1 // Created on: 1998-11-30
2 // Created by: Igor FEOKTISTOV
3 // Copyright (c) 1998-1999 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 #include <AppDef_LinearCriteria.ixx>
19 #include <PLib_Base.hxx>
20 #include <PLib_JacobiPolynomial.hxx>
21 #include <PLib_HermitJacobi.hxx>
22 #include <GeomAbs_Shape.hxx>
23 #include <TColStd_HArray2OfReal.hxx>
24 #include <FEmTool_LinearTension.hxx>
25 #include <FEmTool_LinearFlexion.hxx>
26 #include <FEmTool_LinearJerk.hxx>
27 #include <TColgp_Array1OfPnt.hxx>
28 #include <TColgp_Array1OfPnt2d.hxx>
29 #include <gp_Pnt2d.hxx>
31 #include <math_Matrix.hxx>
32 #include <math_Gauss.hxx>
33 #include <AppDef_MyLineTool.hxx>
35 static Standard_Integer order(const Handle(PLib_Base)& B)
37 return (*( Handle(PLib_HermitJacobi)*)&B)->NivConstr();
41 //=======================================================================
44 //=======================================================================
45 AppDef_LinearCriteria::AppDef_LinearCriteria(const AppDef_MultiLine& SSP,
46 const Standard_Integer FirstPoint,
47 const Standard_Integer LastPoint):
49 myPntWeight(FirstPoint, LastPoint),
56 //=======================================================================
59 //=======================================================================
61 void AppDef_LinearCriteria::SetParameters(const Handle(TColStd_HArray1OfReal)& Parameters)
63 myParameters = Parameters;
64 myE = 0; // Cache become invalid.
69 //=======================================================================
72 //=======================================================================
74 void AppDef_LinearCriteria::SetCurve(const Handle(FEmTool_Curve)& C)
77 if(myCurve.IsNull()) {
80 Standard_Integer MxDeg = myCurve->Base()->WorkDegree(),
81 NbDim = myCurve->Dimension(),
82 Order = order(myCurve->Base());
84 GeomAbs_Shape ConstraintOrder=GeomAbs_C0;
86 case 0 : ConstraintOrder = GeomAbs_C0;
88 case 1 : ConstraintOrder = GeomAbs_C1;
90 case 2 : ConstraintOrder = GeomAbs_C2;
93 myCriteria[0] = new FEmTool_LinearTension(MxDeg, ConstraintOrder);
94 myCriteria[1] = new FEmTool_LinearFlexion(MxDeg, ConstraintOrder);
95 myCriteria[2] = new FEmTool_LinearJerk (MxDeg, ConstraintOrder);
97 Handle(TColStd_HArray2OfReal) Coeff = new TColStd_HArray2OfReal(0, 0, 1, NbDim);
99 myCriteria[0]->Set(Coeff);
100 myCriteria[1]->Set(Coeff);
101 myCriteria[2]->Set(Coeff);
103 else if (myCurve != C) {
105 Standard_Integer OldMxDeg = myCurve->Base()->WorkDegree(),
106 OldNbDim = myCurve->Dimension(),
107 OldOrder = order(myCurve->Base());
111 Standard_Integer MxDeg = myCurve->Base()->WorkDegree(),
112 NbDim = myCurve->Dimension(),
113 Order = order(myCurve->Base());
115 if(MxDeg != OldMxDeg || Order != OldOrder) {
117 GeomAbs_Shape ConstraintOrder=GeomAbs_C0;
119 case 0 : ConstraintOrder = GeomAbs_C0;
121 case 1 : ConstraintOrder = GeomAbs_C1;
123 case 2 : ConstraintOrder = GeomAbs_C2;
126 myCriteria[0] = new FEmTool_LinearTension(MxDeg, ConstraintOrder);
127 myCriteria[1] = new FEmTool_LinearFlexion(MxDeg, ConstraintOrder);
128 myCriteria[2] = new FEmTool_LinearJerk (MxDeg, ConstraintOrder);
130 Handle(TColStd_HArray2OfReal) Coeff = new TColStd_HArray2OfReal(0, 0, 1, NbDim);
132 myCriteria[0]->Set(Coeff);
133 myCriteria[1]->Set(Coeff);
134 myCriteria[2]->Set(Coeff);
136 else if(NbDim != OldNbDim) {
138 Handle(TColStd_HArray2OfReal) Coeff = new TColStd_HArray2OfReal(0, 0, 1, NbDim);
140 myCriteria[0]->Set(Coeff);
141 myCriteria[1]->Set(Coeff);
142 myCriteria[2]->Set(Coeff);
149 //=======================================================================
150 //function : GetCurve
152 //=======================================================================
153 void AppDef_LinearCriteria::GetCurve(Handle(FEmTool_Curve)& C) const
159 //=======================================================================
160 //function : SetEstimation
162 //=======================================================================
163 void AppDef_LinearCriteria::SetEstimation(const Standard_Real E1,
164 const Standard_Real E2,
165 const Standard_Real E3)
167 myEstimation[0] = E1;
168 myEstimation[1] = E2;
169 myEstimation[2] = E3;
172 Standard_Real& AppDef_LinearCriteria::EstLength()
178 //=======================================================================
179 //function : GetEstimation
181 //=======================================================================
182 void AppDef_LinearCriteria::GetEstimation(Standard_Real& E1,
184 Standard_Real& E3) const
186 E1 = myEstimation[0];
187 E2 = myEstimation[1];
188 E3 = myEstimation[2];
193 //=======================================================================
194 //function : AssemblyTable
196 //=======================================================================
197 Handle(FEmTool_HAssemblyTable) AppDef_LinearCriteria::AssemblyTable() const
199 if(myCurve.IsNull()) Standard_DomainError::Raise("AppDef_LinearCriteria::AssemblyTable");
201 Standard_Integer NbDim = myCurve->Dimension(),
202 NbElm = myCurve->NbElements(),
203 nc1 = order(myCurve->Base()) + 1;
204 Standard_Integer MxDeg = myCurve->Base()->WorkDegree() ;
206 Handle(FEmTool_HAssemblyTable) AssTable = new FEmTool_HAssemblyTable(1, NbDim, 1, NbElm);
208 Handle(TColStd_HArray1OfInteger) GlobIndex, Aux;
210 Standard_Integer i, el = 1, dim = 1, NbGlobVar = 0, gi0;
213 // For first element (el = 1)
214 GlobIndex = new TColStd_HArray1OfInteger(0, MxDeg);
216 for(i = 0; i < nc1; i++) {
218 GlobIndex->SetValue(i, NbGlobVar);
220 gi0 = MxDeg - 2 * nc1 + 1;
221 for(i = nc1; i < 2*nc1; i++) {
223 GlobIndex->SetValue(i, NbGlobVar + gi0);
225 for(i = 2*nc1; i <= MxDeg; i++) {
227 GlobIndex->SetValue(i, NbGlobVar - nc1);
229 gi0 = NbGlobVar - nc1 + 1;
230 AssTable->SetValue(dim, el, GlobIndex);
233 for(el = 2; el <= NbElm; el++) {
234 GlobIndex = new TColStd_HArray1OfInteger(0, MxDeg);
235 for(i = 0; i < nc1; i++) GlobIndex->SetValue(i, gi0 + i);
237 gi0 = MxDeg - 2 * nc1 + 1;
238 for(i = nc1; i < 2*nc1; i++) {
240 GlobIndex->SetValue(i, NbGlobVar + gi0);
242 for(i = 2*nc1; i <= MxDeg; i++) {
244 GlobIndex->SetValue(i, NbGlobVar - nc1);
246 gi0 = NbGlobVar - nc1 + 1;
247 AssTable->SetValue(dim, el, GlobIndex);
250 // For other dimensions
252 for(dim = 2; dim <= NbDim; dim++) {
253 for(el = 1; el <= NbElm; el++) {
254 Aux = AssTable->Value(1, el);
255 GlobIndex = new TColStd_HArray1OfInteger(0, MxDeg);
256 for(i = 0; i <= MxDeg; i++) GlobIndex->SetValue(i, Aux->Value(i) + NbGlobVar);
257 AssTable->SetValue(dim, el, GlobIndex);
268 //=======================================================================
271 //=======================================================================
272 Handle(TColStd_HArray2OfInteger) AppDef_LinearCriteria::DependenceTable() const
274 if(myCurve.IsNull()) Standard_DomainError::Raise("AppDef_LinearCriteria::DependenceTable");
276 Standard_Integer Dim = myCurve->Dimension();
278 Handle(TColStd_HArray2OfInteger) DepTab =
279 new TColStd_HArray2OfInteger(1, Dim, 1, Dim, 0);
281 for(i=1; i <= Dim; i++) DepTab->SetValue(i,i,1);
287 //=======================================================================
288 //function : QualityValues
290 //=======================================================================
292 Standard_Integer AppDef_LinearCriteria::QualityValues(const Standard_Real J1min,
293 const Standard_Real J2min,
294 const Standard_Real J3min,
299 if(myCurve.IsNull()) Standard_DomainError::Raise("AppDef_LinearCriteria::QualityValues");
301 Standard_Integer NbDim = myCurve->Dimension(),
302 NbElm = myCurve->NbElements();
304 TColStd_Array1OfReal& Knots = myCurve->Knots();
305 Handle(TColStd_HArray2OfReal) Coeff;
307 Standard_Integer el, deg = 0, curdeg, i;
308 Standard_Real UFirst, ULast;
311 for(el = 1; el <= NbElm; el++) {
313 curdeg = myCurve->Degree(el);
316 Coeff = new TColStd_HArray2OfReal(0, deg, 1, NbDim);
319 myCurve->GetElement(el, Coeff->ChangeArray2());
321 UFirst = Knots(el); ULast = Knots(el + 1);
323 myCriteria[0]->Set(Coeff);
324 myCriteria[0]->Set(UFirst, ULast);
325 J1 = J1 + myCriteria[0]->Value();
327 myCriteria[1]->Set(Coeff);
328 myCriteria[1]->Set(UFirst, ULast);
329 J2 = J2 + myCriteria[1]->Value();
331 myCriteria[2]->Set(Coeff);
332 myCriteria[2]->Set(UFirst, ULast);
333 J3 = J3 + myCriteria[2]->Value();
337 // Calculation of ICDANA - see MOTEST.f
338 // Standard_Real JEsMin[3] = {.01, .001, .001}; // from MOTLIS.f
339 Standard_Real JEsMin[3]; JEsMin[0] = J1min; JEsMin[1] = J2min; JEsMin[2] = J3min;
340 Standard_Real ValCri[3]; ValCri[0] = J1; ValCri[1] = J2; ValCri[2] = J3;
342 Standard_Integer ICDANA = 0;
344 // (2) Test l'amelioration des estimations
345 // (critere sureleve => Non minimisation )
347 for(i = 0; i <= 2; i++)
348 if((ValCri[i] < 0.8 * myEstimation[i]) && (myEstimation[i] > JEsMin[i])) {
349 if(ICDANA < 1) ICDANA = 1;
350 if(ValCri[i] < 0.1 * myEstimation[i]) ICDANA = 2;
351 myEstimation[i] = Max(1.05*ValCri[i], JEsMin[i]);
355 // (3) Mise a jours des Estimation
356 // (critere sous-estimer => mauvais conditionement)
358 if (ValCri[0] > myEstimation[0] * 2) {
359 myEstimation[0] += ValCri[0] * .1;
361 if (ValCri[0] > myEstimation[0] * 10) {
370 if (ValCri[1] > myEstimation[1] * 20) {
371 myEstimation[1] += ValCri[1] * .1;
373 if (ValCri[1] > myEstimation[1] * 100) {
382 if (ValCri[2] > myEstimation[2] * 20) {
383 myEstimation[2] += ValCri[2] * .05;
385 if (ValCri[2] > myEstimation[2] * 100) {
400 //=======================================================================
401 //function : ErrorValues
403 //=======================================================================
405 void AppDef_LinearCriteria::ErrorValues(Standard_Real& MaxError,
406 Standard_Real& QuadraticError,
407 Standard_Real& AverageError)
409 if(myCurve.IsNull()) Standard_DomainError::Raise("AppDef_LinearCriteria::ErrorValues");
411 Standard_Integer NbDim = myCurve->Dimension();
413 Standard_Integer myNbP2d = AppDef_MyLineTool::NbP2d(mySSP), myNbP3d = AppDef_MyLineTool::NbP3d(mySSP);
415 if(NbDim != (2*myNbP2d + 3*myNbP3d)) Standard_DomainError::Raise("AppDef_LinearCriteria::ErrorValues");
417 TColgp_Array1OfPnt TabP3d(1, Max(1,myNbP3d));
418 TColgp_Array1OfPnt2d TabP2d(1, Max(1,myNbP2d));
419 TColStd_Array1OfReal BasePoint(1,NbDim);
423 Standard_Integer i, ipnt, c0 = 0;
424 Standard_Real SqrDist, Dist;
426 MaxError = QuadraticError = AverageError = 0.;
428 for(i = myParameters->Lower(); i <= myParameters->Upper(); i++) {
430 myCurve->D0(myParameters->Value(i), BasePoint);
434 AppDef_MyLineTool::Value(mySSP, i, TabP3d);
435 for(ipnt = 1; ipnt <= myNbP3d; ipnt++) {
436 P3d.SetCoord(BasePoint(c0+1), BasePoint(c0+2), BasePoint(c0+3));
437 SqrDist = P3d.SquareDistance(TabP3d(ipnt)); Dist = Sqrt(SqrDist);
438 MaxError = Max(MaxError, Dist);
439 QuadraticError += SqrDist;
440 AverageError += Dist;
444 if(myNbP3d == 0) AppDef_MyLineTool::Value(mySSP, i, TabP2d);
445 else AppDef_MyLineTool::Value(mySSP, i, TabP3d, TabP2d);
446 for(ipnt = 1; ipnt <= myNbP2d; ipnt++) {
447 P2d.SetCoord(BasePoint(c0+1), BasePoint(c0+2));
448 SqrDist = P2d.SquareDistance(TabP2d(ipnt)); Dist = Sqrt(SqrDist);
449 MaxError = Max(MaxError, Dist);
450 QuadraticError += SqrDist;
451 AverageError += Dist;
458 //=======================================================================
461 //=======================================================================
463 void AppDef_LinearCriteria::Hessian(const Standard_Integer Element,
464 const Standard_Integer Dimension1,
465 const Standard_Integer Dimension2,
468 if(myCurve.IsNull()) Standard_DomainError::Raise("AppDef_LinearCriteria::Hessian");
470 if(DependenceTable()->Value(Dimension1, Dimension2) == 0)
471 Standard_DomainError::Raise("AppDef_LinearCriteria::Hessian");
473 Standard_Integer //NbDim = myCurve->Dimension(),
474 MxDeg = myCurve->Base()->WorkDegree(),
475 // Deg = myCurve->Degree(Element),
476 Order = order(myCurve->Base());
479 math_Matrix AuxH(0, H.RowNumber()-1, 0, H.ColNumber()-1, 0.);
481 TColStd_Array1OfReal& Knots = myCurve->Knots();
482 Standard_Real UFirst, ULast;
484 UFirst = Knots(Element); ULast = Knots(Element + 1);
486 Standard_Integer icrit;
488 // Quality criterion part of Hessian
492 for(icrit = 0; icrit <= 2; icrit++) {
493 myCriteria[icrit]->Set(UFirst, ULast);
494 myCriteria[icrit]->Hessian(Dimension1, Dimension2, AuxH);
495 H += (myQualityWeight*myPercent[icrit]/myEstimation[icrit]) * AuxH;
498 // Least square part of Hessian
502 Standard_Real coeff = (ULast - UFirst)/2., curcoeff, poid;
503 Standard_Integer ipnt, ii, degH = 2 * Order+1;
506 Handle(PLib_Base) myBase = myCurve->Base();
507 Standard_Integer k1, k2, i, j, i0 = H.LowerRow(), j0 = H.LowerCol(), i1, j1,
508 di = myPntWeight.Lower() - myParameters->Lower();
511 if (myE != Element) BuildCache(Element);
513 // Compute the least square Hessian
514 for(ii=1, ipnt = IF; ipnt <= IL; ipnt++, ii+=(MxDeg+1)) {
515 poid = myPntWeight(di + ipnt) * 2.;
516 const Standard_Real * BV = &myCache->Value(ii);
518 // Hermite*Hermite part of matrix
519 for(i = 0; i <= degH; i++) {
520 k1 = (i <= Order)? i : i - Order - 1;
521 curcoeff = Pow(coeff, k1) * poid * BV[i];
523 // Hermite*Hermite part of matrix
524 for(j = i; j <= degH; j++) {
525 k2 = (j <= Order)? j : j - Order - 1;
526 AuxH(i, j) += curcoeff * Pow(coeff, k2) * BV[j];
528 // Hermite*Jacobi part of matrix
529 for(j = degH + 1; j <= MxDeg; j++) {
530 AuxH(i, j) += curcoeff * BV[j];
534 // Jacoby*Jacobi part of matrix
535 for(i = degH+1; i <= MxDeg; i++) {
536 curcoeff = BV[i] * poid;
537 for(j = i; j <= MxDeg; j++) {
538 AuxH(i, j) += curcoeff * BV[j];
544 for(i = 0; i <= MxDeg; i++) {
546 for(j = i; j <= MxDeg; j++) {
547 H(i1, j1) += myQuadraticWeight * AuxH(i, j);
548 H(j1, i1) = H(i1, j1);
556 //=======================================================================
557 //function : Gradient
559 //=======================================================================
560 void AppDef_LinearCriteria::Gradient(const Standard_Integer Element,
561 const Standard_Integer Dimension,
565 Standard_DomainError::Raise("AppDef_LinearCriteria::ErrorValues");
567 Standard_Integer myNbP2d = AppDef_MyLineTool::NbP2d(mySSP), myNbP3d = AppDef_MyLineTool::NbP3d(mySSP);
569 if(Dimension > (2*myNbP2d + 3*myNbP3d))
570 Standard_DomainError::Raise("AppDef_LinearCriteria::ErrorValues");
572 TColgp_Array1OfPnt TabP3d(1, Max(1,myNbP3d));
573 TColgp_Array1OfPnt2d TabP2d(1, Max(1,myNbP2d));
575 Standard_Boolean In3d;
576 Standard_Integer IndPnt, IndCrd;
578 if(Dimension <= 3*myNbP3d) {
579 In3d = Standard_True;
580 IndCrd = Dimension % 3;
581 IndPnt = Dimension / 3;
582 if(IndCrd == 0) IndCrd = 3;
586 In3d = Standard_False;
587 IndCrd = (Dimension - 3*myNbP3d) % 2;
588 IndPnt = (Dimension - 3*myNbP3d) / 2;
589 if(IndCrd == 0) IndCrd = 2;
593 TColStd_Array1OfReal& Knots = myCurve->Knots();
594 Standard_Real UFirst, ULast, Pnt;
595 UFirst = Knots(Element); ULast = Knots(Element + 1);
596 Standard_Real coeff = (ULast-UFirst)/2;
598 Standard_Integer //Deg = myCurve->Degree(Element),
599 Order = order(myCurve->Base());
601 Handle(PLib_Base) myBase = myCurve->Base();
602 Standard_Integer MxDeg = myBase->WorkDegree();
604 Standard_Real curcoeff;
605 Standard_Integer degH = 2 * Order + 1;
606 Standard_Integer ipnt, k, i, ii, i0 = G.Lower(),
607 di = myPntWeight.Lower() - myParameters->Lower();
609 if (myE != Element) BuildCache(Element);
610 const Standard_Real * BV = &myCache->Value(1);
615 for(ii=1,ipnt = IF; ipnt <= IL; ipnt++) {
617 AppDef_MyLineTool::Value(mySSP, ipnt, TabP3d);
618 Pnt = TabP3d(IndPnt).Coord(IndCrd);
621 if(myNbP3d == 0) AppDef_MyLineTool::Value(mySSP, ipnt, TabP2d);
622 else AppDef_MyLineTool::Value(mySSP, ipnt, TabP3d, TabP2d);
623 Pnt = TabP2d(IndPnt).Coord(IndCrd);
626 curcoeff = Pnt * myPntWeight(di + ipnt);
627 for(i = 0; i <= MxDeg; i++,ii++)
628 G(i0 + i) += BV[ii] * curcoeff;
632 G *= 2. * myQuadraticWeight;
634 for(i = 0; i <= degH; i++) {
635 k = (i <= Order)? i : i - Order - 1;
636 curcoeff = Pow(coeff, k);
637 G(i0 + i) *= curcoeff;
642 //=======================================================================
643 //function : InputVector
645 //=======================================================================
646 void AppDef_LinearCriteria::InputVector(const math_Vector& X,
647 const Handle(FEmTool_HAssemblyTable)& AssTable)
649 Standard_Integer NbDim = myCurve->Dimension(),
650 NbElm = myCurve->NbElements() ;
651 Standard_Integer MxDeg = 0 ;
652 MxDeg = myCurve->Base()->WorkDegree();
653 TColStd_Array2OfReal CoeffEl(0, MxDeg, 1, NbDim);
656 Handle(TColStd_HArray1OfInteger) GlobIndex;
658 Standard_Integer el, dim, i, i0 = X.Lower() - 1;
660 for(el = 1; el <= NbElm; el++) {
661 for(dim = 1; dim <= NbDim; dim++) {
662 GlobIndex = AssTable->Value(dim, el);
663 for(i = 0; i <= MxDeg; i++) CoeffEl(i, dim) = X(i0 + GlobIndex->Value(i));
665 myCurve->SetDegree(el, MxDeg);
666 myCurve->SetElement(el, CoeffEl);
671 //=======================================================================
672 //function : SetWeight
674 //=======================================================================
675 void AppDef_LinearCriteria::SetWeight(const Standard_Real QuadraticWeight,
676 const Standard_Real QualityWeight,
677 const Standard_Real percentJ1,
678 const Standard_Real percentJ2,
679 const Standard_Real percentJ3)
681 if (QuadraticWeight < 0. || QualityWeight < 0.)
682 Standard_DomainError::Raise("AppDef_LinearCriteria::SetWeight");
683 if (percentJ1 < 0. || percentJ2 < 0. || percentJ3 < 0.)
684 Standard_DomainError::Raise("AppDef_LinearCriteria::SetWeight");
686 myQuadraticWeight = QuadraticWeight; myQualityWeight = QualityWeight;
688 Standard_Real Total = percentJ1 + percentJ2 + percentJ3;
689 myPercent[0] = percentJ1 / Total;
690 myPercent[1] = percentJ2 / Total;
691 myPercent[2] = percentJ3 / Total;
695 //=======================================================================
696 //function : GetWeight
698 //=======================================================================
699 void AppDef_LinearCriteria::GetWeight(Standard_Real& QuadraticWeight,
700 Standard_Real& QualityWeight) const
703 QuadraticWeight = myQuadraticWeight; QualityWeight = myQualityWeight;
707 //=======================================================================
708 //function : SetWeight
710 //=======================================================================
711 void AppDef_LinearCriteria::SetWeight(const TColStd_Array1OfReal& Weight)
713 myPntWeight = Weight;
717 //=======================================================================
718 //function : BuildCache
720 //=======================================================================
721 void AppDef_LinearCriteria::BuildCache(const Standard_Integer Element)
724 Standard_Real UFirst, ULast;
725 Standard_Integer ipnt;
727 UFirst = myCurve->Knots()(Element);
728 ULast = myCurve->Knots()(Element + 1);
731 for(ipnt = myParameters->Lower(); ipnt <= myParameters->Upper(); ipnt++) {
732 t = myParameters->Value(ipnt);
733 if((t > UFirst && t <= ULast) || (Element == 1 && t == UFirst)) {
734 if (IF == 0) IF=ipnt;
737 else if (t>ULast) break;
741 Handle(PLib_Base) myBase = myCurve->Base();
742 Standard_Integer order = myBase->WorkDegree()+1, ii;
743 myCache = new TColStd_HArray1OfReal (1, (IL-IF+1)*(order));
746 for(ipnt = IF, ii=1; ipnt <= IL; ipnt++, ii+=order) {
747 Standard_Real * cache = &myCache->ChangeValue(ii);
748 TColStd_Array1OfReal BasicValue(cache[0], 0, order-1);
749 t = myParameters->Value(ipnt);
750 Standard_Real coeff = 2./(ULast - UFirst), c0 = -(ULast + UFirst)/2., s;
751 s = (t + c0) * coeff;
752 myBase->D0(s, BasicValue);
755 else { //pas de points dans l'interval.