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1 | // Created on: 1998-05-12 |
2 | // Created by: Philippe NOUAILLE |
3 | // Copyright (c) 1998-1999 Matra Datavision |
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4 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
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5 | // |
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6 | // This file is part of Open CASCADE Technology software library. |
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7 | // |
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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 |
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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. |
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13 | // |
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14 | // Alternatively, this file may be used under the terms of Open CASCADE |
15 | // commercial license or contractual agreement. |
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16 | |
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17 | |
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18 | #include <Blend_AppFunction.hxx> |
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19 | #include <Blend_Point.hxx> |
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20 | #include <BRepBlend_AppFuncRoot.hxx> |
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21 | #include <BRepBlend_Line.hxx> |
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22 | #include <gp_Pnt.hxx> |
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23 | #include <math_FunctionSetRoot.hxx> |
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24 | #include <Standard_OutOfRange.hxx> |
25 | #include <Standard_Type.hxx> |
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26 | #include <TColgp_HArray1OfPnt.hxx> |
27 | #include <TColgp_HArray1OfPnt2d.hxx> |
28 | #include <TColgp_HArray1OfVec.hxx> |
29 | #include <TColgp_HArray1OfVec2d.hxx> |
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30 | #include <TColStd_HArray1OfInteger.hxx> |
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31 | #include <TColStd_HArray1OfReal.hxx> |
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32 | |
33 | BRepBlend_AppFuncRoot::BRepBlend_AppFuncRoot(Handle(BRepBlend_Line)& Line, |
34 | Blend_AppFunction& Func, |
35 | const Standard_Real Tol3d, |
36 | const Standard_Real Tol2d) |
37 | :myLine(Line), |
38 | myFunc(&Func), |
39 | myTolerance(1,Func.NbVariables()), |
40 | X1(1,Func.NbVariables()), |
41 | X2(1,Func.NbVariables()), |
42 | XInit(1,Func.NbVariables()), |
43 | Sol(1,Func.NbVariables()) |
44 | { |
45 | Standard_Integer NbPoles, NbKnots, Degree, NbPoles2d; |
46 | Standard_Integer ii; |
47 | |
48 | // Tolerances |
49 | Func.GetTolerance(myTolerance, Tol3d); |
50 | Standard_Integer dim = Func.NbVariables(); |
51 | for (ii=1; ii<= dim; ii++) { |
52 | if (myTolerance(ii)>Tol2d) { myTolerance(ii) = Tol2d;} |
53 | } |
54 | |
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55 | // Tables |
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56 | Func.GetShape( NbPoles, NbKnots, Degree, NbPoles2d); |
57 | |
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58 | // Calculation of BaryCentre (rationnal case). |
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59 | if (Func.IsRational()) { |
60 | Standard_Real Xmax =-1.e100, Xmin = 1.e100, |
61 | Ymax =-1.e100, Ymin = 1.e100, |
62 | Zmax =-1.e100, Zmin = 1.e100; |
63 | Blend_Point P; |
64 | for (ii=1; ii<=myLine->NbPoints(); ii++) { |
65 | P = myLine->Point(ii); |
66 | Xmax = Max ( Max(P.PointOnS1().X(), P.PointOnS2().X()), Xmax); |
67 | Xmin = Min ( Min(P.PointOnS1().X(), P.PointOnS2().X()), Xmin); |
68 | Ymax = Max ( Max(P.PointOnS1().Y(), P.PointOnS2().Y()), Ymax); |
69 | Ymin = Min ( Min(P.PointOnS1().Y(), P.PointOnS2().Y()), Ymin); |
70 | Zmax = Max ( Max(P.PointOnS1().Z(), P.PointOnS2().Z()), Zmax); |
71 | Zmin = Min ( Min(P.PointOnS1().Z(), P.PointOnS2().Z()), Zmin); |
72 | |
73 | myBary.SetCoord((Xmax+Xmin)/2, (Ymax+Ymin)/2, (Zmax+Zmin)/2); |
74 | } |
75 | } |
76 | else {myBary.SetCoord(0,0,0);} |
77 | } |
78 | |
79 | //================================================================================ |
80 | // Function: D0 |
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81 | // Purpose : Calculation of section for v = Param, if calculation fails |
82 | // Standard_False is raised. |
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83 | //================================================================================ |
84 | Standard_Boolean BRepBlend_AppFuncRoot::D0(const Standard_Real Param, |
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85 | const Standard_Real /*First*/, |
86 | const Standard_Real /*Last*/, |
87 | TColgp_Array1OfPnt& Poles, |
88 | TColgp_Array1OfPnt2d& Poles2d, |
89 | TColStd_Array1OfReal& Weigths) |
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90 | { |
91 | Standard_Boolean Ok=Standard_True; |
92 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
93 | Ok = SearchPoint( *Func, Param, myPnt); |
94 | |
95 | if (Ok) (*Func).Section(myPnt, |
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96 | Poles, |
97 | Poles2d, |
98 | Weigths); |
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99 | return Ok; |
100 | } |
101 | |
102 | //================================================================================ |
103 | // Function: D1 |
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104 | // Purpose : Calculation of the partial derivative of the section corresponding to v |
105 | // for v = Param, if the calculation fails Standard_False is raised. |
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106 | //================================================================================ |
107 | Standard_Boolean BRepBlend_AppFuncRoot::D1(const Standard_Real Param, |
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108 | const Standard_Real /*First*/, |
109 | const Standard_Real /*Last*/, |
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110 | TColgp_Array1OfPnt& Poles, |
111 | TColgp_Array1OfVec& DPoles, |
112 | TColgp_Array1OfPnt2d& Poles2d, |
113 | TColgp_Array1OfVec2d& DPoles2d, |
114 | TColStd_Array1OfReal& Weigths, |
115 | TColStd_Array1OfReal& DWeigths) |
116 | { |
117 | Standard_Boolean Ok=Standard_True; |
118 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
119 | |
120 | Ok = SearchPoint( *Func, Param, myPnt); |
121 | |
122 | if (Ok) { |
123 | Ok = (*Func).Section(myPnt, |
124 | Poles, DPoles, |
125 | Poles2d, DPoles2d, |
126 | Weigths, DWeigths); |
127 | } |
128 | |
129 | return Ok; |
130 | } |
131 | |
132 | //=========================================================================== |
133 | // Function: D2 |
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134 | // Purpose : Calculation of the derivative and second partial of the |
135 | // section corresponding to v. |
136 | // For v = Param, if the calculation fails Standard_False is raised. |
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137 | //=========================================================================== |
138 | Standard_Boolean BRepBlend_AppFuncRoot::D2(const Standard_Real Param, |
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139 | const Standard_Real /*First*/, |
140 | const Standard_Real /*Last*/, |
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141 | TColgp_Array1OfPnt& Poles, |
142 | TColgp_Array1OfVec& DPoles, |
143 | TColgp_Array1OfVec& D2Poles, |
144 | TColgp_Array1OfPnt2d& Poles2d, |
145 | TColgp_Array1OfVec2d& DPoles2d, |
146 | TColgp_Array1OfVec2d& D2Poles2d, |
147 | TColStd_Array1OfReal& Weigths, |
148 | TColStd_Array1OfReal& DWeigths, |
149 | TColStd_Array1OfReal& D2Weigths) |
150 | { |
151 | Standard_Boolean Ok=Standard_True; |
152 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
153 | |
154 | Ok = SearchPoint( *Func, Param, myPnt); |
155 | if (Ok) { |
156 | Ok = (*Func).Section(myPnt, |
157 | Poles, DPoles, D2Poles, |
158 | Poles2d, DPoles2d, D2Poles2d, |
159 | Weigths, DWeigths, D2Weigths); |
160 | } |
161 | return Ok; |
162 | } |
163 | |
164 | Standard_Integer BRepBlend_AppFuncRoot::Nb2dCurves() const |
165 | { |
166 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
167 | Standard_Integer i,j,k,nbpol2d; |
168 | (*Func).GetShape(i,j,k,nbpol2d); |
169 | return nbpol2d; |
170 | } |
171 | |
172 | void BRepBlend_AppFuncRoot::SectionShape(Standard_Integer& NbPoles, |
173 | Standard_Integer& NbKnots, |
174 | Standard_Integer& Degree) const |
175 | { |
176 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
177 | Standard_Integer ii; |
178 | (*Func).GetShape( NbPoles, NbKnots, Degree, ii); |
179 | } |
180 | |
181 | void BRepBlend_AppFuncRoot::Knots(TColStd_Array1OfReal& TKnots) const |
182 | { |
183 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
184 | Func->Knots(TKnots); |
185 | } |
186 | |
187 | void BRepBlend_AppFuncRoot::Mults(TColStd_Array1OfInteger& TMults) const |
188 | { |
189 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
190 | Func->Mults(TMults); |
191 | } |
192 | |
193 | Standard_Boolean BRepBlend_AppFuncRoot::IsRational() const |
194 | { |
195 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
196 | return (*Func).IsRational(); |
197 | } |
198 | |
199 | Standard_Integer BRepBlend_AppFuncRoot::NbIntervals(const GeomAbs_Shape S) const |
200 | { |
201 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
202 | return Func->NbIntervals(S); |
203 | } |
204 | |
205 | void BRepBlend_AppFuncRoot::Intervals(TColStd_Array1OfReal& T,const GeomAbs_Shape S) const |
206 | { |
207 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
208 | Func->Intervals(T, S); |
209 | } |
210 | |
211 | void BRepBlend_AppFuncRoot::SetInterval(const Standard_Real First,const Standard_Real Last) |
212 | { |
213 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
214 | Func->Set(First, Last); |
215 | } |
216 | |
217 | void BRepBlend_AppFuncRoot::Resolution(const Standard_Integer Index, |
218 | const Standard_Real Tol, |
219 | Standard_Real& TolU, |
220 | Standard_Real& TolV) const |
221 | { |
222 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
223 | Func->Resolution(Index,Tol,TolU,TolV); |
224 | } |
225 | |
226 | void BRepBlend_AppFuncRoot::GetTolerance(const Standard_Real BoundTol, |
227 | const Standard_Real SurfTol, |
228 | const Standard_Real AngleTol, |
229 | TColStd_Array1OfReal& Tol3d) const |
230 | { |
231 | Standard_Integer ii; |
232 | math_Vector V3d(1, Tol3d.Length()), V1d(1, Tol3d.Length()); |
233 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
234 | |
235 | Func->GetTolerance(BoundTol, SurfTol, AngleTol, V3d, V1d); |
236 | for (ii=1; ii<=Tol3d.Length(); ii++) Tol3d(ii) = V3d(ii); |
237 | } |
238 | |
239 | void BRepBlend_AppFuncRoot::SetTolerance(const Standard_Real Tol3d, |
240 | const Standard_Real Tol2d) |
241 | { |
242 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
243 | Standard_Integer ii, dim = Func->NbVariables(); |
244 | Func->GetTolerance(myTolerance, Tol3d); |
245 | for (ii=1; ii<=dim; ii++) { |
246 | if (myTolerance(ii)>Tol2d) { myTolerance(ii) = Tol2d;} |
247 | } |
248 | } |
249 | |
250 | gp_Pnt BRepBlend_AppFuncRoot::BarycentreOfSurf() const |
251 | { |
252 | return myBary; |
253 | } |
254 | |
255 | Standard_Real BRepBlend_AppFuncRoot::MaximalSection() const |
256 | { |
257 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
258 | return Func->GetSectionSize(); |
259 | } |
260 | |
261 | void BRepBlend_AppFuncRoot::GetMinimalWeight(TColStd_Array1OfReal& Weigths) const |
262 | { |
263 | Blend_AppFunction* Func = (Blend_AppFunction*)myFunc; |
264 | Func->GetMinimalWeight(Weigths); |
265 | } |
266 | |
267 | |
268 | //================================================================================ |
269 | // |
270 | // Function : SearchPoint |
271 | // |
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272 | // Purpose : Find point solution with parameter Param (on 2 Surfaces) |
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273 | // |
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274 | // Algorithm : |
275 | // 1) Approximative solution is found from already calculated Points |
276 | // 2) Convergence is done by a method of type Newton |
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277 | // |
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278 | // Possible causes of fails : |
279 | // - Singularity on surfaces. |
280 | // - no information oin the "line" resulting from processing. |
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281 | // |
282 | //================================================================================ |
283 | |
284 | Standard_Boolean BRepBlend_AppFuncRoot::SearchPoint(Blend_AppFunction& Func, |
285 | const Standard_Real Param, |
286 | Blend_Point& Pnt) |
287 | { |
288 | Standard_Boolean Trouve; |
289 | Standard_Integer dim = Func.NbVariables(); |
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290 | // (1) Find a point of init |
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291 | Standard_Integer I1=1, I2=myLine->NbPoints(), Index; |
292 | Standard_Real t1, t2; |
293 | |
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294 | // (1.a) It is checked if it is inside |
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295 | if (Param < myLine->Point(I1).Parameter()) {return Standard_False;} |
296 | if (Param > myLine->Point(I2).Parameter()) {return Standard_False;} |
297 | |
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298 | // (1.b) Find the interval |
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299 | Trouve = SearchLocation(Param, I1, I2, Index); |
300 | |
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301 | // (1.c) If the point is already calculated it is returned |
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302 | if (Trouve) { |
303 | Pnt = myLine->Point(Index); |
304 | Vec(XInit,Pnt); |
305 | } |
306 | else { |
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307 | // (1.d) Intialisation by linear interpolation |
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308 | Pnt = myLine->Point(Index); |
309 | Vec(X1,Pnt); |
310 | t1 = Pnt.Parameter(); |
311 | |
312 | Pnt = myLine->Point(Index+1); |
313 | Vec(X2,Pnt); |
314 | t2 = Pnt.Parameter(); |
315 | |
316 | Standard_Real Parammt1 = (Param-t1) / (t2-t1); |
317 | Standard_Real t2mParam = (t2-Param) / (t2-t1); |
318 | for(Standard_Integer i = 1; i <= dim; i++){ |
319 | XInit(i) = X2(i) * Parammt1 + X1(i) * t2mParam; |
320 | } |
321 | } |
322 | |
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323 | // (2) Calculation of the solution ------------------------ |
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324 | Func.Set(Param); |
325 | Func.GetBounds(X1, X2); |
326 | math_FunctionSetRoot rsnld(Func, myTolerance, 30); |
327 | |
328 | rsnld.Perform(Func, XInit, X1, X2); |
329 | |
330 | if (!rsnld.IsDone()) { |
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331 | # ifdef BREPBLEND_DEB |
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332 | cout << "AppFunc : RNLD Not done en t = " << Param << endl; |
333 | # endif |
334 | return Standard_False; |
335 | } |
336 | rsnld.Root(Sol); |
337 | |
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338 | // (3) Storage of the point |
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339 | Point(Func,Param,Sol,Pnt); |
340 | |
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341 | // (4) Insertion of the point if the calculation seems long. |
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342 | if ((!Trouve)&&(rsnld.NbIterations()>3)) { |
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343 | #ifdef OCCT_DEBUG |
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344 | cout << "Evaluation in t = " << Param << "given" << endl; |
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345 | rsnld.Dump(cout); |
346 | #endif |
347 | myLine->InsertBefore(Index+1, Pnt); |
348 | } |
349 | return Standard_True; |
350 | } |
351 | |
352 | |
353 | //============================================================================= |
354 | // |
355 | // Function : SearchLocation |
356 | // |
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357 | // Purpose : Binary search of the line of the parametric interval containing |
358 | // Param in the list of calculated points (myline) |
359 | // if the point of parameter Param is already stored in the list |
360 | // True is raised and ParamIndex corresponds to line of Point. |
361 | // Complexity of this algorithm is log(n)/log(2) |
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362 | //================================================================================ |
363 | Standard_Boolean BRepBlend_AppFuncRoot::SearchLocation(const Standard_Real Param, |
364 | const Standard_Integer FirstIndex, |
365 | const Standard_Integer LastIndex, |
366 | Standard_Integer& ParamIndex) const |
367 | { |
368 | Standard_Integer Ideb = FirstIndex, Ifin = LastIndex, Idemi; |
369 | Standard_Real Valeur; |
370 | |
371 | Valeur = myLine->Point(Ideb).Parameter(); |
372 | if (Param == Valeur) { |
373 | ParamIndex = Ideb; |
374 | return Standard_True; |
375 | } |
376 | |
377 | Valeur = myLine->Point(Ifin).Parameter(); |
378 | if (Param == Valeur) { |
379 | ParamIndex = Ifin; |
380 | return Standard_True; |
381 | } |
382 | |
383 | while ( Ideb+1 != Ifin) { |
384 | Idemi = (Ideb+Ifin)/2; |
385 | Valeur = myLine->Point(Idemi).Parameter(); |
386 | if (Valeur < Param) {Ideb = Idemi;} |
387 | else { |
388 | if ( Valeur > Param) { Ifin = Idemi;} |
389 | else { ParamIndex = Idemi; |
390 | return Standard_True;} |
391 | } |
392 | } |
393 | |
394 | ParamIndex = Ideb; |
395 | return Standard_False; |
396 | } |
397 | |