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b311480e | 1 | // Created on: 1995-08-28 |
2 | // Created by: Laurent BOURESCHE | |
3 | // Copyright (c) 1995-1999 Matra Datavision | |
973c2be1 | 4 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
b311480e | 5 | // |
973c2be1 | 6 | // This file is part of Open CASCADE Technology software library. |
b311480e | 7 | // |
973c2be1 | 8 | // This library is free software; you can redistribute it and / or modify it |
9 | // under the terms of the GNU Lesser General Public 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. | |
b311480e | 13 | // |
973c2be1 | 14 | // Alternatively, this file may be used under the terms of Open CASCADE |
15 | // commercial license or contractual agreement. | |
b311480e | 16 | |
7fd59977 | 17 | // Modified: 28/02/1996 by PMN : HermiteCoefficients added |
18 | // Modified: 18/06/1996 by PMN : NULL reference. | |
19 | // Modified: 19/02/1997 by JCT : EvalPoly2Var added | |
20 | ||
7fd59977 | 21 | #include <PLib.ixx> |
f7b4312f | 22 | #include <NCollection_LocalArray.hxx> |
7fd59977 | 23 | #include <math_Matrix.hxx> |
24 | #include <math_Gauss.hxx> | |
25 | #include <Standard_ConstructionError.hxx> | |
26 | #include <GeomAbs_Shape.hxx> | |
27 | ||
105aae76 | 28 | #include <math_Gauss.hxx> |
29 | #include <math.hxx> | |
30 | ||
7fd59977 | 31 | // To convert points array into Real .. |
32 | // ********************************* | |
33 | ||
105aae76 | 34 | //======================================================================= |
35 | //function : SetPoles | |
36 | //purpose : | |
37 | //======================================================================= | |
38 | ||
39 | void PLib::SetPoles(const TColgp_Array1OfPnt2d& Poles, | |
40 | TColStd_Array1OfReal& FP) | |
41 | { | |
42 | Standard_Integer j = FP .Lower(); | |
43 | Standard_Integer PLower = Poles.Lower(); | |
44 | Standard_Integer PUpper = Poles.Upper(); | |
45 | ||
46 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
47 | const gp_Pnt2d& P = Poles(i); | |
48 | FP(j) = P.Coord(1); j++; | |
49 | FP(j) = P.Coord(2); j++; | |
50 | } | |
51 | } | |
52 | ||
53 | //======================================================================= | |
54 | //function : SetPoles | |
55 | //purpose : | |
56 | //======================================================================= | |
57 | ||
58 | void PLib::SetPoles(const TColgp_Array1OfPnt2d& Poles, | |
59 | const TColStd_Array1OfReal& Weights, | |
60 | TColStd_Array1OfReal& FP) | |
61 | { | |
62 | Standard_Integer j = FP .Lower(); | |
63 | Standard_Integer PLower = Poles.Lower(); | |
64 | Standard_Integer PUpper = Poles.Upper(); | |
65 | ||
66 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
67 | Standard_Real w = Weights(i); | |
68 | const gp_Pnt2d& P = Poles(i); | |
69 | FP(j) = P.Coord(1) * w; j++; | |
70 | FP(j) = P.Coord(2) * w; j++; | |
71 | FP(j) = w; j++; | |
72 | } | |
73 | } | |
74 | ||
75 | //======================================================================= | |
76 | //function : GetPoles | |
77 | //purpose : | |
78 | //======================================================================= | |
7fd59977 | 79 | |
105aae76 | 80 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, |
81 | TColgp_Array1OfPnt2d& Poles) | |
82 | { | |
83 | Standard_Integer j = FP .Lower(); | |
84 | Standard_Integer PLower = Poles.Lower(); | |
85 | Standard_Integer PUpper = Poles.Upper(); | |
86 | ||
87 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
88 | gp_Pnt2d& P = Poles(i); | |
89 | P.SetCoord(1,FP(j)); j++; | |
90 | P.SetCoord(2,FP(j)); j++; | |
91 | } | |
92 | } | |
7fd59977 | 93 | |
105aae76 | 94 | //======================================================================= |
95 | //function : GetPoles | |
96 | //purpose : | |
97 | //======================================================================= | |
7fd59977 | 98 | |
105aae76 | 99 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, |
100 | TColgp_Array1OfPnt2d& Poles, | |
101 | TColStd_Array1OfReal& Weights) | |
102 | { | |
103 | Standard_Integer j = FP .Lower(); | |
104 | Standard_Integer PLower = Poles.Lower(); | |
105 | Standard_Integer PUpper = Poles.Upper(); | |
106 | ||
107 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
108 | Standard_Real w = FP(j + 2); | |
109 | Weights(i) = w; | |
110 | gp_Pnt2d& P = Poles(i); | |
111 | P.SetCoord(1,FP(j) / w); j++; | |
112 | P.SetCoord(2,FP(j) / w); j++; | |
113 | j++; | |
114 | } | |
115 | } | |
7fd59977 | 116 | |
105aae76 | 117 | //======================================================================= |
118 | //function : SetPoles | |
119 | //purpose : | |
120 | //======================================================================= | |
7fd59977 | 121 | |
105aae76 | 122 | void PLib::SetPoles(const TColgp_Array1OfPnt& Poles, |
123 | TColStd_Array1OfReal& FP) | |
124 | { | |
125 | Standard_Integer j = FP .Lower(); | |
126 | Standard_Integer PLower = Poles.Lower(); | |
127 | Standard_Integer PUpper = Poles.Upper(); | |
7fd59977 | 128 | |
105aae76 | 129 | for (Standard_Integer i = PLower; i <= PUpper; i++) { |
130 | const gp_Pnt& P = Poles(i); | |
131 | FP(j) = P.Coord(1); j++; | |
132 | FP(j) = P.Coord(2); j++; | |
133 | FP(j) = P.Coord(3); j++; | |
134 | } | |
135 | } | |
136 | ||
137 | //======================================================================= | |
138 | //function : SetPoles | |
139 | //purpose : | |
140 | //======================================================================= | |
141 | ||
142 | void PLib::SetPoles(const TColgp_Array1OfPnt& Poles, | |
143 | const TColStd_Array1OfReal& Weights, | |
144 | TColStd_Array1OfReal& FP) | |
145 | { | |
146 | Standard_Integer j = FP .Lower(); | |
147 | Standard_Integer PLower = Poles.Lower(); | |
148 | Standard_Integer PUpper = Poles.Upper(); | |
149 | ||
150 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
151 | Standard_Real w = Weights(i); | |
152 | const gp_Pnt& P = Poles(i); | |
153 | FP(j) = P.Coord(1) * w; j++; | |
154 | FP(j) = P.Coord(2) * w; j++; | |
155 | FP(j) = P.Coord(3) * w; j++; | |
156 | FP(j) = w; j++; | |
157 | } | |
158 | } | |
159 | ||
160 | //======================================================================= | |
161 | //function : GetPoles | |
162 | //purpose : | |
163 | //======================================================================= | |
164 | ||
165 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, | |
166 | TColgp_Array1OfPnt& Poles) | |
167 | { | |
168 | Standard_Integer j = FP .Lower(); | |
169 | Standard_Integer PLower = Poles.Lower(); | |
170 | Standard_Integer PUpper = Poles.Upper(); | |
171 | ||
172 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
173 | gp_Pnt& P = Poles(i); | |
174 | P.SetCoord(1,FP(j)); j++; | |
175 | P.SetCoord(2,FP(j)); j++; | |
176 | P.SetCoord(3,FP(j)); j++; | |
177 | } | |
178 | } | |
179 | ||
180 | //======================================================================= | |
181 | //function : GetPoles | |
182 | //purpose : | |
183 | //======================================================================= | |
184 | ||
185 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, | |
186 | TColgp_Array1OfPnt& Poles, | |
187 | TColStd_Array1OfReal& Weights) | |
188 | { | |
189 | Standard_Integer j = FP .Lower(); | |
190 | Standard_Integer PLower = Poles.Lower(); | |
191 | Standard_Integer PUpper = Poles.Upper(); | |
192 | ||
193 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
194 | Standard_Real w = FP(j + 3); | |
195 | Weights(i) = w; | |
196 | gp_Pnt& P = Poles(i); | |
197 | P.SetCoord(1,FP(j) / w); j++; | |
198 | P.SetCoord(2,FP(j) / w); j++; | |
199 | P.SetCoord(3,FP(j) / w); j++; | |
200 | j++; | |
201 | } | |
202 | } | |
203 | ||
204 | // specialized allocator | |
205 | namespace | |
206 | { | |
7fd59977 | 207 | |
41194117 | 208 | class BinomAllocator |
7fd59977 | 209 | { |
41194117 K |
210 | public: |
211 | ||
212 | //! Main constructor | |
213 | BinomAllocator (const Standard_Integer theMaxBinom) | |
214 | : myBinom (NULL), | |
215 | myMaxBinom (theMaxBinom) | |
216 | { | |
217 | Standard_Integer i, im1, ip1, id2, md2, md3, j, k; | |
218 | Standard_Integer np1 = myMaxBinom + 1; | |
219 | myBinom = new Standard_Integer*[np1]; | |
220 | myBinom[0] = new Standard_Integer[1]; | |
221 | myBinom[0][0] = 1; | |
222 | for (i = 1; i < np1; ++i) | |
223 | { | |
7fd59977 | 224 | im1 = i - 1; |
225 | ip1 = i + 1; | |
226 | id2 = i >> 1; | |
227 | md2 = im1 >> 1; | |
228 | md3 = ip1 >> 1; | |
229 | k = 0; | |
41194117 | 230 | myBinom[i] = new Standard_Integer[ip1]; |
7fd59977 | 231 | |
41194117 K |
232 | for (j = 0; j < id2; ++j) |
233 | { | |
234 | myBinom[i][j] = k + myBinom[im1][j]; | |
235 | k = myBinom[im1][j]; | |
7fd59977 | 236 | } |
237 | j = id2; | |
238 | if (j > md2) j = im1 - j; | |
41194117 | 239 | myBinom[i][id2] = k + myBinom[im1][j]; |
7fd59977 | 240 | |
41194117 K |
241 | for (j = ip1 - md3; j < ip1; j++) |
242 | { | |
243 | myBinom[i][j] = myBinom[i][i - j]; | |
7fd59977 | 244 | } |
245 | } | |
7fd59977 | 246 | } |
7fd59977 | 247 | |
41194117 K |
248 | //! Destructor |
249 | ~BinomAllocator() | |
250 | { | |
251 | // free memory | |
252 | for (Standard_Integer i = 0; i <= myMaxBinom; ++i) | |
253 | { | |
254 | delete[] myBinom[i]; | |
255 | } | |
256 | delete[] myBinom; | |
257 | } | |
7fd59977 | 258 | |
41194117 K |
259 | Standard_Real Value (const Standard_Integer N, |
260 | const Standard_Integer P) const | |
261 | { | |
262 | Standard_OutOfRange_Raise_if (N > myMaxBinom, | |
263 | "PLib, BinomAllocator: requested degree is greater than maximum supported"); | |
264 | return Standard_Real (myBinom[N][P]); | |
7fd59977 | 265 | } |
41194117 K |
266 | |
267 | private: | |
268 | Standard_Integer** myBinom; | |
269 | Standard_Integer myMaxBinom; | |
270 | ||
271 | }; | |
272 | ||
41194117 K |
273 | // we do not call BSplCLib here to avoid Cyclic dependency detection by WOK |
274 | //static BinomAllocator THE_BINOM (BSplCLib::MaxDegree() + 1); | |
275 | static BinomAllocator THE_BINOM (25 + 1); | |
276 | }; | |
277 | ||
278 | //======================================================================= | |
279 | //function : Bin | |
280 | //purpose : | |
281 | //======================================================================= | |
282 | ||
283 | Standard_Real PLib::Bin(const Standard_Integer N, | |
284 | const Standard_Integer P) | |
285 | { | |
286 | return THE_BINOM.Value (N, P); | |
7fd59977 | 287 | } |
288 | ||
289 | //======================================================================= | |
290 | //function : RationalDerivative | |
291 | //purpose : | |
292 | //======================================================================= | |
293 | ||
294 | void PLib::RationalDerivative(const Standard_Integer Degree, | |
295 | const Standard_Integer DerivativeRequest, | |
296 | const Standard_Integer Dimension, | |
297 | Standard_Real& Ders, | |
298 | Standard_Real& RDers, | |
299 | const Standard_Boolean All) | |
300 | { | |
301 | // | |
302 | // Our purpose is to compute f = (u/v) derivated N = DerivativeRequest times | |
303 | // | |
304 | // We Write u = fv | |
305 | // Let C(N,P) be the binomial | |
306 | // | |
307 | // then we have | |
308 | // | |
309 | // (q) (p) (q-p) | |
310 | // u = SUM C (q,p) f v | |
311 | // p = 0 to q | |
312 | // | |
313 | // | |
314 | // Therefore | |
315 | // | |
316 | // | |
317 | // (q) ( (q) (p) (q-p) ) | |
318 | // f = (1/v) ( u - SUM C (q,p) f v ) | |
319 | // ( p = 0 to q-1 ) | |
320 | // | |
321 | // | |
322 | // make arrays for the binomial since computing it each time could raise a performance | |
323 | // issue | |
324 | // As oppose to the method below the <Der> array is organized in the following | |
325 | // fashion : | |
326 | // | |
327 | // u (1) u (2) .... u (Dimension) v (1) | |
328 | // | |
329 | // (1) (1) (1) (1) | |
330 | // u (1) u (2) .... u (Dimension) v (1) | |
331 | // | |
332 | // ............................................ | |
333 | // | |
334 | // (Degree) (Degree) (Degree) (Degree) | |
335 | // u (1) u (2) .... u (Dimension) v (1) | |
336 | // | |
337 | // | |
338 | Standard_Real Inverse; | |
339 | Standard_Real *PolesArray = &Ders; | |
340 | Standard_Real *RationalArray = &RDers; | |
341 | Standard_Real Factor ; | |
342 | Standard_Integer ii, Index, OtherIndex, Index1, Index2, jj; | |
f7b4312f | 343 | NCollection_LocalArray<Standard_Real> binomial_array; |
344 | NCollection_LocalArray<Standard_Real> derivative_storage; | |
7fd59977 | 345 | if (Dimension == 3) { |
346 | Standard_Integer DeRequest1 = DerivativeRequest + 1; | |
347 | Standard_Integer MinDegRequ = DerivativeRequest; | |
348 | if (MinDegRequ > Degree) MinDegRequ = Degree; | |
41194117 | 349 | binomial_array.Allocate (DeRequest1); |
7fd59977 | 350 | |
351 | for (ii = 0 ; ii < DeRequest1 ; ii++) { | |
352 | binomial_array[ii] = 1.0e0 ; | |
353 | } | |
354 | if (!All) { | |
355 | Standard_Integer DimDeRequ1 = (DeRequest1 << 1) + DeRequest1; | |
41194117 | 356 | derivative_storage.Allocate (DimDeRequ1); |
7fd59977 | 357 | RationalArray = derivative_storage ; |
358 | } | |
359 | ||
360 | Inverse = 1.0e0 / PolesArray[3] ; | |
361 | Index = 0 ; | |
362 | Index2 = - 6; | |
363 | OtherIndex = 0 ; | |
364 | ||
365 | for (ii = 0 ; ii <= MinDegRequ ; ii++) { | |
366 | Index2 += 3; | |
367 | Index1 = Index2; | |
368 | RationalArray[Index] = PolesArray[OtherIndex]; Index++; OtherIndex++; | |
369 | RationalArray[Index] = PolesArray[OtherIndex]; Index++; OtherIndex++; | |
370 | RationalArray[Index] = PolesArray[OtherIndex]; | |
371 | Index -= 2; | |
372 | OtherIndex += 2; | |
373 | ||
374 | for (jj = ii - 1 ; jj >= 0 ; jj--) { | |
375 | Factor = binomial_array[jj] * PolesArray[((ii-jj) << 2) + 3]; | |
376 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
377 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
378 | RationalArray[Index] -= Factor * RationalArray[Index1]; | |
379 | Index -= 2; | |
380 | Index1 -= 5; | |
381 | } | |
382 | ||
383 | for (jj = ii ; jj >= 1 ; jj--) { | |
384 | binomial_array[jj] += binomial_array[jj - 1] ; | |
385 | } | |
386 | RationalArray[Index] *= Inverse ; Index++; | |
387 | RationalArray[Index] *= Inverse ; Index++; | |
388 | RationalArray[Index] *= Inverse ; Index++; | |
389 | } | |
390 | ||
391 | for (ii= MinDegRequ + 1; ii <= DerivativeRequest ; ii++){ | |
392 | Index2 += 3; | |
393 | Index1 = Index2; | |
394 | RationalArray[Index] = 0.0e0; Index++; | |
395 | RationalArray[Index] = 0.0e0; Index++; | |
396 | RationalArray[Index] = 0.0e0; | |
397 | Index -= 2; | |
398 | ||
399 | for (jj = ii - 1 ; jj >= ii - MinDegRequ ; jj--) { | |
400 | Factor = binomial_array[jj] * PolesArray[((ii-jj) << 2) + 3]; | |
401 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
402 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
403 | RationalArray[Index] -= Factor * RationalArray[Index1]; | |
404 | Index -= 2; | |
405 | Index1 -= 5; | |
406 | } | |
407 | ||
408 | for (jj = ii ; jj >= 1 ; jj--) { | |
409 | binomial_array[jj] += binomial_array[jj - 1] ; | |
410 | } | |
411 | RationalArray[Index] *= Inverse; Index++; | |
412 | RationalArray[Index] *= Inverse; Index++; | |
413 | RationalArray[Index] *= Inverse; Index++; | |
414 | } | |
415 | ||
416 | if (!All) { | |
417 | RationalArray = &RDers ; | |
418 | Standard_Integer DimDeRequ = (DerivativeRequest << 1) + DerivativeRequest; | |
419 | RationalArray[0] = derivative_storage[DimDeRequ]; DimDeRequ++; | |
420 | RationalArray[1] = derivative_storage[DimDeRequ]; DimDeRequ++; | |
421 | RationalArray[2] = derivative_storage[DimDeRequ]; | |
422 | } | |
423 | } | |
424 | else { | |
425 | Standard_Integer kk; | |
426 | Standard_Integer Dimension1 = Dimension + 1; | |
427 | Standard_Integer Dimension2 = Dimension << 1; | |
428 | Standard_Integer DeRequest1 = DerivativeRequest + 1; | |
429 | Standard_Integer MinDegRequ = DerivativeRequest; | |
430 | if (MinDegRequ > Degree) MinDegRequ = Degree; | |
41194117 | 431 | binomial_array.Allocate (DeRequest1); |
7fd59977 | 432 | |
433 | for (ii = 0 ; ii < DeRequest1 ; ii++) { | |
434 | binomial_array[ii] = 1.0e0 ; | |
435 | } | |
436 | if (!All) { | |
437 | Standard_Integer DimDeRequ1 = Dimension * DeRequest1; | |
41194117 | 438 | derivative_storage.Allocate (DimDeRequ1); |
7fd59977 | 439 | RationalArray = derivative_storage ; |
440 | } | |
441 | ||
442 | Inverse = 1.0e0 / PolesArray[Dimension] ; | |
443 | Index = 0 ; | |
444 | Index2 = - Dimension2; | |
445 | OtherIndex = 0 ; | |
446 | ||
447 | for (ii = 0 ; ii <= MinDegRequ ; ii++) { | |
448 | Index2 += Dimension; | |
449 | Index1 = Index2; | |
450 | ||
451 | for (kk = 0 ; kk < Dimension ; kk++) { | |
452 | RationalArray[Index] = PolesArray[OtherIndex]; Index++; OtherIndex++; | |
453 | } | |
454 | Index -= Dimension; | |
455 | OtherIndex ++;; | |
456 | ||
457 | for (jj = ii - 1 ; jj >= 0 ; jj--) { | |
458 | Factor = binomial_array[jj] * PolesArray[(ii-jj) * Dimension1 + Dimension]; | |
459 | ||
460 | for (kk = 0 ; kk < Dimension ; kk++) { | |
461 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
462 | } | |
463 | Index -= Dimension ; | |
464 | Index1 -= Dimension2 ; | |
465 | } | |
466 | ||
467 | for (jj = ii ; jj >= 1 ; jj--) { | |
468 | binomial_array[jj] += binomial_array[jj - 1] ; | |
469 | } | |
470 | ||
471 | for (kk = 0 ; kk < Dimension ; kk++) { | |
472 | RationalArray[Index] *= Inverse ; Index++; | |
473 | } | |
474 | } | |
475 | ||
476 | for (ii= MinDegRequ + 1; ii <= DerivativeRequest ; ii++){ | |
477 | Index2 += Dimension; | |
478 | Index1 = Index2; | |
479 | ||
480 | for (kk = 0 ; kk < Dimension ; kk++) { | |
481 | RationalArray[Index] = 0.0e0 ; Index++; | |
482 | } | |
483 | Index -= Dimension; | |
484 | ||
485 | for (jj = ii - 1 ; jj >= ii - MinDegRequ ; jj--) { | |
486 | Factor = binomial_array[jj] * PolesArray[(ii-jj) * Dimension1 + Dimension]; | |
487 | ||
488 | for (kk = 0 ; kk < Dimension ; kk++) { | |
489 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
490 | } | |
491 | Index -= Dimension ; | |
492 | Index1 -= Dimension2 ; | |
493 | } | |
494 | ||
495 | for (jj = ii ; jj >= 1 ; jj--) { | |
496 | binomial_array[jj] += binomial_array[jj - 1] ; | |
497 | } | |
498 | ||
499 | for (kk = 0 ; kk < Dimension ; kk++) { | |
500 | RationalArray[Index] *= Inverse; Index++; | |
501 | } | |
502 | } | |
503 | ||
504 | if (!All) { | |
505 | RationalArray = &RDers ; | |
506 | Standard_Integer DimDeRequ = Dimension * DerivativeRequest; | |
507 | ||
508 | for (kk = 0 ; kk < Dimension ; kk++) { | |
509 | RationalArray[kk] = derivative_storage[DimDeRequ]; DimDeRequ++; | |
510 | } | |
511 | } | |
512 | } | |
513 | } | |
514 | ||
515 | //======================================================================= | |
516 | //function : RationalDerivatives | |
517 | //purpose : Uses Homogeneous Poles Derivatives and Deivatives of Weights | |
518 | //======================================================================= | |
519 | ||
520 | void PLib::RationalDerivatives(const Standard_Integer DerivativeRequest, | |
521 | const Standard_Integer Dimension, | |
522 | Standard_Real& PolesDerivates, | |
523 | // must be an array with | |
524 | // (DerivativeRequest + 1) * Dimension slots | |
525 | Standard_Real& WeightsDerivates, | |
526 | // must be an array with | |
527 | // (DerivativeRequest + 1) slots | |
528 | Standard_Real& RationalDerivates) | |
529 | { | |
530 | // | |
531 | // Our purpose is to compute f = (u/v) derivated N times | |
532 | // | |
533 | // We Write u = fv | |
534 | // Let C(N,P) be the binomial | |
535 | // | |
536 | // then we have | |
537 | // | |
538 | // (q) (p) (q-p) | |
539 | // u = SUM C (q,p) f v | |
540 | // p = 0 to q | |
541 | // | |
542 | // | |
543 | // Therefore | |
544 | // | |
545 | // | |
546 | // (q) ( (q) (p) (q-p) ) | |
547 | // f = (1/v) ( u - SUM C (q,p) f v ) | |
548 | // ( p = 0 to q-1 ) | |
549 | // | |
550 | // | |
551 | // make arrays for the binomial since computing it each time could | |
552 | // raize a performance issue | |
553 | // | |
554 | Standard_Real Inverse; | |
555 | Standard_Real *PolesArray = &PolesDerivates; | |
556 | Standard_Real *WeightsArray = &WeightsDerivates; | |
557 | Standard_Real *RationalArray = &RationalDerivates; | |
558 | Standard_Real Factor ; | |
559 | ||
560 | Standard_Integer ii, Index, Index1, Index2, jj; | |
561 | Standard_Integer DeRequest1 = DerivativeRequest + 1; | |
562 | ||
f7b4312f | 563 | NCollection_LocalArray<Standard_Real> binomial_array (DeRequest1); |
564 | NCollection_LocalArray<Standard_Real> derivative_storage; | |
7fd59977 | 565 | |
566 | for (ii = 0 ; ii < DeRequest1 ; ii++) { | |
567 | binomial_array[ii] = 1.0e0 ; | |
568 | } | |
569 | Inverse = 1.0e0 / WeightsArray[0] ; | |
570 | if (Dimension == 3) { | |
571 | Index = 0 ; | |
572 | Index2 = - 6 ; | |
573 | ||
574 | for (ii = 0 ; ii < DeRequest1 ; ii++) { | |
575 | Index2 += 3; | |
576 | Index1 = Index2; | |
577 | RationalArray[Index] = PolesArray[Index] ; Index++; | |
578 | RationalArray[Index] = PolesArray[Index] ; Index++; | |
579 | RationalArray[Index] = PolesArray[Index] ; | |
580 | Index -= 2; | |
581 | ||
582 | for (jj = ii - 1 ; jj >= 0 ; jj--) { | |
583 | Factor = binomial_array[jj] * WeightsArray[ii - jj] ; | |
584 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
585 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
586 | RationalArray[Index] -= Factor * RationalArray[Index1]; | |
587 | Index -= 2; | |
588 | Index1 -= 5; | |
589 | } | |
590 | ||
591 | for (jj = ii ; jj >= 1 ; jj--) { | |
592 | binomial_array[jj] += binomial_array[jj - 1] ; | |
593 | } | |
594 | RationalArray[Index] *= Inverse ; Index++; | |
595 | RationalArray[Index] *= Inverse ; Index++; | |
596 | RationalArray[Index] *= Inverse ; Index++; | |
597 | } | |
598 | } | |
599 | else { | |
600 | Standard_Integer kk; | |
601 | Standard_Integer Dimension2 = Dimension << 1; | |
602 | Index = 0 ; | |
603 | Index2 = - Dimension2; | |
604 | ||
605 | for (ii = 0 ; ii < DeRequest1 ; ii++) { | |
606 | Index2 += Dimension; | |
607 | Index1 = Index2; | |
608 | ||
609 | for (kk = 0 ; kk < Dimension ; kk++) { | |
610 | RationalArray[Index] = PolesArray[Index]; Index++; | |
611 | } | |
612 | Index -= Dimension; | |
613 | ||
614 | for (jj = ii - 1 ; jj >= 0 ; jj--) { | |
615 | Factor = binomial_array[jj] * WeightsArray[ii - jj] ; | |
616 | ||
617 | for (kk = 0 ; kk < Dimension ; kk++) { | |
618 | RationalArray[Index] -= Factor * RationalArray[Index1]; Index++; Index1++; | |
619 | } | |
620 | Index -= Dimension; | |
621 | Index1 -= Dimension2; | |
622 | } | |
623 | ||
624 | for (jj = ii ; jj >= 1 ; jj--) { | |
625 | binomial_array[jj] += binomial_array[jj - 1] ; | |
626 | } | |
627 | ||
628 | for (kk = 0 ; kk < Dimension ; kk++) { | |
629 | RationalArray[Index] *= Inverse ; Index++; | |
630 | } | |
631 | } | |
632 | } | |
633 | } | |
634 | ||
635 | //======================================================================= | |
636 | //function : This evaluates a polynomial and its derivatives | |
637 | //purpose : up to the requested order | |
638 | //======================================================================= | |
639 | ||
640 | void PLib::EvalPolynomial(const Standard_Real Par, | |
641 | const Standard_Integer DerivativeRequest, | |
642 | const Standard_Integer Degree, | |
643 | const Standard_Integer Dimension, | |
644 | Standard_Real& PolynomialCoeff, | |
645 | Standard_Real& Results) | |
646 | // | |
647 | // the polynomial coefficients are assumed to be stored as follows : | |
648 | // 0 | |
649 | // [0] [Dimension -1] X coefficient | |
650 | // 1 | |
651 | // [Dimension] [Dimension + Dimension -1] X coefficient | |
652 | // 2 | |
653 | // [2 * Dimension] [2 * Dimension + Dimension-1] X coefficient | |
654 | // | |
655 | // ................................................... | |
656 | // | |
657 | // | |
658 | // d | |
659 | // [d * Dimension] [d * Dimension + Dimension-1] X coefficient | |
660 | // | |
661 | // where d is the Degree | |
662 | // | |
663 | { | |
664 | Standard_Integer DegreeDimension = Degree * Dimension; | |
665 | ||
666 | Standard_Integer jj; | |
667 | Standard_Real *RA = &Results ; | |
668 | Standard_Real *PA = &PolynomialCoeff ; | |
669 | Standard_Real *tmpRA = RA; | |
670 | Standard_Real *tmpPA = PA + DegreeDimension; | |
671 | ||
672 | switch (Dimension) { | |
673 | ||
674 | case 1 : { | |
675 | *tmpRA = *tmpPA; | |
676 | if (DerivativeRequest > 0 ) { | |
677 | tmpRA++ ; | |
678 | Standard_Real *valRA; | |
679 | Standard_Integer ii, LocalRequest; | |
680 | Standard_Integer Index1, Index2; | |
681 | Standard_Integer MaxIndex1, MaxIndex2; | |
682 | if (DerivativeRequest < Degree) { | |
683 | LocalRequest = DerivativeRequest; | |
684 | MaxIndex2 = MaxIndex1 = LocalRequest; | |
685 | } | |
686 | else { | |
687 | LocalRequest = Degree; | |
688 | MaxIndex2 = MaxIndex1 = Degree; | |
689 | } | |
690 | MaxIndex2 --; | |
691 | ||
692 | for (ii = 1; ii <= LocalRequest; ii++) { | |
693 | *tmpRA = 0.0e0; tmpRA ++ ; | |
694 | } | |
695 | ||
696 | for (jj = Degree ; jj > 0 ; jj--) { | |
697 | tmpPA --; | |
698 | Index1 = MaxIndex1; | |
699 | Index2 = MaxIndex2; | |
700 | ||
701 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
702 | valRA = &RA[Index1]; | |
703 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
704 | Index1 --; | |
705 | Index2 --; | |
706 | } | |
707 | valRA = &RA[Index1]; | |
708 | *valRA = Par * (*valRA) + (*tmpPA); | |
709 | } | |
710 | } | |
711 | else { | |
712 | ||
713 | for (jj = Degree ; jj > 0 ; jj--) { | |
714 | tmpPA --; | |
715 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
716 | } | |
717 | } | |
718 | break; | |
719 | } | |
720 | case 2 : { | |
721 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
722 | *tmpRA = *tmpPA; tmpRA++; | |
723 | tmpPA --; | |
724 | if (DerivativeRequest > 0 ) { | |
725 | Standard_Real *valRA; | |
726 | Standard_Integer ii, LocalRequest; | |
727 | Standard_Integer Index1, Index2; | |
728 | Standard_Integer MaxIndex1, MaxIndex2; | |
729 | if (DerivativeRequest < Degree) { | |
730 | LocalRequest = DerivativeRequest; | |
731 | MaxIndex2 = MaxIndex1 = LocalRequest << 1; | |
732 | } | |
733 | else { | |
734 | LocalRequest = Degree; | |
735 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
736 | } | |
737 | MaxIndex2 -= 2; | |
738 | ||
739 | for (ii = 1; ii <= LocalRequest; ii++) { | |
740 | *tmpRA = 0.0e0; tmpRA++; | |
741 | *tmpRA = 0.0e0; tmpRA++; | |
742 | } | |
743 | ||
744 | for (jj = Degree ; jj > 0 ; jj--) { | |
745 | tmpPA -= 2; | |
746 | ||
747 | Index1 = MaxIndex1; | |
748 | Index2 = MaxIndex2; | |
749 | ||
750 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
751 | valRA = &RA[Index1]; | |
752 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
753 | Index1 -= 2; | |
754 | Index2 -= 2; | |
755 | } | |
756 | valRA = &RA[Index1]; | |
757 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
758 | ||
759 | Index1 = MaxIndex1 + 1; | |
760 | Index2 = MaxIndex2 + 1; | |
761 | ||
762 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
763 | valRA = &RA[Index1]; | |
764 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
765 | Index1 -= 2; | |
766 | Index2 -= 2; | |
767 | } | |
768 | valRA = &RA[Index1]; | |
769 | *valRA = Par * (*valRA) + (*tmpPA); | |
770 | ||
771 | tmpPA --; | |
772 | } | |
773 | } | |
774 | else { | |
775 | ||
776 | for (jj = Degree ; jj > 0 ; jj--) { | |
777 | tmpPA -= 2; | |
778 | tmpRA = RA; | |
779 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
780 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
781 | tmpPA --; | |
782 | } | |
783 | } | |
784 | break; | |
785 | } | |
786 | case 3 : { | |
787 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
788 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
789 | *tmpRA = *tmpPA; tmpRA++; | |
790 | tmpPA -= 2; | |
791 | if (DerivativeRequest > 0 ) { | |
792 | Standard_Real *valRA; | |
793 | Standard_Integer ii, LocalRequest; | |
794 | Standard_Integer Index1, Index2; | |
795 | Standard_Integer MaxIndex1, MaxIndex2; | |
796 | if (DerivativeRequest < Degree) { | |
797 | LocalRequest = DerivativeRequest; | |
798 | MaxIndex2 = MaxIndex1 = (LocalRequest << 1) + LocalRequest; | |
799 | } | |
800 | else { | |
801 | LocalRequest = Degree; | |
802 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
803 | } | |
804 | MaxIndex2 -= 3; | |
805 | ||
806 | for (ii = 1; ii <= LocalRequest; ii++) { | |
807 | *tmpRA = 0.0e0; tmpRA++; | |
808 | *tmpRA = 0.0e0; tmpRA++; | |
809 | *tmpRA = 0.0e0; tmpRA++; | |
810 | } | |
811 | ||
812 | for (jj = Degree ; jj > 0 ; jj--) { | |
813 | tmpPA -= 3; | |
814 | ||
815 | Index1 = MaxIndex1; | |
816 | Index2 = MaxIndex2; | |
817 | ||
818 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
819 | valRA = &RA[Index1]; | |
820 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
821 | Index1 -= 3; | |
822 | Index2 -= 3; | |
823 | } | |
824 | valRA = &RA[Index1]; | |
825 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
826 | ||
827 | Index1 = MaxIndex1 + 1; | |
828 | Index2 = MaxIndex2 + 1; | |
829 | ||
830 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
831 | valRA = &RA[Index1]; | |
832 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
833 | Index1 -= 3; | |
834 | Index2 -= 3; | |
835 | } | |
836 | valRA = &RA[Index1]; | |
837 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
838 | ||
839 | Index1 = MaxIndex1 + 2; | |
840 | Index2 = MaxIndex2 + 2; | |
841 | ||
842 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
843 | valRA = &RA[Index1]; | |
844 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
845 | Index1 -= 3; | |
846 | Index2 -= 3; | |
847 | } | |
848 | valRA = &RA[Index1]; | |
849 | *valRA = Par * (*valRA) + (*tmpPA); | |
850 | ||
851 | tmpPA -= 2; | |
852 | } | |
853 | } | |
854 | else { | |
855 | ||
856 | for (jj = Degree ; jj > 0 ; jj--) { | |
857 | tmpPA -= 3; | |
858 | tmpRA = RA; | |
859 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
860 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
861 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
862 | tmpPA -= 2; | |
863 | } | |
864 | } | |
865 | break; | |
866 | } | |
867 | case 6 : { | |
868 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
869 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
870 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
871 | ||
872 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
873 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
874 | *tmpRA = *tmpPA; tmpRA++; | |
875 | tmpPA -= 5; | |
876 | if (DerivativeRequest > 0 ) { | |
877 | Standard_Real *valRA; | |
878 | Standard_Integer ii, LocalRequest; | |
879 | Standard_Integer Index1, Index2; | |
880 | Standard_Integer MaxIndex1, MaxIndex2; | |
881 | if (DerivativeRequest < Degree) { | |
882 | LocalRequest = DerivativeRequest; | |
883 | MaxIndex2 = MaxIndex1 = (LocalRequest << 2) + (LocalRequest << 1); | |
884 | } | |
885 | else { | |
886 | LocalRequest = Degree; | |
887 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
888 | } | |
889 | MaxIndex2 -= 6; | |
890 | ||
891 | for (ii = 1; ii <= LocalRequest; ii++) { | |
892 | *tmpRA = 0.0e0; tmpRA++; | |
893 | *tmpRA = 0.0e0; tmpRA++; | |
894 | *tmpRA = 0.0e0; tmpRA++; | |
895 | ||
896 | *tmpRA = 0.0e0; tmpRA++; | |
897 | *tmpRA = 0.0e0; tmpRA++; | |
898 | *tmpRA = 0.0e0; tmpRA++; | |
899 | } | |
900 | ||
901 | for (jj = Degree ; jj > 0 ; jj--) { | |
902 | tmpPA -= 6; | |
903 | ||
904 | Index1 = MaxIndex1; | |
905 | Index2 = MaxIndex2; | |
906 | ||
907 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
908 | valRA = &RA[Index1]; | |
909 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
910 | Index1 -= 6; | |
911 | Index2 -= 6; | |
912 | } | |
913 | valRA = &RA[Index1]; | |
914 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
915 | ||
916 | Index1 = MaxIndex1 + 1; | |
917 | Index2 = MaxIndex2 + 1; | |
918 | ||
919 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
920 | valRA = &RA[Index1]; | |
921 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
922 | Index1 -= 6; | |
923 | Index2 -= 6; | |
924 | } | |
925 | valRA = &RA[Index1]; | |
926 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
927 | ||
928 | Index1 = MaxIndex1 + 2; | |
929 | Index2 = MaxIndex2 + 2; | |
930 | ||
931 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
932 | valRA = &RA[Index1]; | |
933 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
934 | Index1 -= 6; | |
935 | Index2 -= 6; | |
936 | } | |
937 | valRA = &RA[Index1]; | |
938 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
939 | ||
940 | Index1 = MaxIndex1 + 3; | |
941 | Index2 = MaxIndex2 + 3; | |
942 | ||
943 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
944 | valRA = &RA[Index1]; | |
945 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
946 | Index1 -= 6; | |
947 | Index2 -= 6; | |
948 | } | |
949 | valRA = &RA[Index1]; | |
950 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
951 | ||
952 | Index1 = MaxIndex1 + 4; | |
953 | Index2 = MaxIndex2 + 4; | |
954 | ||
955 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
956 | valRA = &RA[Index1]; | |
957 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
958 | Index1 -= 6; | |
959 | Index2 -= 6; | |
960 | } | |
961 | valRA = &RA[Index1]; | |
962 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
963 | ||
964 | Index1 = MaxIndex1 + 5; | |
965 | Index2 = MaxIndex2 + 5; | |
966 | ||
967 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
968 | valRA = &RA[Index1]; | |
969 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
970 | Index1 -= 6; | |
971 | Index2 -= 6; | |
972 | } | |
973 | valRA = &RA[Index1]; | |
974 | *valRA = Par * (*valRA) + (*tmpPA); | |
975 | ||
976 | tmpPA -= 5; | |
977 | } | |
978 | } | |
979 | else { | |
980 | ||
981 | for (jj = Degree ; jj > 0 ; jj--) { | |
982 | tmpPA -= 6; | |
983 | tmpRA = RA; | |
984 | ||
985 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
986 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
987 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
988 | ||
989 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
990 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
991 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
992 | tmpPA -= 5; | |
993 | } | |
994 | } | |
995 | break; | |
996 | } | |
997 | case 9 : { | |
998 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
999 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1000 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1001 | ||
1002 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1003 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1004 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1005 | ||
1006 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1007 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1008 | *tmpRA = *tmpPA; tmpRA++; | |
1009 | tmpPA -= 8; | |
1010 | if (DerivativeRequest > 0 ) { | |
1011 | Standard_Real *valRA; | |
1012 | Standard_Integer ii, LocalRequest; | |
1013 | Standard_Integer Index1, Index2; | |
1014 | Standard_Integer MaxIndex1, MaxIndex2; | |
1015 | if (DerivativeRequest < Degree) { | |
1016 | LocalRequest = DerivativeRequest; | |
1017 | MaxIndex2 = MaxIndex1 = (LocalRequest << 3) + LocalRequest; | |
1018 | } | |
1019 | else { | |
1020 | LocalRequest = Degree; | |
1021 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
1022 | } | |
1023 | MaxIndex2 -= 9; | |
1024 | ||
1025 | for (ii = 1; ii <= LocalRequest; ii++) { | |
1026 | *tmpRA = 0.0e0; tmpRA++; | |
1027 | *tmpRA = 0.0e0; tmpRA++; | |
1028 | *tmpRA = 0.0e0; tmpRA++; | |
1029 | ||
1030 | *tmpRA = 0.0e0; tmpRA++; | |
1031 | *tmpRA = 0.0e0; tmpRA++; | |
1032 | *tmpRA = 0.0e0; tmpRA++; | |
1033 | ||
1034 | *tmpRA = 0.0e0; tmpRA++; | |
1035 | *tmpRA = 0.0e0; tmpRA++; | |
1036 | *tmpRA = 0.0e0; tmpRA++; | |
1037 | } | |
1038 | ||
1039 | for (jj = Degree ; jj > 0 ; jj--) { | |
1040 | tmpPA -= 9; | |
1041 | ||
1042 | Index1 = MaxIndex1; | |
1043 | Index2 = MaxIndex2; | |
1044 | ||
1045 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1046 | valRA = &RA[Index1]; | |
1047 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1048 | Index1 -= 9; | |
1049 | Index2 -= 9; | |
1050 | } | |
1051 | valRA = &RA[Index1]; | |
1052 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1053 | ||
1054 | Index1 = MaxIndex1 + 1; | |
1055 | Index2 = MaxIndex2 + 1; | |
1056 | ||
1057 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1058 | valRA = &RA[Index1]; | |
1059 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1060 | Index1 -= 9; | |
1061 | Index2 -= 9; | |
1062 | } | |
1063 | valRA = &RA[Index1]; | |
1064 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1065 | ||
1066 | Index1 = MaxIndex1 + 2; | |
1067 | Index2 = MaxIndex2 + 2; | |
1068 | ||
1069 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1070 | valRA = &RA[Index1]; | |
1071 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1072 | Index1 -= 9; | |
1073 | Index2 -= 9; | |
1074 | } | |
1075 | valRA = &RA[Index1]; | |
1076 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1077 | ||
1078 | Index1 = MaxIndex1 + 3; | |
1079 | Index2 = MaxIndex2 + 3; | |
1080 | ||
1081 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1082 | valRA = &RA[Index1]; | |
1083 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1084 | Index1 -= 9; | |
1085 | Index2 -= 9; | |
1086 | } | |
1087 | valRA = &RA[Index1]; | |
1088 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1089 | ||
1090 | Index1 = MaxIndex1 + 4; | |
1091 | Index2 = MaxIndex2 + 4; | |
1092 | ||
1093 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1094 | valRA = &RA[Index1]; | |
1095 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1096 | Index1 -= 9; | |
1097 | Index2 -= 9; | |
1098 | } | |
1099 | valRA = &RA[Index1]; | |
1100 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1101 | ||
1102 | Index1 = MaxIndex1 + 5; | |
1103 | Index2 = MaxIndex2 + 5; | |
1104 | ||
1105 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1106 | valRA = &RA[Index1]; | |
1107 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1108 | Index1 -= 9; | |
1109 | Index2 -= 9; | |
1110 | } | |
1111 | valRA = &RA[Index1]; | |
1112 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1113 | ||
1114 | Index1 = MaxIndex1 + 6; | |
1115 | Index2 = MaxIndex2 + 6; | |
1116 | ||
1117 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1118 | valRA = &RA[Index1]; | |
1119 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1120 | Index1 -= 9; | |
1121 | Index2 -= 9; | |
1122 | } | |
1123 | valRA = &RA[Index1]; | |
1124 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1125 | ||
1126 | Index1 = MaxIndex1 + 7; | |
1127 | Index2 = MaxIndex2 + 7; | |
1128 | ||
1129 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1130 | valRA = &RA[Index1]; | |
1131 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1132 | Index1 -= 9; | |
1133 | Index2 -= 9; | |
1134 | } | |
1135 | valRA = &RA[Index1]; | |
1136 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1137 | ||
1138 | Index1 = MaxIndex1 + 8; | |
1139 | Index2 = MaxIndex2 + 8; | |
1140 | ||
1141 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1142 | valRA = &RA[Index1]; | |
1143 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1144 | Index1 -= 9; | |
1145 | Index2 -= 9; | |
1146 | } | |
1147 | valRA = &RA[Index1]; | |
1148 | *valRA = Par * (*valRA) + (*tmpPA); | |
1149 | ||
1150 | tmpPA -= 8; | |
1151 | } | |
1152 | } | |
1153 | else { | |
1154 | ||
1155 | for (jj = Degree ; jj > 0 ; jj--) { | |
1156 | tmpPA -= 9; | |
1157 | tmpRA = RA; | |
1158 | ||
1159 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1160 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1161 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1162 | ||
1163 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1164 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1165 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1166 | ||
1167 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1168 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1169 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1170 | tmpPA -= 8; | |
1171 | } | |
1172 | } | |
1173 | break; | |
1174 | } | |
1175 | case 12 : { | |
1176 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1177 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1178 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1179 | ||
1180 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1181 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1182 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1183 | ||
1184 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1185 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1186 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1187 | ||
1188 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1189 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1190 | *tmpRA = *tmpPA; tmpRA++; | |
1191 | tmpPA -= 11; | |
1192 | if (DerivativeRequest > 0 ) { | |
1193 | Standard_Real *valRA; | |
1194 | Standard_Integer ii, LocalRequest; | |
1195 | Standard_Integer Index1, Index2; | |
1196 | Standard_Integer MaxIndex1, MaxIndex2; | |
1197 | if (DerivativeRequest < Degree) { | |
1198 | LocalRequest = DerivativeRequest; | |
1199 | MaxIndex2 = MaxIndex1 = (LocalRequest << 3) + (LocalRequest << 2); | |
1200 | } | |
1201 | else { | |
1202 | LocalRequest = Degree; | |
1203 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
1204 | } | |
1205 | MaxIndex2 -= 12; | |
1206 | ||
1207 | for (ii = 1; ii <= LocalRequest; ii++) { | |
1208 | *tmpRA = 0.0e0; tmpRA++; | |
1209 | *tmpRA = 0.0e0; tmpRA++; | |
1210 | *tmpRA = 0.0e0; tmpRA++; | |
1211 | ||
1212 | *tmpRA = 0.0e0; tmpRA++; | |
1213 | *tmpRA = 0.0e0; tmpRA++; | |
1214 | *tmpRA = 0.0e0; tmpRA++; | |
1215 | ||
1216 | *tmpRA = 0.0e0; tmpRA++; | |
1217 | *tmpRA = 0.0e0; tmpRA++; | |
1218 | *tmpRA = 0.0e0; tmpRA++; | |
1219 | ||
1220 | *tmpRA = 0.0e0; tmpRA++; | |
1221 | *tmpRA = 0.0e0; tmpRA++; | |
1222 | *tmpRA = 0.0e0; tmpRA++; | |
1223 | } | |
1224 | ||
1225 | for (jj = Degree ; jj > 0 ; jj--) { | |
1226 | tmpPA -= 12; | |
1227 | ||
1228 | Index1 = MaxIndex1; | |
1229 | Index2 = MaxIndex2; | |
1230 | ||
1231 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1232 | valRA = &RA[Index1]; | |
1233 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1234 | Index1 -= 12; | |
1235 | Index2 -= 12; | |
1236 | } | |
1237 | valRA = &RA[Index1]; | |
1238 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1239 | ||
1240 | Index1 = MaxIndex1 + 1; | |
1241 | Index2 = MaxIndex2 + 1; | |
1242 | ||
1243 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1244 | valRA = &RA[Index1]; | |
1245 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1246 | Index1 -= 12; | |
1247 | Index2 -= 12; | |
1248 | } | |
1249 | valRA = &RA[Index1]; | |
1250 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1251 | ||
1252 | Index1 = MaxIndex1 + 2; | |
1253 | Index2 = MaxIndex2 + 2; | |
1254 | ||
1255 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1256 | valRA = &RA[Index1]; | |
1257 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1258 | Index1 -= 12; | |
1259 | Index2 -= 12; | |
1260 | } | |
1261 | valRA = &RA[Index1]; | |
1262 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1263 | ||
1264 | Index1 = MaxIndex1 + 3; | |
1265 | Index2 = MaxIndex2 + 3; | |
1266 | ||
1267 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1268 | valRA = &RA[Index1]; | |
1269 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1270 | Index1 -= 12; | |
1271 | Index2 -= 12; | |
1272 | } | |
1273 | valRA = &RA[Index1]; | |
1274 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1275 | ||
1276 | Index1 = MaxIndex1 + 4; | |
1277 | Index2 = MaxIndex2 + 4; | |
1278 | ||
1279 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1280 | valRA = &RA[Index1]; | |
1281 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1282 | Index1 -= 12; | |
1283 | Index2 -= 12; | |
1284 | } | |
1285 | valRA = &RA[Index1]; | |
1286 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1287 | ||
1288 | Index1 = MaxIndex1 + 5; | |
1289 | Index2 = MaxIndex2 + 5; | |
1290 | ||
1291 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1292 | valRA = &RA[Index1]; | |
1293 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1294 | Index1 -= 12; | |
1295 | Index2 -= 12; | |
1296 | } | |
1297 | valRA = &RA[Index1]; | |
1298 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1299 | ||
1300 | Index1 = MaxIndex1 + 6; | |
1301 | Index2 = MaxIndex2 + 6; | |
1302 | ||
1303 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1304 | valRA = &RA[Index1]; | |
1305 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1306 | Index1 -= 12; | |
1307 | Index2 -= 12; | |
1308 | } | |
1309 | valRA = &RA[Index1]; | |
1310 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1311 | ||
1312 | Index1 = MaxIndex1 + 7; | |
1313 | Index2 = MaxIndex2 + 7; | |
1314 | ||
1315 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1316 | valRA = &RA[Index1]; | |
1317 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1318 | Index1 -= 12; | |
1319 | Index2 -= 12; | |
1320 | } | |
1321 | valRA = &RA[Index1]; | |
1322 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1323 | ||
1324 | Index1 = MaxIndex1 + 8; | |
1325 | Index2 = MaxIndex2 + 8; | |
1326 | ||
1327 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1328 | valRA = &RA[Index1]; | |
1329 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1330 | Index1 -= 12; | |
1331 | Index2 -= 12; | |
1332 | } | |
1333 | valRA = &RA[Index1]; | |
1334 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1335 | ||
1336 | Index1 = MaxIndex1 + 9; | |
1337 | Index2 = MaxIndex2 + 9; | |
1338 | ||
1339 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1340 | valRA = &RA[Index1]; | |
1341 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1342 | Index1 -= 12; | |
1343 | Index2 -= 12; | |
1344 | } | |
1345 | valRA = &RA[Index1]; | |
1346 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1347 | ||
1348 | Index1 = MaxIndex1 + 10; | |
1349 | Index2 = MaxIndex2 + 10; | |
1350 | ||
1351 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1352 | valRA = &RA[Index1]; | |
1353 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1354 | Index1 -= 12; | |
1355 | Index2 -= 12; | |
1356 | } | |
1357 | valRA = &RA[Index1]; | |
1358 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1359 | ||
1360 | Index1 = MaxIndex1 + 11; | |
1361 | Index2 = MaxIndex2 + 11; | |
1362 | ||
1363 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1364 | valRA = &RA[Index1]; | |
1365 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1366 | Index1 -= 12; | |
1367 | Index2 -= 12; | |
1368 | } | |
1369 | valRA = &RA[Index1]; | |
1370 | *valRA = Par * (*valRA) + (*tmpPA); | |
1371 | ||
1372 | tmpPA -= 11; | |
1373 | } | |
1374 | } | |
1375 | else { | |
1376 | ||
1377 | for (jj = Degree ; jj > 0 ; jj--) { | |
1378 | tmpPA -= 12; | |
1379 | tmpRA = RA; | |
1380 | ||
1381 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1382 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1383 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1384 | ||
1385 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1386 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1387 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1388 | ||
1389 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1390 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1391 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1392 | ||
1393 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1394 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1395 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1396 | tmpPA -= 11; | |
1397 | } | |
1398 | } | |
1399 | break; | |
7fd59977 | 1400 | } |
1401 | case 15 : { | |
1402 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1403 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1404 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1405 | ||
1406 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1407 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1408 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1409 | ||
1410 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1411 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1412 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1413 | ||
1414 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1415 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1416 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1417 | ||
1418 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1419 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1420 | *tmpRA = *tmpPA; tmpRA++; | |
1421 | tmpPA -= 14; | |
1422 | if (DerivativeRequest > 0 ) { | |
1423 | Standard_Real *valRA; | |
1424 | Standard_Integer ii, LocalRequest; | |
1425 | Standard_Integer Index1, Index2; | |
1426 | Standard_Integer MaxIndex1, MaxIndex2; | |
1427 | if (DerivativeRequest < Degree) { | |
1428 | LocalRequest = DerivativeRequest; | |
1429 | MaxIndex2 = MaxIndex1 = (LocalRequest << 4) - LocalRequest; | |
1430 | } | |
1431 | else { | |
1432 | LocalRequest = Degree; | |
1433 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
1434 | } | |
1435 | MaxIndex2 -= 15; | |
1436 | ||
1437 | for (ii = 1; ii <= LocalRequest; ii++) { | |
1438 | *tmpRA = 0.0e0; tmpRA++; | |
1439 | *tmpRA = 0.0e0; tmpRA++; | |
1440 | *tmpRA = 0.0e0; tmpRA++; | |
1441 | ||
1442 | *tmpRA = 0.0e0; tmpRA++; | |
1443 | *tmpRA = 0.0e0; tmpRA++; | |
1444 | *tmpRA = 0.0e0; tmpRA++; | |
1445 | ||
1446 | *tmpRA = 0.0e0; tmpRA++; | |
1447 | *tmpRA = 0.0e0; tmpRA++; | |
1448 | *tmpRA = 0.0e0; tmpRA++; | |
1449 | ||
1450 | *tmpRA = 0.0e0; tmpRA++; | |
1451 | *tmpRA = 0.0e0; tmpRA++; | |
1452 | *tmpRA = 0.0e0; tmpRA++; | |
1453 | ||
1454 | *tmpRA = 0.0e0; tmpRA++; | |
1455 | *tmpRA = 0.0e0; tmpRA++; | |
1456 | *tmpRA = 0.0e0; tmpRA++; | |
1457 | } | |
1458 | ||
1459 | for (jj = Degree ; jj > 0 ; jj--) { | |
1460 | tmpPA -= 15; | |
1461 | ||
1462 | Index1 = MaxIndex1; | |
1463 | Index2 = MaxIndex2; | |
1464 | ||
1465 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1466 | valRA = &RA[Index1]; | |
1467 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1468 | Index1 -= 15; | |
1469 | Index2 -= 15; | |
1470 | } | |
1471 | valRA = &RA[Index1]; | |
1472 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1473 | ||
1474 | Index1 = MaxIndex1 + 1; | |
1475 | Index2 = MaxIndex2 + 1; | |
1476 | ||
1477 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1478 | valRA = &RA[Index1]; | |
1479 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1480 | Index1 -= 15; | |
1481 | Index2 -= 15; | |
1482 | } | |
1483 | valRA = &RA[Index1]; | |
1484 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1485 | ||
1486 | Index1 = MaxIndex1 + 2; | |
1487 | Index2 = MaxIndex2 + 2; | |
1488 | ||
1489 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1490 | valRA = &RA[Index1]; | |
1491 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1492 | Index1 -= 15; | |
1493 | Index2 -= 15; | |
1494 | } | |
1495 | valRA = &RA[Index1]; | |
1496 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1497 | ||
1498 | Index1 = MaxIndex1 + 3; | |
1499 | Index2 = MaxIndex2 + 3; | |
1500 | ||
1501 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1502 | valRA = &RA[Index1]; | |
1503 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1504 | Index1 -= 15; | |
1505 | Index2 -= 15; | |
1506 | } | |
1507 | valRA = &RA[Index1]; | |
1508 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1509 | ||
1510 | Index1 = MaxIndex1 + 4; | |
1511 | Index2 = MaxIndex2 + 4; | |
1512 | ||
1513 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1514 | valRA = &RA[Index1]; | |
1515 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1516 | Index1 -= 15; | |
1517 | Index2 -= 15; | |
1518 | } | |
1519 | valRA = &RA[Index1]; | |
1520 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1521 | ||
1522 | Index1 = MaxIndex1 + 5; | |
1523 | Index2 = MaxIndex2 + 5; | |
1524 | ||
1525 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1526 | valRA = &RA[Index1]; | |
1527 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1528 | Index1 -= 15; | |
1529 | Index2 -= 15; | |
1530 | } | |
1531 | valRA = &RA[Index1]; | |
1532 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1533 | ||
1534 | Index1 = MaxIndex1 + 6; | |
1535 | Index2 = MaxIndex2 + 6; | |
1536 | ||
1537 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1538 | valRA = &RA[Index1]; | |
1539 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1540 | Index1 -= 15; | |
1541 | Index2 -= 15; | |
1542 | } | |
1543 | valRA = &RA[Index1]; | |
1544 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1545 | ||
1546 | Index1 = MaxIndex1 + 7; | |
1547 | Index2 = MaxIndex2 + 7; | |
1548 | ||
1549 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1550 | valRA = &RA[Index1]; | |
1551 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1552 | Index1 -= 15; | |
1553 | Index2 -= 15; | |
1554 | } | |
1555 | valRA = &RA[Index1]; | |
1556 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1557 | ||
1558 | Index1 = MaxIndex1 + 8; | |
1559 | Index2 = MaxIndex2 + 8; | |
1560 | ||
1561 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1562 | valRA = &RA[Index1]; | |
1563 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1564 | Index1 -= 15; | |
1565 | Index2 -= 15; | |
1566 | } | |
1567 | valRA = &RA[Index1]; | |
1568 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1569 | ||
1570 | Index1 = MaxIndex1 + 9; | |
1571 | Index2 = MaxIndex2 + 9; | |
1572 | ||
1573 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1574 | valRA = &RA[Index1]; | |
1575 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1576 | Index1 -= 15; | |
1577 | Index2 -= 15; | |
1578 | } | |
1579 | valRA = &RA[Index1]; | |
1580 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1581 | ||
1582 | Index1 = MaxIndex1 + 10; | |
1583 | Index2 = MaxIndex2 + 10; | |
1584 | ||
1585 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1586 | valRA = &RA[Index1]; | |
1587 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1588 | Index1 -= 15; | |
1589 | Index2 -= 15; | |
1590 | } | |
1591 | valRA = &RA[Index1]; | |
1592 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1593 | ||
1594 | Index1 = MaxIndex1 + 11; | |
1595 | Index2 = MaxIndex2 + 11; | |
1596 | ||
1597 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1598 | valRA = &RA[Index1]; | |
1599 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1600 | Index1 -= 15; | |
1601 | Index2 -= 15; | |
1602 | } | |
1603 | valRA = &RA[Index1]; | |
1604 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1605 | ||
1606 | Index1 = MaxIndex1 + 12; | |
1607 | Index2 = MaxIndex2 + 12; | |
1608 | ||
1609 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1610 | valRA = &RA[Index1]; | |
1611 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1612 | Index1 -= 15; | |
1613 | Index2 -= 15; | |
1614 | } | |
1615 | valRA = &RA[Index1]; | |
1616 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1617 | ||
1618 | Index1 = MaxIndex1 + 13; | |
1619 | Index2 = MaxIndex2 + 13; | |
1620 | ||
1621 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1622 | valRA = &RA[Index1]; | |
1623 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1624 | Index1 -= 15; | |
1625 | Index2 -= 15; | |
1626 | } | |
1627 | valRA = &RA[Index1]; | |
1628 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1629 | ||
1630 | Index1 = MaxIndex1 + 14; | |
1631 | Index2 = MaxIndex2 + 14; | |
1632 | ||
1633 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1634 | valRA = &RA[Index1]; | |
1635 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1636 | Index1 -= 15; | |
1637 | Index2 -= 15; | |
1638 | } | |
1639 | valRA = &RA[Index1]; | |
1640 | *valRA = Par * (*valRA) + (*tmpPA); | |
1641 | ||
1642 | tmpPA -= 14; | |
1643 | } | |
1644 | } | |
1645 | else { | |
1646 | ||
1647 | for (jj = Degree ; jj > 0 ; jj--) { | |
1648 | tmpPA -= 15; | |
1649 | tmpRA = RA; | |
1650 | ||
1651 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1652 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1653 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1654 | ||
1655 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1656 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1657 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1658 | ||
1659 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1660 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1661 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1662 | ||
1663 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1664 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1665 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1666 | ||
1667 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1668 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1669 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1670 | tmpPA -= 14; | |
1671 | } | |
1672 | } | |
1673 | break; | |
1674 | } | |
1675 | default : { | |
1676 | Standard_Integer kk ; | |
1677 | for ( kk = 0 ; kk < Dimension ; kk++) { | |
1678 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1679 | } | |
1680 | tmpPA -= Dimension; | |
1681 | if (DerivativeRequest > 0 ) { | |
1682 | Standard_Real *valRA; | |
1683 | Standard_Integer ii, LocalRequest; | |
1684 | Standard_Integer Index1, Index2; | |
1685 | Standard_Integer MaxIndex1, MaxIndex2; | |
1686 | if (DerivativeRequest < Degree) { | |
1687 | LocalRequest = DerivativeRequest; | |
1688 | MaxIndex2 = MaxIndex1 = LocalRequest * Dimension; | |
1689 | } | |
1690 | else { | |
1691 | LocalRequest = Degree; | |
1692 | MaxIndex2 = MaxIndex1 = DegreeDimension; | |
1693 | } | |
1694 | MaxIndex2 -= Dimension; | |
1695 | ||
1696 | for (ii = 1; ii <= MaxIndex1; ii++) { | |
1697 | *tmpRA = 0.0e0; tmpRA++; | |
1698 | } | |
1699 | ||
1700 | for (jj = Degree ; jj > 0 ; jj--) { | |
1701 | tmpPA -= Dimension; | |
1702 | ||
1703 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1704 | Index1 = MaxIndex1 + kk; | |
1705 | Index2 = MaxIndex2 + kk; | |
1706 | ||
1707 | for (ii = LocalRequest ; ii > 0 ; ii--) { | |
1708 | valRA = &RA[Index1]; | |
1709 | *valRA = Par * (*valRA) + ((Standard_Real)ii) * RA[Index2] ; | |
1710 | Index1 -= Dimension; | |
1711 | Index2 -= Dimension; | |
1712 | } | |
1713 | valRA = &RA[Index1]; | |
1714 | *valRA = Par * (*valRA) + (*tmpPA); tmpPA++; | |
1715 | } | |
1716 | tmpPA -= Dimension; | |
1717 | } | |
1718 | } | |
1719 | else { | |
1720 | ||
1721 | for (jj = Degree ; jj > 0 ; jj--) { | |
1722 | tmpPA -= Dimension; | |
1723 | tmpRA = RA; | |
1724 | ||
1725 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1726 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1727 | } | |
1728 | tmpPA -= Dimension; | |
1729 | } | |
1730 | } | |
1731 | } | |
1732 | } | |
1733 | } | |
1734 | ||
1735 | //======================================================================= | |
1736 | //function : This evaluates a polynomial without derivative | |
1737 | //purpose : | |
1738 | //======================================================================= | |
1739 | ||
1740 | void PLib::NoDerivativeEvalPolynomial(const Standard_Real Par, | |
1741 | const Standard_Integer Degree, | |
1742 | const Standard_Integer Dimension, | |
1743 | const Standard_Integer DegreeDimension, | |
1744 | Standard_Real& PolynomialCoeff, | |
1745 | Standard_Real& Results) | |
1746 | { | |
1747 | Standard_Integer jj; | |
1748 | Standard_Real *RA = &Results ; | |
1749 | Standard_Real *PA = &PolynomialCoeff ; | |
1750 | Standard_Real *tmpRA = RA; | |
1751 | Standard_Real *tmpPA = PA + DegreeDimension; | |
1752 | ||
1753 | switch (Dimension) { | |
1754 | ||
1755 | case 1 : { | |
1756 | *tmpRA = *tmpPA; | |
1757 | ||
1758 | for (jj = Degree ; jj > 0 ; jj--) { | |
1759 | tmpPA--; | |
1760 | ||
1761 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1762 | } | |
1763 | break; | |
1764 | } | |
1765 | case 2 : { | |
1766 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1767 | *tmpRA = *tmpPA; | |
1768 | tmpPA--; | |
1769 | ||
1770 | for (jj = Degree ; jj > 0 ; jj--) { | |
1771 | tmpPA -= 2; | |
1772 | tmpRA = RA; | |
1773 | ||
1774 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1775 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1776 | tmpPA--; | |
1777 | } | |
1778 | break; | |
1779 | } | |
1780 | case 3 : { | |
1781 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1782 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1783 | *tmpRA = *tmpPA; | |
1784 | tmpPA -= 2; | |
1785 | ||
1786 | for (jj = Degree ; jj > 0 ; jj--) { | |
1787 | tmpPA -= 3; | |
1788 | tmpRA = RA; | |
1789 | ||
1790 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1791 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1792 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1793 | tmpPA -= 2; | |
1794 | } | |
1795 | break; | |
1796 | } | |
1797 | case 6 : { | |
1798 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1799 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1800 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1801 | ||
1802 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1803 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1804 | *tmpRA = *tmpPA; | |
1805 | tmpPA -= 5; | |
1806 | ||
1807 | for (jj = Degree ; jj > 0 ; jj--) { | |
1808 | tmpPA -= 6; | |
1809 | tmpRA = RA; | |
1810 | ||
1811 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1812 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1813 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1814 | ||
1815 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1816 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1817 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1818 | tmpPA -= 5; | |
1819 | } | |
1820 | break; | |
1821 | } | |
1822 | case 9 : { | |
1823 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1824 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1825 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1826 | ||
1827 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1828 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1829 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1830 | ||
1831 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1832 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1833 | *tmpRA = *tmpPA; | |
1834 | tmpPA -= 8; | |
1835 | ||
1836 | for (jj = Degree ; jj > 0 ; jj--) { | |
1837 | tmpPA -= 9; | |
1838 | tmpRA = RA; | |
1839 | ||
1840 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1841 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1842 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1843 | ||
1844 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1845 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1846 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1847 | ||
1848 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1849 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1850 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1851 | tmpPA -= 8; | |
1852 | } | |
1853 | break; | |
1854 | } | |
1855 | case 12 : { | |
1856 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1857 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1858 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1859 | ||
1860 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1861 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1862 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1863 | ||
1864 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1865 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1866 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1867 | ||
1868 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1869 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1870 | *tmpRA = *tmpPA; | |
1871 | tmpPA -= 11; | |
1872 | ||
1873 | for (jj = Degree ; jj > 0 ; jj--) { | |
1874 | tmpPA -= 12; | |
1875 | tmpRA = RA; | |
1876 | ||
1877 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1878 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1879 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1880 | ||
1881 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1882 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1883 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1884 | ||
1885 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1886 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1887 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1888 | ||
1889 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1890 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1891 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1892 | tmpPA -= 11; | |
1893 | } | |
1894 | break; | |
1895 | } | |
1896 | case 15 : { | |
1897 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1898 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1899 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1900 | ||
1901 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1902 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1903 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1904 | ||
1905 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1906 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1907 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1908 | ||
1909 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1910 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1911 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1912 | ||
1913 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1914 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1915 | *tmpRA = *tmpPA; | |
1916 | tmpPA -= 14; | |
1917 | ||
1918 | for (jj = Degree ; jj > 0 ; jj--) { | |
1919 | tmpPA -= 15; | |
1920 | tmpRA = RA; | |
1921 | ||
1922 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1923 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1924 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1925 | ||
1926 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1927 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1928 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1929 | ||
1930 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1931 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1932 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1933 | ||
1934 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1935 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1936 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1937 | ||
1938 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1939 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1940 | *tmpRA = Par * (*tmpRA) + (*tmpPA); | |
1941 | tmpPA -= 14; | |
1942 | } | |
1943 | break; | |
1944 | } | |
1945 | default : { | |
1946 | Standard_Integer kk ; | |
1947 | for ( kk = 0 ; kk < Dimension ; kk++) { | |
1948 | *tmpRA = *tmpPA; tmpRA++; tmpPA++; | |
1949 | } | |
1950 | tmpPA -= Dimension; | |
1951 | ||
1952 | for (jj = Degree ; jj > 0 ; jj--) { | |
1953 | tmpPA -= Dimension; | |
1954 | tmpRA = RA; | |
1955 | ||
1956 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1957 | *tmpRA = Par * (*tmpRA) + (*tmpPA); tmpPA++; tmpRA++; | |
1958 | } | |
1959 | tmpPA -= Dimension; | |
1960 | } | |
1961 | } | |
1962 | } | |
1963 | } | |
1964 | ||
1965 | //======================================================================= | |
1966 | //function : This evaluates a polynomial of 2 variables | |
1967 | //purpose : or its derivative at the requested orders | |
1968 | //======================================================================= | |
1969 | ||
1970 | void PLib::EvalPoly2Var(const Standard_Real UParameter, | |
1971 | const Standard_Real VParameter, | |
1972 | const Standard_Integer UDerivativeRequest, | |
1973 | const Standard_Integer VDerivativeRequest, | |
1974 | const Standard_Integer UDegree, | |
1975 | const Standard_Integer VDegree, | |
1976 | const Standard_Integer Dimension, | |
1977 | Standard_Real& PolynomialCoeff, | |
1978 | Standard_Real& Results) | |
1979 | // | |
1980 | // the polynomial coefficients are assumed to be stored as follows : | |
1981 | // 0 0 | |
1982 | // [0] [Dimension -1] U V coefficient | |
1983 | // 1 0 | |
1984 | // [Dimension] [Dimension + Dimension -1] U V coefficient | |
1985 | // 2 0 | |
1986 | // [2 * Dimension] [2 * Dimension + Dimension-1] U V coefficient | |
1987 | // | |
1988 | // ................................................... | |
1989 | // | |
1990 | // | |
1991 | // m 0 | |
1992 | // [m * Dimension] [m * Dimension + Dimension-1] U V coefficient | |
1993 | // | |
1994 | // where m = UDegree | |
1995 | // | |
1996 | // 0 1 | |
1997 | // [(m+1) * Dimension] [(m+1) * Dimension + Dimension-1] U V coefficient | |
1998 | // | |
1999 | // ................................................... | |
2000 | // | |
2001 | // m 1 | |
2002 | // [2*m * Dimension] [2*m * Dimension + Dimension-1] U V coefficient | |
2003 | // | |
2004 | // ................................................... | |
2005 | // | |
2006 | // m n | |
2007 | // [m*n * Dimension] [m*n * Dimension + Dimension-1] U V coefficient | |
2008 | // | |
2009 | // where n = VDegree | |
2010 | { | |
2011 | Standard_Integer Udim = (VDegree+1)*Dimension, | |
2012 | index = Udim*UDerivativeRequest; | |
2013 | TColStd_Array1OfReal Curve(1, Udim*(UDerivativeRequest+1)); | |
2014 | TColStd_Array1OfReal Point(1, Dimension*(VDerivativeRequest+1)); | |
2015 | Standard_Real * Result = (Standard_Real *) &Curve.ChangeValue(1); | |
2016 | Standard_Real * Digit = (Standard_Real *) &Point.ChangeValue(1); | |
2017 | Standard_Real * ResultArray ; | |
2018 | ResultArray = &Results ; | |
2019 | ||
2020 | PLib::EvalPolynomial(UParameter, | |
2021 | UDerivativeRequest, | |
2022 | UDegree, | |
2023 | Udim, | |
2024 | PolynomialCoeff, | |
2025 | Result[0]); | |
2026 | ||
2027 | PLib::EvalPolynomial(VParameter, | |
2028 | VDerivativeRequest, | |
2029 | VDegree, | |
2030 | Dimension, | |
2031 | Result[index], | |
2032 | Digit[0]); | |
2033 | ||
2034 | index = Dimension*VDerivativeRequest; | |
2035 | ||
2036 | for (Standard_Integer i=0;i<Dimension;i++) { | |
2037 | ResultArray[i] = Digit[index+i]; | |
2038 | } | |
2039 | } | |
2040 | ||
2041 | ||
7fd59977 | 2042 | |
2043 | //======================================================================= | |
2044 | //function : This evaluates the lagrange polynomial and its derivatives | |
2045 | //purpose : up to the requested order that interpolates a series of | |
2046 | //points of dimension <Dimension> with given assigned parameters | |
2047 | //======================================================================= | |
2048 | ||
2049 | Standard_Integer | |
2050 | PLib::EvalLagrange(const Standard_Real Parameter, | |
2051 | const Standard_Integer DerivativeRequest, | |
2052 | const Standard_Integer Degree, | |
2053 | const Standard_Integer Dimension, | |
2054 | Standard_Real& Values, | |
2055 | Standard_Real& Parameters, | |
2056 | Standard_Real& Results) | |
2057 | { | |
2058 | // | |
2059 | // the points are assumed to be stored as follows in the Values array : | |
2060 | // | |
2061 | // [0] [Dimension -1] first point coefficients | |
2062 | // | |
2063 | // [Dimension] [Dimension + Dimension -1] second point coefficients | |
2064 | // | |
2065 | // [2 * Dimension] [2 * Dimension + Dimension-1] third point coefficients | |
2066 | // | |
2067 | // ................................................... | |
2068 | // | |
2069 | // | |
2070 | // | |
2071 | // [d * Dimension] [d * Dimension + Dimension-1] d + 1 point coefficients | |
2072 | // | |
2073 | // where d is the Degree | |
2074 | // | |
2075 | // The ParameterArray stores the parameter value assign to each point in | |
2076 | // order described above, that is | |
2077 | // [0] is assign to first point | |
2078 | // [1] is assign to second point | |
2079 | // | |
2080 | Standard_Integer ii, jj, kk, Index, Index1, ReturnCode=0; | |
2081 | Standard_Integer local_request = DerivativeRequest; | |
2082 | Standard_Real *ParameterArray; | |
2083 | Standard_Real difference; | |
2084 | Standard_Real *PointsArray; | |
2085 | Standard_Real *ResultArray ; | |
2086 | ||
2087 | PointsArray = &Values ; | |
2088 | ParameterArray = &Parameters ; | |
2089 | ResultArray = &Results ; | |
2090 | if (local_request >= Degree) { | |
2091 | local_request = Degree ; | |
41194117 | 2092 | } |
f7b4312f | 2093 | NCollection_LocalArray<Standard_Real> divided_differences_array ((Degree + 1) * Dimension); |
7fd59977 | 2094 | // |
2095 | // Build the divided differences array | |
2096 | // | |
2097 | ||
2098 | for (ii = 0 ; ii < (Degree + 1) * Dimension ; ii++) { | |
2099 | divided_differences_array[ii] = PointsArray[ii] ; | |
2100 | } | |
2101 | ||
2102 | for (ii = Degree ; ii >= 0 ; ii--) { | |
2103 | ||
2104 | for (jj = Degree ; jj > Degree - ii ; jj--) { | |
2105 | Index = jj * Dimension ; | |
2106 | Index1 = Index - Dimension ; | |
2107 | ||
2108 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2109 | divided_differences_array[Index + kk] -= | |
2110 | divided_differences_array[Index1 + kk] ; | |
2111 | } | |
2112 | difference = | |
2113 | ParameterArray[jj] - ParameterArray[jj - Degree -1 + ii] ; | |
2114 | if (Abs(difference) < RealSmall()) { | |
2115 | ReturnCode = 1 ; | |
2116 | goto FINISH ; | |
2117 | } | |
2118 | difference = 1.0e0 / difference ; | |
2119 | ||
2120 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2121 | divided_differences_array[Index + kk] *= difference ; | |
2122 | } | |
2123 | } | |
2124 | } | |
2125 | // | |
2126 | // | |
2127 | // Evaluate the divided difference array polynomial which expresses as | |
2128 | // | |
2129 | // P(t) = [t1] P + (t - t1) [t1,t2] P + (t - t1)(t - t2)[t1,t2,t3] P + ... | |
2130 | // + (t - t1)(t - t2)(t - t3)...(t - td) [t1,t2,...,td+1] P | |
2131 | // | |
2132 | // The ith slot in the divided_differences_array is [t1,t2,...,ti+1] | |
2133 | // | |
2134 | // | |
2135 | Index = Degree * Dimension ; | |
2136 | ||
2137 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2138 | ResultArray[kk] = divided_differences_array[Index + kk] ; | |
2139 | } | |
2140 | ||
2141 | for (ii = Dimension ; ii < (local_request + 1) * Dimension ; ii++) { | |
2142 | ResultArray[ii] = 0.0e0 ; | |
2143 | } | |
2144 | ||
2145 | for (ii = Degree ; ii >= 1 ; ii--) { | |
2146 | difference = Parameter - ParameterArray[ii - 1] ; | |
2147 | ||
2148 | for (jj = local_request ; jj > 0 ; jj--) { | |
2149 | Index = jj * Dimension ; | |
2150 | Index1 = Index - Dimension ; | |
2151 | ||
2152 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2153 | ResultArray[Index + kk] *= difference ; | |
2154 | ResultArray[Index + kk] += ResultArray[Index1+kk]*(Standard_Real) jj ; | |
2155 | } | |
2156 | } | |
2157 | Index = (ii -1) * Dimension ; | |
2158 | ||
2159 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2160 | ResultArray[kk] *= difference ; | |
2161 | ResultArray[kk] += divided_differences_array[Index+kk] ; | |
2162 | } | |
2163 | } | |
2164 | FINISH : | |
2165 | return (ReturnCode) ; | |
2166 | } | |
2167 | ||
2168 | //======================================================================= | |
2169 | //function : This evaluates the hermite polynomial and its derivatives | |
2170 | //purpose : up to the requested order that interpolates a series of | |
2171 | //points of dimension <Dimension> with given assigned parameters | |
2172 | //======================================================================= | |
2173 | ||
2174 | Standard_Integer PLib::EvalCubicHermite | |
2175 | (const Standard_Real Parameter, | |
2176 | const Standard_Integer DerivativeRequest, | |
2177 | const Standard_Integer Dimension, | |
2178 | Standard_Real& Values, | |
2179 | Standard_Real& Derivatives, | |
2180 | Standard_Real& theParameters, | |
2181 | Standard_Real& Results) | |
2182 | { | |
2183 | // | |
2184 | // the points are assumed to be stored as follows in the Values array : | |
2185 | // | |
2186 | // [0] [Dimension -1] first point coefficients | |
2187 | // | |
2188 | // [Dimension] [Dimension + Dimension -1] last point coefficients | |
2189 | // | |
2190 | // | |
2191 | // the derivatives are assumed to be stored as follows in | |
2192 | // the Derivatives array : | |
2193 | // | |
2194 | // [0] [Dimension -1] first point coefficients | |
2195 | // | |
2196 | // [Dimension] [Dimension + Dimension -1] last point coefficients | |
2197 | // | |
2198 | // The ParameterArray stores the parameter value assign to each point in | |
2199 | // order described above, that is | |
2200 | // [0] is assign to first point | |
2201 | // [1] is assign to last point | |
2202 | // | |
2203 | Standard_Integer ii, jj, kk, pp, Index, Index1, Degree, ReturnCode; | |
2204 | Standard_Integer local_request = DerivativeRequest ; | |
2205 | ||
2206 | ReturnCode = 0 ; | |
2207 | Degree = 3 ; | |
2208 | Standard_Real ParametersArray[4]; | |
2209 | Standard_Real difference; | |
2210 | Standard_Real inverse; | |
2211 | Standard_Real *FirstLast; | |
2212 | Standard_Real *PointsArray; | |
2213 | Standard_Real *DerivativesArray; | |
2214 | Standard_Real *ResultArray ; | |
2215 | ||
2216 | DerivativesArray = &Derivatives ; | |
2217 | PointsArray = &Values ; | |
2218 | FirstLast = &theParameters ; | |
2219 | ResultArray = &Results ; | |
2220 | if (local_request >= Degree) { | |
2221 | local_request = Degree ; | |
2222 | } | |
f7b4312f | 2223 | NCollection_LocalArray<Standard_Real> divided_differences_array ((Degree + 1) * Dimension); |
7fd59977 | 2224 | |
2225 | for (ii = 0, jj = 0 ; ii < 2 ; ii++, jj+= 2) { | |
2226 | ParametersArray[jj] = | |
2227 | ParametersArray[jj+1] = FirstLast[ii] ; | |
2228 | } | |
2229 | // | |
2230 | // Build the divided differences array | |
2231 | // | |
2232 | // | |
2233 | // initialise it at the stage 2 of the building algorithm | |
2234 | // for devided differences | |
2235 | // | |
2236 | inverse = FirstLast[1] - FirstLast[0] ; | |
2237 | inverse = 1.0e0 / inverse ; | |
2238 | ||
2239 | for (ii = 0, jj = Dimension, kk = 2 * Dimension, pp = 3 * Dimension ; | |
2240 | ii < Dimension ; | |
2241 | ii++, jj++, kk++, pp++) { | |
2242 | divided_differences_array[ii] = PointsArray[ii] ; | |
2243 | divided_differences_array[kk] = inverse * | |
2244 | (PointsArray[jj] - PointsArray[ii]) ; | |
2245 | divided_differences_array[jj] = DerivativesArray[ii] ; | |
2246 | divided_differences_array[pp] = DerivativesArray[jj] ; | |
2247 | } | |
2248 | ||
2249 | for (ii = 1 ; ii <= Degree ; ii++) { | |
2250 | ||
2251 | for (jj = Degree ; jj >= ii+1 ; jj--) { | |
2252 | Index = jj * Dimension ; | |
2253 | Index1 = Index - Dimension ; | |
2254 | ||
2255 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2256 | divided_differences_array[Index + kk] -= | |
2257 | divided_differences_array[Index1 + kk] ; | |
2258 | } | |
2259 | ||
2260 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2261 | divided_differences_array[Index + kk] *= inverse ; | |
2262 | } | |
2263 | } | |
2264 | } | |
2265 | // | |
2266 | // | |
2267 | // Evaluate the divided difference array polynomial which expresses as | |
2268 | // | |
2269 | // P(t) = [t1] P + (t - t1) [t1,t2] P + (t - t1)(t - t2)[t1,t2,t3] P + ... | |
2270 | // + (t - t1)(t - t2)(t - t3)...(t - td) [t1,t2,...,td+1] P | |
2271 | // | |
2272 | // The ith slot in the divided_differences_array is [t1,t2,...,ti+1] | |
2273 | // | |
2274 | // | |
2275 | Index = Degree * Dimension ; | |
2276 | ||
2277 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2278 | ResultArray[kk] = divided_differences_array[Index + kk] ; | |
2279 | } | |
2280 | ||
2281 | for (ii = Dimension ; ii < (local_request + 1) * Dimension ; ii++) { | |
2282 | ResultArray[ii] = 0.0e0 ; | |
2283 | } | |
2284 | ||
2285 | for (ii = Degree ; ii >= 1 ; ii--) { | |
2286 | difference = Parameter - ParametersArray[ii - 1] ; | |
2287 | ||
2288 | for (jj = local_request ; jj > 0 ; jj--) { | |
2289 | Index = jj * Dimension ; | |
2290 | Index1 = Index - Dimension ; | |
2291 | ||
2292 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2293 | ResultArray[Index + kk] *= difference ; | |
2294 | ResultArray[Index + kk] += ResultArray[Index1+kk]*(Standard_Real) jj; | |
2295 | } | |
2296 | } | |
2297 | Index = (ii -1) * Dimension ; | |
2298 | ||
2299 | for (kk = 0 ; kk < Dimension ; kk++) { | |
2300 | ResultArray[kk] *= difference ; | |
2301 | ResultArray[kk] += divided_differences_array[Index+kk] ; | |
2302 | } | |
2303 | } | |
2304 | // FINISH : | |
2305 | return (ReturnCode) ; | |
2306 | } | |
2307 | ||
2308 | //======================================================================= | |
2309 | //function : HermiteCoefficients | |
2310 | //purpose : calcul des polynomes d'Hermite | |
2311 | //======================================================================= | |
2312 | ||
2313 | Standard_Boolean PLib::HermiteCoefficients(const Standard_Real FirstParameter, | |
2314 | const Standard_Real LastParameter, | |
2315 | const Standard_Integer FirstOrder, | |
2316 | const Standard_Integer LastOrder, | |
2317 | math_Matrix& MatrixCoefs) | |
2318 | { | |
2319 | Standard_Integer NbCoeff = FirstOrder + LastOrder + 2, Ordre[2]; | |
2320 | Standard_Integer ii, jj, pp, cote, iof=0; | |
2321 | Standard_Real Prod, TBorne = FirstParameter; | |
2322 | math_Vector Coeff(1,NbCoeff), B(1, NbCoeff, 0.0); | |
2323 | math_Matrix MAT(1,NbCoeff, 1,NbCoeff, 0.0); | |
2324 | ||
2325 | // Test de validites | |
2326 | ||
2327 | if ((FirstOrder < 0) || (LastOrder < 0)) return Standard_False; | |
2328 | Standard_Real D1 = fabs(FirstParameter), D2 = fabs(LastParameter); | |
2329 | if (D1 > 100 || D2 > 100) return Standard_False; | |
2330 | D2 += D1; | |
2331 | if (D2 < 0.01) return Standard_False; | |
2332 | if (fabs(LastParameter - FirstParameter) / D2 < 0.01) return Standard_False; | |
2333 | ||
2334 | // Calcul de la matrice a inverser (MAT) | |
2335 | ||
2336 | Ordre[0] = FirstOrder+1; | |
2337 | Ordre[1] = LastOrder+1; | |
2338 | ||
2339 | for (cote=0; cote<=1; cote++) { | |
2340 | Coeff.Init(1); | |
2341 | ||
2342 | for (pp=1; pp<=Ordre[cote]; pp++) { | |
2343 | ii = pp + iof; | |
2344 | Prod = 1; | |
2345 | ||
2346 | for (jj=pp; jj<=NbCoeff; jj++) { | |
2347 | // tout se passe dans les 3 lignes suivantes | |
2348 | MAT(ii, jj) = Coeff(jj) * Prod; | |
2349 | Coeff(jj) *= jj - pp; | |
2350 | Prod *= TBorne; | |
2351 | } | |
2352 | } | |
2353 | TBorne = LastParameter; | |
2354 | iof = Ordre[0]; | |
2355 | } | |
2356 | ||
2357 | // resolution du systemes | |
2358 | math_Gauss ResolCoeff(MAT, 1.0e-10); | |
2359 | if (!ResolCoeff.IsDone()) return Standard_False; | |
2360 | ||
2361 | for (ii=1; ii<=NbCoeff; ii++) { | |
2362 | B(ii) = 1; | |
2363 | ResolCoeff.Solve(B, Coeff); | |
2364 | MatrixCoefs.SetRow( ii, Coeff); | |
2365 | B(ii) = 0; | |
2366 | } | |
2367 | return Standard_True; | |
2368 | } | |
2369 | ||
2370 | //======================================================================= | |
2371 | //function : CoefficientsPoles | |
2372 | //purpose : | |
2373 | //======================================================================= | |
2374 | ||
2375 | void PLib::CoefficientsPoles (const TColgp_Array1OfPnt& Coefs, | |
2376 | const TColStd_Array1OfReal& WCoefs, | |
2377 | TColgp_Array1OfPnt& Poles, | |
2378 | TColStd_Array1OfReal& Weights) | |
2379 | { | |
2380 | TColStd_Array1OfReal tempC(1,3*Coefs.Length()); | |
2381 | PLib::SetPoles(Coefs,tempC); | |
2382 | TColStd_Array1OfReal tempP(1,3*Poles.Length()); | |
2383 | PLib::SetPoles(Coefs,tempP); | |
2384 | PLib::CoefficientsPoles(3,tempC,WCoefs,tempP,Weights); | |
2385 | PLib::GetPoles(tempP,Poles); | |
2386 | } | |
2387 | ||
2388 | //======================================================================= | |
2389 | //function : CoefficientsPoles | |
2390 | //purpose : | |
2391 | //======================================================================= | |
2392 | ||
2393 | void PLib::CoefficientsPoles (const TColgp_Array1OfPnt2d& Coefs, | |
2394 | const TColStd_Array1OfReal& WCoefs, | |
2395 | TColgp_Array1OfPnt2d& Poles, | |
2396 | TColStd_Array1OfReal& Weights) | |
2397 | { | |
2398 | TColStd_Array1OfReal tempC(1,2*Coefs.Length()); | |
2399 | PLib::SetPoles(Coefs,tempC); | |
2400 | TColStd_Array1OfReal tempP(1,2*Poles.Length()); | |
2401 | PLib::SetPoles(Coefs,tempP); | |
2402 | PLib::CoefficientsPoles(2,tempC,WCoefs,tempP,Weights); | |
2403 | PLib::GetPoles(tempP,Poles); | |
2404 | } | |
2405 | ||
2406 | //======================================================================= | |
2407 | //function : CoefficientsPoles | |
2408 | //purpose : | |
2409 | //======================================================================= | |
2410 | ||
2411 | void PLib::CoefficientsPoles (const TColStd_Array1OfReal& Coefs, | |
2412 | const TColStd_Array1OfReal& WCoefs, | |
2413 | TColStd_Array1OfReal& Poles, | |
2414 | TColStd_Array1OfReal& Weights) | |
2415 | { | |
2416 | PLib::CoefficientsPoles(1,Coefs,WCoefs,Poles,Weights); | |
2417 | } | |
2418 | ||
2419 | //======================================================================= | |
2420 | //function : CoefficientsPoles | |
2421 | //purpose : | |
2422 | //======================================================================= | |
2423 | ||
2424 | void PLib::CoefficientsPoles (const Standard_Integer dim, | |
2425 | const TColStd_Array1OfReal& Coefs, | |
2426 | const TColStd_Array1OfReal& WCoefs, | |
2427 | TColStd_Array1OfReal& Poles, | |
2428 | TColStd_Array1OfReal& Weights) | |
2429 | { | |
2430 | Standard_Boolean rat = &WCoefs != NULL; | |
2431 | Standard_Integer loc = Coefs.Lower(); | |
2432 | Standard_Integer lop = Poles.Lower(); | |
2433 | Standard_Integer lowc=0; | |
2434 | Standard_Integer lowp=0; | |
2435 | Standard_Integer upc = Coefs.Upper(); | |
2436 | Standard_Integer upp = Poles.Upper(); | |
2437 | Standard_Integer upwc=0; | |
2438 | Standard_Integer upwp=0; | |
2439 | Standard_Integer reflen = Coefs.Length()/dim; | |
2440 | Standard_Integer i,j,k; | |
2441 | //Les Extremites. | |
2442 | if (rat) { | |
2443 | lowc = WCoefs.Lower(); lowp = Weights.Lower(); | |
2444 | upwc = WCoefs.Upper(); upwp = Weights.Upper(); | |
2445 | } | |
2446 | ||
2447 | for (i = 0; i < dim; i++){ | |
2448 | Poles (lop + i) = Coefs (loc + i); | |
2449 | Poles (upp - i) = Coefs (upc - i); | |
2450 | } | |
2451 | if (rat) { | |
2452 | Weights (lowp) = WCoefs (lowc); | |
2453 | Weights (upwp) = WCoefs (upwc); | |
2454 | } | |
2455 | ||
2456 | Standard_Real Cnp; | |
7fd59977 | 2457 | for (i = 2; i < reflen; i++ ) { |
2458 | Cnp = PLib::Bin(reflen - 1, i - 1); | |
2459 | if (rat) Weights (lowp + i - 1) = WCoefs (lowc + i - 1) / Cnp; | |
2460 | ||
2461 | for(j = 0; j < dim; j++){ | |
2462 | Poles(lop + dim * (i-1) + j)= Coefs(loc + dim * (i-1) + j) / Cnp; | |
2463 | } | |
2464 | } | |
2465 | ||
2466 | for (i = 1; i <= reflen - 1; i++) { | |
2467 | ||
2468 | for (j = reflen - 1; j >= i; j--) { | |
2469 | if (rat) Weights (lowp + j) += Weights (lowp + j -1); | |
2470 | ||
2471 | for(k = 0; k < dim; k++){ | |
2472 | Poles(lop + dim * j + k) += Poles(lop + dim * (j - 1) + k); | |
2473 | } | |
2474 | } | |
2475 | } | |
2476 | if (rat) { | |
2477 | ||
2478 | for (i = 1; i <= reflen; i++) { | |
2479 | ||
2480 | for(j = 0; j < dim; j++){ | |
2481 | Poles(lop + dim * (i-1) + j) /= Weights(lowp + i -1); | |
2482 | } | |
2483 | } | |
2484 | } | |
2485 | } | |
2486 | ||
2487 | //======================================================================= | |
2488 | //function : Trimming | |
2489 | //purpose : | |
2490 | //======================================================================= | |
2491 | ||
2492 | void PLib::Trimming(const Standard_Real U1, | |
2493 | const Standard_Real U2, | |
2494 | TColgp_Array1OfPnt& Coefs, | |
2495 | TColStd_Array1OfReal& WCoefs) | |
2496 | { | |
2497 | TColStd_Array1OfReal temp(1,3*Coefs.Length()); | |
2498 | PLib::SetPoles(Coefs,temp); | |
2499 | PLib::Trimming(U1,U2,3,temp,WCoefs); | |
2500 | PLib::GetPoles(temp,Coefs); | |
2501 | } | |
2502 | ||
2503 | //======================================================================= | |
2504 | //function : Trimming | |
2505 | //purpose : | |
2506 | //======================================================================= | |
2507 | ||
2508 | void PLib::Trimming(const Standard_Real U1, | |
2509 | const Standard_Real U2, | |
2510 | TColgp_Array1OfPnt2d& Coefs, | |
2511 | TColStd_Array1OfReal& WCoefs) | |
2512 | { | |
2513 | TColStd_Array1OfReal temp(1,2*Coefs.Length()); | |
2514 | PLib::SetPoles(Coefs,temp); | |
2515 | PLib::Trimming(U1,U2,2,temp,WCoefs); | |
2516 | PLib::GetPoles(temp,Coefs); | |
2517 | } | |
2518 | ||
2519 | //======================================================================= | |
2520 | //function : Trimming | |
2521 | //purpose : | |
2522 | //======================================================================= | |
2523 | ||
2524 | void PLib::Trimming(const Standard_Real U1, | |
2525 | const Standard_Real U2, | |
2526 | TColStd_Array1OfReal& Coefs, | |
2527 | TColStd_Array1OfReal& WCoefs) | |
2528 | { | |
2529 | PLib::Trimming(U1,U2,1,Coefs,WCoefs); | |
2530 | } | |
2531 | ||
2532 | //======================================================================= | |
2533 | //function : Trimming | |
2534 | //purpose : | |
2535 | //======================================================================= | |
2536 | ||
2537 | void PLib::Trimming(const Standard_Real U1, | |
2538 | const Standard_Real U2, | |
2539 | const Standard_Integer dim, | |
2540 | TColStd_Array1OfReal& Coefs, | |
2541 | TColStd_Array1OfReal& WCoefs) | |
2542 | { | |
2543 | ||
2544 | // principe : | |
2545 | // on fait le changement de variable v = (u-U1) / (U2-U1) | |
2546 | // on exprime u = f(v) que l'on remplace dans l'expression polynomiale | |
2547 | // decomposee sous la forme du schema iteratif de horner. | |
2548 | ||
2549 | Standard_Real lsp = U2 - U1; | |
2550 | Standard_Integer indc, indw=0; | |
2551 | Standard_Integer upc = Coefs.Upper() - dim + 1, upw=0; | |
2552 | Standard_Integer len = Coefs.Length()/dim; | |
2553 | Standard_Boolean rat = &WCoefs != NULL; | |
2554 | ||
2555 | if (rat) { | |
2556 | if(len != WCoefs.Length()) | |
2557 | Standard_Failure::Raise("PLib::Trimming : nbcoefs/dim != nbweights !!!"); | |
2558 | upw = WCoefs.Upper(); | |
2559 | } | |
2560 | len --; | |
2561 | ||
2562 | for (Standard_Integer i = 1; i <= len; i++) { | |
2563 | Standard_Integer j ; | |
2564 | indc = upc - dim*(i-1); | |
2565 | if (rat) indw = upw - i + 1; | |
2566 | //calcul du coefficient de degre le plus faible a l'iteration i | |
2567 | ||
2568 | for( j = 0; j < dim; j++){ | |
2569 | Coefs(indc - dim + j) += U1 * Coefs(indc + j); | |
2570 | } | |
2571 | if (rat) WCoefs(indw - 1) += U1 * WCoefs(indw); | |
2572 | ||
2573 | //calcul des coefficients intermediaires : | |
2574 | ||
2575 | while (indc < upc){ | |
2576 | indc += dim; | |
2577 | ||
2578 | for(Standard_Integer k = 0; k < dim; k++){ | |
2579 | Coefs(indc - dim + k) = | |
2580 | U1 * Coefs(indc + k) + lsp * Coefs(indc - dim + k); | |
2581 | } | |
2582 | if (rat) { | |
2583 | indw ++; | |
2584 | WCoefs(indw - 1) = U1 * WCoefs(indw) + lsp * WCoefs(indw - 1); | |
2585 | } | |
2586 | } | |
2587 | ||
2588 | //calcul du coefficient de degre le plus eleve : | |
2589 | ||
2590 | for(j = 0; j < dim; j++){ | |
2591 | Coefs(upc + j) *= lsp; | |
2592 | } | |
2593 | if (rat) WCoefs(upw) *= lsp; | |
2594 | } | |
2595 | } | |
2596 | ||
2597 | //======================================================================= | |
2598 | //function : CoefficientsPoles | |
2599 | //purpose : | |
2600 | // Modified: 21/10/1996 by PMN : PolesCoefficient (PRO5852). | |
2601 | // on ne bidouille plus les u et v c'est a l'appelant de savoir ce qu'il | |
2602 | // fait avec BuildCache ou plus simplement d'utiliser PolesCoefficients | |
2603 | //======================================================================= | |
2604 | ||
2605 | void PLib::CoefficientsPoles (const TColgp_Array2OfPnt& Coefs, | |
2606 | const TColStd_Array2OfReal& WCoefs, | |
2607 | TColgp_Array2OfPnt& Poles, | |
2608 | TColStd_Array2OfReal& Weights) | |
2609 | { | |
2610 | Standard_Boolean rat = (&WCoefs != NULL); | |
2611 | Standard_Integer LowerRow = Poles.LowerRow(); | |
2612 | Standard_Integer UpperRow = Poles.UpperRow(); | |
2613 | Standard_Integer LowerCol = Poles.LowerCol(); | |
2614 | Standard_Integer UpperCol = Poles.UpperCol(); | |
2615 | Standard_Integer ColLength = Poles.ColLength(); | |
2616 | Standard_Integer RowLength = Poles.RowLength(); | |
2617 | ||
2618 | // Bidouille pour retablir u et v pour les coefs calcules | |
2619 | // par buildcache | |
2620 | // Standard_Boolean inv = Standard_False; //ColLength != Coefs.ColLength(); | |
2621 | ||
2622 | Standard_Integer Row, Col; | |
2623 | Standard_Real W, Cnp; | |
2624 | ||
2625 | Standard_Integer I1, I2; | |
2626 | Standard_Integer NPoleu , NPolev; | |
2627 | gp_XYZ Temp; | |
7fd59977 | 2628 | |
2629 | for (NPoleu = LowerRow; NPoleu <= UpperRow; NPoleu++){ | |
2630 | Poles (NPoleu, LowerCol) = Coefs (NPoleu, LowerCol); | |
2631 | if (rat) { | |
2632 | Weights (NPoleu, LowerCol) = WCoefs (NPoleu, LowerCol); | |
2633 | } | |
2634 | ||
2635 | for (Col = LowerCol + 1; Col <= UpperCol - 1; Col++) { | |
2636 | Cnp = PLib::Bin(RowLength - 1,Col - LowerCol); | |
2637 | Temp = Coefs (NPoleu, Col).XYZ(); | |
2638 | Temp.Divide (Cnp); | |
2639 | Poles (NPoleu, Col).SetXYZ (Temp); | |
2640 | if (rat) { | |
2641 | Weights (NPoleu, Col) = WCoefs (NPoleu, Col) / Cnp; | |
2642 | } | |
2643 | } | |
2644 | Poles (NPoleu, UpperCol) = Coefs (NPoleu, UpperCol); | |
2645 | if (rat) { | |
2646 | Weights (NPoleu, UpperCol) = WCoefs (NPoleu, UpperCol); | |
2647 | } | |
2648 | ||
2649 | for (I1 = 1; I1 <= RowLength - 1; I1++) { | |
2650 | ||
2651 | for (I2 = UpperCol; I2 >= LowerCol + I1; I2--) { | |
2652 | Temp.SetLinearForm | |
2653 | (Poles (NPoleu, I2).XYZ(), Poles (NPoleu, I2-1).XYZ()); | |
2654 | Poles (NPoleu, I2).SetXYZ (Temp); | |
2655 | if (rat) Weights(NPoleu, I2) += Weights(NPoleu, I2-1); | |
2656 | } | |
2657 | } | |
2658 | } | |
7fd59977 | 2659 | |
2660 | for (NPolev = LowerCol; NPolev <= UpperCol; NPolev++){ | |
2661 | ||
2662 | for (Row = LowerRow + 1; Row <= UpperRow - 1; Row++) { | |
2663 | Cnp = PLib::Bin(ColLength - 1,Row - LowerRow); | |
2664 | Temp = Poles (Row, NPolev).XYZ(); | |
2665 | Temp.Divide (Cnp); | |
2666 | Poles (Row, NPolev).SetXYZ (Temp); | |
2667 | if (rat) Weights(Row, NPolev) /= Cnp; | |
2668 | } | |
2669 | ||
2670 | for (I1 = 1; I1 <= ColLength - 1; I1++) { | |
2671 | ||
2672 | for (I2 = UpperRow; I2 >= LowerRow + I1; I2--) { | |
2673 | Temp.SetLinearForm | |
2674 | (Poles (I2, NPolev).XYZ(), Poles (I2-1, NPolev).XYZ()); | |
2675 | Poles (I2, NPolev).SetXYZ (Temp); | |
2676 | if (rat) Weights(I2, NPolev) += Weights(I2-1, NPolev); | |
2677 | } | |
2678 | } | |
2679 | } | |
2680 | if (rat) { | |
2681 | ||
2682 | for (Row = LowerRow; Row <= UpperRow; Row++) { | |
2683 | ||
2684 | for (Col = LowerCol; Col <= UpperCol; Col++) { | |
2685 | W = Weights (Row, Col); | |
2686 | Temp = Poles(Row, Col).XYZ(); | |
2687 | Temp.Divide (W); | |
2688 | Poles(Row, Col).SetXYZ (Temp); | |
2689 | } | |
2690 | } | |
2691 | } | |
2692 | } | |
2693 | ||
2694 | //======================================================================= | |
2695 | //function : UTrimming | |
2696 | //purpose : | |
2697 | //======================================================================= | |
2698 | ||
2699 | void PLib::UTrimming(const Standard_Real U1, | |
2700 | const Standard_Real U2, | |
2701 | TColgp_Array2OfPnt& Coeffs, | |
2702 | TColStd_Array2OfReal& WCoeffs) | |
2703 | { | |
2704 | Standard_Boolean rat = &WCoeffs != NULL; | |
2705 | Standard_Integer lr = Coeffs.LowerRow(); | |
2706 | Standard_Integer ur = Coeffs.UpperRow(); | |
2707 | Standard_Integer lc = Coeffs.LowerCol(); | |
2708 | Standard_Integer uc = Coeffs.UpperCol(); | |
2709 | TColgp_Array1OfPnt Temp (lr,ur); | |
2710 | TColStd_Array1OfReal Temw (lr,ur); | |
2711 | ||
2712 | for (Standard_Integer icol = lc; icol <= uc; icol++) { | |
2713 | Standard_Integer irow ; | |
2714 | for ( irow = lr; irow <= ur; irow++) { | |
2715 | Temp (irow) = Coeffs (irow, icol); | |
2716 | if (rat) Temw (irow) = WCoeffs (irow, icol); | |
2717 | } | |
2718 | if (rat) PLib::Trimming (U1, U2, Temp, Temw); | |
2719 | else PLib::Trimming (U1, U2, Temp, PLib::NoWeights()); | |
2720 | ||
2721 | for (irow = lr; irow <= ur; irow++) { | |
2722 | Coeffs (irow, icol) = Temp (irow); | |
2723 | if (rat) WCoeffs (irow, icol) = Temw (irow); | |
2724 | } | |
2725 | } | |
2726 | } | |
2727 | ||
2728 | //======================================================================= | |
2729 | //function : VTrimming | |
2730 | //purpose : | |
2731 | //======================================================================= | |
2732 | ||
2733 | void PLib::VTrimming(const Standard_Real V1, | |
2734 | const Standard_Real V2, | |
2735 | TColgp_Array2OfPnt& Coeffs, | |
2736 | TColStd_Array2OfReal& WCoeffs) | |
2737 | { | |
2738 | Standard_Boolean rat = &WCoeffs != NULL; | |
2739 | Standard_Integer lr = Coeffs.LowerRow(); | |
2740 | Standard_Integer ur = Coeffs.UpperRow(); | |
2741 | Standard_Integer lc = Coeffs.LowerCol(); | |
2742 | Standard_Integer uc = Coeffs.UpperCol(); | |
2743 | TColgp_Array1OfPnt Temp (lc,uc); | |
2744 | TColStd_Array1OfReal Temw (lc,uc); | |
2745 | ||
2746 | for (Standard_Integer irow = lr; irow <= ur; irow++) { | |
2747 | Standard_Integer icol ; | |
2748 | for ( icol = lc; icol <= uc; icol++) { | |
2749 | Temp (icol) = Coeffs (irow, icol); | |
2750 | if (rat) Temw (icol) = WCoeffs (irow, icol); | |
2751 | } | |
2752 | if (rat) PLib::Trimming (V1, V2, Temp, Temw); | |
2753 | else PLib::Trimming (V1, V2, Temp, PLib::NoWeights()); | |
2754 | ||
2755 | for (icol = lc; icol <= uc; icol++) { | |
2756 | Coeffs (irow, icol) = Temp (icol); | |
2757 | if (rat) WCoeffs (irow, icol) = Temw (icol); | |
2758 | } | |
2759 | } | |
2760 | } | |
2761 | ||
2762 | //======================================================================= | |
2763 | //function : HermiteInterpolate | |
2764 | //purpose : | |
2765 | //======================================================================= | |
2766 | ||
2767 | Standard_Boolean PLib::HermiteInterpolate | |
2768 | (const Standard_Integer Dimension, | |
2769 | const Standard_Real FirstParameter, | |
2770 | const Standard_Real LastParameter, | |
2771 | const Standard_Integer FirstOrder, | |
2772 | const Standard_Integer LastOrder, | |
2773 | const TColStd_Array2OfReal& FirstConstr, | |
2774 | const TColStd_Array2OfReal& LastConstr, | |
2775 | TColStd_Array1OfReal& Coefficients) | |
2776 | { | |
2777 | Standard_Real Pattern[3][6]; | |
2778 | ||
2779 | // portage HP : il faut les initialiser 1 par 1 | |
2780 | ||
2781 | Pattern[0][0] = 1; | |
2782 | Pattern[0][1] = 1; | |
2783 | Pattern[0][2] = 1; | |
2784 | Pattern[0][3] = 1; | |
2785 | Pattern[0][4] = 1; | |
2786 | Pattern[0][5] = 1; | |
2787 | Pattern[1][0] = 0; | |
2788 | Pattern[1][1] = 1; | |
2789 | Pattern[1][2] = 2; | |
2790 | Pattern[1][3] = 3; | |
2791 | Pattern[1][4] = 4; | |
2792 | Pattern[1][5] = 5; | |
2793 | Pattern[2][0] = 0; | |
2794 | Pattern[2][1] = 0; | |
2795 | Pattern[2][2] = 2; | |
2796 | Pattern[2][3] = 6; | |
2797 | Pattern[2][4] = 12; | |
2798 | Pattern[2][5] = 20; | |
2799 | ||
2800 | math_Matrix A(0,FirstOrder+LastOrder+1, 0,FirstOrder+LastOrder+1); | |
2801 | // The initialisation of the matrix A | |
2802 | Standard_Integer irow ; | |
2803 | for ( irow=0; irow<=FirstOrder; irow++) { | |
2804 | Standard_Real FirstVal = 1.; | |
2805 | ||
2806 | for (Standard_Integer icol=0; icol<=FirstOrder+LastOrder+1; icol++) { | |
2807 | A(irow,icol) = Pattern[irow][icol]*FirstVal; | |
2808 | if (irow <= icol) FirstVal *= FirstParameter; | |
2809 | } | |
2810 | } | |
2811 | ||
2812 | for (irow=0; irow<=LastOrder; irow++) { | |
2813 | Standard_Real LastVal = 1.; | |
2814 | ||
2815 | for (Standard_Integer icol=0; icol<=FirstOrder+LastOrder+1; icol++) { | |
2816 | A(irow+FirstOrder+1,icol) = Pattern[irow][icol]*LastVal; | |
2817 | if (irow <= icol) LastVal *= LastParameter; | |
2818 | } | |
2819 | } | |
2820 | // | |
2821 | // The filled matrix A for FirstOrder=LastOrder=2 is: | |
2822 | // | |
2823 | // 1 FP FP**2 FP**3 FP**4 FP**5 | |
2824 | // 0 1 2*FP 3*FP**2 4*FP**3 5*FP**4 FP - FirstParameter | |
2825 | // 0 0 2 6*FP 12*FP**2 20*FP**3 | |
2826 | // 1 LP LP**2 LP**3 LP**4 LP**5 | |
2827 | // 0 1 2*LP 3*LP**2 4*LP**3 5*LP**4 LP - LastParameter | |
2828 | // 0 0 2 6*LP 12*LP**2 20*LP**3 | |
2829 | // | |
2830 | // If FirstOrder or LastOrder <=2 then some rows and columns are missing. | |
2831 | // For example: | |
2832 | // If FirstOrder=1 then 3th row and 6th column are missing | |
2833 | // If FirstOrder=LastOrder=0 then 2,3,5,6th rows and 3,4,5,6th columns are missing | |
2834 | ||
2835 | math_Gauss Equations(A); | |
2836 | // cout << "A=" << A << endl; | |
2837 | ||
2838 | for (Standard_Integer idim=1; idim<=Dimension; idim++) { | |
2839 | // cout << "idim=" << idim << endl; | |
2840 | ||
2841 | math_Vector B(0,FirstOrder+LastOrder+1); | |
2842 | Standard_Integer icol ; | |
2843 | for ( icol=0; icol<=FirstOrder; icol++) | |
2844 | B(icol) = FirstConstr(idim,icol); | |
2845 | ||
2846 | for (icol=0; icol<=LastOrder; icol++) | |
2847 | B(FirstOrder+1+icol) = LastConstr(idim,icol); | |
2848 | // cout << "B=" << B << endl; | |
2849 | ||
2850 | // The solving of equations system A * X = B. Then B = X | |
2851 | Equations.Solve(B); | |
2852 | // cout << "After Solving" << endl << "B=" << B << endl; | |
2853 | ||
2854 | if (Equations.IsDone()==Standard_False) return Standard_False; | |
2855 | ||
2856 | // the filling of the Coefficients | |
2857 | ||
2858 | for (icol=0; icol<=FirstOrder+LastOrder+1; icol++) | |
2859 | Coefficients(Dimension*icol+idim-1) = B(icol); | |
2860 | } | |
2861 | return Standard_True; | |
2862 | } | |
2863 | ||
2864 | //======================================================================= | |
2865 | //function : JacobiParameters | |
2866 | //purpose : | |
2867 | //======================================================================= | |
2868 | ||
2869 | void PLib::JacobiParameters(const GeomAbs_Shape ConstraintOrder, | |
2870 | const Standard_Integer MaxDegree, | |
2871 | const Standard_Integer Code, | |
2872 | Standard_Integer& NbGaussPoints, | |
2873 | Standard_Integer& WorkDegree) | |
2874 | { | |
2875 | // ConstraintOrder: Ordre de contrainte aux extremites : | |
2876 | // C0 = contraintes de passage aux bornes; | |
2877 | // C1 = C0 + contraintes de derivees 1eres; | |
2878 | // C2 = C1 + contraintes de derivees 2ndes. | |
2879 | // MaxDegree: Nombre maxi de coeff de la "courbe" polynomiale | |
2880 | // d' approximation (doit etre superieur ou egal a | |
2881 | // 2*NivConstr+2 et inferieur ou egal a 50). | |
2882 | // Code: Code d' init. des parametres de discretisation. | |
2883 | // (choix de NBPNTS et de NDGJAC de MAPF1C,MAPFXC). | |
2884 | // = -5 Calcul tres rapide mais peu precis (8pts) | |
2885 | // = -4 ' ' ' ' ' ' (10pts) | |
2886 | // = -3 ' ' ' ' ' ' (15pts) | |
2887 | // = -2 ' ' ' ' ' ' (20pts) | |
2888 | // = -1 ' ' ' ' ' ' (25pts) | |
2889 | // = 1 calcul rapide avec precision moyenne (30pts). | |
2890 | // = 2 calcul rapide avec meilleure precision (40pts). | |
2891 | // = 3 calcul un peu plus lent avec bonne precision (50 pts). | |
2892 | // = 4 calcul lent avec la meilleure precision possible | |
2893 | // (61pts). | |
2894 | ||
2895 | // The possible values of NbGaussPoints | |
2896 | ||
2897 | const Standard_Integer NDEG8=8, NDEG10=10, NDEG15=15, NDEG20=20, NDEG25=25, | |
2898 | NDEG30=30, NDEG40=40, NDEG50=50, NDEG61=61; | |
2899 | ||
2900 | Standard_Integer NivConstr=0; | |
2901 | switch (ConstraintOrder) { | |
2902 | case GeomAbs_C0: NivConstr = 0; break; | |
2903 | case GeomAbs_C1: NivConstr = 1; break; | |
2904 | case GeomAbs_C2: NivConstr = 2; break; | |
2905 | default: | |
2906 | Standard_ConstructionError::Raise("Invalid ConstraintOrder"); | |
2907 | } | |
2908 | if (MaxDegree < 2*NivConstr+1) | |
2909 | Standard_ConstructionError::Raise("Invalid MaxDegree"); | |
2910 | ||
2911 | if (Code >= 1) | |
2912 | WorkDegree = MaxDegree + 9; | |
2913 | else | |
2914 | WorkDegree = MaxDegree + 6; | |
2915 | ||
2916 | //---> Nbre mini de points necessaires. | |
2917 | Standard_Integer IPMIN=0; | |
2918 | if (WorkDegree < NDEG8) | |
2919 | IPMIN=NDEG8; | |
2920 | else if (WorkDegree < NDEG10) | |
2921 | IPMIN=NDEG10; | |
2922 | else if (WorkDegree < NDEG15) | |
2923 | IPMIN=NDEG15; | |
2924 | else if (WorkDegree < NDEG20) | |
2925 | IPMIN=NDEG20; | |
2926 | else if (WorkDegree < NDEG25) | |
2927 | IPMIN=NDEG25; | |
2928 | else if (WorkDegree < NDEG30) | |
2929 | IPMIN=NDEG30; | |
2930 | else if (WorkDegree < NDEG40) | |
2931 | IPMIN=NDEG40; | |
2932 | else if (WorkDegree < NDEG50) | |
2933 | IPMIN=NDEG50; | |
2934 | else if (WorkDegree < NDEG61) | |
2935 | IPMIN=NDEG61; | |
2936 | else | |
2937 | Standard_ConstructionError::Raise("Invalid MaxDegree"); | |
2938 | // ---> Nbre de points voulus. | |
2939 | Standard_Integer IWANT=0; | |
2940 | switch (Code) { | |
2941 | case -5: IWANT=NDEG8; break; | |
2942 | case -4: IWANT=NDEG10; break; | |
2943 | case -3: IWANT=NDEG15; break; | |
2944 | case -2: IWANT=NDEG20; break; | |
2945 | case -1: IWANT=NDEG25; break; | |
2946 | case 1: IWANT=NDEG30; break; | |
2947 | case 2: IWANT=NDEG40; break; | |
2948 | case 3: IWANT=NDEG50; break; | |
2949 | case 4: IWANT=NDEG61; break; | |
2950 | default: | |
2951 | Standard_ConstructionError::Raise("Invalid Code"); | |
2952 | } | |
2953 | //--> NbGaussPoints est le nombre de points de discretisation de la fonction, | |
2954 | // il ne peut prendre que les valeurs 8,10,15,20,25,30,40,50 ou 61. | |
2955 | // NbGaussPoints doit etre superieur strictement a WorkDegree. | |
2956 | NbGaussPoints = Max(IPMIN,IWANT); | |
2957 | // NbGaussPoints +=2; | |
2958 | } | |
2959 | ||
2960 | //======================================================================= | |
2961 | //function : NivConstr | |
2962 | //purpose : translates from GeomAbs_Shape to Integer | |
2963 | //======================================================================= | |
2964 | ||
2965 | Standard_Integer PLib::NivConstr(const GeomAbs_Shape ConstraintOrder) | |
2966 | { | |
2967 | Standard_Integer NivConstr=0; | |
2968 | switch (ConstraintOrder) { | |
2969 | case GeomAbs_C0: NivConstr = 0; break; | |
2970 | case GeomAbs_C1: NivConstr = 1; break; | |
2971 | case GeomAbs_C2: NivConstr = 2; break; | |
2972 | default: | |
2973 | Standard_ConstructionError::Raise("Invalid ConstraintOrder"); | |
2974 | } | |
2975 | return NivConstr; | |
2976 | } | |
2977 | ||
2978 | //======================================================================= | |
2979 | //function : ConstraintOrder | |
2980 | //purpose : translates from Integer to GeomAbs_Shape | |
2981 | //======================================================================= | |
2982 | ||
2983 | GeomAbs_Shape PLib::ConstraintOrder(const Standard_Integer NivConstr) | |
2984 | { | |
2985 | GeomAbs_Shape ConstraintOrder=GeomAbs_C0; | |
2986 | switch (NivConstr) { | |
2987 | case 0: ConstraintOrder = GeomAbs_C0; break; | |
2988 | case 1: ConstraintOrder = GeomAbs_C1; break; | |
2989 | case 2: ConstraintOrder = GeomAbs_C2; break; | |
2990 | default: | |
2991 | Standard_ConstructionError::Raise("Invalid NivConstr"); | |
2992 | } | |
2993 | return ConstraintOrder; | |
2994 | } | |
2995 | ||
2996 | //======================================================================= | |
2997 | //function : EvalLength | |
2998 | //purpose : | |
2999 | //======================================================================= | |
3000 | ||
3001 | void PLib::EvalLength(const Standard_Integer Degree, const Standard_Integer Dimension, | |
3002 | Standard_Real& PolynomialCoeff, | |
3003 | const Standard_Real U1, const Standard_Real U2, | |
3004 | Standard_Real& Length) | |
3005 | { | |
3006 | Standard_Integer i,j,idim, degdim; | |
3007 | Standard_Real C1,C2,Sum,Tran,X1,X2,Der1,Der2,D1,D2,DD; | |
3008 | ||
3009 | Standard_Real *PolynomialArray = &PolynomialCoeff ; | |
3010 | ||
3011 | Standard_Integer NbGaussPoints = 4 * Min((Degree/4)+1,10); | |
3012 | ||
3013 | math_Vector GaussPoints(1,NbGaussPoints); | |
3014 | math::GaussPoints(NbGaussPoints,GaussPoints); | |
3015 | ||
3016 | math_Vector GaussWeights(1,NbGaussPoints); | |
3017 | math::GaussWeights(NbGaussPoints,GaussWeights); | |
3018 | ||
3019 | C1 = (U2 + U1) / 2.; | |
3020 | C2 = (U2 - U1) / 2.; | |
3021 | ||
3022 | //----------------------------------------------------------- | |
3023 | //****** Integration - Boucle sur les intervalles de GAUSS ** | |
3024 | //----------------------------------------------------------- | |
3025 | ||
3026 | Sum = 0; | |
3027 | ||
3028 | for (j=1; j<=NbGaussPoints/2; j++) { | |
3029 | // Integration en tenant compte de la symetrie | |
3030 | Tran = C2 * GaussPoints(j); | |
3031 | X1 = C1 + Tran; | |
3032 | X2 = C1 - Tran; | |
3033 | ||
3034 | //****** Derivation sur la dimension de l'espace ** | |
3035 | ||
3036 | degdim = Degree*Dimension; | |
3037 | Der1 = Der2 = 0.; | |
3038 | for (idim=0; idim<Dimension; idim++) { | |
3039 | D1 = D2 = Degree * PolynomialArray [idim + degdim]; | |
3040 | for (i=Degree-1; i>=1; i--) { | |
3041 | DD = i * PolynomialArray [idim + i*Dimension]; | |
3042 | D1 = D1 * X1 + DD; | |
3043 | D2 = D2 * X2 + DD; | |
3044 | } | |
3045 | Der1 += D1 * D1; | |
3046 | Der2 += D2 * D2; | |
3047 | } | |
3048 | ||
3049 | //****** Integration ** | |
3050 | ||
3051 | Sum += GaussWeights(j) * C2 * (Sqrt(Der1) + Sqrt(Der2)); | |
3052 | ||
3053 | //****** Fin de boucle dur les intervalles de GAUSS ** | |
3054 | } | |
3055 | Length = Sum; | |
3056 | } | |
3057 | ||
3058 | ||
3059 | //======================================================================= | |
3060 | //function : EvalLength | |
3061 | //purpose : | |
3062 | //======================================================================= | |
3063 | ||
3064 | void PLib::EvalLength(const Standard_Integer Degree, const Standard_Integer Dimension, | |
3065 | Standard_Real& PolynomialCoeff, | |
3066 | const Standard_Real U1, const Standard_Real U2, | |
3067 | const Standard_Real Tol, | |
3068 | Standard_Real& Length, Standard_Real& Error) | |
3069 | { | |
3070 | Standard_Integer i; | |
3071 | Standard_Integer NbSubInt = 1, // Current number of subintervals | |
3072 | MaxNbIter = 13, // Max number of iterations | |
3073 | NbIter = 1; // Current number of iterations | |
3074 | Standard_Real dU,OldLen,LenI; | |
3075 | ||
3076 | PLib::EvalLength(Degree,Dimension, PolynomialCoeff, U1,U2, Length); | |
3077 | ||
3078 | do { | |
3079 | OldLen = Length; | |
3080 | Length = 0.; | |
3081 | NbSubInt *= 2; | |
3082 | dU = (U2-U1)/NbSubInt; | |
3083 | for (i=1; i<=NbSubInt; i++) { | |
3084 | PLib::EvalLength(Degree,Dimension, PolynomialCoeff, U1+(i-1)*dU,U1+i*dU, LenI); | |
3085 | Length += LenI; | |
3086 | } | |
3087 | NbIter++; | |
3088 | Error = Abs(OldLen-Length); | |
3089 | } | |
3090 | while (Error > Tol && NbIter <= MaxNbIter); | |
3091 | } |