() < 3) {
197 throw Standard_ConstructionError();
199 if (PointsArray.Length() == 3) {
202 if (!TangentFlags.Value(1)) {
203 point_array = (Standard_Real *) &PointsArray.Value(PointsArray.Lower()) ;
205 (Standard_Real *) &ParametersArray.Value(1) ;
206 TangentFlags.SetValue(1,Standard_True) ;
207 PLib::EvalLagrange(ParametersArray.Value(1),
214 for (ii = 1 ; ii <= 2 ; ii++) {
215 a_vector.SetCoord(ii,eval_result[1][ii-1]) ;
217 TangentsArray.SetValue(1,a_vector) ;
219 if (! TangentFlags.Value(TangentFlags.Upper())) {
221 (Standard_Real *) &PointsArray.Value(PointsArray.Upper() - degree) ;
222 TangentFlags.SetValue(TangentFlags.Upper(),Standard_True) ;
224 (Standard_Real *)&ParametersArray.Value(ParametersArray.Upper() - degree) ;
225 PLib::EvalLagrange(ParametersArray.Value(ParametersArray.Upper()),
232 for (ii = 1 ; ii <= 2 ; ii++) {
233 a_vector.SetCoord(ii,eval_result[1][ii-1]) ;
235 TangentsArray.SetValue(TangentsArray.Upper(),a_vector) ;
238 //=======================================================================
239 //function : BuildTangents
240 //purpose : scale the given tangent so that they have the length of
241 // the size of the derivative of the lagrange interpolation
243 //=======================================================================
244 static void ScaleTangents(const TColgp_Array1OfPnt2d& PointsArray,
245 TColgp_Array1OfVec2d& TangentsArray,
246 const TColStd_Array1OfBoolean& TangentFlags,
247 const TColStd_Array1OfReal& ParametersArray)
255 Standard_Real *point_array,
263 num_points = PointsArray.Length() ;
264 if (num_points == 2) {
267 else if (num_points >= 3) {
271 index = PointsArray.Lower() ;
272 for (ii = TangentFlags.Lower() ; ii <= TangentFlags.Upper() ; ii++) {
273 if (TangentFlags.Value(ii)) {
275 (Standard_Real *) &PointsArray.Value(index) ;
277 (Standard_Real *) &ParametersArray.Value(index) ;
278 PLib::EvalLagrange(ParametersArray.Value(ii),
287 for (jj = 1 ; jj <= 2 ; jj++) {
288 value[0] += Abs(TangentsArray.Value(ii).Coord(jj)) ;
289 value[1] += Abs(eval_result[1][jj-1]) ;
291 ratio = value[1] / value[0] ;
292 for (jj = 1 ; jj <= 2 ; jj++) {
293 a_vector.SetCoord(jj, ratio *
294 TangentsArray.Value(ii).Coord(jj)) ;
296 TangentsArray.SetValue(ii, a_vector) ;
297 if (ii != TangentFlags.Lower()) {
300 if (index > PointsArray.Upper() - degree) {
301 index = PointsArray.Upper() - degree ;
308 //=======================================================================
309 //function : Geom2dAPI_Interpolate
311 //=======================================================================
313 Geom2dAPI_Interpolate::Geom2dAPI_Interpolate
314 (const Handle(TColgp_HArray1OfPnt2d)& PointsPtr,
315 const Standard_Boolean PeriodicFlag,
316 const Standard_Real Tolerance) :
317 myTolerance(Tolerance),
319 myIsDone(Standard_False),
320 myPeriodic(PeriodicFlag),
321 myTangentRequest(Standard_False)
324 Standard_Integer ii ;
325 Standard_Boolean result =
326 CheckPoints(PointsPtr->Array1(),
329 new TColgp_HArray1OfVec2d(myPoints->Lower(),
332 new TColStd_HArray1OfBoolean(myPoints->Lower(),
336 throw Standard_ConstructionError();
338 BuildParameters(PeriodicFlag,
342 for (ii = myPoints->Lower() ; ii <= myPoints->Upper() ; ii++) {
343 myTangentFlags->SetValue(ii,Standard_False) ;
350 //=======================================================================
351 //function : Geom2dAPI_Interpolate
353 //=======================================================================
355 Geom2dAPI_Interpolate::Geom2dAPI_Interpolate
356 (const Handle(TColgp_HArray1OfPnt2d)& PointsPtr,
357 const Handle(TColStd_HArray1OfReal)& ParametersPtr,
358 const Standard_Boolean PeriodicFlag,
359 const Standard_Real Tolerance) :
360 myTolerance(Tolerance),
362 myIsDone(Standard_False),
363 myParameters(ParametersPtr),
364 myPeriodic(PeriodicFlag),
365 myTangentRequest(Standard_False)
367 Standard_Integer ii ;
370 Standard_Boolean result =
371 CheckPoints(PointsPtr->Array1(),
375 if ((PointsPtr->Length()) + 1 != ParametersPtr->Length()) {
376 throw Standard_ConstructionError();
380 new TColgp_HArray1OfVec2d(myPoints->Lower(),
383 new TColStd_HArray1OfBoolean(myPoints->Lower(),
387 throw Standard_ConstructionError();
391 CheckParameters(ParametersPtr->Array1()) ;
393 throw Standard_ConstructionError();
396 for (ii = myPoints->Lower() ; ii <= myPoints->Upper() ; ii++) {
397 myTangentFlags->SetValue(ii,Standard_False) ;
401 //=======================================================================
404 //=======================================================================
406 void Geom2dAPI_Interpolate::Load(
407 const TColgp_Array1OfVec2d& Tangents,
408 const Handle(TColStd_HArray1OfBoolean)& TangentFlagsPtr,
409 const Standard_Boolean Scale)
412 Standard_Boolean result ;
413 Standard_Integer ii ;
414 myTangentRequest = Standard_True ;
415 myTangentFlags = TangentFlagsPtr ;
416 if (Tangents.Length() != myPoints->Length() ||
417 TangentFlagsPtr->Length() != myPoints->Length()) {
418 throw Standard_ConstructionError();
421 CheckTangents(Tangents,
422 TangentFlagsPtr->Array1(),
426 new TColgp_HArray1OfVec2d(Tangents.Lower(),Tangents.Upper()) ;
427 for (ii = Tangents.Lower() ; ii <= Tangents.Upper() ; ii++ ) {
428 myTangents->SetValue(ii,Tangents.Value(ii)) ;
431 ScaleTangents(myPoints->Array1(),
432 myTangents->ChangeArray1(),
433 TangentFlagsPtr->Array1(),
434 myParameters->Array1()) ;
438 throw Standard_ConstructionError();
444 //=======================================================================
447 //=======================================================================
449 void Geom2dAPI_Interpolate::Load(const gp_Vec2d& InitialTangent,
450 const gp_Vec2d& FinalTangent,
451 const Standard_Boolean Scale)
453 Standard_Boolean result ;
454 myTangentRequest = Standard_True ;
455 myTangentFlags->SetValue(1,Standard_True) ;
456 myTangentFlags->SetValue(myPoints->Length(),Standard_True) ;
457 myTangents->SetValue(1,InitialTangent) ;
458 myTangents->SetValue(myPoints->Length(),FinalTangent);
460 CheckTangents(myTangents->Array1(),
461 myTangentFlags->Array1(),
464 throw Standard_ConstructionError();
467 ScaleTangents(myPoints->Array1(),
468 myTangents->ChangeArray1(),
469 myTangentFlags->Array1(),
470 myParameters->Array1()) ;
474 //=======================================================================
477 //=======================================================================
479 void Geom2dAPI_Interpolate::Perform()
485 PerformNonPeriodic() ;
488 //=======================================================================
489 //function : PerformPeriodic
491 //=======================================================================
493 void Geom2dAPI_Interpolate::PerformPeriodic()
495 Standard_Integer degree,
508 Standard_Real period ;
512 num_points = myPoints->Length() ;
513 period = myParameters->Value(myParameters->Upper()) -
514 myParameters->Value(myParameters->Lower()) ;
515 num_poles = num_points + 1 ;
516 if (num_points == 2 && !myTangentRequest) {
518 // build a periodic curve of degree 1
522 TColStd_Array1OfInteger deg1_mults(1,num_poles) ;
523 for (ii = 1 ; ii <= num_poles ; ii++) {
524 deg1_mults.SetValue(ii,1) ;
528 new Geom2d_BSplineCurve(myPoints->Array1(),
529 myParameters->Array1(),
533 myIsDone = Standard_True ;
537 num_distinct_knots = num_points + 1 ;
541 if (myTangentRequest)
542 for (ii = myTangentFlags->Lower() + 1 ;
543 ii <= myTangentFlags->Upper() ; ii++) {
544 if (myTangentFlags->Value(ii)) {
549 TColStd_Array1OfReal parameters(1,num_poles) ;
550 TColStd_Array1OfReal flatknots(1,num_poles + degree + 1) ;
551 TColStd_Array1OfInteger mults(1,num_distinct_knots) ;
552 TColStd_Array1OfInteger contact_order_array(1, num_poles) ;
553 TColgp_Array1OfPnt2d poles(1,num_poles) ;
555 for (ii = 1 ; ii <= half_order ; ii++) {
556 flatknots.SetValue(ii,myParameters->Value(myParameters->Upper() -1) -
558 flatknots.SetValue(ii + half_order,myParameters->
559 Value(myParameters->Lower())) ;
560 flatknots.SetValue(num_poles + ii,
561 myParameters->Value(myParameters->Upper())) ;
562 flatknots.SetValue(num_poles + half_order + ii,
563 myParameters->Value(half_order) + period) ;
565 for (ii = 1 ; ii <= num_poles ; ii++) {
566 contact_order_array.SetValue(ii,0) ;
568 for (ii = 2 ; ii < num_distinct_knots ; ii++) {
569 mults.SetValue(ii,1) ;
571 mults.SetValue(1,half_order) ;
572 mults.SetValue(num_distinct_knots ,half_order) ;
573 if (num_points >= 3) {
576 // only enter here if there are more than 3 points otherwise
577 // it means we have already the tangent
579 BuildPeriodicTangent(myPoints->Array1(),
580 myTangents->ChangeArray1(),
581 myTangentFlags->ChangeArray1(),
582 myParameters->Array1()) ;
584 contact_order_array.SetValue(2,1) ;
585 parameters.SetValue(1,myParameters->Value(1)) ;
586 parameters.SetValue(2,myParameters->Value(1)) ;
587 poles.SetValue(1,myPoints->Value(1)) ;
588 for (jj = 1 ; jj <= 2 ; jj++) {
589 a_point.SetCoord(jj,myTangents->Value(1).Coord(jj)) ;
591 poles.SetValue(2,a_point) ;
595 index1 = degree + 2 ;
596 if (myTangentRequest) {
597 for (ii = myTangentFlags->Lower() + 1 ;
598 ii <= myTangentFlags->Upper() ; ii++) {
599 parameters.SetValue(index,myParameters->Value(ii)) ;
600 flatknots.SetValue(index1,myParameters->Value(ii)) ;
601 poles.SetValue(index,myPoints->Value(ii)) ;
604 if (myTangentFlags->Value(ii)) {
605 mults.SetValue(mult_index,mults.Value(mult_index) + 1) ;
606 contact_order_array(index) = 1 ;
608 parameters.SetValue(index,
609 myParameters->Value(ii)) ;
610 flatknots.SetValue(index1,myParameters->Value(ii)) ;
611 for (jj = 1 ; jj <= 2 ; jj++) {
612 a_point.SetCoord(jj,myTangents->Value(ii).Coord(jj)) ;
614 poles.SetValue(index,a_point) ;
624 for(ii = myParameters->Lower() ; ii <= myParameters->Upper() ; ii++) {
625 parameters.SetValue(index1,
626 myParameters->Value(ii)) ;
627 flatknots.SetValue(index,
628 myParameters->Value(ii)) ;
633 for (ii = myPoints->Lower() + 1 ; ii <= myPoints->Upper() ; ii++) {
635 // copy all the given points since the last one will be initialized
636 // below by the first point in the array myPoints
638 poles.SetValue(index,
639 myPoints->Value(ii)) ;
644 contact_order_array.SetValue(num_poles - 1, 1) ;
645 parameters.SetValue(num_poles-1,
646 myParameters->Value(myParameters->Upper())) ;
648 // for the periodic curve ONLY the tangent of the first point
649 // will be used since the curve should close itself at the first
650 // point See BuildPeriodicTangent
652 for (jj = 1 ; jj <= 2 ; jj++) {
653 a_point.SetCoord(jj,myTangents->Value(1).Coord(jj)) ;
655 poles.SetValue(num_poles-1,a_point) ;
657 parameters.SetValue(num_poles,
658 myParameters->Value(myParameters->Upper())) ;
660 poles.SetValue(num_poles,
661 myPoints->Value(1)) ;
664 BSplCLib::Interpolate(degree,
670 if (!inversion_problem) {
671 TColgp_Array1OfPnt2d newpoles(poles.Value(1),
675 new Geom2d_BSplineCurve(newpoles,
676 myParameters->Array1(),
680 myIsDone = Standard_True ;
686 //=======================================================================
687 //function : PerformNonPeriodic
689 //=======================================================================
691 void Geom2dAPI_Interpolate::PerformNonPeriodic()
693 Standard_Integer degree,
710 num_poles = myPoints->Length() ;
711 if (num_poles == 2 && !myTangentRequest) {
714 else if (num_poles == 3 && !myTangentRequest) {
716 num_distinct_knots = 2 ;
721 if (myTangentRequest)
722 for (ii = myTangentFlags->Lower() + 1 ;
723 ii < myTangentFlags->Upper() ; ii++) {
724 if (myTangentFlags->Value(ii)) {
731 TColStd_Array1OfReal parameters(1,num_poles) ;
732 TColStd_Array1OfReal flatknots(1,num_poles + degree + 1) ;
733 TColStd_Array1OfInteger mults(1,num_distinct_knots) ;
734 TColStd_Array1OfReal knots(1,num_distinct_knots) ;
735 TColStd_Array1OfInteger contact_order_array(1, num_poles) ;
736 TColgp_Array1OfPnt2d poles(1,num_poles) ;
738 for (ii = 1 ; ii <= degree + 1 ; ii++) {
739 flatknots.SetValue(ii,myParameters->Value(1)) ;
740 flatknots.SetValue(ii + num_poles,
741 myParameters->Value(num_points)) ;
743 for (ii = 1 ; ii <= num_poles ; ii++) {
744 contact_order_array.SetValue(ii,0) ;
746 for (ii = 2 ; ii < num_distinct_knots ; ii++) {
747 mults.SetValue(ii,1) ;
749 mults.SetValue(1,degree + 1) ;
750 mults.SetValue(num_distinct_knots ,degree + 1) ;
754 for (ii = 1 ; ii <= num_poles ; ii++) {
755 poles.SetValue(ii ,myPoints->Value(ii)) ;
758 new Geom2d_BSplineCurve(poles,
759 myParameters->Array1(),
762 myIsDone = Standard_True ;
765 knots.SetValue(1,myParameters->Value(1)) ;
766 knots.SetValue(2,myParameters->Value(3)) ;
767 for (ii = 1 ; ii <= num_poles ; ii++) {
768 poles.SetValue(ii,myPoints->Value(ii)) ;
771 BSplCLib::Interpolate(degree,
773 myParameters->Array1(),
777 if (!inversion_problem) {
779 new Geom2d_BSplineCurve(poles,
783 myIsDone = Standard_True ;
788 // check if the boundary conditions are set
790 if (num_points >= 3) {
792 // cannot build the tangents with degree 3 with only 2 points
793 // if those where not given in advance
795 BuildTangents(myPoints->Array1(),
796 myTangents->ChangeArray1(),
797 myTangentFlags->ChangeArray1(),
798 myParameters->Array1()) ;
800 contact_order_array.SetValue(2,1) ;
801 parameters.SetValue(1,myParameters->Value(1)) ;
802 parameters.SetValue(2,myParameters->Value(1)) ;
803 poles.SetValue(1,myPoints->Value(1)) ;
804 for (jj = 1 ; jj <= 2 ; jj++) {
805 a_point.SetCoord(jj,myTangents->Value(1).Coord(jj)) ;
808 poles.SetValue(2,a_point) ;
812 index2 = myPoints->Lower() + 1 ;
813 index3 = degree + 2 ;
814 if (myTangentRequest) {
815 for (ii = myParameters->Lower() + 1 ;
816 ii < myParameters->Upper() ; ii++) {
817 parameters.SetValue(index,myParameters->Value(ii)) ;
818 poles.SetValue(index,myPoints->Value(index2)) ;
819 flatknots.SetValue(index3,myParameters->Value(ii)) ;
822 if (myTangentFlags->Value(index1)) {
824 // set the multiplicities, the order of the contact, the
827 mults.SetValue(mult_index,mults.Value(mult_index) + 1) ;
828 contact_order_array(index) = 1 ;
829 flatknots.SetValue(index3, myParameters->Value(ii)) ;
830 parameters.SetValue(index,
831 myParameters->Value(ii)) ;
832 for (jj = 1 ; jj <= 2 ; jj++) {
833 a_point.SetCoord(jj,myTangents->Value(ii).Coord(jj)) ;
835 poles.SetValue(index,a_point) ;
847 for(ii = myParameters->Lower() ; ii <= myParameters->Upper() ; ii++) {
848 parameters.SetValue(index1,
849 myParameters->Value(ii)) ;
853 for (ii = myPoints->Lower() + 1 ; ii <= myPoints->Upper() - 1 ; ii++) {
854 poles.SetValue(index,
855 myPoints->Value(ii)) ;
861 for(ii = myParameters->Lower() ; ii <= myParameters->Upper() ; ii++) {
862 flatknots.SetValue(index,
863 myParameters->Value(ii)) ;
867 for (jj = 1 ; jj <= 2 ; jj++) {
869 myTangents->Value(num_points).Coord(jj)) ;
871 poles.SetValue(num_poles-1 ,a_point) ;
873 contact_order_array.SetValue(num_poles - 1,1) ;
874 parameters.SetValue(num_poles,
875 myParameters->Value(myParameters->Upper())) ;
876 parameters.SetValue(num_poles -1,
877 myParameters->Value(myParameters->Upper())) ;
879 poles.SetValue(num_poles,
880 myPoints->Value(num_points)) ;
882 BSplCLib::Interpolate(degree,
888 if (!inversion_problem) {
890 new Geom2d_BSplineCurve(poles,
891 myParameters->Array1(),
894 myIsDone = Standard_True ;
900 //=======================================================================
901 //function : Handle(Geom2d_BSplineCurve)&
903 //=======================================================================
905 const Handle(Geom2d_BSplineCurve)& Geom2dAPI_Interpolate::Curve() const
908 throw StdFail_NotDone(" ");
914 //=======================================================================
915 //function : Geom2d_BSplineCurve
917 //=======================================================================
919 Geom2dAPI_Interpolate::operator Handle(Geom2d_BSplineCurve)() const
925 //=======================================================================
928 //=======================================================================
930 Standard_Boolean Geom2dAPI_Interpolate::IsDone() const