1 // File: Approx_CurvlinFunc.cxx
2 // Created: Tue May 12 14:03:09 1998
3 // Author: Roman BORISOV
7 #include <Approx_CurvlinFunc.ixx>
8 #include <Adaptor3d_CurveOnSurface.hxx>
9 #include <Adaptor3d_HCurveOnSurface.hxx>
10 #include <TColStd_SequenceOfReal.hxx>
11 #include <GeomLib.hxx>
12 #include <GCPnts_AbscissaPoint.hxx>
13 #include <Precision.hxx>
15 #ifdef __OCC_DEBUG_CHRONO
16 #include <OSD_Timer.hxx>
17 static OSD_Chronometer chr_uparam;
18 Standard_EXPORT Standard_Integer uparam_count;
19 Standard_EXPORT Standard_Real t_uparam;
21 //Standard_IMPORT extern void InitChron(OSD_Chronometer& ch);
22 Standard_IMPORT void InitChron(OSD_Chronometer& ch);
23 //Standard_IMPORT extern void ResultChron( OSD_Chronometer & ch, Standard_Real & time);
24 Standard_IMPORT void ResultChron( OSD_Chronometer & ch, Standard_Real & time);
27 static Standard_Real cubic(const Standard_Real X, const Standard_Real *Xi, const Standard_Real *Yi)
29 Standard_Real I1, I2, I3, I21, I22, I31, Result;
31 I1 = (Yi[0] - Yi[1])/(Xi[0] - Xi[1]);
32 I2 = (Yi[1] - Yi[2])/(Xi[1] - Xi[2]);
33 I3 = (Yi[2] - Yi[3])/(Xi[2] - Xi[3]);
35 I21 = (I1 - I2)/(Xi[0] - Xi[2]);
36 I22 = (I2 - I3)/(Xi[1] - Xi[3]);
38 I31 = (I21 - I22)/(Xi[0] - Xi[3]);
40 Result = Yi[0] + (X - Xi[0])*(I1 + (X - Xi[1])*(I21 + (X - Xi[2])*I31));
45 //static void findfourpoints(const Standard_Real S,
46 static void findfourpoints(const Standard_Real ,
47 Standard_Integer NInterval,
48 const Handle(TColStd_HArray1OfReal)& Si,
49 Handle(TColStd_HArray1OfReal)& Ui,
50 const Standard_Real prevS,
51 const Standard_Real prevU, Standard_Real *Xi,
54 Standard_Integer i, j;
55 Standard_Integer NbInt = Si->Length() - 1;
56 if (NbInt < 3) Standard_ConstructionError::Raise("Approx_CurvlinFunc::GetUParameter");
58 if(NInterval < 1) NInterval = 1;
59 else if(NInterval > NbInt - 2) NInterval = NbInt - 2;
61 for(i = 0; i < 4; i++) {
62 Xi[i] = Si->Value(NInterval - 1 + i);
63 Yi[i] = Ui->Value(NInterval - 1 + i);
65 // try to insert (S, U)
66 for(i = 0; i < 3; i++) {
67 if(Xi[i] < prevS && prevS < Xi[i+1]) {
68 for(j = 0; j < i; j++) {
79 /*static Standard_Real curvature(const Standard_Real U, const Adaptor3d_Curve& C)
81 Standard_Real k, tau, mod1, mod2, OMEGA;
84 C.D3(U, P, D1, D2, D3);
85 mod1 = D1.Magnitude();
86 mod2 = D1.Crossed(D2).Magnitude();
87 k = mod2/(mod1*mod1*mod1);
88 tau = D1.Dot(D2.Crossed(D3));
90 OMEGA = Sqrt(k*k + tau*tau);
96 Approx_CurvlinFunc::Approx_CurvlinFunc(const Handle(Adaptor3d_HCurve)& C, const Standard_Real Tol) : myC3D(C),
107 Approx_CurvlinFunc::Approx_CurvlinFunc(const Handle(Adaptor2d_HCurve2d)& C2D, const Handle(Adaptor3d_HSurface)& S, const Standard_Real Tol) :
120 Approx_CurvlinFunc::Approx_CurvlinFunc(const Handle(Adaptor2d_HCurve2d)& C2D1, const Handle(Adaptor2d_HCurve2d)& C2D2, const Handle(Adaptor3d_HSurface)& S1, const Handle(Adaptor3d_HSurface)& S2, const Standard_Real Tol) :
135 void Approx_CurvlinFunc::Init()
137 Adaptor3d_CurveOnSurface CurOnSur;
141 Init(myC3D->GetCurve(), mySi_1, myUi_1);
142 myFirstU1 = myC3D->FirstParameter();
143 myLastU1 = myC3D->LastParameter();
144 myFirstU2 = myLastU2 = 0;
147 CurOnSur.Load(myC2D1);
148 CurOnSur.Load(mySurf1);
149 Init(CurOnSur, mySi_1, myUi_1);
150 myFirstU1 = CurOnSur.FirstParameter();
151 myLastU1 = CurOnSur.LastParameter();
152 myFirstU2 = myLastU2 = 0;
155 CurOnSur.Load(myC2D1);
156 CurOnSur.Load(mySurf1);
157 Init(CurOnSur, mySi_1, myUi_1);
158 myFirstU1 = CurOnSur.FirstParameter();
159 myLastU1 = CurOnSur.LastParameter();
160 CurOnSur.Load(myC2D2);
161 CurOnSur.Load(mySurf2);
162 Init(CurOnSur, mySi_2, myUi_2);
163 myFirstU2 = CurOnSur.FirstParameter();
164 myLastU2 = CurOnSur.LastParameter();
171 //=======================================================================
173 //purpose : Init the values
174 //history : 23/10/1998 PMN : Cut at curve's discontinuities
175 //=======================================================================
176 void Approx_CurvlinFunc::Init(Adaptor3d_Curve& C, Handle(TColStd_HArray1OfReal)& Si,
177 Handle(TColStd_HArray1OfReal)& Ui) const
179 Standard_Real Step, FirstU, LastU;
180 Standard_Integer i, j, k, NbInt, NbIntC3;
181 FirstU = C.FirstParameter();
182 LastU = C.LastParameter();
185 NbIntC3 = C.NbIntervals(GeomAbs_C3);
186 TColStd_Array1OfReal Disc(1, NbIntC3+1);
189 C.Intervals(Disc, GeomAbs_C3);
196 Ui = new TColStd_HArray1OfReal (0,NbIntC3*NbInt);
197 Si = new TColStd_HArray1OfReal (0,NbIntC3*NbInt);
199 Ui->SetValue(0, FirstU);
202 for(j = 1, i=1; j<=NbIntC3; j++) {
203 Step = (Disc(j+1) - Disc(j))/NbInt;
204 for(k = 1; k <= NbInt; k++, i++) {
205 Ui->ChangeValue(i) = Ui->Value(i-1) + Step;
206 Si->ChangeValue(i) = Si->Value(i-1) + Length(C, Ui->Value(i-1), Ui->Value(i));
210 Standard_Real Len = Si->Value(Si->Upper());
211 for(i = Si->Lower(); i<= Si->Upper(); i++)
212 Si->ChangeValue(i) /= Len;
214 // TODO - fields should be mutable
215 const_cast<Approx_CurvlinFunc*>(this)->myPrevS = myFirstS;
216 const_cast<Approx_CurvlinFunc*>(this)->myPrevU = FirstU;
219 void Approx_CurvlinFunc::SetTol(const Standard_Real Tol)
224 Standard_Real Approx_CurvlinFunc::FirstParameter() const
229 Standard_Real Approx_CurvlinFunc::LastParameter() const
234 Standard_Integer Approx_CurvlinFunc::NbIntervals(const GeomAbs_Shape S) const
236 Adaptor3d_CurveOnSurface CurOnSur;
240 return myC3D->NbIntervals(S);
242 CurOnSur.Load(myC2D1);
243 CurOnSur.Load(mySurf1);
244 return CurOnSur.NbIntervals(S);
246 Standard_Integer NbInt;
247 CurOnSur.Load(myC2D1);
248 CurOnSur.Load(mySurf1);
249 NbInt = CurOnSur.NbIntervals(S);
250 TColStd_Array1OfReal T1(1, NbInt+1);
251 CurOnSur.Intervals(T1, S);
252 CurOnSur.Load(myC2D2);
253 CurOnSur.Load(mySurf2);
254 NbInt = CurOnSur.NbIntervals(S);
255 TColStd_Array1OfReal T2(1, NbInt+1);
256 CurOnSur.Intervals(T2, S);
258 TColStd_SequenceOfReal Fusion;
259 GeomLib::FuseIntervals(T1, T2, Fusion);
260 return Fusion.Length() - 1;
267 void Approx_CurvlinFunc::Intervals(TColStd_Array1OfReal& T, const GeomAbs_Shape S) const
269 Adaptor3d_CurveOnSurface CurOnSur;
274 myC3D->Intervals(T, S);
277 CurOnSur.Load(myC2D1);
278 CurOnSur.Load(mySurf1);
279 CurOnSur.Intervals(T, S);
282 Standard_Integer NbInt;
283 CurOnSur.Load(myC2D1);
284 CurOnSur.Load(mySurf1);
285 NbInt = CurOnSur.NbIntervals(S);
286 TColStd_Array1OfReal T1(1, NbInt+1);
287 CurOnSur.Intervals(T1, S);
288 CurOnSur.Load(myC2D2);
289 CurOnSur.Load(mySurf2);
290 NbInt = CurOnSur.NbIntervals(S);
291 TColStd_Array1OfReal T2(1, NbInt+1);
292 CurOnSur.Intervals(T2, S);
294 TColStd_SequenceOfReal Fusion;
295 GeomLib::FuseIntervals(T1, T2, Fusion);
297 for (i = 1; i <= Fusion.Length(); i++)
298 T.ChangeValue(i) = Fusion.Value(i);
301 for(i = 1; i <= T.Length(); i++)
302 T.ChangeValue(i) = GetSParameter(T.Value(i));
305 void Approx_CurvlinFunc::Trim(const Standard_Real First, const Standard_Real Last, const Standard_Real Tol)
307 if (First < 0 || Last >1) Standard_OutOfRange::Raise("Approx_CurvlinFunc::Trim");
308 if ((Last - First) < Tol) return;
310 Standard_Real FirstU, LastU;
311 Adaptor3d_CurveOnSurface CurOnSur;
312 Handle(Adaptor3d_HCurve) HCurOnSur;
316 myC3D = myC3D->Trim(myFirstU1, myLastU1, Tol);
317 FirstU = GetUParameter(myC3D->GetCurve(), First, 1);
318 LastU = GetUParameter(myC3D->GetCurve(), Last, 1);
319 myC3D = myC3D->Trim(FirstU, LastU, Tol);
322 CurOnSur.Load(myC2D2);
323 CurOnSur.Load(mySurf2);
324 HCurOnSur = CurOnSur.Trim(myFirstU2, myLastU2, Tol);
325 myC2D2 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetCurve();
326 mySurf2 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetSurface();
327 CurOnSur.Load(myC2D2);
328 CurOnSur.Load(mySurf2);
330 FirstU = GetUParameter(CurOnSur, First, 1);
331 LastU = GetUParameter(CurOnSur, Last, 1);
332 HCurOnSur = CurOnSur.Trim(FirstU, LastU, Tol);
333 myC2D2 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetCurve();
334 mySurf2 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetSurface();
337 CurOnSur.Load(myC2D1);
338 CurOnSur.Load(mySurf1);
339 HCurOnSur = CurOnSur.Trim(myFirstU1, myLastU1, Tol);
340 myC2D1 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetCurve();
341 mySurf1 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetSurface();
342 CurOnSur.Load(myC2D1);
343 CurOnSur.Load(mySurf1);
345 FirstU = GetUParameter(CurOnSur, First, 1);
346 LastU = GetUParameter(CurOnSur, Last, 1);
347 HCurOnSur = CurOnSur.Trim(FirstU, LastU, Tol);
348 myC2D1 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetCurve();
349 mySurf1 = ((Adaptor3d_CurveOnSurface *)(&(HCurOnSur->Curve())))->GetSurface();
355 void Approx_CurvlinFunc::Length()
357 Adaptor3d_CurveOnSurface CurOnSur;
358 Standard_Real FirstU, LastU;
362 FirstU = myC3D->FirstParameter();
363 LastU = myC3D->LastParameter();
364 myLength = Length(myC3D->GetCurve(), FirstU, LastU);
365 myLength1 = myLength2 = 0;
368 CurOnSur.Load(myC2D1);
369 CurOnSur.Load(mySurf1);
370 FirstU = CurOnSur.FirstParameter();
371 LastU = CurOnSur.LastParameter();
372 myLength = Length(CurOnSur, FirstU, LastU);
373 myLength1 = myLength2 = 0;
376 CurOnSur.Load(myC2D1);
377 CurOnSur.Load(mySurf1);
378 FirstU = CurOnSur.FirstParameter();
379 LastU = CurOnSur.LastParameter();
380 myLength1 = Length(CurOnSur, FirstU, LastU);
381 CurOnSur.Load(myC2D2);
382 CurOnSur.Load(mySurf2);
383 FirstU = CurOnSur.FirstParameter();
384 LastU = CurOnSur.LastParameter();
385 myLength2 = Length(CurOnSur, FirstU, LastU);
386 myLength = (myLength1 + myLength2)/2;
391 Standard_Real Approx_CurvlinFunc::Length(Adaptor3d_Curve& C, const Standard_Real FirstU, const Standard_Real LastU) const
393 Standard_Real Length;
395 Length = GCPnts_AbscissaPoint::Length(C, FirstU, LastU, myTolLen);
400 Standard_Real Approx_CurvlinFunc::GetLength() const
405 Standard_Real Approx_CurvlinFunc::GetSParameter(const Standard_Real U) const
407 Standard_Real S=0, S1, S2;
408 Adaptor3d_CurveOnSurface CurOnSur;
412 S = GetSParameter(myC3D->GetCurve(), U, myLength);
415 CurOnSur.Load(myC2D1);
416 CurOnSur.Load(mySurf1);
417 S = GetSParameter(CurOnSur, U, myLength);
420 CurOnSur.Load(myC2D1);
421 CurOnSur.Load(mySurf1);
422 S1 = GetSParameter(CurOnSur, U, myLength1);
423 CurOnSur.Load(myC2D2);
424 CurOnSur.Load(mySurf2);
425 S2 = GetSParameter(CurOnSur, U, myLength2);
433 Standard_Real Approx_CurvlinFunc::GetUParameter(Adaptor3d_Curve& C,
434 const Standard_Real S,
435 const Standard_Integer NumberOfCurve) const
437 Standard_Real deltaS, base, U, Length;
438 Standard_Integer NbInt, NInterval, i;
439 Handle(TColStd_HArray1OfReal) InitUArray, InitSArray;
440 #ifdef __OCC_DEBUG_CHRONO
441 InitChron(chr_uparam);
443 if(S < 0 || S > 1) Standard_ConstructionError::Raise("Approx_CurvlinFunc::GetUParameter");
445 if(NumberOfCurve == 1) {
459 NbInt = InitUArray->Length() - 1;
461 if(S == 1) NInterval = NbInt - 1;
463 for(i = 0; i < NbInt; i++) {
464 if((InitSArray->Value(i) <= S && S < InitSArray->Value(i+1)))
469 if(S==InitSArray->Value(NInterval)) {
470 return InitUArray->Value(NInterval);
472 if(S==InitSArray->Value(NInterval+1)) {
473 return InitUArray->Value(NInterval+1);
476 base = InitUArray->Value(NInterval);
477 deltaS = (S - InitSArray->Value(NInterval))*Length;
479 // to find an initial point
480 Standard_Real Xi[4], Yi[4], UGuess;
481 findfourpoints(S, NInterval, InitSArray, InitUArray, myPrevS, myPrevU, Xi, Yi);
482 UGuess = cubic(S , Xi, Yi);
484 U = GCPnts_AbscissaPoint(C, deltaS, base, UGuess, myTolLen).Parameter();
486 // TODO - fields should be mutable
487 const_cast<Approx_CurvlinFunc*>(this)->myPrevS = S;
488 const_cast<Approx_CurvlinFunc*>(this)->myPrevU = U;
490 #ifdef __OCC_DEBUG_CHRONO
491 ResultChron(chr_uparam, t_uparam);
498 Standard_Real Approx_CurvlinFunc::GetSParameter(Adaptor3d_Curve& C, const Standard_Real U, const Standard_Real Len) const
500 Standard_Real S, Origin;
502 Origin = C.FirstParameter();
503 S = myFirstS + Length(C, Origin, U)/Len;
507 Standard_Boolean Approx_CurvlinFunc::EvalCase1(const Standard_Real S, const Standard_Integer Order, TColStd_Array1OfReal& Result) const
509 if(myCase != 1) Standard_ConstructionError::Raise("Approx_CurvlinFunc::EvalCase1");
512 gp_Vec dC_dU, dC_dS, d2C_dU2, d2C_dS2;
513 Standard_Real U, Mag, dU_dS, d2U_dS2;
515 U = GetUParameter(myC3D->GetCurve(), S, 1);
528 myC3D->D1(U, C, dC_dU);
529 Mag = dC_dU.Magnitude();
530 dU_dS = myLength/Mag;
533 Result(0) = dC_dS.X();
534 Result(1) = dC_dS.Y();
535 Result(2) = dC_dS.Z();
539 myC3D->D2(U, C, dC_dU, d2C_dU2);
540 Mag = dC_dU.Magnitude();
541 dU_dS = myLength/Mag;
542 d2U_dS2 = -myLength*dC_dU.Dot(d2C_dU2)*dU_dS/(Mag*Mag*Mag);
543 d2C_dS2 = d2C_dU2*dU_dS*dU_dS + dC_dU*d2U_dS2;
545 Result(0) = d2C_dS2.X();
546 Result(1) = d2C_dS2.Y();
547 Result(2) = d2C_dS2.Z();
550 default: Result(0) = Result(1) = Result(2) = 0;
551 return Standard_False;
553 return Standard_True;
556 Standard_Boolean Approx_CurvlinFunc::EvalCase2(const Standard_Real S, const Standard_Integer Order, TColStd_Array1OfReal& Result) const
558 if(myCase != 2) Standard_ConstructionError::Raise("Approx_CurvlinFunc::EvalCase2");
560 Standard_Boolean Done;
562 Done = EvalCurOnSur(S, Order, Result, 1);
567 Standard_Boolean Approx_CurvlinFunc::EvalCase3(const Standard_Real S, const Standard_Integer Order, TColStd_Array1OfReal& Result)
569 if(myCase != 3) Standard_ConstructionError::Raise("Approx_CurvlinFunc::EvalCase3");
571 TColStd_Array1OfReal tmpRes1(0, 4), tmpRes2(0, 4);
572 Standard_Boolean Done;
574 Done = EvalCurOnSur(S, Order, tmpRes1, 1);
576 Done = EvalCurOnSur(S, Order, tmpRes2, 2) && Done;
578 Result(0) = tmpRes1(0);
579 Result(1) = tmpRes1(1);
580 Result(2) = tmpRes2(0);
581 Result(3) = tmpRes2(1);
582 Result(4) = 0.5*(tmpRes1(2) + tmpRes2(2));
583 Result(5) = 0.5*(tmpRes1(3) + tmpRes2(3));
584 Result(6) = 0.5*(tmpRes1(4) + tmpRes2(4));
589 Standard_Boolean Approx_CurvlinFunc::EvalCurOnSur(const Standard_Real S, const Standard_Integer Order, TColStd_Array1OfReal& Result, const Standard_Integer NumberOfCurve) const
591 Handle(Adaptor2d_HCurve2d) Cur2D;
592 Handle(Adaptor3d_HSurface) Surf;
593 Standard_Real U=0, Length=0;
595 if (NumberOfCurve == 1) {
598 Adaptor3d_CurveOnSurface CurOnSur(myC2D1, mySurf1);
599 U = GetUParameter(CurOnSur, S, 1);
600 if(myCase == 3) Length = myLength1;
601 else Length = myLength;
603 else if (NumberOfCurve == 2) {
606 Adaptor3d_CurveOnSurface CurOnSur(myC2D2, mySurf2);
607 U = GetUParameter(CurOnSur, S, 2);
611 Standard_ConstructionError::Raise("Approx_CurvlinFunc::EvalCurOnSur");
613 Standard_Real Mag, dU_dS, d2U_dS2, dV_dU, dW_dU, dV_dS, dW_dS, d2V_dS2, d2W_dS2, d2V_dU2, d2W_dU2;
616 gp_Vec2d dC2D_dU, d2C2D_dU2;
617 gp_Vec dC_dU, d2C_dU2, dC_dS, d2C_dS2, dS_dV, dS_dW, d2S_dV2, d2S_dW2, d2S_dVdW;
622 Surf->D0(C2D.X(), C2D.Y(), C);
632 Cur2D->D1(U, C2D, dC2D_dU);
635 Surf->D1(C2D.X(), C2D.Y(), C, dS_dV, dS_dW);
636 dC_dU = dS_dV*dV_dU + dS_dW*dW_dU;
637 Mag = dC_dU.Magnitude();
646 Result(2) = dC_dS.X();
647 Result(3) = dC_dS.Y();
648 Result(4) = dC_dS.Z();
652 Cur2D->D2(U, C2D, dC2D_dU, d2C2D_dU2);
655 d2V_dU2 = d2C2D_dU2.X();
656 d2W_dU2 = d2C2D_dU2.Y();
657 Surf->D2(C2D.X(), C2D.Y(), C, dS_dV, dS_dW, d2S_dV2, d2S_dW2, d2S_dVdW);
658 dC_dU = dS_dV*dV_dU + dS_dW*dW_dU;
659 d2C_dU2 = (d2S_dV2*dV_dU + d2S_dVdW*dW_dU)*dV_dU + dS_dV*d2V_dU2 +
660 (d2S_dVdW*dV_dU + d2S_dW2*dW_dU)*dW_dU + dS_dW*d2W_dU2;
661 Mag = dC_dU.Magnitude();
663 d2U_dS2 = -Length*dC_dU.Dot(d2C_dU2)*dU_dS/(Mag*Mag*Mag);
665 dV_dS = dV_dU * dU_dS;
666 dW_dS = dW_dU * dU_dS;
667 d2V_dS2 = d2V_dU2*dU_dS*dU_dS + dV_dU*d2U_dS2;
668 d2W_dS2 = d2W_dU2*dU_dS*dU_dS + dW_dU*d2U_dS2;
670 d2U_dS2 = -dC_dU.Dot(d2C_dU2)*dU_dS/(Mag*Mag);
671 d2C_dS2 = (d2S_dV2 * dV_dS + d2S_dVdW * dW_dS) * dV_dS + dS_dV * d2V_dS2 +
672 (d2S_dW2 * dW_dS + d2S_dVdW * dV_dS) * dW_dS + dS_dW * d2W_dS2;
676 Result(2) = d2C_dS2.X();
677 Result(3) = d2C_dS2.Y();
678 Result(4) = d2C_dS2.Z();
681 default: Result(0) = Result(1) = Result(2) = Result(3) = Result(4) = 0;
682 return Standard_False;
684 return Standard_True;