1 // Created on: 1993-12-02
2 // Created by: Jacques GOUSSARD
3 // Copyright (c) 1993-1999 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.
18 #include <Adaptor2d_HCurve2d.hxx>
19 #include <Adaptor3d_HCurve.hxx>
20 #include <Adaptor3d_HSurface.hxx>
21 #include <BlendFunc_RuledInv.hxx>
22 #include <math_Matrix.hxx>
23 #include <Precision.hxx>
25 BlendFunc_RuledInv::BlendFunc_RuledInv(const Handle(Adaptor3d_HSurface)& S1,
26 const Handle(Adaptor3d_HSurface)& S2,
27 const Handle(Adaptor3d_HCurve)& C) :
28 surf1(S1),surf2(S2),curv(C)
31 void BlendFunc_RuledInv::Set(const Standard_Boolean OnFirst,
32 const Handle(Adaptor2d_HCurve2d)& C)
38 Standard_Integer BlendFunc_RuledInv::NbEquations () const
43 void BlendFunc_RuledInv::GetTolerance(math_Vector& Tolerance,
44 const Standard_Real Tol) const
46 Tolerance(1) = csurf->Resolution(Tol);
47 Tolerance(2) = curv->Resolution(Tol);
49 Tolerance(3) = surf2->UResolution(Tol);
50 Tolerance(4) = surf2->VResolution(Tol);
53 Tolerance(3) = surf1->UResolution(Tol);
54 Tolerance(4) = surf1->VResolution(Tol);
58 void BlendFunc_RuledInv::GetBounds(math_Vector& InfBound,
59 math_Vector& SupBound) const
61 InfBound(1) = csurf->FirstParameter();
62 InfBound(2) = curv->FirstParameter();
63 SupBound(1) = csurf->LastParameter();
64 SupBound(2) = curv->LastParameter();
67 InfBound(3) = surf2->FirstUParameter();
68 InfBound(4) = surf2->FirstVParameter();
69 SupBound(3) = surf2->LastUParameter();
70 SupBound(4) = surf2->LastVParameter();
71 if(!Precision::IsInfinite(InfBound(3)) &&
72 !Precision::IsInfinite(SupBound(3))) {
73 const Standard_Real range = (SupBound(3) - InfBound(3));
77 if(!Precision::IsInfinite(InfBound(4)) &&
78 !Precision::IsInfinite(SupBound(4))) {
79 const Standard_Real range = (SupBound(4) - InfBound(4));
85 InfBound(3) = surf1->FirstUParameter();
86 InfBound(4) = surf1->FirstVParameter();
87 SupBound(3) = surf1->LastUParameter();
88 SupBound(4) = surf1->LastVParameter();
89 if(!Precision::IsInfinite(InfBound(3)) &&
90 !Precision::IsInfinite(SupBound(3))) {
91 const Standard_Real range = (SupBound(3) - InfBound(3));
95 if(!Precision::IsInfinite(InfBound(4)) &&
96 !Precision::IsInfinite(SupBound(4))) {
97 const Standard_Real range = (SupBound(4) - InfBound(4));
104 Standard_Boolean BlendFunc_RuledInv::IsSolution(const math_Vector& Sol,
105 const Standard_Real Tol)
107 math_Vector valsol(1,4);
109 if (Abs(valsol(1)) <= Tol &&
110 Abs(valsol(2)) <= Tol &&
111 Abs(valsol(3)) <= Tol &&
112 Abs(valsol(4)) <= Tol)
113 return Standard_True;
115 return Standard_False;
119 Standard_Boolean BlendFunc_RuledInv::Value(const math_Vector& X,
124 curv->D1(X(2),ptcur,d1cur);
126 const gp_XYZ nplan = d1cur.Normalized().XYZ();
127 const Standard_Real theD = -(nplan.Dot(ptcur.XYZ()));
128 const gp_Pnt2d pt2d(csurf->Value(X(1)));
131 gp_Vec d1u1,d1v1,d1u2,d1v2;
134 surf1->D1(pt2d.X(),pt2d.Y(),pts1,d1u1,d1v1);
135 surf2->D1(X(3),X(4),pts2,d1u2,d1v2);
139 surf1->D1(X(3),X(4),pts1,d1u1,d1v1);
140 surf2->D1(pt2d.X(),pt2d.Y(),pts2,d1u2,d1v2);
143 const gp_XYZ temp(pts2.XYZ()-pts1.XYZ());
145 gp_XYZ ns1 = d1u1.Crossed(d1v1).XYZ();
146 gp_XYZ ns2 = d1u2.Crossed(d1v2).XYZ();
147 const Standard_Real norm1 = nplan.Crossed(ns1).Modulus();
148 const Standard_Real norm2 = nplan.Crossed(ns2).Modulus();
149 ns1.SetLinearForm(nplan.Dot(ns1)/norm1,nplan, -1./norm1,ns1);
150 ns2.SetLinearForm(nplan.Dot(ns2)/norm2,nplan, -1./norm2,ns2);
152 F(1) = (nplan.Dot(pts1.XYZ())) + theD;
153 F(2) = (nplan.Dot(pts2.XYZ())) + theD;
155 F(3) = temp.Dot(ns1);
156 F(4) = temp.Dot(ns2);
158 return Standard_True;
161 Standard_Boolean BlendFunc_RuledInv::Derivatives(const math_Vector& X,
166 curv->D2(X(2),ptcur,d1cur,d2cur);
168 const Standard_Real normtgcur = d1cur.Magnitude();
169 const gp_Vec nplan = d1cur.Normalized();
172 dnplan.SetLinearForm(-nplan.Dot(d2cur),nplan,d2cur);
177 csurf->D1(X(1),p2d,v2d);
180 gp_Vec d1u1,d1v1,d1u2,d1v2;
181 gp_Vec d2u1,d2v1,d2u2,d2v2,d2uv1,d2uv2;
185 surf1->D2(p2d.X(),p2d.Y(),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
186 surf2->D2(X(3),X(4),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);
187 dpdt.SetLinearForm(v2d.X(),d1u1,v2d.Y(),d1v1);
188 p1p2 = gp_Vec(pts1,pts2);
189 D(1,1) = dpdt.Dot(nplan);
190 D(1,2) = dnplan.XYZ().Dot(pts1.XYZ()-ptcur.XYZ()) - normtgcur;
195 D(2,2) = dnplan.XYZ().Dot(pts2.XYZ()-ptcur.XYZ()) - normtgcur;
196 D(2,3) = d1u2.Dot(nplan);
197 D(2,4) = d1v2.Dot(nplan);
201 surf1->D2(X(3),X(4),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
202 surf2->D2(p2d.X(),p2d.Y(),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);
203 dpdt.SetLinearForm(v2d.X(),d1u2,v2d.Y(),d1v2);
204 p1p2 = gp_Vec(pts1,pts2);
206 D(1,2) = dnplan.XYZ().Dot(pts1.XYZ()-ptcur.XYZ()) - normtgcur;
207 D(1,3) = d1u1.Dot(nplan);
208 D(1,4) = d1v1.Dot(nplan);
210 D(2,1) = dpdt.Dot(nplan);
211 D(2,2) = dnplan.XYZ().Dot(pts2.XYZ()-ptcur.XYZ()) - normtgcur;
216 const gp_Vec ns1 = d1u1.Crossed(d1v1);
217 const gp_Vec ns2 = d1u2.Crossed(d1v2);
218 const gp_Vec ncrossns1 = nplan.Crossed(ns1);
219 const gp_Vec ncrossns2 = nplan.Crossed(ns2);
220 const Standard_Real norm1 = ncrossns1.Magnitude();
221 const Standard_Real norm2 = ncrossns2.Magnitude();
223 const Standard_Real ndotns1 = nplan.Dot(ns1);
224 const Standard_Real ndotns2 = nplan.Dot(ns2);
227 nor1.SetLinearForm(ndotns1/norm1,nplan,-1./norm1,ns1);
228 nor2.SetLinearForm(ndotns2/norm2,nplan,-1./norm2,ns2);
231 D(3,3) = d1u2.Dot(nor1);
232 D(3,4) = d1v2.Dot(nor1);
234 D(4,1) = -(dpdt.Dot(nor2));
237 D(3,1) = dpdt.Dot(nor1);
239 D(4,3) = -(d1u1.Dot(nor2));
240 D(4,4) = -(d1v1.Dot(nor2));
243 gp_Vec resul1,resul2,temp;
244 Standard_Real grosterme;
246 // Derivee de nor1 par rapport a u1
248 temp = d2u1.Crossed(d1v1).Added(d1u1.Crossed(d2uv1));
249 grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
250 resul1.SetLinearForm(-(grosterme*ndotns1-nplan.Dot(temp))/norm1,nplan,
254 // Derivee par rapport a v1
256 temp = d2uv1.Crossed(d1v1).Added(d1u1.Crossed(d2v1));
257 grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
258 resul2.SetLinearForm(-(grosterme*ndotns1-nplan.Dot(temp))/norm1,nplan,
263 resul1.SetLinearForm(v2d.X(),resul1,v2d.Y(),resul2);
264 D(3,1) = p1p2.Dot(resul1) - (dpdt.Dot(nor1));
267 D(3,3) = -(d1u1.Dot(nor1)) + p1p2.Dot(resul1);
268 D(3,4) = -(d1v1.Dot(nor1)) + p1p2.Dot(resul2);
271 // Derivee de nor2 par rapport a u2
272 temp = d2u2.Crossed(d1v2).Added(d1u2.Crossed(d2uv2));
273 grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
274 resul1.SetLinearForm(-(grosterme*ndotns2-nplan.Dot(temp))/norm2,nplan,
278 // Derivee par rapport a v2
279 temp = d2uv2.Crossed(d1v2).Added(d1u2.Crossed(d2v2));
280 grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
281 resul2.SetLinearForm(-(grosterme*ndotns2-nplan.Dot(temp))/norm2,nplan,
286 D(4,3) = d1u2.Dot(nor2) + p1p2.Dot(resul1);
287 D(4,4) = d1v2.Dot(nor2) + p1p2.Dot(resul2);
290 resul1.SetLinearForm(v2d.X(),resul1,v2d.Y(),resul2);
291 D(4,1) = p1p2.Dot(resul1) + dpdt.Dot(nor2) ;
295 // derivee par rapport a w (parametre sur ligne guide)
297 grosterme = ncrossns1.Dot(dnplan.Crossed(ns1))/norm1/norm1;
298 resul1.SetLinearForm(-(grosterme*ndotns1-dnplan.Dot(ns1))/norm1,nplan,
299 ndotns1/norm1,dnplan,
300 grosterme/norm1,ns1);
303 grosterme = ncrossns2.Dot(dnplan.Crossed(ns2))/norm2/norm2;
304 resul2.SetLinearForm(-(grosterme*ndotns2-dnplan.Dot(ns2))/norm2,nplan,
305 ndotns2/norm2,dnplan,
306 grosterme/norm2,ns2);
308 D(3,2) = p1p2.Dot(resul1);
309 D(4,2) = p1p2.Dot(resul2);
311 return Standard_True;
315 Standard_Boolean BlendFunc_RuledInv::Values(const math_Vector& X,
321 curv->D2(X(2),ptcur,d1cur,d2cur);
323 const Standard_Real normtgcur = d1cur.Magnitude();
324 const gp_Vec nplan = d1cur.Normalized();
325 const Standard_Real theD = -(nplan.XYZ().Dot(ptcur.XYZ()));
328 dnplan.SetLinearForm(-nplan.Dot(d2cur),nplan,d2cur);
333 csurf->D1(X(1),p2d,v2d);
336 gp_Vec d1u1,d1v1,d1u2,d1v2;
337 gp_Vec d2u1,d2v1,d2u2,d2v2,d2uv1,d2uv2;
341 surf1->D2(p2d.X(),p2d.Y(),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
342 surf2->D2(X(3),X(4),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);
343 dpdt.SetLinearForm(v2d.X(),d1u1,v2d.Y(),d1v1);
344 p1p2 = gp_Vec(pts1,pts2);
345 D(1,1) = dpdt.Dot(nplan);
346 D(1,2) = dnplan.XYZ().Dot(pts1.XYZ()-ptcur.XYZ()) - normtgcur;
351 D(2,2) = dnplan.XYZ().Dot(pts2.XYZ()-ptcur.XYZ()) - normtgcur;
352 D(2,3) = d1u2.Dot(nplan);
353 D(2,4) = d1v2.Dot(nplan);
357 surf1->D2(X(3),X(4),pts1,d1u1,d1v1,d2u1,d2v1,d2uv1);
358 surf2->D2(p2d.X(),p2d.Y(),pts2,d1u2,d1v2,d2u2,d2v2,d2uv2);
359 dpdt.SetLinearForm(v2d.X(),d1u2,v2d.Y(),d1v2);
360 p1p2 = gp_Vec(pts1,pts2);
362 D(1,2) = dnplan.XYZ().Dot(pts1.XYZ()-ptcur.XYZ()) - normtgcur;
363 D(1,3) = d1u1.Dot(nplan);
364 D(1,4) = d1v1.Dot(nplan);
366 D(2,1) = dpdt.Dot(nplan);
367 D(2,2) = dnplan.XYZ().Dot(pts2.XYZ()-ptcur.XYZ()) - normtgcur;
372 const gp_Vec ns1 = d1u1.Crossed(d1v1);
373 const gp_Vec ns2 = d1u2.Crossed(d1v2);
374 const gp_Vec ncrossns1 = nplan.Crossed(ns1);
375 const gp_Vec ncrossns2 = nplan.Crossed(ns2);
376 const Standard_Real norm1 = ncrossns1.Magnitude();
377 const Standard_Real norm2 = ncrossns2.Magnitude();
379 const Standard_Real ndotns1 = nplan.Dot(ns1);
380 const Standard_Real ndotns2 = nplan.Dot(ns2);
383 nor1.SetLinearForm(ndotns1/norm1,nplan,-1./norm1,ns1);
384 nor2.SetLinearForm(ndotns2/norm2,nplan,-1./norm2,ns2);
386 F(1) = (nplan.Dot(pts1.XYZ())) + theD;
387 F(2) = (nplan.Dot(pts2.XYZ())) + theD;
389 F(3) = p1p2.Dot(nor1);
390 F(4) = p1p2.Dot(nor2);
393 D(3,3) = d1u2.Dot(nor1);
394 D(3,4) = d1v2.Dot(nor1);
396 D(4,1) = -(dpdt.Dot(nor2));
399 D(3,1) = dpdt.Dot(nor1);
401 D(4,3) = -(d1u1.Dot(nor2));
402 D(4,4) = -(d1v1.Dot(nor2));
405 gp_Vec resul1,resul2,temp;
406 Standard_Real grosterme;
408 // Derivee de nor1 par rapport a u1
410 temp = d2u1.Crossed(d1v1).Added(d1u1.Crossed(d2uv1));
411 grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
412 resul1.SetLinearForm(-(grosterme*ndotns1-nplan.Dot(temp))/norm1,nplan,
416 // Derivee par rapport a v1
418 temp = d2uv1.Crossed(d1v1).Added(d1u1.Crossed(d2v1));
419 grosterme = ncrossns1.Dot(nplan.Crossed(temp))/norm1/norm1;
420 resul2.SetLinearForm(-(grosterme*ndotns1-nplan.Dot(temp))/norm1,nplan,
425 resul1.SetLinearForm(v2d.X(),resul1,v2d.Y(),resul2);
426 D(3,1) = p1p2.Dot(resul1) - (dpdt.Dot(nor1));
429 D(3,3) = -(d1u1.Dot(nor1)) + p1p2.Dot(resul1);
430 D(3,4) = -(d1v1.Dot(nor1)) + p1p2.Dot(resul2);
433 // Derivee de nor2 par rapport a u2
434 temp = d2u2.Crossed(d1v2).Added(d1u2.Crossed(d2uv2));
435 grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
436 resul1.SetLinearForm(-(grosterme*ndotns2-nplan.Dot(temp))/norm2,nplan,
440 // Derivee par rapport a v2
441 temp = d2uv2.Crossed(d1v2).Added(d1u2.Crossed(d2v2));
442 grosterme = ncrossns2.Dot(nplan.Crossed(temp))/norm2/norm2;
443 resul2.SetLinearForm(-(grosterme*ndotns2-nplan.Dot(temp))/norm2,nplan,
448 D(4,3) = d1u2.Dot(nor2) + p1p2.Dot(resul1);
449 D(4,4) = d1v2.Dot(nor2) + p1p2.Dot(resul2);
452 resul1.SetLinearForm(v2d.X(),resul1,v2d.Y(),resul2);
453 D(4,1) = p1p2.Dot(resul1) + dpdt.Dot(nor2) ;
457 // derivee par rapport a w (parametre sur ligne guide)
459 grosterme = ncrossns1.Dot(dnplan.Crossed(ns1))/norm1/norm1;
460 resul1.SetLinearForm(-(grosterme*ndotns1-dnplan.Dot(ns1))/norm1,nplan,
461 ndotns1/norm1,dnplan,
462 grosterme/norm1,ns1);
465 grosterme = ncrossns2.Dot(dnplan.Crossed(ns2))/norm2/norm2;
466 resul2.SetLinearForm(-(grosterme*ndotns2-dnplan.Dot(ns2))/norm2,nplan,
467 ndotns2/norm2,dnplan,
468 grosterme/norm2,ns2);
470 D(3,2) = p1p2.Dot(resul1);
471 D(4,2) = p1p2.Dot(resul2);
473 return Standard_True;