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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 | // |
d5f74e42 | 8 | // This library is free software; you can redistribute it and/or modify it under |
9 | // the terms of the GNU Lesser General Public License version 2.1 as published | |
973c2be1 | 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 <GeomAbs_Shape.hxx> |
105aae76 | 22 | #include <math.hxx> |
42cf5bc1 | 23 | #include <math_Gauss.hxx> |
24 | #include <math_Matrix.hxx> | |
25 | #include <NCollection_LocalArray.hxx> | |
26 | #include <PLib.hxx> | |
27 | #include <Standard_ConstructionError.hxx> | |
105aae76 | 28 | |
7fd59977 | 29 | // To convert points array into Real .. |
30 | // ********************************* | |
105aae76 | 31 | //======================================================================= |
32 | //function : SetPoles | |
33 | //purpose : | |
34 | //======================================================================= | |
105aae76 | 35 | void PLib::SetPoles(const TColgp_Array1OfPnt2d& Poles, |
36 | TColStd_Array1OfReal& FP) | |
37 | { | |
38 | Standard_Integer j = FP .Lower(); | |
39 | Standard_Integer PLower = Poles.Lower(); | |
40 | Standard_Integer PUpper = Poles.Upper(); | |
41 | ||
42 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
43 | const gp_Pnt2d& P = Poles(i); | |
44 | FP(j) = P.Coord(1); j++; | |
45 | FP(j) = P.Coord(2); j++; | |
46 | } | |
47 | } | |
48 | ||
49 | //======================================================================= | |
50 | //function : SetPoles | |
51 | //purpose : | |
52 | //======================================================================= | |
53 | ||
54 | void PLib::SetPoles(const TColgp_Array1OfPnt2d& Poles, | |
55 | const TColStd_Array1OfReal& Weights, | |
56 | TColStd_Array1OfReal& FP) | |
57 | { | |
58 | Standard_Integer j = FP .Lower(); | |
59 | Standard_Integer PLower = Poles.Lower(); | |
60 | Standard_Integer PUpper = Poles.Upper(); | |
61 | ||
62 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
63 | Standard_Real w = Weights(i); | |
64 | const gp_Pnt2d& P = Poles(i); | |
65 | FP(j) = P.Coord(1) * w; j++; | |
66 | FP(j) = P.Coord(2) * w; j++; | |
67 | FP(j) = w; j++; | |
68 | } | |
69 | } | |
70 | ||
71 | //======================================================================= | |
72 | //function : GetPoles | |
73 | //purpose : | |
74 | //======================================================================= | |
7fd59977 | 75 | |
105aae76 | 76 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, |
77 | TColgp_Array1OfPnt2d& Poles) | |
78 | { | |
79 | Standard_Integer j = FP .Lower(); | |
80 | Standard_Integer PLower = Poles.Lower(); | |
81 | Standard_Integer PUpper = Poles.Upper(); | |
82 | ||
83 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
84 | gp_Pnt2d& P = Poles(i); | |
85 | P.SetCoord(1,FP(j)); j++; | |
86 | P.SetCoord(2,FP(j)); j++; | |
87 | } | |
88 | } | |
7fd59977 | 89 | |
105aae76 | 90 | //======================================================================= |
91 | //function : GetPoles | |
92 | //purpose : | |
93 | //======================================================================= | |
7fd59977 | 94 | |
105aae76 | 95 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, |
96 | TColgp_Array1OfPnt2d& Poles, | |
97 | TColStd_Array1OfReal& Weights) | |
98 | { | |
99 | Standard_Integer j = FP .Lower(); | |
100 | Standard_Integer PLower = Poles.Lower(); | |
101 | Standard_Integer PUpper = Poles.Upper(); | |
102 | ||
103 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
104 | Standard_Real w = FP(j + 2); | |
105 | Weights(i) = w; | |
106 | gp_Pnt2d& P = Poles(i); | |
107 | P.SetCoord(1,FP(j) / w); j++; | |
108 | P.SetCoord(2,FP(j) / w); j++; | |
109 | j++; | |
110 | } | |
111 | } | |
7fd59977 | 112 | |
105aae76 | 113 | //======================================================================= |
114 | //function : SetPoles | |
115 | //purpose : | |
116 | //======================================================================= | |
7fd59977 | 117 | |
105aae76 | 118 | void PLib::SetPoles(const TColgp_Array1OfPnt& Poles, |
119 | TColStd_Array1OfReal& FP) | |
120 | { | |
121 | Standard_Integer j = FP .Lower(); | |
122 | Standard_Integer PLower = Poles.Lower(); | |
123 | Standard_Integer PUpper = Poles.Upper(); | |
7fd59977 | 124 | |
105aae76 | 125 | for (Standard_Integer i = PLower; i <= PUpper; i++) { |
126 | const gp_Pnt& P = Poles(i); | |
127 | FP(j) = P.Coord(1); j++; | |
128 | FP(j) = P.Coord(2); j++; | |
129 | FP(j) = P.Coord(3); j++; | |
130 | } | |
131 | } | |
132 | ||
133 | //======================================================================= | |
134 | //function : SetPoles | |
135 | //purpose : | |
136 | //======================================================================= | |
137 | ||
138 | void PLib::SetPoles(const TColgp_Array1OfPnt& Poles, | |
139 | const TColStd_Array1OfReal& Weights, | |
140 | TColStd_Array1OfReal& FP) | |
141 | { | |
142 | Standard_Integer j = FP .Lower(); | |
143 | Standard_Integer PLower = Poles.Lower(); | |
144 | Standard_Integer PUpper = Poles.Upper(); | |
145 | ||
146 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
147 | Standard_Real w = Weights(i); | |
148 | const gp_Pnt& P = Poles(i); | |
149 | FP(j) = P.Coord(1) * w; j++; | |
150 | FP(j) = P.Coord(2) * w; j++; | |
151 | FP(j) = P.Coord(3) * w; j++; | |
152 | FP(j) = w; j++; | |
153 | } | |
154 | } | |
155 | ||
156 | //======================================================================= | |
157 | //function : GetPoles | |
158 | //purpose : | |
159 | //======================================================================= | |
160 | ||
161 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, | |
162 | TColgp_Array1OfPnt& Poles) | |
163 | { | |
164 | Standard_Integer j = FP .Lower(); | |
165 | Standard_Integer PLower = Poles.Lower(); | |
166 | Standard_Integer PUpper = Poles.Upper(); | |
167 | ||
168 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
169 | gp_Pnt& P = Poles(i); | |
170 | P.SetCoord(1,FP(j)); j++; | |
171 | P.SetCoord(2,FP(j)); j++; | |
172 | P.SetCoord(3,FP(j)); j++; | |
173 | } | |
174 | } | |
175 | ||
176 | //======================================================================= | |
177 | //function : GetPoles | |
178 | //purpose : | |
179 | //======================================================================= | |
180 | ||
181 | void PLib::GetPoles(const TColStd_Array1OfReal& FP, | |
182 | TColgp_Array1OfPnt& Poles, | |
183 | TColStd_Array1OfReal& Weights) | |
184 | { | |
185 | Standard_Integer j = FP .Lower(); | |
186 | Standard_Integer PLower = Poles.Lower(); | |
187 | Standard_Integer PUpper = Poles.Upper(); | |
188 | ||
189 | for (Standard_Integer i = PLower; i <= PUpper; i++) { | |
190 | Standard_Real w = FP(j + 3); | |
191 | Weights(i) = w; | |
192 | gp_Pnt& P = Poles(i); | |
193 | P.SetCoord(1,FP(j) / w); j++; | |
194 | P.SetCoord(2,FP(j) / w); j++; | |
195 | P.SetCoord(3,FP(j) / w); j++; | |
196 | j++; | |
197 | } | |
198 | } | |
199 | ||
200 | // specialized allocator | |
201 | namespace | |
202 | { | |
7fd59977 | 203 | |
41194117 | 204 | class BinomAllocator |
7fd59977 | 205 | { |
41194117 K |
206 | public: |
207 | ||
208 | //! Main constructor | |
209 | BinomAllocator (const Standard_Integer theMaxBinom) | |
210 | : myBinom (NULL), | |
211 | myMaxBinom (theMaxBinom) | |
212 | { | |
213 | Standard_Integer i, im1, ip1, id2, md2, md3, j, k; | |
214 | Standard_Integer np1 = myMaxBinom + 1; | |
215 | myBinom = new Standard_Integer*[np1]; | |
216 | myBinom[0] = new Standard_Integer[1]; | |
217 | myBinom[0][0] = 1; | |
218 | for (i = 1; i < np1; ++i) | |
219 | { | |
7fd59977 | 220 | im1 = i - 1; |
221 | ip1 = i + 1; | |
222 | id2 = i >> 1; | |
223 | md2 = im1 >> 1; | |
224 | md3 = ip1 >> 1; | |
225 | k = 0; | |
41194117 | 226 | myBinom[i] = new Standard_Integer[ip1]; |
7fd59977 | 227 | |
41194117 K |
228 | for (j = 0; j < id2; ++j) |
229 | { | |
230 | myBinom[i][j] = k + myBinom[im1][j]; | |
231 | k = myBinom[im1][j]; | |
7fd59977 | 232 | } |
233 | j = id2; | |
234 | if (j > md2) j = im1 - j; | |
41194117 | 235 | myBinom[i][id2] = k + myBinom[im1][j]; |
7fd59977 | 236 | |
41194117 K |
237 | for (j = ip1 - md3; j < ip1; j++) |
238 | { | |
239 | myBinom[i][j] = myBinom[i][i - j]; | |
7fd59977 | 240 | } |
241 | } | |
7fd59977 | 242 | } |
7fd59977 | 243 | |
41194117 K |
244 | //! Destructor |
245 | ~BinomAllocator() | |
246 | { | |
247 | // free memory | |
248 | for (Standard_Integer i = 0; i <= myMaxBinom; ++i) | |
249 | { | |
250 | delete[] myBinom[i]; | |
251 | } | |
252 | delete[] myBinom; | |
253 | } | |
7fd59977 | 254 | |
41194117 K |
255 | Standard_Real Value (const Standard_Integer N, |
256 | const Standard_Integer P) const | |
257 | { | |
258 | Standard_OutOfRange_Raise_if (N > myMaxBinom, | |
259 | "PLib, BinomAllocator: requested degree is greater than maximum supported"); | |
260 | return Standard_Real (myBinom[N][P]); | |
7fd59977 | 261 | } |
41194117 | 262 | |
6a38ff48 | 263 | private: |
264 | BinomAllocator (const BinomAllocator&); | |
265 | BinomAllocator& operator= (const BinomAllocator&); | |
266 | ||
41194117 K |
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); | |
5640d653 | 276 | } |
41194117 K |
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; | |
8c2d3314 | 455 | ++OtherIndex; |
7fd59977 | 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 | ||
d721c8eb | 635 | //======================================================================= |
636 | // Auxiliary template functions used for optimized evaluation of polynome | |
637 | // and its derivatives for smaller dimensions of the polynome | |
638 | //======================================================================= | |
639 | ||
640 | namespace { | |
641 | // recursive template for evaluating value or first derivative | |
642 | template<int dim> | |
643 | inline void eval_step1 (double* poly, double par, double* coef) | |
644 | { | |
645 | eval_step1<dim - 1> (poly, par, coef); | |
646 | poly[dim] = poly[dim] * par + coef[dim]; | |
647 | } | |
648 | ||
649 | // recursion end | |
650 | template<> | |
651 | inline void eval_step1<-1> (double*, double, double*) | |
652 | { | |
653 | } | |
654 | ||
655 | // recursive template for evaluating second derivative | |
656 | template<int dim> | |
657 | inline void eval_step2 (double* poly, double par, double* coef) | |
658 | { | |
659 | eval_step2<dim - 1> (poly, par, coef); | |
660 | poly[dim] = poly[dim] * par + coef[dim] * 2.; | |
661 | } | |
662 | ||
663 | // recursion end | |
664 | template<> | |
665 | inline void eval_step2<-1> (double*, double, double*) | |
666 | { | |
667 | } | |
668 | ||
669 | // evaluation of only value | |
670 | template<int dim> | |
671 | inline void eval_poly0 (double* aRes, double* aCoeffs, int Degree, double Par) | |
672 | { | |
673 | Standard_Real* aRes0 = aRes; | |
674 | memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * dim); | |
675 | ||
676 | for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++) | |
677 | { | |
678 | aCoeffs -= dim; | |
679 | // Calculating the value of the polynomial | |
680 | eval_step1<dim-1> (aRes0, Par, aCoeffs); | |
681 | } | |
682 | } | |
683 | ||
684 | // evaluation of value and first derivative | |
685 | template<int dim> | |
686 | inline void eval_poly1 (double* aRes, double* aCoeffs, int Degree, double Par) | |
687 | { | |
688 | Standard_Real* aRes0 = aRes; | |
689 | Standard_Real* aRes1 = aRes + dim; | |
690 | ||
691 | memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * dim); | |
692 | memset(aRes1, 0, sizeof(Standard_Real) * dim); | |
693 | ||
694 | for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++) | |
695 | { | |
696 | aCoeffs -= dim; | |
697 | // Calculating derivatives of the polynomial | |
698 | eval_step1<dim-1> (aRes1, Par, aRes0); | |
699 | // Calculating the value of the polynomial | |
700 | eval_step1<dim-1> (aRes0, Par, aCoeffs); | |
701 | } | |
702 | } | |
703 | ||
704 | // evaluation of value and first and second derivatives | |
705 | template<int dim> | |
706 | inline void eval_poly2 (double* aRes, double* aCoeffs, int Degree, double Par) | |
707 | { | |
708 | Standard_Real* aRes0 = aRes; | |
709 | Standard_Real* aRes1 = aRes + dim; | |
710 | Standard_Real* aRes2 = aRes + 2 * dim; | |
711 | ||
712 | memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * dim); | |
713 | memset(aRes1, 0, sizeof(Standard_Real) * dim); | |
714 | memset(aRes2, 0, sizeof(Standard_Real) * dim); | |
715 | ||
716 | for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++) | |
717 | { | |
718 | aCoeffs -= dim; | |
719 | // Calculating second derivatives of the polynomial | |
720 | eval_step2<dim-1> (aRes2, Par, aRes1); | |
721 | // Calculating derivatives of the polynomial | |
722 | eval_step1<dim-1> (aRes1, Par, aRes0); | |
723 | // Calculating the value of the polynomial | |
724 | eval_step1<dim-1> (aRes0, Par, aCoeffs); | |
725 | } | |
726 | } | |
727 | } | |
728 | ||
7fd59977 | 729 | //======================================================================= |
730 | //function : This evaluates a polynomial and its derivatives | |
731 | //purpose : up to the requested order | |
732 | //======================================================================= | |
733 | ||
734 | void PLib::EvalPolynomial(const Standard_Real Par, | |
d721c8eb | 735 | const Standard_Integer DerivativeRequest, |
736 | const Standard_Integer Degree, | |
737 | const Standard_Integer Dimension, | |
738 | Standard_Real& PolynomialCoeff, | |
739 | Standard_Real& Results) | |
7fd59977 | 740 | // |
741 | // the polynomial coefficients are assumed to be stored as follows : | |
742 | // 0 | |
743 | // [0] [Dimension -1] X coefficient | |
744 | // 1 | |
745 | // [Dimension] [Dimension + Dimension -1] X coefficient | |
746 | // 2 | |
747 | // [2 * Dimension] [2 * Dimension + Dimension-1] X coefficient | |
748 | // | |
749 | // ................................................... | |
750 | // | |
751 | // | |
752 | // d | |
753 | // [d * Dimension] [d * Dimension + Dimension-1] X coefficient | |
754 | // | |
755 | // where d is the Degree | |
756 | // | |
757 | { | |
d721c8eb | 758 | Standard_Real* aCoeffs = &PolynomialCoeff + Degree * Dimension; |
759 | Standard_Real* aRes = &Results; | |
760 | Standard_Real* anOriginal; | |
761 | Standard_Integer ind = 0; | |
762 | switch (DerivativeRequest) | |
763 | { | |
764 | case 1: | |
765 | { | |
766 | switch (Dimension) | |
767 | { | |
768 | case 1: eval_poly1<1> (aRes, aCoeffs, Degree, Par); break; | |
769 | case 2: eval_poly1<2> (aRes, aCoeffs, Degree, Par); break; | |
770 | case 3: eval_poly1<3> (aRes, aCoeffs, Degree, Par); break; | |
771 | case 4: eval_poly1<4> (aRes, aCoeffs, Degree, Par); break; | |
772 | case 5: eval_poly1<5> (aRes, aCoeffs, Degree, Par); break; | |
773 | case 6: eval_poly1<6> (aRes, aCoeffs, Degree, Par); break; | |
774 | case 7: eval_poly1<7> (aRes, aCoeffs, Degree, Par); break; | |
775 | case 8: eval_poly1<8> (aRes, aCoeffs, Degree, Par); break; | |
776 | case 9: eval_poly1<9> (aRes, aCoeffs, Degree, Par); break; | |
777 | case 10: eval_poly1<10> (aRes, aCoeffs, Degree, Par); break; | |
778 | case 11: eval_poly1<11> (aRes, aCoeffs, Degree, Par); break; | |
779 | case 12: eval_poly1<12> (aRes, aCoeffs, Degree, Par); break; | |
780 | case 13: eval_poly1<13> (aRes, aCoeffs, Degree, Par); break; | |
781 | case 14: eval_poly1<14> (aRes, aCoeffs, Degree, Par); break; | |
782 | case 15: eval_poly1<15> (aRes, aCoeffs, Degree, Par); break; | |
783 | default: | |
784 | { | |
785 | Standard_Real* aRes0 = aRes; | |
786 | Standard_Real* aRes1 = aRes + Dimension; | |
7fd59977 | 787 | |
d721c8eb | 788 | memcpy(aRes0, aCoeffs, sizeof(Standard_Real) * Dimension); |
789 | memset(aRes1, 0, sizeof(Standard_Real) * Dimension); | |
790 | ||
791 | for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++) | |
792 | { | |
793 | aCoeffs -= Dimension; | |
794 | // Calculating derivatives of the polynomial | |
795 | for (ind = 0; ind < Dimension; ind++) | |
796 | aRes1[ind] = aRes1[ind] * Par + aRes0[ind]; | |
797 | // Calculating the value of the polynomial | |
798 | for (ind = 0; ind < Dimension; ind++) | |
799 | aRes0[ind] = aRes0[ind] * Par + aCoeffs[ind]; | |
800 | } | |
7fd59977 | 801 | } |
802 | } | |
803 | break; | |
7fd59977 | 804 | } |
d721c8eb | 805 | case 2: |
806 | { | |
807 | switch (Dimension) | |
808 | { | |
809 | case 1: eval_poly2<1> (aRes, aCoeffs, Degree, Par); break; | |
810 | case 2: eval_poly2<2> (aRes, aCoeffs, Degree, Par); break; | |
811 | case 3: eval_poly2<3> (aRes, aCoeffs, Degree, Par); break; | |
812 | case 4: eval_poly2<4> (aRes, aCoeffs, Degree, Par); break; | |
813 | case 5: eval_poly2<5> (aRes, aCoeffs, Degree, Par); break; | |
814 | case 6: eval_poly2<6> (aRes, aCoeffs, Degree, Par); break; | |
815 | case 7: eval_poly2<7> (aRes, aCoeffs, Degree, Par); break; | |
816 | case 8: eval_poly2<8> (aRes, aCoeffs, Degree, Par); break; | |
817 | case 9: eval_poly2<9> (aRes, aCoeffs, Degree, Par); break; | |
818 | case 10: eval_poly2<10> (aRes, aCoeffs, Degree, Par); break; | |
819 | case 11: eval_poly2<11> (aRes, aCoeffs, Degree, Par); break; | |
820 | case 12: eval_poly2<12> (aRes, aCoeffs, Degree, Par); break; | |
821 | case 13: eval_poly2<13> (aRes, aCoeffs, Degree, Par); break; | |
822 | case 14: eval_poly2<14> (aRes, aCoeffs, Degree, Par); break; | |
823 | case 15: eval_poly2<15> (aRes, aCoeffs, Degree, Par); break; | |
824 | default: | |
825 | { | |
826 | Standard_Real* aRes0 = aRes; | |
827 | Standard_Real* aRes1 = aRes + Dimension; | |
828 | Standard_Real* aRes2 = aRes1 + Dimension; | |
829 | ||
830 | // Nullify the results | |
831 | Standard_Integer aSize = 2 * Dimension; | |
832 | memcpy(aRes, aCoeffs, sizeof(Standard_Real) * Dimension); | |
833 | memset(aRes1, 0, sizeof(Standard_Real) * aSize); | |
834 | ||
835 | for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++) | |
836 | { | |
837 | aCoeffs -= Dimension; | |
838 | // Calculating derivatives of the polynomial | |
839 | for (ind = 0; ind < Dimension; ind++) | |
840 | aRes2[ind] = aRes2[ind] * Par + aRes1[ind] * 2.0; | |
841 | for (ind = 0; ind < Dimension; ind++) | |
842 | aRes1[ind] = aRes1[ind] * Par + aRes0[ind]; | |
843 | // Calculating the value of the polynomial | |
844 | for (ind = 0; ind < Dimension; ind++) | |
845 | aRes0[ind] = aRes0[ind] * Par + aCoeffs[ind]; | |
846 | } | |
847 | break; | |
7fd59977 | 848 | } |
849 | } | |
850 | break; | |
851 | } | |
d721c8eb | 852 | default: |
853 | { | |
854 | // Nullify the results | |
855 | Standard_Integer aResSize = (1 + DerivativeRequest) * Dimension; | |
856 | memset(aRes, 0, sizeof(Standard_Real) * aResSize); | |
857 | ||
858 | for (Standard_Integer aDeg = 0; aDeg <= Degree; aDeg++) | |
859 | { | |
860 | aRes = &Results + aResSize - Dimension; | |
861 | // Calculating derivatives of the polynomial | |
862 | for (Standard_Integer aDeriv = DerivativeRequest; aDeriv > 0; aDeriv--) | |
863 | { | |
864 | anOriginal = aRes - Dimension; // pointer to the derivative minus 1 | |
865 | for (ind = 0; ind < Dimension; ind++) | |
866 | aRes[ind] = aRes[ind] * Par + anOriginal[ind] * aDeriv; | |
867 | aRes = anOriginal; | |
868 | } | |
869 | // Calculating the value of the polynomial | |
870 | for (ind = 0; ind < Dimension; ind++) | |
871 | aRes[ind] = aRes[ind] * Par + aCoeffs[ind]; | |
872 | aCoeffs -= Dimension; | |
7fd59977 | 873 | } |
874 | } | |
875 | } | |
876 | } | |
877 | ||
878 | //======================================================================= | |
879 | //function : This evaluates a polynomial without derivative | |
880 | //purpose : | |
881 | //======================================================================= | |
882 | ||
883 | void PLib::NoDerivativeEvalPolynomial(const Standard_Real Par, | |
d721c8eb | 884 | const Standard_Integer Degree, |
885 | const Standard_Integer Dimension, | |
886 | const Standard_Integer DegreeDimension, | |
887 | Standard_Real& PolynomialCoeff, | |
888 | Standard_Real& Results) | |
7fd59977 | 889 | { |
d721c8eb | 890 | Standard_Real* aCoeffs = &PolynomialCoeff + DegreeDimension; |
891 | Standard_Real* aRes = &Results; | |
7fd59977 | 892 | |
d721c8eb | 893 | switch (Dimension) |
894 | { | |
895 | case 1: eval_poly0<1> (aRes, aCoeffs, Degree, Par); break; | |
896 | case 2: eval_poly0<2> (aRes, aCoeffs, Degree, Par); break; | |
897 | case 3: eval_poly0<3> (aRes, aCoeffs, Degree, Par); break; | |
898 | case 4: eval_poly0<4> (aRes, aCoeffs, Degree, Par); break; | |
899 | case 5: eval_poly0<5> (aRes, aCoeffs, Degree, Par); break; | |
900 | case 6: eval_poly0<6> (aRes, aCoeffs, Degree, Par); break; | |
901 | case 7: eval_poly0<7> (aRes, aCoeffs, Degree, Par); break; | |
902 | case 8: eval_poly0<8> (aRes, aCoeffs, Degree, Par); break; | |
903 | case 9: eval_poly0<9> (aRes, aCoeffs, Degree, Par); break; | |
904 | case 10: eval_poly0<10> (aRes, aCoeffs, Degree, Par); break; | |
905 | case 11: eval_poly0<11> (aRes, aCoeffs, Degree, Par); break; | |
906 | case 12: eval_poly0<12> (aRes, aCoeffs, Degree, Par); break; | |
907 | case 13: eval_poly0<13> (aRes, aCoeffs, Degree, Par); break; | |
908 | case 14: eval_poly0<14> (aRes, aCoeffs, Degree, Par); break; | |
909 | case 15: eval_poly0<15> (aRes, aCoeffs, Degree, Par); break; | |
910 | default: | |
911 | { | |
912 | memcpy(aRes, aCoeffs, sizeof(Standard_Real) * Dimension); | |
913 | for (Standard_Integer aDeg = 0; aDeg < Degree; aDeg++) | |
914 | { | |
915 | aCoeffs -= Dimension; | |
916 | for (Standard_Integer ind = 0; ind < Dimension; ind++) | |
917 | aRes[ind] = aRes[ind] * Par + aCoeffs[ind]; | |
7fd59977 | 918 | } |
919 | } | |
920 | } | |
921 | } | |
922 | ||
923 | //======================================================================= | |
924 | //function : This evaluates a polynomial of 2 variables | |
925 | //purpose : or its derivative at the requested orders | |
926 | //======================================================================= | |
927 | ||
928 | void PLib::EvalPoly2Var(const Standard_Real UParameter, | |
929 | const Standard_Real VParameter, | |
930 | const Standard_Integer UDerivativeRequest, | |
931 | const Standard_Integer VDerivativeRequest, | |
932 | const Standard_Integer UDegree, | |
933 | const Standard_Integer VDegree, | |
934 | const Standard_Integer Dimension, | |
935 | Standard_Real& PolynomialCoeff, | |
936 | Standard_Real& Results) | |
937 | // | |
938 | // the polynomial coefficients are assumed to be stored as follows : | |
939 | // 0 0 | |
940 | // [0] [Dimension -1] U V coefficient | |
941 | // 1 0 | |
942 | // [Dimension] [Dimension + Dimension -1] U V coefficient | |
943 | // 2 0 | |
944 | // [2 * Dimension] [2 * Dimension + Dimension-1] U V coefficient | |
945 | // | |
946 | // ................................................... | |
947 | // | |
948 | // | |
949 | // m 0 | |
950 | // [m * Dimension] [m * Dimension + Dimension-1] U V coefficient | |
951 | // | |
952 | // where m = UDegree | |
953 | // | |
954 | // 0 1 | |
955 | // [(m+1) * Dimension] [(m+1) * Dimension + Dimension-1] U V coefficient | |
956 | // | |
957 | // ................................................... | |
958 | // | |
959 | // m 1 | |
960 | // [2*m * Dimension] [2*m * Dimension + Dimension-1] U V coefficient | |
961 | // | |
962 | // ................................................... | |
963 | // | |
964 | // m n | |
965 | // [m*n * Dimension] [m*n * Dimension + Dimension-1] U V coefficient | |
966 | // | |
967 | // where n = VDegree | |
968 | { | |
969 | Standard_Integer Udim = (VDegree+1)*Dimension, | |
970 | index = Udim*UDerivativeRequest; | |
971 | TColStd_Array1OfReal Curve(1, Udim*(UDerivativeRequest+1)); | |
972 | TColStd_Array1OfReal Point(1, Dimension*(VDerivativeRequest+1)); | |
973 | Standard_Real * Result = (Standard_Real *) &Curve.ChangeValue(1); | |
974 | Standard_Real * Digit = (Standard_Real *) &Point.ChangeValue(1); | |
975 | Standard_Real * ResultArray ; | |
976 | ResultArray = &Results ; | |
977 | ||
978 | PLib::EvalPolynomial(UParameter, | |
979 | UDerivativeRequest, | |
980 | UDegree, | |
981 | Udim, | |
982 | PolynomialCoeff, | |
983 | Result[0]); | |
984 | ||
985 | PLib::EvalPolynomial(VParameter, | |
986 | VDerivativeRequest, | |
987 | VDegree, | |
988 | Dimension, | |
989 | Result[index], | |
990 | Digit[0]); | |
991 | ||
992 | index = Dimension*VDerivativeRequest; | |
993 | ||
994 | for (Standard_Integer i=0;i<Dimension;i++) { | |
995 | ResultArray[i] = Digit[index+i]; | |
996 | } | |
997 | } | |
998 | ||
999 | ||
7fd59977 | 1000 | |
1001 | //======================================================================= | |
1002 | //function : This evaluates the lagrange polynomial and its derivatives | |
1003 | //purpose : up to the requested order that interpolates a series of | |
1004 | //points of dimension <Dimension> with given assigned parameters | |
1005 | //======================================================================= | |
1006 | ||
1007 | Standard_Integer | |
1008 | PLib::EvalLagrange(const Standard_Real Parameter, | |
1009 | const Standard_Integer DerivativeRequest, | |
1010 | const Standard_Integer Degree, | |
1011 | const Standard_Integer Dimension, | |
1012 | Standard_Real& Values, | |
1013 | Standard_Real& Parameters, | |
1014 | Standard_Real& Results) | |
1015 | { | |
1016 | // | |
1017 | // the points are assumed to be stored as follows in the Values array : | |
1018 | // | |
1019 | // [0] [Dimension -1] first point coefficients | |
1020 | // | |
1021 | // [Dimension] [Dimension + Dimension -1] second point coefficients | |
1022 | // | |
1023 | // [2 * Dimension] [2 * Dimension + Dimension-1] third point coefficients | |
1024 | // | |
1025 | // ................................................... | |
1026 | // | |
1027 | // | |
1028 | // | |
1029 | // [d * Dimension] [d * Dimension + Dimension-1] d + 1 point coefficients | |
1030 | // | |
1031 | // where d is the Degree | |
1032 | // | |
1033 | // The ParameterArray stores the parameter value assign to each point in | |
1034 | // order described above, that is | |
1035 | // [0] is assign to first point | |
1036 | // [1] is assign to second point | |
1037 | // | |
1038 | Standard_Integer ii, jj, kk, Index, Index1, ReturnCode=0; | |
1039 | Standard_Integer local_request = DerivativeRequest; | |
1040 | Standard_Real *ParameterArray; | |
1041 | Standard_Real difference; | |
1042 | Standard_Real *PointsArray; | |
1043 | Standard_Real *ResultArray ; | |
1044 | ||
1045 | PointsArray = &Values ; | |
1046 | ParameterArray = &Parameters ; | |
1047 | ResultArray = &Results ; | |
1048 | if (local_request >= Degree) { | |
1049 | local_request = Degree ; | |
41194117 | 1050 | } |
f7b4312f | 1051 | NCollection_LocalArray<Standard_Real> divided_differences_array ((Degree + 1) * Dimension); |
7fd59977 | 1052 | // |
1053 | // Build the divided differences array | |
1054 | // | |
1055 | ||
1056 | for (ii = 0 ; ii < (Degree + 1) * Dimension ; ii++) { | |
1057 | divided_differences_array[ii] = PointsArray[ii] ; | |
1058 | } | |
1059 | ||
1060 | for (ii = Degree ; ii >= 0 ; ii--) { | |
1061 | ||
1062 | for (jj = Degree ; jj > Degree - ii ; jj--) { | |
1063 | Index = jj * Dimension ; | |
1064 | Index1 = Index - Dimension ; | |
1065 | ||
1066 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1067 | divided_differences_array[Index + kk] -= | |
1068 | divided_differences_array[Index1 + kk] ; | |
1069 | } | |
1070 | difference = | |
1071 | ParameterArray[jj] - ParameterArray[jj - Degree -1 + ii] ; | |
1072 | if (Abs(difference) < RealSmall()) { | |
1073 | ReturnCode = 1 ; | |
1074 | goto FINISH ; | |
1075 | } | |
1076 | difference = 1.0e0 / difference ; | |
1077 | ||
1078 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1079 | divided_differences_array[Index + kk] *= difference ; | |
1080 | } | |
1081 | } | |
1082 | } | |
1083 | // | |
1084 | // | |
1085 | // Evaluate the divided difference array polynomial which expresses as | |
1086 | // | |
1087 | // P(t) = [t1] P + (t - t1) [t1,t2] P + (t - t1)(t - t2)[t1,t2,t3] P + ... | |
1088 | // + (t - t1)(t - t2)(t - t3)...(t - td) [t1,t2,...,td+1] P | |
1089 | // | |
1090 | // The ith slot in the divided_differences_array is [t1,t2,...,ti+1] | |
1091 | // | |
1092 | // | |
1093 | Index = Degree * Dimension ; | |
1094 | ||
1095 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1096 | ResultArray[kk] = divided_differences_array[Index + kk] ; | |
1097 | } | |
1098 | ||
1099 | for (ii = Dimension ; ii < (local_request + 1) * Dimension ; ii++) { | |
1100 | ResultArray[ii] = 0.0e0 ; | |
1101 | } | |
1102 | ||
1103 | for (ii = Degree ; ii >= 1 ; ii--) { | |
1104 | difference = Parameter - ParameterArray[ii - 1] ; | |
1105 | ||
1106 | for (jj = local_request ; jj > 0 ; jj--) { | |
1107 | Index = jj * Dimension ; | |
1108 | Index1 = Index - Dimension ; | |
1109 | ||
1110 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1111 | ResultArray[Index + kk] *= difference ; | |
1112 | ResultArray[Index + kk] += ResultArray[Index1+kk]*(Standard_Real) jj ; | |
1113 | } | |
1114 | } | |
1115 | Index = (ii -1) * Dimension ; | |
1116 | ||
1117 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1118 | ResultArray[kk] *= difference ; | |
1119 | ResultArray[kk] += divided_differences_array[Index+kk] ; | |
1120 | } | |
1121 | } | |
1122 | FINISH : | |
1123 | return (ReturnCode) ; | |
1124 | } | |
1125 | ||
1126 | //======================================================================= | |
1127 | //function : This evaluates the hermite polynomial and its derivatives | |
1128 | //purpose : up to the requested order that interpolates a series of | |
1129 | //points of dimension <Dimension> with given assigned parameters | |
1130 | //======================================================================= | |
1131 | ||
1132 | Standard_Integer PLib::EvalCubicHermite | |
1133 | (const Standard_Real Parameter, | |
1134 | const Standard_Integer DerivativeRequest, | |
1135 | const Standard_Integer Dimension, | |
1136 | Standard_Real& Values, | |
1137 | Standard_Real& Derivatives, | |
1138 | Standard_Real& theParameters, | |
1139 | Standard_Real& Results) | |
1140 | { | |
1141 | // | |
1142 | // the points are assumed to be stored as follows in the Values array : | |
1143 | // | |
1144 | // [0] [Dimension -1] first point coefficients | |
1145 | // | |
1146 | // [Dimension] [Dimension + Dimension -1] last point coefficients | |
1147 | // | |
1148 | // | |
1149 | // the derivatives are assumed to be stored as follows in | |
1150 | // the Derivatives array : | |
1151 | // | |
1152 | // [0] [Dimension -1] first point coefficients | |
1153 | // | |
1154 | // [Dimension] [Dimension + Dimension -1] last point coefficients | |
1155 | // | |
1156 | // The ParameterArray stores the parameter value assign to each point in | |
1157 | // order described above, that is | |
1158 | // [0] is assign to first point | |
1159 | // [1] is assign to last point | |
1160 | // | |
1161 | Standard_Integer ii, jj, kk, pp, Index, Index1, Degree, ReturnCode; | |
1162 | Standard_Integer local_request = DerivativeRequest ; | |
1163 | ||
1164 | ReturnCode = 0 ; | |
1165 | Degree = 3 ; | |
1166 | Standard_Real ParametersArray[4]; | |
1167 | Standard_Real difference; | |
1168 | Standard_Real inverse; | |
1169 | Standard_Real *FirstLast; | |
1170 | Standard_Real *PointsArray; | |
1171 | Standard_Real *DerivativesArray; | |
1172 | Standard_Real *ResultArray ; | |
1173 | ||
1174 | DerivativesArray = &Derivatives ; | |
1175 | PointsArray = &Values ; | |
1176 | FirstLast = &theParameters ; | |
1177 | ResultArray = &Results ; | |
1178 | if (local_request >= Degree) { | |
1179 | local_request = Degree ; | |
1180 | } | |
f7b4312f | 1181 | NCollection_LocalArray<Standard_Real> divided_differences_array ((Degree + 1) * Dimension); |
7fd59977 | 1182 | |
1183 | for (ii = 0, jj = 0 ; ii < 2 ; ii++, jj+= 2) { | |
1184 | ParametersArray[jj] = | |
1185 | ParametersArray[jj+1] = FirstLast[ii] ; | |
1186 | } | |
1187 | // | |
1188 | // Build the divided differences array | |
1189 | // | |
1190 | // | |
1191 | // initialise it at the stage 2 of the building algorithm | |
1192 | // for devided differences | |
1193 | // | |
1194 | inverse = FirstLast[1] - FirstLast[0] ; | |
1195 | inverse = 1.0e0 / inverse ; | |
1196 | ||
1197 | for (ii = 0, jj = Dimension, kk = 2 * Dimension, pp = 3 * Dimension ; | |
1198 | ii < Dimension ; | |
1199 | ii++, jj++, kk++, pp++) { | |
1200 | divided_differences_array[ii] = PointsArray[ii] ; | |
1201 | divided_differences_array[kk] = inverse * | |
1202 | (PointsArray[jj] - PointsArray[ii]) ; | |
1203 | divided_differences_array[jj] = DerivativesArray[ii] ; | |
1204 | divided_differences_array[pp] = DerivativesArray[jj] ; | |
1205 | } | |
1206 | ||
1207 | for (ii = 1 ; ii <= Degree ; ii++) { | |
1208 | ||
1209 | for (jj = Degree ; jj >= ii+1 ; jj--) { | |
1210 | Index = jj * Dimension ; | |
1211 | Index1 = Index - Dimension ; | |
1212 | ||
1213 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1214 | divided_differences_array[Index + kk] -= | |
1215 | divided_differences_array[Index1 + kk] ; | |
1216 | } | |
1217 | ||
1218 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1219 | divided_differences_array[Index + kk] *= inverse ; | |
1220 | } | |
1221 | } | |
1222 | } | |
1223 | // | |
1224 | // | |
1225 | // Evaluate the divided difference array polynomial which expresses as | |
1226 | // | |
1227 | // P(t) = [t1] P + (t - t1) [t1,t2] P + (t - t1)(t - t2)[t1,t2,t3] P + ... | |
1228 | // + (t - t1)(t - t2)(t - t3)...(t - td) [t1,t2,...,td+1] P | |
1229 | // | |
1230 | // The ith slot in the divided_differences_array is [t1,t2,...,ti+1] | |
1231 | // | |
1232 | // | |
1233 | Index = Degree * Dimension ; | |
1234 | ||
1235 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1236 | ResultArray[kk] = divided_differences_array[Index + kk] ; | |
1237 | } | |
1238 | ||
1239 | for (ii = Dimension ; ii < (local_request + 1) * Dimension ; ii++) { | |
1240 | ResultArray[ii] = 0.0e0 ; | |
1241 | } | |
1242 | ||
1243 | for (ii = Degree ; ii >= 1 ; ii--) { | |
1244 | difference = Parameter - ParametersArray[ii - 1] ; | |
1245 | ||
1246 | for (jj = local_request ; jj > 0 ; jj--) { | |
1247 | Index = jj * Dimension ; | |
1248 | Index1 = Index - Dimension ; | |
1249 | ||
1250 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1251 | ResultArray[Index + kk] *= difference ; | |
1252 | ResultArray[Index + kk] += ResultArray[Index1+kk]*(Standard_Real) jj; | |
1253 | } | |
1254 | } | |
1255 | Index = (ii -1) * Dimension ; | |
1256 | ||
1257 | for (kk = 0 ; kk < Dimension ; kk++) { | |
1258 | ResultArray[kk] *= difference ; | |
1259 | ResultArray[kk] += divided_differences_array[Index+kk] ; | |
1260 | } | |
1261 | } | |
1262 | // FINISH : | |
1263 | return (ReturnCode) ; | |
1264 | } | |
1265 | ||
1266 | //======================================================================= | |
1267 | //function : HermiteCoefficients | |
1268 | //purpose : calcul des polynomes d'Hermite | |
1269 | //======================================================================= | |
1270 | ||
1271 | Standard_Boolean PLib::HermiteCoefficients(const Standard_Real FirstParameter, | |
1272 | const Standard_Real LastParameter, | |
1273 | const Standard_Integer FirstOrder, | |
1274 | const Standard_Integer LastOrder, | |
1275 | math_Matrix& MatrixCoefs) | |
1276 | { | |
1277 | Standard_Integer NbCoeff = FirstOrder + LastOrder + 2, Ordre[2]; | |
1278 | Standard_Integer ii, jj, pp, cote, iof=0; | |
1279 | Standard_Real Prod, TBorne = FirstParameter; | |
1280 | math_Vector Coeff(1,NbCoeff), B(1, NbCoeff, 0.0); | |
1281 | math_Matrix MAT(1,NbCoeff, 1,NbCoeff, 0.0); | |
1282 | ||
1283 | // Test de validites | |
1284 | ||
1285 | if ((FirstOrder < 0) || (LastOrder < 0)) return Standard_False; | |
1286 | Standard_Real D1 = fabs(FirstParameter), D2 = fabs(LastParameter); | |
1287 | if (D1 > 100 || D2 > 100) return Standard_False; | |
1288 | D2 += D1; | |
1289 | if (D2 < 0.01) return Standard_False; | |
1290 | if (fabs(LastParameter - FirstParameter) / D2 < 0.01) return Standard_False; | |
1291 | ||
1292 | // Calcul de la matrice a inverser (MAT) | |
1293 | ||
1294 | Ordre[0] = FirstOrder+1; | |
1295 | Ordre[1] = LastOrder+1; | |
1296 | ||
1297 | for (cote=0; cote<=1; cote++) { | |
1298 | Coeff.Init(1); | |
1299 | ||
1300 | for (pp=1; pp<=Ordre[cote]; pp++) { | |
1301 | ii = pp + iof; | |
1302 | Prod = 1; | |
1303 | ||
1304 | for (jj=pp; jj<=NbCoeff; jj++) { | |
1305 | // tout se passe dans les 3 lignes suivantes | |
1306 | MAT(ii, jj) = Coeff(jj) * Prod; | |
1307 | Coeff(jj) *= jj - pp; | |
1308 | Prod *= TBorne; | |
1309 | } | |
1310 | } | |
1311 | TBorne = LastParameter; | |
1312 | iof = Ordre[0]; | |
1313 | } | |
1314 | ||
1315 | // resolution du systemes | |
1316 | math_Gauss ResolCoeff(MAT, 1.0e-10); | |
1317 | if (!ResolCoeff.IsDone()) return Standard_False; | |
1318 | ||
1319 | for (ii=1; ii<=NbCoeff; ii++) { | |
1320 | B(ii) = 1; | |
1321 | ResolCoeff.Solve(B, Coeff); | |
1322 | MatrixCoefs.SetRow( ii, Coeff); | |
1323 | B(ii) = 0; | |
1324 | } | |
1325 | return Standard_True; | |
1326 | } | |
1327 | ||
1328 | //======================================================================= | |
1329 | //function : CoefficientsPoles | |
1330 | //purpose : | |
1331 | //======================================================================= | |
1332 | ||
1333 | void PLib::CoefficientsPoles (const TColgp_Array1OfPnt& Coefs, | |
0e14656b | 1334 | const TColStd_Array1OfReal* WCoefs, |
7fd59977 | 1335 | TColgp_Array1OfPnt& Poles, |
0e14656b | 1336 | TColStd_Array1OfReal* Weights) |
7fd59977 | 1337 | { |
1338 | TColStd_Array1OfReal tempC(1,3*Coefs.Length()); | |
1339 | PLib::SetPoles(Coefs,tempC); | |
1340 | TColStd_Array1OfReal tempP(1,3*Poles.Length()); | |
1341 | PLib::SetPoles(Coefs,tempP); | |
1342 | PLib::CoefficientsPoles(3,tempC,WCoefs,tempP,Weights); | |
1343 | PLib::GetPoles(tempP,Poles); | |
1344 | } | |
1345 | ||
1346 | //======================================================================= | |
1347 | //function : CoefficientsPoles | |
1348 | //purpose : | |
1349 | //======================================================================= | |
1350 | ||
1351 | void PLib::CoefficientsPoles (const TColgp_Array1OfPnt2d& Coefs, | |
0e14656b | 1352 | const TColStd_Array1OfReal* WCoefs, |
7fd59977 | 1353 | TColgp_Array1OfPnt2d& Poles, |
0e14656b | 1354 | TColStd_Array1OfReal* Weights) |
7fd59977 | 1355 | { |
1356 | TColStd_Array1OfReal tempC(1,2*Coefs.Length()); | |
1357 | PLib::SetPoles(Coefs,tempC); | |
1358 | TColStd_Array1OfReal tempP(1,2*Poles.Length()); | |
1359 | PLib::SetPoles(Coefs,tempP); | |
1360 | PLib::CoefficientsPoles(2,tempC,WCoefs,tempP,Weights); | |
1361 | PLib::GetPoles(tempP,Poles); | |
1362 | } | |
1363 | ||
1364 | //======================================================================= | |
1365 | //function : CoefficientsPoles | |
1366 | //purpose : | |
1367 | //======================================================================= | |
1368 | ||
1369 | void PLib::CoefficientsPoles (const TColStd_Array1OfReal& Coefs, | |
0e14656b | 1370 | const TColStd_Array1OfReal* WCoefs, |
7fd59977 | 1371 | TColStd_Array1OfReal& Poles, |
0e14656b | 1372 | TColStd_Array1OfReal* Weights) |
7fd59977 | 1373 | { |
1374 | PLib::CoefficientsPoles(1,Coefs,WCoefs,Poles,Weights); | |
1375 | } | |
1376 | ||
1377 | //======================================================================= | |
1378 | //function : CoefficientsPoles | |
1379 | //purpose : | |
1380 | //======================================================================= | |
1381 | ||
1382 | void PLib::CoefficientsPoles (const Standard_Integer dim, | |
1383 | const TColStd_Array1OfReal& Coefs, | |
0e14656b | 1384 | const TColStd_Array1OfReal* WCoefs, |
7fd59977 | 1385 | TColStd_Array1OfReal& Poles, |
0e14656b | 1386 | TColStd_Array1OfReal* Weights) |
7fd59977 | 1387 | { |
0e14656b | 1388 | Standard_Boolean rat = WCoefs != NULL; |
7fd59977 | 1389 | Standard_Integer loc = Coefs.Lower(); |
1390 | Standard_Integer lop = Poles.Lower(); | |
1391 | Standard_Integer lowc=0; | |
1392 | Standard_Integer lowp=0; | |
1393 | Standard_Integer upc = Coefs.Upper(); | |
1394 | Standard_Integer upp = Poles.Upper(); | |
1395 | Standard_Integer upwc=0; | |
1396 | Standard_Integer upwp=0; | |
1397 | Standard_Integer reflen = Coefs.Length()/dim; | |
1398 | Standard_Integer i,j,k; | |
1399 | //Les Extremites. | |
1400 | if (rat) { | |
0e14656b | 1401 | lowc = WCoefs->Lower(); lowp = Weights->Lower(); |
1402 | upwc = WCoefs->Upper(); upwp = Weights->Upper(); | |
7fd59977 | 1403 | } |
1404 | ||
1405 | for (i = 0; i < dim; i++){ | |
1406 | Poles (lop + i) = Coefs (loc + i); | |
1407 | Poles (upp - i) = Coefs (upc - i); | |
1408 | } | |
1409 | if (rat) { | |
0e14656b | 1410 | (*Weights) (lowp) = (*WCoefs) (lowc); |
1411 | (*Weights) (upwp) = (*WCoefs) (upwc); | |
7fd59977 | 1412 | } |
1413 | ||
1414 | Standard_Real Cnp; | |
7fd59977 | 1415 | for (i = 2; i < reflen; i++ ) { |
1416 | Cnp = PLib::Bin(reflen - 1, i - 1); | |
0e14656b | 1417 | if (rat) (*Weights)(lowp + i - 1) = (*WCoefs)(lowc + i - 1) / Cnp; |
7fd59977 | 1418 | |
1419 | for(j = 0; j < dim; j++){ | |
1420 | Poles(lop + dim * (i-1) + j)= Coefs(loc + dim * (i-1) + j) / Cnp; | |
1421 | } | |
1422 | } | |
1423 | ||
1424 | for (i = 1; i <= reflen - 1; i++) { | |
1425 | ||
1426 | for (j = reflen - 1; j >= i; j--) { | |
0e14656b | 1427 | if (rat) (*Weights)(lowp + j) += (*Weights)(lowp + j - 1); |
7fd59977 | 1428 | |
1429 | for(k = 0; k < dim; k++){ | |
1430 | Poles(lop + dim * j + k) += Poles(lop + dim * (j - 1) + k); | |
1431 | } | |
1432 | } | |
1433 | } | |
1434 | if (rat) { | |
1435 | ||
1436 | for (i = 1; i <= reflen; i++) { | |
1437 | ||
1438 | for(j = 0; j < dim; j++){ | |
0e14656b | 1439 | Poles(lop + dim * (i-1) + j) /= (*Weights)(lowp + i -1); |
7fd59977 | 1440 | } |
1441 | } | |
1442 | } | |
1443 | } | |
1444 | ||
1445 | //======================================================================= | |
1446 | //function : Trimming | |
1447 | //purpose : | |
1448 | //======================================================================= | |
1449 | ||
1450 | void PLib::Trimming(const Standard_Real U1, | |
1451 | const Standard_Real U2, | |
1452 | TColgp_Array1OfPnt& Coefs, | |
0e14656b | 1453 | TColStd_Array1OfReal* WCoefs) |
7fd59977 | 1454 | { |
1455 | TColStd_Array1OfReal temp(1,3*Coefs.Length()); | |
1456 | PLib::SetPoles(Coefs,temp); | |
1457 | PLib::Trimming(U1,U2,3,temp,WCoefs); | |
1458 | PLib::GetPoles(temp,Coefs); | |
1459 | } | |
1460 | ||
1461 | //======================================================================= | |
1462 | //function : Trimming | |
1463 | //purpose : | |
1464 | //======================================================================= | |
1465 | ||
1466 | void PLib::Trimming(const Standard_Real U1, | |
1467 | const Standard_Real U2, | |
1468 | TColgp_Array1OfPnt2d& Coefs, | |
0e14656b | 1469 | TColStd_Array1OfReal* WCoefs) |
7fd59977 | 1470 | { |
1471 | TColStd_Array1OfReal temp(1,2*Coefs.Length()); | |
1472 | PLib::SetPoles(Coefs,temp); | |
1473 | PLib::Trimming(U1,U2,2,temp,WCoefs); | |
1474 | PLib::GetPoles(temp,Coefs); | |
1475 | } | |
1476 | ||
1477 | //======================================================================= | |
1478 | //function : Trimming | |
1479 | //purpose : | |
1480 | //======================================================================= | |
1481 | ||
1482 | void PLib::Trimming(const Standard_Real U1, | |
1483 | const Standard_Real U2, | |
1484 | TColStd_Array1OfReal& Coefs, | |
0e14656b | 1485 | TColStd_Array1OfReal* WCoefs) |
7fd59977 | 1486 | { |
1487 | PLib::Trimming(U1,U2,1,Coefs,WCoefs); | |
1488 | } | |
1489 | ||
1490 | //======================================================================= | |
1491 | //function : Trimming | |
1492 | //purpose : | |
1493 | //======================================================================= | |
1494 | ||
1495 | void PLib::Trimming(const Standard_Real U1, | |
1496 | const Standard_Real U2, | |
1497 | const Standard_Integer dim, | |
1498 | TColStd_Array1OfReal& Coefs, | |
0e14656b | 1499 | TColStd_Array1OfReal* WCoefs) |
7fd59977 | 1500 | { |
1501 | ||
1502 | // principe : | |
1503 | // on fait le changement de variable v = (u-U1) / (U2-U1) | |
1504 | // on exprime u = f(v) que l'on remplace dans l'expression polynomiale | |
1505 | // decomposee sous la forme du schema iteratif de horner. | |
1506 | ||
1507 | Standard_Real lsp = U2 - U1; | |
1508 | Standard_Integer indc, indw=0; | |
1509 | Standard_Integer upc = Coefs.Upper() - dim + 1, upw=0; | |
1510 | Standard_Integer len = Coefs.Length()/dim; | |
0e14656b | 1511 | Standard_Boolean rat = WCoefs != NULL; |
7fd59977 | 1512 | |
1513 | if (rat) { | |
0e14656b | 1514 | if(len != WCoefs->Length()) |
9775fa61 | 1515 | throw Standard_Failure("PLib::Trimming : nbcoefs/dim != nbweights !!!"); |
0e14656b | 1516 | upw = WCoefs->Upper(); |
7fd59977 | 1517 | } |
1518 | len --; | |
1519 | ||
1520 | for (Standard_Integer i = 1; i <= len; i++) { | |
1521 | Standard_Integer j ; | |
1522 | indc = upc - dim*(i-1); | |
1523 | if (rat) indw = upw - i + 1; | |
1524 | //calcul du coefficient de degre le plus faible a l'iteration i | |
1525 | ||
1526 | for( j = 0; j < dim; j++){ | |
1527 | Coefs(indc - dim + j) += U1 * Coefs(indc + j); | |
1528 | } | |
0e14656b | 1529 | if (rat) (*WCoefs)(indw - 1) += U1 * (*WCoefs)(indw); |
7fd59977 | 1530 | |
1531 | //calcul des coefficients intermediaires : | |
1532 | ||
1533 | while (indc < upc){ | |
1534 | indc += dim; | |
1535 | ||
1536 | for(Standard_Integer k = 0; k < dim; k++){ | |
1537 | Coefs(indc - dim + k) = | |
1538 | U1 * Coefs(indc + k) + lsp * Coefs(indc - dim + k); | |
1539 | } | |
1540 | if (rat) { | |
1541 | indw ++; | |
0e14656b | 1542 | (*WCoefs)(indw - 1) = U1 * (*WCoefs)(indw) + lsp * (*WCoefs)(indw - 1); |
7fd59977 | 1543 | } |
1544 | } | |
1545 | ||
1546 | //calcul du coefficient de degre le plus eleve : | |
1547 | ||
1548 | for(j = 0; j < dim; j++){ | |
1549 | Coefs(upc + j) *= lsp; | |
1550 | } | |
0e14656b | 1551 | if (rat) (*WCoefs)(upw) *= lsp; |
7fd59977 | 1552 | } |
1553 | } | |
1554 | ||
1555 | //======================================================================= | |
1556 | //function : CoefficientsPoles | |
1557 | //purpose : | |
1558 | // Modified: 21/10/1996 by PMN : PolesCoefficient (PRO5852). | |
1559 | // on ne bidouille plus les u et v c'est a l'appelant de savoir ce qu'il | |
1560 | // fait avec BuildCache ou plus simplement d'utiliser PolesCoefficients | |
1561 | //======================================================================= | |
1562 | ||
1563 | void PLib::CoefficientsPoles (const TColgp_Array2OfPnt& Coefs, | |
0e14656b | 1564 | const TColStd_Array2OfReal* WCoefs, |
7fd59977 | 1565 | TColgp_Array2OfPnt& Poles, |
0e14656b | 1566 | TColStd_Array2OfReal* Weights) |
7fd59977 | 1567 | { |
0e14656b | 1568 | Standard_Boolean rat = (WCoefs != NULL); |
7fd59977 | 1569 | Standard_Integer LowerRow = Poles.LowerRow(); |
1570 | Standard_Integer UpperRow = Poles.UpperRow(); | |
1571 | Standard_Integer LowerCol = Poles.LowerCol(); | |
1572 | Standard_Integer UpperCol = Poles.UpperCol(); | |
1573 | Standard_Integer ColLength = Poles.ColLength(); | |
1574 | Standard_Integer RowLength = Poles.RowLength(); | |
1575 | ||
1576 | // Bidouille pour retablir u et v pour les coefs calcules | |
1577 | // par buildcache | |
1578 | // Standard_Boolean inv = Standard_False; //ColLength != Coefs.ColLength(); | |
1579 | ||
1580 | Standard_Integer Row, Col; | |
1581 | Standard_Real W, Cnp; | |
1582 | ||
1583 | Standard_Integer I1, I2; | |
1584 | Standard_Integer NPoleu , NPolev; | |
1585 | gp_XYZ Temp; | |
7fd59977 | 1586 | |
1587 | for (NPoleu = LowerRow; NPoleu <= UpperRow; NPoleu++){ | |
1588 | Poles (NPoleu, LowerCol) = Coefs (NPoleu, LowerCol); | |
1589 | if (rat) { | |
0e14656b | 1590 | (*Weights) (NPoleu, LowerCol) = (*WCoefs) (NPoleu, LowerCol); |
7fd59977 | 1591 | } |
1592 | ||
1593 | for (Col = LowerCol + 1; Col <= UpperCol - 1; Col++) { | |
1594 | Cnp = PLib::Bin(RowLength - 1,Col - LowerCol); | |
1595 | Temp = Coefs (NPoleu, Col).XYZ(); | |
1596 | Temp.Divide (Cnp); | |
1597 | Poles (NPoleu, Col).SetXYZ (Temp); | |
1598 | if (rat) { | |
0e14656b | 1599 | (*Weights) (NPoleu, Col) = (*WCoefs) (NPoleu, Col) / Cnp; |
7fd59977 | 1600 | } |
1601 | } | |
1602 | Poles (NPoleu, UpperCol) = Coefs (NPoleu, UpperCol); | |
1603 | if (rat) { | |
0e14656b | 1604 | (*Weights) (NPoleu, UpperCol) = (*WCoefs) (NPoleu, UpperCol); |
7fd59977 | 1605 | } |
1606 | ||
1607 | for (I1 = 1; I1 <= RowLength - 1; I1++) { | |
1608 | ||
1609 | for (I2 = UpperCol; I2 >= LowerCol + I1; I2--) { | |
1610 | Temp.SetLinearForm | |
1611 | (Poles (NPoleu, I2).XYZ(), Poles (NPoleu, I2-1).XYZ()); | |
1612 | Poles (NPoleu, I2).SetXYZ (Temp); | |
0e14656b | 1613 | if (rat) (*Weights)(NPoleu, I2) += (*Weights)(NPoleu, I2-1); |
7fd59977 | 1614 | } |
1615 | } | |
1616 | } | |
7fd59977 | 1617 | |
1618 | for (NPolev = LowerCol; NPolev <= UpperCol; NPolev++){ | |
1619 | ||
1620 | for (Row = LowerRow + 1; Row <= UpperRow - 1; Row++) { | |
1621 | Cnp = PLib::Bin(ColLength - 1,Row - LowerRow); | |
1622 | Temp = Poles (Row, NPolev).XYZ(); | |
1623 | Temp.Divide (Cnp); | |
1624 | Poles (Row, NPolev).SetXYZ (Temp); | |
0e14656b | 1625 | if (rat) (*Weights)(Row, NPolev) /= Cnp; |
7fd59977 | 1626 | } |
1627 | ||
1628 | for (I1 = 1; I1 <= ColLength - 1; I1++) { | |
1629 | ||
1630 | for (I2 = UpperRow; I2 >= LowerRow + I1; I2--) { | |
1631 | Temp.SetLinearForm | |
1632 | (Poles (I2, NPolev).XYZ(), Poles (I2-1, NPolev).XYZ()); | |
1633 | Poles (I2, NPolev).SetXYZ (Temp); | |
0e14656b | 1634 | if (rat) (*Weights)(I2, NPolev) += (*Weights)(I2-1, NPolev); |
7fd59977 | 1635 | } |
1636 | } | |
1637 | } | |
1638 | if (rat) { | |
1639 | ||
1640 | for (Row = LowerRow; Row <= UpperRow; Row++) { | |
1641 | ||
1642 | for (Col = LowerCol; Col <= UpperCol; Col++) { | |
0e14656b | 1643 | W = (*Weights) (Row, Col); |
7fd59977 | 1644 | Temp = Poles(Row, Col).XYZ(); |
1645 | Temp.Divide (W); | |
1646 | Poles(Row, Col).SetXYZ (Temp); | |
1647 | } | |
1648 | } | |
1649 | } | |
1650 | } | |
1651 | ||
1652 | //======================================================================= | |
1653 | //function : UTrimming | |
1654 | //purpose : | |
1655 | //======================================================================= | |
1656 | ||
1657 | void PLib::UTrimming(const Standard_Real U1, | |
1658 | const Standard_Real U2, | |
1659 | TColgp_Array2OfPnt& Coeffs, | |
0e14656b | 1660 | TColStd_Array2OfReal* WCoeffs) |
7fd59977 | 1661 | { |
0e14656b | 1662 | Standard_Boolean rat = WCoeffs != NULL; |
7fd59977 | 1663 | Standard_Integer lr = Coeffs.LowerRow(); |
1664 | Standard_Integer ur = Coeffs.UpperRow(); | |
1665 | Standard_Integer lc = Coeffs.LowerCol(); | |
1666 | Standard_Integer uc = Coeffs.UpperCol(); | |
1667 | TColgp_Array1OfPnt Temp (lr,ur); | |
1668 | TColStd_Array1OfReal Temw (lr,ur); | |
1669 | ||
1670 | for (Standard_Integer icol = lc; icol <= uc; icol++) { | |
1671 | Standard_Integer irow ; | |
1672 | for ( irow = lr; irow <= ur; irow++) { | |
1673 | Temp (irow) = Coeffs (irow, icol); | |
0e14656b | 1674 | if (rat) Temw (irow) = (*WCoeffs) (irow, icol); |
7fd59977 | 1675 | } |
0e14656b | 1676 | if (rat) PLib::Trimming (U1, U2, Temp, &Temw); |
7fd59977 | 1677 | else PLib::Trimming (U1, U2, Temp, PLib::NoWeights()); |
1678 | ||
1679 | for (irow = lr; irow <= ur; irow++) { | |
1680 | Coeffs (irow, icol) = Temp (irow); | |
0e14656b | 1681 | if (rat) (*WCoeffs) (irow, icol) = Temw (irow); |
7fd59977 | 1682 | } |
1683 | } | |
1684 | } | |
1685 | ||
1686 | //======================================================================= | |
1687 | //function : VTrimming | |
1688 | //purpose : | |
1689 | //======================================================================= | |
1690 | ||
1691 | void PLib::VTrimming(const Standard_Real V1, | |
1692 | const Standard_Real V2, | |
1693 | TColgp_Array2OfPnt& Coeffs, | |
0e14656b | 1694 | TColStd_Array2OfReal* WCoeffs) |
7fd59977 | 1695 | { |
0e14656b | 1696 | Standard_Boolean rat = WCoeffs != NULL; |
7fd59977 | 1697 | Standard_Integer lr = Coeffs.LowerRow(); |
1698 | Standard_Integer ur = Coeffs.UpperRow(); | |
1699 | Standard_Integer lc = Coeffs.LowerCol(); | |
1700 | Standard_Integer uc = Coeffs.UpperCol(); | |
1701 | TColgp_Array1OfPnt Temp (lc,uc); | |
1702 | TColStd_Array1OfReal Temw (lc,uc); | |
1703 | ||
1704 | for (Standard_Integer irow = lr; irow <= ur; irow++) { | |
1705 | Standard_Integer icol ; | |
1706 | for ( icol = lc; icol <= uc; icol++) { | |
1707 | Temp (icol) = Coeffs (irow, icol); | |
0e14656b | 1708 | if (rat) Temw (icol) = (*WCoeffs) (irow, icol); |
7fd59977 | 1709 | } |
0e14656b | 1710 | if (rat) PLib::Trimming (V1, V2, Temp, &Temw); |
7fd59977 | 1711 | else PLib::Trimming (V1, V2, Temp, PLib::NoWeights()); |
1712 | ||
1713 | for (icol = lc; icol <= uc; icol++) { | |
1714 | Coeffs (irow, icol) = Temp (icol); | |
0e14656b | 1715 | if (rat) (*WCoeffs) (irow, icol) = Temw (icol); |
7fd59977 | 1716 | } |
1717 | } | |
1718 | } | |
1719 | ||
1720 | //======================================================================= | |
1721 | //function : HermiteInterpolate | |
1722 | //purpose : | |
1723 | //======================================================================= | |
1724 | ||
1725 | Standard_Boolean PLib::HermiteInterpolate | |
1726 | (const Standard_Integer Dimension, | |
1727 | const Standard_Real FirstParameter, | |
1728 | const Standard_Real LastParameter, | |
1729 | const Standard_Integer FirstOrder, | |
1730 | const Standard_Integer LastOrder, | |
1731 | const TColStd_Array2OfReal& FirstConstr, | |
1732 | const TColStd_Array2OfReal& LastConstr, | |
1733 | TColStd_Array1OfReal& Coefficients) | |
1734 | { | |
1735 | Standard_Real Pattern[3][6]; | |
1736 | ||
1737 | // portage HP : il faut les initialiser 1 par 1 | |
1738 | ||
1739 | Pattern[0][0] = 1; | |
1740 | Pattern[0][1] = 1; | |
1741 | Pattern[0][2] = 1; | |
1742 | Pattern[0][3] = 1; | |
1743 | Pattern[0][4] = 1; | |
1744 | Pattern[0][5] = 1; | |
1745 | Pattern[1][0] = 0; | |
1746 | Pattern[1][1] = 1; | |
1747 | Pattern[1][2] = 2; | |
1748 | Pattern[1][3] = 3; | |
1749 | Pattern[1][4] = 4; | |
1750 | Pattern[1][5] = 5; | |
1751 | Pattern[2][0] = 0; | |
1752 | Pattern[2][1] = 0; | |
1753 | Pattern[2][2] = 2; | |
1754 | Pattern[2][3] = 6; | |
1755 | Pattern[2][4] = 12; | |
1756 | Pattern[2][5] = 20; | |
1757 | ||
1758 | math_Matrix A(0,FirstOrder+LastOrder+1, 0,FirstOrder+LastOrder+1); | |
1759 | // The initialisation of the matrix A | |
1760 | Standard_Integer irow ; | |
1761 | for ( irow=0; irow<=FirstOrder; irow++) { | |
1762 | Standard_Real FirstVal = 1.; | |
1763 | ||
1764 | for (Standard_Integer icol=0; icol<=FirstOrder+LastOrder+1; icol++) { | |
1765 | A(irow,icol) = Pattern[irow][icol]*FirstVal; | |
1766 | if (irow <= icol) FirstVal *= FirstParameter; | |
1767 | } | |
1768 | } | |
1769 | ||
1770 | for (irow=0; irow<=LastOrder; irow++) { | |
1771 | Standard_Real LastVal = 1.; | |
1772 | ||
1773 | for (Standard_Integer icol=0; icol<=FirstOrder+LastOrder+1; icol++) { | |
1774 | A(irow+FirstOrder+1,icol) = Pattern[irow][icol]*LastVal; | |
1775 | if (irow <= icol) LastVal *= LastParameter; | |
1776 | } | |
1777 | } | |
1778 | // | |
1779 | // The filled matrix A for FirstOrder=LastOrder=2 is: | |
1780 | // | |
1781 | // 1 FP FP**2 FP**3 FP**4 FP**5 | |
1782 | // 0 1 2*FP 3*FP**2 4*FP**3 5*FP**4 FP - FirstParameter | |
1783 | // 0 0 2 6*FP 12*FP**2 20*FP**3 | |
1784 | // 1 LP LP**2 LP**3 LP**4 LP**5 | |
1785 | // 0 1 2*LP 3*LP**2 4*LP**3 5*LP**4 LP - LastParameter | |
1786 | // 0 0 2 6*LP 12*LP**2 20*LP**3 | |
1787 | // | |
1788 | // If FirstOrder or LastOrder <=2 then some rows and columns are missing. | |
1789 | // For example: | |
1790 | // If FirstOrder=1 then 3th row and 6th column are missing | |
1791 | // If FirstOrder=LastOrder=0 then 2,3,5,6th rows and 3,4,5,6th columns are missing | |
1792 | ||
1793 | math_Gauss Equations(A); | |
04232180 | 1794 | // std::cout << "A=" << A << std::endl; |
7fd59977 | 1795 | |
1796 | for (Standard_Integer idim=1; idim<=Dimension; idim++) { | |
04232180 | 1797 | // std::cout << "idim=" << idim << std::endl; |
7fd59977 | 1798 | |
1799 | math_Vector B(0,FirstOrder+LastOrder+1); | |
1800 | Standard_Integer icol ; | |
1801 | for ( icol=0; icol<=FirstOrder; icol++) | |
1802 | B(icol) = FirstConstr(idim,icol); | |
1803 | ||
1804 | for (icol=0; icol<=LastOrder; icol++) | |
1805 | B(FirstOrder+1+icol) = LastConstr(idim,icol); | |
04232180 | 1806 | // std::cout << "B=" << B << std::endl; |
7fd59977 | 1807 | |
1808 | // The solving of equations system A * X = B. Then B = X | |
1809 | Equations.Solve(B); | |
04232180 | 1810 | // std::cout << "After Solving" << std::endl << "B=" << B << std::endl; |
7fd59977 | 1811 | |
1812 | if (Equations.IsDone()==Standard_False) return Standard_False; | |
1813 | ||
1814 | // the filling of the Coefficients | |
1815 | ||
1816 | for (icol=0; icol<=FirstOrder+LastOrder+1; icol++) | |
1817 | Coefficients(Dimension*icol+idim-1) = B(icol); | |
1818 | } | |
1819 | return Standard_True; | |
1820 | } | |
1821 | ||
1822 | //======================================================================= | |
1823 | //function : JacobiParameters | |
1824 | //purpose : | |
1825 | //======================================================================= | |
1826 | ||
1827 | void PLib::JacobiParameters(const GeomAbs_Shape ConstraintOrder, | |
1828 | const Standard_Integer MaxDegree, | |
1829 | const Standard_Integer Code, | |
1830 | Standard_Integer& NbGaussPoints, | |
1831 | Standard_Integer& WorkDegree) | |
1832 | { | |
1833 | // ConstraintOrder: Ordre de contrainte aux extremites : | |
1834 | // C0 = contraintes de passage aux bornes; | |
1835 | // C1 = C0 + contraintes de derivees 1eres; | |
1836 | // C2 = C1 + contraintes de derivees 2ndes. | |
1837 | // MaxDegree: Nombre maxi de coeff de la "courbe" polynomiale | |
1838 | // d' approximation (doit etre superieur ou egal a | |
1839 | // 2*NivConstr+2 et inferieur ou egal a 50). | |
1840 | // Code: Code d' init. des parametres de discretisation. | |
1841 | // (choix de NBPNTS et de NDGJAC de MAPF1C,MAPFXC). | |
1842 | // = -5 Calcul tres rapide mais peu precis (8pts) | |
1843 | // = -4 ' ' ' ' ' ' (10pts) | |
1844 | // = -3 ' ' ' ' ' ' (15pts) | |
1845 | // = -2 ' ' ' ' ' ' (20pts) | |
1846 | // = -1 ' ' ' ' ' ' (25pts) | |
1847 | // = 1 calcul rapide avec precision moyenne (30pts). | |
1848 | // = 2 calcul rapide avec meilleure precision (40pts). | |
1849 | // = 3 calcul un peu plus lent avec bonne precision (50 pts). | |
1850 | // = 4 calcul lent avec la meilleure precision possible | |
1851 | // (61pts). | |
1852 | ||
1853 | // The possible values of NbGaussPoints | |
1854 | ||
1855 | const Standard_Integer NDEG8=8, NDEG10=10, NDEG15=15, NDEG20=20, NDEG25=25, | |
1856 | NDEG30=30, NDEG40=40, NDEG50=50, NDEG61=61; | |
1857 | ||
1858 | Standard_Integer NivConstr=0; | |
1859 | switch (ConstraintOrder) { | |
1860 | case GeomAbs_C0: NivConstr = 0; break; | |
1861 | case GeomAbs_C1: NivConstr = 1; break; | |
1862 | case GeomAbs_C2: NivConstr = 2; break; | |
1863 | default: | |
9775fa61 | 1864 | throw Standard_ConstructionError("Invalid ConstraintOrder"); |
7fd59977 | 1865 | } |
1866 | if (MaxDegree < 2*NivConstr+1) | |
9775fa61 | 1867 | throw Standard_ConstructionError("Invalid MaxDegree"); |
7fd59977 | 1868 | |
1869 | if (Code >= 1) | |
1870 | WorkDegree = MaxDegree + 9; | |
1871 | else | |
1872 | WorkDegree = MaxDegree + 6; | |
1873 | ||
1874 | //---> Nbre mini de points necessaires. | |
1875 | Standard_Integer IPMIN=0; | |
1876 | if (WorkDegree < NDEG8) | |
1877 | IPMIN=NDEG8; | |
1878 | else if (WorkDegree < NDEG10) | |
1879 | IPMIN=NDEG10; | |
1880 | else if (WorkDegree < NDEG15) | |
1881 | IPMIN=NDEG15; | |
1882 | else if (WorkDegree < NDEG20) | |
1883 | IPMIN=NDEG20; | |
1884 | else if (WorkDegree < NDEG25) | |
1885 | IPMIN=NDEG25; | |
1886 | else if (WorkDegree < NDEG30) | |
1887 | IPMIN=NDEG30; | |
1888 | else if (WorkDegree < NDEG40) | |
1889 | IPMIN=NDEG40; | |
1890 | else if (WorkDegree < NDEG50) | |
1891 | IPMIN=NDEG50; | |
1892 | else if (WorkDegree < NDEG61) | |
1893 | IPMIN=NDEG61; | |
1894 | else | |
9775fa61 | 1895 | throw Standard_ConstructionError("Invalid MaxDegree"); |
7fd59977 | 1896 | // ---> Nbre de points voulus. |
1897 | Standard_Integer IWANT=0; | |
1898 | switch (Code) { | |
1899 | case -5: IWANT=NDEG8; break; | |
1900 | case -4: IWANT=NDEG10; break; | |
1901 | case -3: IWANT=NDEG15; break; | |
1902 | case -2: IWANT=NDEG20; break; | |
1903 | case -1: IWANT=NDEG25; break; | |
1904 | case 1: IWANT=NDEG30; break; | |
1905 | case 2: IWANT=NDEG40; break; | |
1906 | case 3: IWANT=NDEG50; break; | |
1907 | case 4: IWANT=NDEG61; break; | |
1908 | default: | |
9775fa61 | 1909 | throw Standard_ConstructionError("Invalid Code"); |
7fd59977 | 1910 | } |
1911 | //--> NbGaussPoints est le nombre de points de discretisation de la fonction, | |
1912 | // il ne peut prendre que les valeurs 8,10,15,20,25,30,40,50 ou 61. | |
1913 | // NbGaussPoints doit etre superieur strictement a WorkDegree. | |
1914 | NbGaussPoints = Max(IPMIN,IWANT); | |
1915 | // NbGaussPoints +=2; | |
1916 | } | |
1917 | ||
1918 | //======================================================================= | |
1919 | //function : NivConstr | |
1920 | //purpose : translates from GeomAbs_Shape to Integer | |
1921 | //======================================================================= | |
1922 | ||
1923 | Standard_Integer PLib::NivConstr(const GeomAbs_Shape ConstraintOrder) | |
1924 | { | |
1925 | Standard_Integer NivConstr=0; | |
1926 | switch (ConstraintOrder) { | |
1927 | case GeomAbs_C0: NivConstr = 0; break; | |
1928 | case GeomAbs_C1: NivConstr = 1; break; | |
1929 | case GeomAbs_C2: NivConstr = 2; break; | |
1930 | default: | |
9775fa61 | 1931 | throw Standard_ConstructionError("Invalid ConstraintOrder"); |
7fd59977 | 1932 | } |
1933 | return NivConstr; | |
1934 | } | |
1935 | ||
1936 | //======================================================================= | |
1937 | //function : ConstraintOrder | |
1938 | //purpose : translates from Integer to GeomAbs_Shape | |
1939 | //======================================================================= | |
1940 | ||
1941 | GeomAbs_Shape PLib::ConstraintOrder(const Standard_Integer NivConstr) | |
1942 | { | |
1943 | GeomAbs_Shape ConstraintOrder=GeomAbs_C0; | |
1944 | switch (NivConstr) { | |
1945 | case 0: ConstraintOrder = GeomAbs_C0; break; | |
1946 | case 1: ConstraintOrder = GeomAbs_C1; break; | |
1947 | case 2: ConstraintOrder = GeomAbs_C2; break; | |
1948 | default: | |
9775fa61 | 1949 | throw Standard_ConstructionError("Invalid NivConstr"); |
7fd59977 | 1950 | } |
1951 | return ConstraintOrder; | |
1952 | } | |
1953 | ||
1954 | //======================================================================= | |
1955 | //function : EvalLength | |
1956 | //purpose : | |
1957 | //======================================================================= | |
1958 | ||
1959 | void PLib::EvalLength(const Standard_Integer Degree, const Standard_Integer Dimension, | |
1960 | Standard_Real& PolynomialCoeff, | |
1961 | const Standard_Real U1, const Standard_Real U2, | |
1962 | Standard_Real& Length) | |
1963 | { | |
1964 | Standard_Integer i,j,idim, degdim; | |
1965 | Standard_Real C1,C2,Sum,Tran,X1,X2,Der1,Der2,D1,D2,DD; | |
1966 | ||
1967 | Standard_Real *PolynomialArray = &PolynomialCoeff ; | |
1968 | ||
1969 | Standard_Integer NbGaussPoints = 4 * Min((Degree/4)+1,10); | |
1970 | ||
1971 | math_Vector GaussPoints(1,NbGaussPoints); | |
1972 | math::GaussPoints(NbGaussPoints,GaussPoints); | |
1973 | ||
1974 | math_Vector GaussWeights(1,NbGaussPoints); | |
1975 | math::GaussWeights(NbGaussPoints,GaussWeights); | |
1976 | ||
1977 | C1 = (U2 + U1) / 2.; | |
1978 | C2 = (U2 - U1) / 2.; | |
1979 | ||
1980 | //----------------------------------------------------------- | |
1981 | //****** Integration - Boucle sur les intervalles de GAUSS ** | |
1982 | //----------------------------------------------------------- | |
1983 | ||
1984 | Sum = 0; | |
1985 | ||
1986 | for (j=1; j<=NbGaussPoints/2; j++) { | |
1987 | // Integration en tenant compte de la symetrie | |
1988 | Tran = C2 * GaussPoints(j); | |
1989 | X1 = C1 + Tran; | |
1990 | X2 = C1 - Tran; | |
1991 | ||
1992 | //****** Derivation sur la dimension de l'espace ** | |
1993 | ||
1994 | degdim = Degree*Dimension; | |
1995 | Der1 = Der2 = 0.; | |
1996 | for (idim=0; idim<Dimension; idim++) { | |
1997 | D1 = D2 = Degree * PolynomialArray [idim + degdim]; | |
1998 | for (i=Degree-1; i>=1; i--) { | |
1999 | DD = i * PolynomialArray [idim + i*Dimension]; | |
2000 | D1 = D1 * X1 + DD; | |
2001 | D2 = D2 * X2 + DD; | |
2002 | } | |
2003 | Der1 += D1 * D1; | |
2004 | Der2 += D2 * D2; | |
2005 | } | |
2006 | ||
2007 | //****** Integration ** | |
2008 | ||
2009 | Sum += GaussWeights(j) * C2 * (Sqrt(Der1) + Sqrt(Der2)); | |
2010 | ||
2011 | //****** Fin de boucle dur les intervalles de GAUSS ** | |
2012 | } | |
2013 | Length = Sum; | |
2014 | } | |
2015 | ||
2016 | ||
2017 | //======================================================================= | |
2018 | //function : EvalLength | |
2019 | //purpose : | |
2020 | //======================================================================= | |
2021 | ||
2022 | void PLib::EvalLength(const Standard_Integer Degree, const Standard_Integer Dimension, | |
2023 | Standard_Real& PolynomialCoeff, | |
2024 | const Standard_Real U1, const Standard_Real U2, | |
2025 | const Standard_Real Tol, | |
2026 | Standard_Real& Length, Standard_Real& Error) | |
2027 | { | |
2028 | Standard_Integer i; | |
2029 | Standard_Integer NbSubInt = 1, // Current number of subintervals | |
2030 | MaxNbIter = 13, // Max number of iterations | |
2031 | NbIter = 1; // Current number of iterations | |
2032 | Standard_Real dU,OldLen,LenI; | |
2033 | ||
2034 | PLib::EvalLength(Degree,Dimension, PolynomialCoeff, U1,U2, Length); | |
2035 | ||
2036 | do { | |
2037 | OldLen = Length; | |
2038 | Length = 0.; | |
2039 | NbSubInt *= 2; | |
2040 | dU = (U2-U1)/NbSubInt; | |
2041 | for (i=1; i<=NbSubInt; i++) { | |
2042 | PLib::EvalLength(Degree,Dimension, PolynomialCoeff, U1+(i-1)*dU,U1+i*dU, LenI); | |
2043 | Length += LenI; | |
2044 | } | |
2045 | NbIter++; | |
2046 | Error = Abs(OldLen-Length); | |
2047 | } | |
2048 | while (Error > Tol && NbIter <= MaxNbIter); | |
2049 | } |