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b311480e | 1 | // Created on: 1991-08-26 |
2 | // Created by: JCV | |
3 | // Copyright (c) 1991-1999 Matra Datavision | |
4 | // Copyright (c) 1999-2012 OPEN CASCADE SAS | |
5 | // | |
6 | // The content of this file is subject to the Open CASCADE Technology Public | |
7 | // License Version 6.5 (the "License"). You may not use the content of this file | |
8 | // except in compliance with the License. Please obtain a copy of the License | |
9 | // at http://www.opencascade.org and read it completely before using this file. | |
10 | // | |
11 | // The Initial Developer of the Original Code is Open CASCADE S.A.S., having its | |
12 | // main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France. | |
13 | // | |
14 | // The Original Code and all software distributed under the License is | |
15 | // distributed on an "AS IS" basis, without warranty of any kind, and the | |
16 | // Initial Developer hereby disclaims all such warranties, including without | |
17 | // limitation, any warranties of merchantability, fitness for a particular | |
18 | // purpose or non-infringement. Please see the License for the specific terms | |
19 | // and conditions governing the rights and limitations under the License. | |
20 | ||
7fd59977 | 21 | |
22 | // Modifed RLE Aug 93 - Complete rewrite | |
23 | // xab 21-Mar-95 implemented cache mecanism | |
24 | // pmn 25-09-96 Interpolation | |
25 | // jct 25-09-96 : Correction de l'alloc de LocalArray dans RationalDerivative. | |
26 | // pmn 07-10-96 : Correction de DN dans le cas rationnal. | |
27 | // pmn 06-02-97 : Correction des poids dans RationalDerivative. (PRO700) | |
28 | ||
7fd59977 | 29 | #include <BSplSLib.ixx> |
30 | #include <PLib.hxx> | |
f7b4312f | 31 | #include <NCollection_LocalArray.hxx> |
7fd59977 | 32 | #include <BSplCLib.hxx> |
33 | #include <TColgp_Array2OfXYZ.hxx> | |
34 | #include <TColgp_Array1OfXYZ.hxx> | |
35 | #include <TColStd_HArray1OfInteger.hxx> | |
36 | #include <Standard_NotImplemented.hxx> | |
37 | #include <Standard_ConstructionError.hxx> | |
38 | #include <math_Matrix.hxx> | |
39 | ||
40 | // for null derivatives | |
41194117 | 41 | static Standard_Real BSplSLib_zero[3] = {0.0, 0.0, 0.0}; |
7fd59977 | 42 | #ifdef WNT |
43 | #define M_SQRT2 1.4142135623730950488016887 | |
44 | #endif | |
45 | ||
46 | //======================================================================= | |
47 | //struct : BSplCLib_DataContainer | |
48 | //purpose: Auxiliary structure providing buffers for poles and knots used in | |
49 | // evaluation of bspline (allocated in the stack) | |
50 | //======================================================================= | |
51 | ||
41194117 | 52 | struct BSplSLib_DataContainer |
7fd59977 | 53 | { |
41194117 | 54 | BSplSLib_DataContainer (Standard_Integer UDegree, Standard_Integer VDegree) |
7fd59977 | 55 | { |
105aae76 | 56 | (void)UDegree; (void)VDegree; // just to avoid compiler warning in Release mode |
41194117 K |
57 | Standard_OutOfRange_Raise_if (UDegree > BSplCLib::MaxDegree() || |
58 | VDegree > BSplCLib::MaxDegree() || BSplCLib::MaxDegree() > 25, | |
59 | "BSplSLib: bspline degree is greater than maximum supported"); | |
7fd59977 | 60 | } |
7fd59977 | 61 | Standard_Real poles[4*(25+1)*(25+1)]; |
62 | Standard_Real knots1[2*25]; | |
63 | Standard_Real knots2[2*25]; | |
64 | Standard_Real ders[48]; | |
65 | }; | |
66 | ||
7fd59977 | 67 | //************************************************************************** |
68 | // Evaluation methods | |
69 | //************************************************************************** | |
70 | ||
71 | //======================================================================= | |
72 | //function : RationalDerivative | |
73 | //purpose : computes the rational derivatives when whe have the | |
74 | // the derivatives of the homogeneous numerator and the | |
75 | // the derivatives of the denominator | |
76 | //======================================================================= | |
77 | ||
78 | void BSplSLib::RationalDerivative(const Standard_Integer UDeg, | |
79 | const Standard_Integer VDeg, | |
80 | const Standard_Integer N, | |
81 | const Standard_Integer M, | |
82 | Standard_Real& HDerivatives, | |
83 | Standard_Real& RDerivatives, | |
84 | const Standard_Boolean All) | |
85 | { | |
86 | // | |
87 | // if All is True all derivatives are computed. if Not only | |
88 | // the requested N, M is computed | |
89 | // | |
90 | // Numerator(u,v) | |
91 | // let f(u,v) be a rational function = ------------------ | |
92 | // Denominator(u,v) | |
93 | // | |
94 | // | |
95 | // Let (N,M) the order of the derivatives we want : then since | |
96 | // we have : | |
97 | // | |
98 | // Numerator = f * Denominator | |
99 | // | |
100 | // we derive : | |
101 | // | |
102 | // (N,M) 1 ( (N M) (p q) (N -p M-q) ) | |
103 | // f = ------------ ( Numerator - SUM SUM a * f * Denominator ) | |
104 | // (0,0) ( p<N q<M p q ) | |
105 | // Denominator | |
106 | // | |
107 | // with : | |
108 | // | |
109 | // ( N ) ( M ) | |
110 | // a = ( ) ( ) | |
111 | // p q ( p ) ( q ) | |
112 | // | |
113 | // | |
114 | // HDerivatives is an array where derivatives are stored in the following form | |
115 | // Numerator is assumee to have 3 functions that is a vector of dimension | |
116 | // 3 | |
117 | // | |
118 | // (0,0) (0,0) (0, DegV) (0, DegV) | |
119 | // Numerator Denominator ... Numerator Denominator | |
120 | // | |
121 | // (1,0) (1,0) (1, DegV) (1, DegV) | |
122 | // Numerator Denominator ... Numerator Denominator | |
123 | // | |
124 | // ........................................................... | |
125 | // | |
126 | // | |
127 | // (DegU,0) (DegU,0) (DegU, DegV) (DegU, DegV) | |
128 | // Numerator Denominator ... Numerator Denominator | |
129 | // | |
130 | // | |
131 | Standard_Integer ii,jj,pp,qq,index,index1,index2; | |
132 | Standard_Integer M1,M3,M4,N1,iiM1,iiM3,jjM1,ppM1,ppM3; | |
133 | Standard_Integer MinN,MinN1,MinM,MinM1; | |
134 | Standard_Integer index_u,index_u1,index_v,index_v1,index_w; | |
135 | ||
136 | M1 = M + 1; | |
137 | N1 = N + 1; | |
138 | ii = N1 * M1; | |
139 | M3 = (M1 << 1) + M1; | |
140 | M4 = (VDeg + 1) << 2; | |
141 | ||
f7b4312f | 142 | NCollection_LocalArray<Standard_Real> StoreDerivatives (All ? 0 : ii * 3); |
7fd59977 | 143 | Standard_Real *RArray = (All ? &RDerivatives : (Standard_Real*)StoreDerivatives); |
f7b4312f | 144 | NCollection_LocalArray<Standard_Real> StoreW (ii); |
7fd59977 | 145 | Standard_Real *HomogeneousArray = &HDerivatives; |
146 | Standard_Real denominator,Pii,Pip,Pjq; | |
147 | ||
148 | denominator = 1.0e0 / HomogeneousArray[3]; | |
149 | index_u = 0; | |
150 | index_u1 = 0; | |
151 | if (UDeg < N) MinN = UDeg; | |
152 | else MinN = N; | |
153 | if (VDeg < M) MinM = VDeg; | |
154 | else MinM = M; | |
155 | MinN1 = MinN + 1; | |
156 | MinM1 = MinM + 1; | |
157 | iiM1 = - M1; | |
158 | ||
159 | for (ii = 0 ; ii < MinN1 ; ii++) { | |
160 | iiM1 += M1; | |
161 | index_v = index_u; | |
162 | index_v1 = index_u1; | |
163 | index_w = iiM1; | |
164 | ||
165 | for (jj = 0 ; jj < MinM1 ; jj++) { | |
174178b9 | 166 | RArray[index_v++] = HomogeneousArray[index_v1++]; |
167 | RArray[index_v++] = HomogeneousArray[index_v1++]; | |
168 | RArray[index_v++] = HomogeneousArray[index_v1++]; | |
169 | StoreW[index_w++] = HomogeneousArray[index_v1++]; | |
7fd59977 | 170 | } |
171 | ||
172 | for (jj = MinM1 ; jj < M1 ; jj++) { | |
174178b9 | 173 | RArray[index_v++] = 0.; |
174 | RArray[index_v++] = 0.; | |
175 | RArray[index_v++] = 0.; | |
176 | StoreW[index_w++] = 0.; | |
7fd59977 | 177 | } |
178 | index_u1 += M4; | |
179 | index_u += M3; | |
180 | } | |
181 | index_v = MinN1 * M3; | |
182 | index_w = MinN1 * M1; | |
183 | ||
184 | for (ii = MinN1 ; ii < N1 ; ii++) { | |
185 | ||
186 | for (jj = 0 ; jj < M1 ; jj++) { | |
174178b9 | 187 | RArray[index_v++] = 0.0e0; |
188 | RArray[index_v++] = 0.0e0; | |
189 | RArray[index_v++] = 0.0e0; | |
190 | StoreW[index_w++] = 0.0e0; | |
7fd59977 | 191 | } |
192 | } | |
193 | ||
0d969553 | 194 | // --------------- Calculation ---------------- |
7fd59977 | 195 | |
196 | iiM1 = - M1; | |
197 | iiM3 = - M3; | |
7fd59977 | 198 | |
199 | for (ii = 0 ; ii <= N ; ii++) { | |
200 | iiM1 += M1; | |
201 | iiM3 += M3; | |
202 | index1 = iiM3 - 3; | |
203 | jjM1 = iiM1; | |
204 | ||
205 | for (jj = 0 ; jj <= M ; jj++) { | |
206 | jjM1 ++; | |
207 | ppM1 = - M1; | |
208 | ppM3 = - M3; | |
209 | index1 += 3; | |
210 | ||
211 | for (pp = 0 ; pp < ii ; pp++) { | |
212 | ppM1 += M1; | |
213 | ppM3 += M3; | |
214 | index = ppM3; | |
215 | index2 = jjM1 - ppM1; | |
216 | Pip = PLib::Bin(ii,pp); | |
217 | ||
218 | for (qq = 0 ; qq <= jj ; qq++) { | |
219 | index2--; | |
220 | Pjq = Pip * PLib::Bin(jj,qq) * StoreW[index2]; | |
221 | RArray[index1] -= Pjq * RArray[index]; index++; index1++; | |
222 | RArray[index1] -= Pjq * RArray[index]; index++; index1++; | |
223 | RArray[index1] -= Pjq * RArray[index]; index++; | |
224 | index1 -= 2; | |
225 | } | |
226 | } | |
227 | index = iiM3; | |
228 | index2 = jj + 1; | |
229 | Pii = PLib::Bin(ii,ii); | |
230 | ||
231 | for (qq = 0 ; qq < jj ; qq++) { | |
232 | index2--; | |
233 | Pjq = Pii * PLib::Bin(jj,qq) * StoreW[index2]; | |
234 | RArray[index1] -= Pjq * RArray[index]; index++; index1++; | |
235 | RArray[index1] -= Pjq * RArray[index]; index++; index1++; | |
236 | RArray[index1] -= Pjq * RArray[index]; index++; | |
237 | index1 -= 2; | |
238 | } | |
239 | RArray[index1] *= denominator; index1++; | |
240 | RArray[index1] *= denominator; index1++; | |
241 | RArray[index1] *= denominator; | |
242 | index1 -= 2; | |
243 | } | |
244 | } | |
245 | if (!All) { | |
246 | RArray = &RDerivatives; | |
247 | index = N * M1 + M; | |
248 | index = (index << 1) + index; | |
249 | RArray[0] = StoreDerivatives[index]; index++; | |
250 | RArray[1] = StoreDerivatives[index]; index++; | |
251 | RArray[2] = StoreDerivatives[index]; | |
252 | } | |
253 | } | |
254 | ||
255 | //======================================================================= | |
256 | //function : PrepareEval | |
257 | //purpose : | |
258 | //======================================================================= | |
259 | ||
260 | // | |
261 | // PrepareEval : | |
262 | // | |
0d969553 | 263 | // Prepare all data for computing points : |
7fd59977 | 264 | // local arrays of knots |
265 | // local array of poles (multiplied by the weights if rational) | |
266 | // | |
267 | // The first direction to compute (smaller degree) is returned | |
268 | // and the poles are stored according to this direction. | |
269 | ||
ab87e6fc | 270 | static Standard_Boolean PrepareEval (const Standard_Real U, |
271 | const Standard_Real V, | |
272 | const Standard_Integer Uindex, | |
273 | const Standard_Integer Vindex, | |
274 | const Standard_Integer UDegree, | |
275 | const Standard_Integer VDegree, | |
276 | const Standard_Boolean URat, | |
277 | const Standard_Boolean VRat, | |
278 | const Standard_Boolean UPer, | |
279 | const Standard_Boolean VPer, | |
280 | const TColgp_Array2OfPnt& Poles, | |
281 | const TColStd_Array2OfReal& Weights, | |
282 | const TColStd_Array1OfReal& UKnots, | |
283 | const TColStd_Array1OfReal& VKnots, | |
284 | const TColStd_Array1OfInteger& UMults, | |
285 | const TColStd_Array1OfInteger& VMults, | |
286 | Standard_Real& u1, // first parameter to use | |
287 | Standard_Real& u2, // second parameter to use | |
288 | Standard_Integer& d1, // first degree | |
289 | Standard_Integer& d2, // second degree | |
290 | Standard_Boolean& rational, | |
291 | BSplSLib_DataContainer& dc) | |
292 | { | |
7fd59977 | 293 | rational = URat || VRat; |
294 | Standard_Integer uindex = Uindex; | |
295 | Standard_Integer vindex = Vindex; | |
296 | Standard_Integer UKLower = UKnots.Lower(); | |
297 | Standard_Integer UKUpper = UKnots.Upper(); | |
298 | Standard_Integer VKLower = VKnots.Lower(); | |
299 | Standard_Integer VKUpper = VKnots.Upper(); | |
ab87e6fc | 300 | |
301 | if (UDegree <= VDegree) | |
302 | { | |
7fd59977 | 303 | // compute the indices |
304 | if (uindex < UKLower || uindex > UKUpper) | |
305 | BSplCLib::LocateParameter(UDegree,UKnots,UMults,U,UPer,uindex,u1); | |
ab87e6fc | 306 | else |
307 | u1 = U; | |
308 | ||
7fd59977 | 309 | if (vindex < VKLower || vindex > VKUpper) |
310 | BSplCLib::LocateParameter(VDegree,VKnots,VMults,V,VPer,vindex,u2); | |
ab87e6fc | 311 | else |
312 | u2 = V; | |
313 | ||
7fd59977 | 314 | // get the knots |
315 | d1 = UDegree; | |
316 | d2 = VDegree; | |
317 | BSplCLib::BuildKnots(UDegree,uindex,UPer,UKnots,UMults,*dc.knots1); | |
318 | BSplCLib::BuildKnots(VDegree,vindex,VPer,VKnots,VMults,*dc.knots2); | |
ab87e6fc | 319 | |
320 | if (&UMults == NULL) | |
321 | uindex -= UKLower + UDegree; | |
322 | else | |
323 | uindex = BSplCLib::PoleIndex(UDegree,uindex,UPer,UMults); | |
324 | ||
325 | if (&VMults == NULL) | |
326 | vindex -= VKLower + VDegree; | |
327 | else | |
328 | vindex = BSplCLib::PoleIndex(VDegree,vindex,VPer,VMults); | |
329 | ||
7fd59977 | 330 | // get the poles |
7fd59977 | 331 | Standard_Integer i,j,ip,jp; |
332 | Standard_Real w, *pole = dc.poles; | |
333 | d1 = UDegree; | |
334 | d2 = VDegree; | |
335 | Standard_Integer PLowerRow = Poles.LowerRow(); | |
336 | Standard_Integer PUpperRow = Poles.UpperRow(); | |
337 | Standard_Integer PLowerCol = Poles.LowerCol(); | |
338 | Standard_Integer PUpperCol = Poles.UpperCol(); | |
ab87e6fc | 339 | |
340 | // verify if locally non rational | |
341 | if (rational) | |
342 | { | |
7fd59977 | 343 | rational = Standard_False; |
344 | ip = PLowerRow + uindex; | |
345 | jp = PLowerCol + vindex; | |
ab87e6fc | 346 | |
347 | if(ip < PLowerRow) ip = PUpperRow; | |
348 | if(jp < PLowerCol) jp = PUpperCol; | |
349 | ||
7fd59977 | 350 | w = Weights.Value(ip,jp); |
351 | Standard_Real eps = Epsilon(w); | |
352 | Standard_Real dw; | |
ab87e6fc | 353 | |
354 | for (i = 0; i <= UDegree && !rational; i++) | |
355 | { | |
356 | jp = PLowerCol + vindex; | |
357 | ||
358 | if(jp < PLowerCol) | |
359 | jp = PUpperCol; | |
360 | ||
361 | for (j = 0; j <= VDegree && !rational; j++) | |
362 | { | |
363 | dw = Weights.Value(ip,jp) - w; | |
364 | if (dw < 0) | |
365 | dw = - dw; | |
366 | ||
367 | rational = (dw > eps); | |
368 | ||
369 | jp++; | |
370 | ||
371 | if (jp > PUpperCol) | |
372 | jp = PLowerCol; | |
373 | } | |
374 | ||
375 | ip++; | |
376 | ||
377 | if (ip > PUpperRow) | |
378 | ip = PLowerRow; | |
379 | ||
380 | } | |
7fd59977 | 381 | } |
ab87e6fc | 382 | |
7fd59977 | 383 | // copy the poles |
384 | ip = PLowerRow + uindex; | |
ab87e6fc | 385 | |
386 | if(ip < PLowerRow) | |
387 | ip = PUpperRow; | |
388 | ||
389 | if (rational) | |
390 | { | |
391 | for (i = 0; i <= d1; i++) | |
392 | { | |
393 | jp = PLowerCol + vindex; | |
394 | ||
395 | if(jp < PLowerCol) | |
396 | jp = PUpperCol; | |
397 | ||
398 | for (j = 0; j <= d2; j++) | |
399 | { | |
400 | const gp_Pnt& P = Poles .Value(ip,jp); | |
401 | pole[3] = w = Weights.Value(ip,jp); | |
402 | pole[0] = P.X() * w; | |
403 | pole[1] = P.Y() * w; | |
404 | pole[2] = P.Z() * w; | |
405 | pole += 4; | |
406 | jp++; | |
407 | ||
408 | if (jp > PUpperCol) | |
409 | jp = PLowerCol; | |
410 | } | |
411 | ||
412 | ip++; | |
413 | ||
414 | if (ip > PUpperRow) | |
415 | ip = PLowerRow; | |
416 | ||
417 | } | |
7fd59977 | 418 | } |
ab87e6fc | 419 | else |
420 | { | |
421 | for (i = 0; i <= d1; i++) | |
422 | { | |
423 | jp = PLowerCol + vindex; | |
424 | ||
425 | if(jp < PLowerCol) | |
426 | jp = PUpperCol; | |
427 | ||
428 | for (j = 0; j <= d2; j++) | |
429 | { | |
430 | const gp_Pnt& P = Poles.Value(ip,jp); | |
431 | pole[0] = P.X(); | |
432 | pole[1] = P.Y(); | |
433 | pole[2] = P.Z(); | |
434 | pole += 3; | |
435 | jp++; | |
436 | ||
437 | if (jp > PUpperCol) | |
438 | jp = PLowerCol; | |
439 | } | |
440 | ||
441 | ip++; | |
442 | ||
443 | if (ip > PUpperRow) | |
444 | ip = PLowerRow; | |
445 | } | |
7fd59977 | 446 | } |
ab87e6fc | 447 | |
7fd59977 | 448 | return Standard_True; |
ab87e6fc | 449 | } |
450 | else | |
451 | { | |
7fd59977 | 452 | // compute the indices |
453 | if (uindex < UKLower || uindex > UKUpper) | |
454 | BSplCLib::LocateParameter(UDegree,UKnots,UMults,U,UPer,uindex,u2); | |
ab87e6fc | 455 | else |
456 | u2 = U; | |
457 | ||
7fd59977 | 458 | if (vindex < VKLower || vindex > VKUpper) |
459 | BSplCLib::LocateParameter(VDegree,VKnots,VMults,V,VPer,vindex,u1); | |
ab87e6fc | 460 | else |
461 | u1 = V; | |
462 | ||
7fd59977 | 463 | // get the knots |
ab87e6fc | 464 | |
7fd59977 | 465 | d2 = UDegree; |
466 | d1 = VDegree; | |
ab87e6fc | 467 | |
7fd59977 | 468 | BSplCLib::BuildKnots(UDegree,uindex,UPer,UKnots,UMults,*dc.knots2); |
469 | BSplCLib::BuildKnots(VDegree,vindex,VPer,VKnots,VMults,*dc.knots1); | |
ab87e6fc | 470 | |
471 | if (&UMults == NULL) | |
472 | uindex -= UKLower + UDegree; | |
473 | else | |
474 | uindex = BSplCLib::PoleIndex(UDegree,uindex,UPer,UMults); | |
475 | ||
476 | if (&VMults == NULL) | |
477 | vindex -= VKLower + VDegree; | |
478 | else | |
479 | vindex = BSplCLib::PoleIndex(VDegree,vindex,VPer,VMults); | |
480 | ||
7fd59977 | 481 | // get the poles |
7fd59977 | 482 | Standard_Integer i,j,ip,jp; |
483 | Standard_Real w, *pole = dc.poles; | |
484 | d1 = VDegree; | |
485 | d2 = UDegree; | |
486 | Standard_Integer PLowerRow = Poles.LowerRow(); | |
487 | Standard_Integer PUpperRow = Poles.UpperRow(); | |
488 | Standard_Integer PLowerCol = Poles.LowerCol(); | |
489 | Standard_Integer PUpperCol = Poles.UpperCol(); | |
ab87e6fc | 490 | |
491 | // verify if locally non rational | |
492 | if (rational) | |
493 | { | |
7fd59977 | 494 | rational = Standard_False; |
495 | ip = PLowerRow + uindex; | |
496 | jp = PLowerCol + vindex; | |
ab87e6fc | 497 | |
498 | if(ip < PLowerRow) | |
499 | ip = PUpperRow; | |
500 | ||
501 | if(jp < PLowerCol) | |
502 | jp = PUpperCol; | |
503 | ||
7fd59977 | 504 | w = Weights.Value(ip,jp); |
505 | Standard_Real eps = Epsilon(w); | |
506 | Standard_Real dw; | |
ab87e6fc | 507 | |
508 | for (i = 0; i <= UDegree && !rational; i++) | |
509 | { | |
510 | jp = PLowerCol + vindex; | |
511 | ||
512 | if(jp < PLowerCol) | |
513 | jp = PUpperCol; | |
514 | ||
515 | for (j = 0; j <= VDegree && !rational; j++) | |
516 | { | |
517 | dw = Weights.Value(ip,jp) - w; | |
518 | if (dw < 0) dw = - dw; | |
519 | rational = dw > eps; | |
520 | ||
521 | jp++; | |
522 | ||
523 | if (jp > PUpperCol) | |
524 | jp = PLowerCol; | |
525 | } | |
526 | ||
527 | ip++; | |
528 | ||
529 | if (ip > PUpperRow) | |
530 | ip = PLowerRow; | |
531 | ||
532 | } | |
7fd59977 | 533 | } |
ab87e6fc | 534 | |
7fd59977 | 535 | // copy the poles |
536 | jp = PLowerCol + vindex; | |
ab87e6fc | 537 | |
538 | if(jp < PLowerCol) | |
539 | jp = PUpperCol; | |
540 | ||
541 | if (rational) | |
542 | { | |
543 | for (i = 0; i <= d1; i++) | |
544 | { | |
545 | ip = PLowerRow + uindex; | |
546 | ||
547 | if(ip < PLowerRow) | |
548 | ip = PUpperRow; | |
549 | ||
550 | for (j = 0; j <= d2; j++) | |
551 | { | |
552 | const gp_Pnt& P = Poles.Value(ip,jp); | |
553 | pole[3] = w = Weights.Value(ip,jp); | |
554 | pole[0] = P.X() * w; | |
555 | pole[1] = P.Y() * w; | |
556 | pole[2] = P.Z() * w; | |
557 | pole += 4; | |
558 | ip++; | |
559 | ||
560 | if (ip > PUpperRow) | |
561 | ip = PLowerRow; | |
562 | ||
563 | } | |
564 | ||
565 | jp++; | |
566 | ||
567 | if (jp > PUpperCol) | |
568 | jp = PLowerCol; | |
569 | ||
570 | } | |
7fd59977 | 571 | } |
ab87e6fc | 572 | else |
573 | { | |
574 | for (i = 0; i <= d1; i++) | |
575 | { | |
576 | ip = PLowerRow + uindex; | |
577 | ||
578 | if(ip < PLowerRow) | |
579 | ip = PUpperRow; | |
580 | ||
581 | for (j = 0; j <= d2; j++) | |
582 | { | |
583 | const gp_Pnt& P = Poles.Value(ip,jp); | |
584 | pole[0] = P.X(); | |
585 | pole[1] = P.Y(); | |
586 | pole[2] = P.Z(); | |
587 | pole += 3; | |
588 | ip++; | |
589 | ||
590 | if (ip > PUpperRow) | |
591 | ip = PLowerRow; | |
592 | } | |
593 | ||
594 | jp++; | |
595 | ||
596 | if (jp > PUpperCol) | |
597 | jp = PLowerCol; | |
598 | ||
599 | } | |
7fd59977 | 600 | } |
ab87e6fc | 601 | |
7fd59977 | 602 | return Standard_False; |
ab87e6fc | 603 | } |
7fd59977 | 604 | } |
7fd59977 | 605 | |
606 | //======================================================================= | |
607 | //function : D0 | |
608 | //purpose : | |
609 | //======================================================================= | |
610 | ||
611 | void BSplSLib::D0 | |
612 | (const Standard_Real U, | |
613 | const Standard_Real V, | |
614 | const Standard_Integer UIndex, | |
615 | const Standard_Integer VIndex, | |
616 | const TColgp_Array2OfPnt& Poles, | |
617 | const TColStd_Array2OfReal& Weights, | |
618 | const TColStd_Array1OfReal& UKnots, | |
619 | const TColStd_Array1OfReal& VKnots, | |
620 | const TColStd_Array1OfInteger& UMults, | |
621 | const TColStd_Array1OfInteger& VMults, | |
622 | const Standard_Integer UDegree, | |
623 | const Standard_Integer VDegree, | |
624 | const Standard_Boolean URat, | |
625 | const Standard_Boolean VRat, | |
626 | const Standard_Boolean UPer, | |
627 | const Standard_Boolean VPer, | |
628 | gp_Pnt& P) | |
629 | { | |
630 | // Standard_Integer k ; | |
631 | Standard_Real W ; | |
632 | HomogeneousD0(U, | |
633 | V, | |
634 | UIndex, | |
635 | VIndex, | |
636 | Poles, | |
637 | Weights, | |
638 | UKnots, | |
639 | VKnots, | |
640 | UMults, | |
641 | VMults, | |
642 | UDegree, | |
643 | VDegree, | |
644 | URat, | |
645 | VRat, | |
646 | UPer, | |
647 | VPer, | |
648 | W, | |
649 | P) ; | |
650 | P.SetX(P.X() / W); | |
651 | P.SetY(P.Y() / W); | |
652 | P.SetZ(P.Z() / W); | |
653 | } | |
654 | ||
655 | //======================================================================= | |
656 | //function : D0 | |
657 | //purpose : | |
658 | //======================================================================= | |
659 | ||
660 | void BSplSLib::HomogeneousD0 | |
661 | (const Standard_Real U, | |
662 | const Standard_Real V, | |
663 | const Standard_Integer UIndex, | |
664 | const Standard_Integer VIndex, | |
665 | const TColgp_Array2OfPnt& Poles, | |
666 | const TColStd_Array2OfReal& Weights, | |
667 | const TColStd_Array1OfReal& UKnots, | |
668 | const TColStd_Array1OfReal& VKnots, | |
669 | const TColStd_Array1OfInteger& UMults, | |
670 | const TColStd_Array1OfInteger& VMults, | |
671 | const Standard_Integer UDegree, | |
672 | const Standard_Integer VDegree, | |
673 | const Standard_Boolean URat, | |
674 | const Standard_Boolean VRat, | |
675 | const Standard_Boolean UPer, | |
676 | const Standard_Boolean VPer, | |
677 | Standard_Real & W, | |
678 | gp_Pnt& P) | |
679 | { | |
680 | Standard_Boolean rational; | |
681 | // Standard_Integer k,dim; | |
682 | Standard_Integer dim; | |
683 | Standard_Real u1,u2; | |
684 | Standard_Integer d1,d2; | |
685 | W = 1.0e0 ; | |
686 | ||
687 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
688 | PrepareEval(U,V,UIndex,VIndex,UDegree,VDegree,URat,VRat,UPer,VPer, | |
689 | Poles,Weights,UKnots,VKnots,UMults,VMults, | |
690 | u1,u2,d1,d2,rational,dc); | |
691 | if (rational) { | |
692 | dim = 4; | |
693 | BSplCLib::Eval(u1,d1,*dc.knots1,dim * (d2 + 1),*dc.poles); | |
694 | BSplCLib::Eval(u2,d2,*dc.knots2,dim,*dc.poles); | |
695 | W = dc.poles[3]; | |
696 | P.SetX(dc.poles[0]); | |
697 | P.SetY(dc.poles[1]); | |
698 | P.SetZ(dc.poles[2]); | |
699 | } | |
700 | else { | |
701 | dim = 3; | |
702 | BSplCLib::Eval(u1,d1,*dc.knots1,dim * (d2 + 1),*dc.poles); | |
703 | BSplCLib::Eval(u2,d2,*dc.knots2,dim,*dc.poles); | |
704 | P.SetX(dc.poles[0]); | |
705 | P.SetY(dc.poles[1]); | |
706 | P.SetZ(dc.poles[2]); | |
707 | } | |
708 | } | |
709 | ||
710 | //======================================================================= | |
711 | //function : D1 | |
712 | //purpose : | |
713 | //======================================================================= | |
714 | ||
715 | void BSplSLib::D1 | |
716 | (const Standard_Real U, | |
717 | const Standard_Real V, | |
718 | const Standard_Integer UIndex, | |
719 | const Standard_Integer VIndex, | |
720 | const TColgp_Array2OfPnt& Poles, | |
721 | const TColStd_Array2OfReal& Weights, | |
722 | const TColStd_Array1OfReal& UKnots, | |
723 | const TColStd_Array1OfReal& VKnots, | |
724 | const TColStd_Array1OfInteger& UMults, | |
725 | const TColStd_Array1OfInteger& VMults, | |
726 | const Standard_Integer UDegree, | |
727 | const Standard_Integer VDegree, | |
728 | const Standard_Boolean URat, | |
729 | const Standard_Boolean VRat, | |
730 | const Standard_Boolean UPer, | |
731 | const Standard_Boolean VPer, | |
732 | gp_Pnt& P, | |
733 | gp_Vec& Vu, | |
734 | gp_Vec& Vv) | |
735 | { | |
736 | Standard_Boolean rational; | |
737 | // Standard_Integer k,dim,dim2; | |
738 | Standard_Integer dim,dim2; | |
739 | Standard_Real u1,u2; | |
740 | Standard_Integer d1,d2; | |
741 | Standard_Real *result, *resVu, *resVv; | |
742 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
743 | if (PrepareEval | |
744 | (U,V,UIndex,VIndex,UDegree,VDegree,URat,VRat,UPer,VPer, | |
745 | Poles,Weights,UKnots,VKnots,UMults,VMults, | |
746 | u1,u2,d1,d2,rational,dc)) { | |
747 | if (rational) { | |
748 | dim = 4; | |
749 | dim2 = (d2 + 1) << 2; | |
750 | BSplCLib::Bohm(u1,d1,1,*dc.knots1,dim2,*dc.poles); | |
751 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*dc.poles); | |
752 | BSplCLib::Eval(u2,d2, *dc.knots2,dim ,*(dc.poles + dim2)); | |
753 | BSplSLib::RationalDerivative(d1,d2,1,1,*dc.poles,*dc.ders); | |
754 | result = dc.ders; | |
755 | resVu = result + 6; | |
756 | resVv = result + 3; | |
757 | } | |
758 | else { | |
759 | dim = 3; | |
760 | dim2 = d2 + 1; | |
761 | dim2 = (dim2 << 1) + dim2; | |
762 | BSplCLib::Bohm(u1,d1,1,*dc.knots1,dim2,*dc.poles); | |
763 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*dc.poles); | |
764 | BSplCLib::Eval(u2,d2, *dc.knots2,dim ,*(dc.poles + dim2)); | |
765 | result = dc.poles; | |
766 | resVu = result + dim2; | |
767 | resVv = result + 3; | |
768 | } | |
769 | } | |
770 | else { | |
771 | if (rational) { | |
772 | dim = 4; | |
773 | dim2 = (d2 + 1) << 2; | |
774 | BSplCLib::Bohm(u1,d1,1,*dc.knots1,dim2,*dc.poles); | |
775 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*dc.poles); | |
776 | BSplCLib::Eval(u2,d2, *dc.knots2,dim ,*(dc.poles + dim2)); | |
777 | BSplSLib::RationalDerivative(d1,d2,1,1,*dc.poles,*dc.ders); | |
778 | result = dc.ders; | |
779 | resVu = result + 3; | |
780 | resVv = result + 6; | |
781 | } | |
782 | else { | |
783 | dim = 3; | |
784 | dim2 = d2 + 1; | |
785 | dim2 = (dim2 << 1) + dim2; | |
786 | BSplCLib::Bohm(u1,d1,1,*dc.knots1,dim2,*dc.poles); | |
787 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*dc.poles); | |
788 | BSplCLib::Eval(u2,d2 ,*dc.knots2,dim ,*(dc.poles + dim2)); | |
789 | result = dc.poles; | |
790 | resVu = result + 3; | |
791 | resVv = result + dim2; | |
792 | } | |
793 | } | |
794 | ||
795 | P .SetX(result[0]); | |
796 | Vu.SetX(resVu [0]); | |
797 | Vv.SetX(resVv [0]); | |
798 | ||
799 | P .SetY(result[1]); | |
800 | Vu.SetY(resVu [1]); | |
801 | Vv.SetY(resVv [1]); | |
802 | ||
803 | P .SetZ(result[2]); | |
804 | Vu.SetZ(resVu [2]); | |
805 | Vv.SetZ(resVv [2]); | |
806 | } | |
807 | ||
808 | //======================================================================= | |
809 | //function : D1 | |
810 | //purpose : | |
811 | //======================================================================= | |
812 | ||
813 | void BSplSLib::HomogeneousD1 | |
814 | (const Standard_Real U, | |
815 | const Standard_Real V, | |
816 | const Standard_Integer UIndex, | |
817 | const Standard_Integer VIndex, | |
818 | const TColgp_Array2OfPnt& Poles, | |
819 | const TColStd_Array2OfReal& Weights, | |
820 | const TColStd_Array1OfReal& UKnots, | |
821 | const TColStd_Array1OfReal& VKnots, | |
822 | const TColStd_Array1OfInteger& UMults, | |
823 | const TColStd_Array1OfInteger& VMults, | |
824 | const Standard_Integer UDegree, | |
825 | const Standard_Integer VDegree, | |
826 | const Standard_Boolean URat, | |
827 | const Standard_Boolean VRat, | |
828 | const Standard_Boolean UPer, | |
829 | const Standard_Boolean VPer, | |
830 | gp_Pnt& N, | |
831 | gp_Vec& Nu, | |
832 | gp_Vec& Nv, | |
833 | Standard_Real& D, | |
834 | Standard_Real& Du, | |
835 | Standard_Real& Dv) | |
836 | { | |
837 | Standard_Boolean rational; | |
838 | // Standard_Integer k,dim; | |
839 | Standard_Integer dim; | |
840 | Standard_Real u1,u2; | |
841 | Standard_Integer d1,d2; | |
842 | ||
843 | D = 1.0e0 ; | |
844 | Du = 0.0e0 ; | |
845 | Dv = 0.0e0 ; | |
846 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
847 | Standard_Boolean ufirst = PrepareEval | |
848 | (U,V,UIndex,VIndex,UDegree,VDegree,URat,VRat,UPer,VPer, | |
849 | Poles,Weights,UKnots,VKnots,UMults,VMults, | |
850 | u1,u2,d1,d2,rational,dc); | |
851 | dim = rational ? 4 : 3; | |
852 | ||
853 | BSplCLib::Bohm(u1,d1,1,*dc.knots1,dim * (d2 + 1),*dc.poles); | |
854 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim,*dc.poles); | |
855 | BSplCLib::Eval(u2,d2,*dc.knots2,dim,*(dc.poles+dim*(d2+1))); | |
856 | ||
857 | Standard_Real *result, *resVu, *resVv; | |
858 | result = dc.poles; | |
859 | resVu = result + (ufirst ? dim*(d2+1) : dim); | |
860 | resVv = result + (ufirst ? dim : dim*(d2+1)); | |
861 | ||
862 | N .SetX(result[0]); | |
863 | Nu.SetX(resVu [0]); | |
864 | Nv.SetX(resVv [0]); | |
865 | ||
866 | N .SetY(result[1]); | |
867 | Nu.SetY(resVu [1]); | |
868 | Nv.SetY(resVv [1]); | |
869 | ||
870 | N .SetZ(result[2]); | |
871 | Nu.SetZ(resVu [2]); | |
872 | Nv.SetZ(resVv [2]); | |
873 | ||
874 | if (rational) { | |
875 | D = result[3]; | |
876 | Du = resVu [3]; | |
877 | Dv = resVv [3]; | |
878 | } | |
879 | } | |
880 | ||
881 | //======================================================================= | |
882 | //function : D2 | |
883 | //purpose : | |
884 | //======================================================================= | |
885 | ||
886 | void BSplSLib::D2 | |
887 | (const Standard_Real U, | |
888 | const Standard_Real V, | |
889 | const Standard_Integer UIndex, | |
890 | const Standard_Integer VIndex, | |
891 | const TColgp_Array2OfPnt& Poles, | |
892 | const TColStd_Array2OfReal& Weights, | |
893 | const TColStd_Array1OfReal& UKnots, | |
894 | const TColStd_Array1OfReal& VKnots, | |
895 | const TColStd_Array1OfInteger& UMults, | |
896 | const TColStd_Array1OfInteger& VMults, | |
897 | const Standard_Integer UDegree, | |
898 | const Standard_Integer VDegree, | |
899 | const Standard_Boolean URat, | |
900 | const Standard_Boolean VRat, | |
901 | const Standard_Boolean UPer, | |
902 | const Standard_Boolean VPer, | |
903 | gp_Pnt& P, | |
904 | gp_Vec& Vu, | |
905 | gp_Vec& Vv, | |
906 | gp_Vec& Vuu, | |
907 | gp_Vec& Vvv, | |
908 | gp_Vec& Vuv) | |
909 | { | |
910 | Standard_Boolean rational; | |
911 | // Standard_Integer k,dim,dim2; | |
912 | Standard_Integer dim,dim2; | |
913 | Standard_Real u1,u2; | |
914 | Standard_Integer d1,d2; | |
915 | Standard_Real *result, *resVu, *resVv, *resVuu, *resVvv, *resVuv; | |
916 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
917 | if (PrepareEval | |
918 | (U,V,UIndex,VIndex,UDegree,VDegree,URat,VRat,UPer,VPer, | |
919 | Poles,Weights,UKnots,VKnots,UMults,VMults, | |
920 | u1,u2,d1,d2,rational,dc)) { | |
921 | if (rational) { | |
922 | dim = 4; | |
923 | dim2 = (d2 + 1) << 2; | |
924 | BSplCLib::Bohm(u1,d1,2,*dc.knots1,dim2,*dc.poles); | |
925 | BSplCLib::Bohm(u2,d2,2,*dc.knots2,dim ,*dc.poles); | |
926 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + dim2)); | |
927 | if (d1 > 1) | |
928 | BSplCLib::Eval(u2,d2,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
929 | BSplSLib::RationalDerivative(d1,d2,2,2,*dc.poles,*dc.ders); | |
930 | result = dc.ders; | |
931 | resVu = result + 9; | |
932 | resVv = result + 3; | |
933 | resVuu = result + 18; | |
934 | resVvv = result + 6; | |
935 | resVuv = result + 12; | |
936 | } | |
937 | else { | |
938 | dim = 3; | |
939 | dim2 = d2 + 1; | |
940 | dim2 = (dim2 << 1) + dim2; | |
941 | BSplCLib::Bohm(u1,d1,2,*dc.knots1,dim2,*dc.poles); | |
942 | BSplCLib::Bohm(u2,d2,2,*dc.knots2,dim ,*dc.poles); | |
943 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + dim2)); | |
944 | if (d1 > 1) | |
945 | BSplCLib::Eval(u2,d2,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
946 | result = dc.poles; | |
947 | resVu = result + dim2; | |
948 | resVv = result + 3; | |
949 | if (UDegree <= 1) resVuu = BSplSLib_zero; | |
950 | else resVuu = result + (dim2 << 1); | |
951 | if (VDegree <= 1) resVvv = BSplSLib_zero; | |
952 | else resVvv = result + 6; | |
953 | resVuv = result + (d2 << 1) + d2 + 6; | |
954 | } | |
955 | } | |
956 | else { | |
957 | if (rational) { | |
958 | dim = 4; | |
959 | dim2 = (d2 + 1) << 2; | |
960 | BSplCLib::Bohm(u1,d1,2,*dc.knots1,dim2,*dc.poles); | |
961 | BSplCLib::Bohm(u2,d2,2,*dc.knots2,dim ,*dc.poles); | |
962 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + dim2)); | |
963 | if (d1 > 1) | |
964 | BSplCLib::Eval(u2,d2,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
965 | BSplSLib::RationalDerivative(d1,d2,2,2,*dc.poles,*dc.ders); | |
966 | result = dc.ders; | |
967 | resVu = result + 3; | |
968 | resVv = result + 9; | |
969 | resVuu = result + 6; | |
970 | resVvv = result + 18; | |
971 | resVuv = result + 12; | |
972 | } | |
973 | else { | |
974 | dim = 3; | |
975 | dim2 = d2 + 1; | |
976 | dim2 = (dim2 << 1) + dim2; | |
977 | BSplCLib::Bohm(u1,d1,2,*dc.knots1,dim2,*dc.poles); | |
978 | BSplCLib::Bohm(u2,d2,2,*dc.knots2,dim ,*dc.poles); | |
979 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + dim2)); | |
980 | if (d1 > 1) | |
981 | BSplCLib::Eval(u2,d2,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
982 | result = dc.poles; | |
983 | resVu = result + 3; | |
984 | resVv = result + dim2; | |
985 | if (UDegree <= 1) resVuu = BSplSLib_zero; | |
986 | else resVuu = result + 6; | |
987 | if (VDegree <= 1) resVvv = BSplSLib_zero; | |
988 | else resVvv = result + (dim2 << 1); | |
989 | resVuv = result + (d2 << 1) + d2 + 6; | |
990 | } | |
991 | } | |
992 | ||
993 | P .SetX(result[0]); | |
994 | Vu .SetX(resVu [0]); | |
995 | Vv .SetX(resVv [0]); | |
996 | Vuu.SetX(resVuu[0]); | |
997 | Vvv.SetX(resVvv[0]); | |
998 | Vuv.SetX(resVuv[0]); | |
999 | ||
1000 | P .SetY(result[1]); | |
1001 | Vu .SetY(resVu [1]); | |
1002 | Vv .SetY(resVv [1]); | |
1003 | Vuu.SetY(resVuu[1]); | |
1004 | Vvv.SetY(resVvv[1]); | |
1005 | Vuv.SetY(resVuv[1]); | |
1006 | ||
1007 | P .SetZ(result[2]); | |
1008 | Vu .SetZ(resVu [2]); | |
1009 | Vv .SetZ(resVv [2]); | |
1010 | Vuu.SetZ(resVuu[2]); | |
1011 | Vvv.SetZ(resVvv[2]); | |
1012 | Vuv.SetZ(resVuv[2]); | |
1013 | } | |
1014 | ||
1015 | //======================================================================= | |
1016 | //function : D3 | |
1017 | //purpose : | |
1018 | //======================================================================= | |
1019 | ||
1020 | void BSplSLib::D3 | |
1021 | (const Standard_Real U, | |
1022 | const Standard_Real V, | |
1023 | const Standard_Integer UIndex, | |
1024 | const Standard_Integer VIndex, | |
1025 | const TColgp_Array2OfPnt& Poles, | |
1026 | const TColStd_Array2OfReal& Weights, | |
1027 | const TColStd_Array1OfReal& UKnots, | |
1028 | const TColStd_Array1OfReal& VKnots, | |
1029 | const TColStd_Array1OfInteger& UMults, | |
1030 | const TColStd_Array1OfInteger& VMults, | |
1031 | const Standard_Integer UDegree, | |
1032 | const Standard_Integer VDegree, | |
1033 | const Standard_Boolean URat, | |
1034 | const Standard_Boolean VRat, | |
1035 | const Standard_Boolean UPer, | |
1036 | const Standard_Boolean VPer, | |
1037 | gp_Pnt& P, | |
1038 | gp_Vec& Vu, | |
1039 | gp_Vec& Vv, | |
1040 | gp_Vec& Vuu, | |
1041 | gp_Vec& Vvv, | |
1042 | gp_Vec& Vuv, | |
1043 | gp_Vec& Vuuu, | |
1044 | gp_Vec& Vvvv, | |
1045 | gp_Vec& Vuuv, | |
1046 | gp_Vec& Vuvv) | |
1047 | { | |
1048 | Standard_Boolean rational; | |
1049 | // Standard_Integer k,dim,dim2; | |
1050 | Standard_Integer dim,dim2; | |
1051 | Standard_Real u1,u2; | |
1052 | Standard_Integer d1,d2; | |
1053 | Standard_Real *result, *resVu, *resVv, *resVuu, *resVvv, *resVuv, | |
1054 | *resVuuu, *resVvvv, *resVuuv, *resVuvv; | |
1055 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
1056 | if (PrepareEval | |
1057 | (U,V,UIndex,VIndex,UDegree,VDegree,URat,VRat,UPer,VPer, | |
1058 | Poles,Weights,UKnots,VKnots,UMults,VMults, | |
1059 | u1,u2,d1,d2,rational,dc)) { | |
1060 | if (rational) { | |
1061 | dim = 4; | |
1062 | dim2 = (d2 + 1) << 2; | |
1063 | BSplCLib::Bohm (u1,d1,3,*dc.knots1,dim2,*dc.poles); | |
1064 | BSplCLib::Bohm (u2,d2,3,*dc.knots2,dim ,*dc.poles); | |
1065 | BSplCLib::Bohm (u2,d2,2,*dc.knots2,dim ,*(dc.poles + dim2)); | |
1066 | if (d1 > 1) | |
1067 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
1068 | if (d1 > 2) | |
1069 | BSplCLib::Eval(u2,d2 ,*dc.knots2,dim ,*(dc.poles + (dim2 << 1) + dim2)); | |
1070 | BSplSLib::RationalDerivative(d1,d2,3,3,*dc.poles,*dc.ders); | |
1071 | result = dc.ders; | |
1072 | resVu = result + 12; | |
1073 | resVv = result + 3; | |
1074 | resVuu = result + 24; | |
1075 | resVvv = result + 6; | |
1076 | resVuv = result + 15; | |
1077 | resVuuu = result + 36; | |
1078 | resVvvv = result + 9; | |
1079 | resVuuv = result + 27; | |
1080 | resVuvv = result + 18; | |
1081 | } | |
1082 | else { | |
1083 | dim = 3; | |
1084 | dim2 = (d2 + 1); | |
1085 | dim2 = (dim2 << 1) + dim2; | |
1086 | BSplCLib::Bohm (u1,d1,3,*dc.knots1,dim2,*dc.poles); | |
1087 | BSplCLib::Bohm (u2,d2,3,*dc.knots2,dim ,*dc.poles); | |
1088 | BSplCLib::Bohm (u2,d2,2,*dc.knots2,dim ,*(dc.poles + dim2)); | |
1089 | if (d1 > 1) | |
1090 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
1091 | if (d1 > 2) | |
1092 | BSplCLib::Eval(u2,d2 ,*dc.knots2,dim ,*(dc.poles + (dim2 << 1) + dim2)); | |
1093 | result = dc.poles; | |
1094 | resVu = result + dim2; | |
1095 | resVv = result + 3; | |
1096 | if (UDegree <= 1) { | |
1097 | resVuu = BSplSLib_zero; | |
1098 | resVuuv = BSplSLib_zero; | |
1099 | } | |
1100 | else { | |
1101 | resVuu = result + (dim2 << 1); | |
1102 | resVuuv = result + (dim2 << 1) + 3; | |
1103 | } | |
1104 | if (VDegree <= 1) { | |
1105 | resVvv = BSplSLib_zero; | |
1106 | resVuvv = BSplSLib_zero; | |
1107 | } | |
1108 | else { | |
1109 | resVvv = result + 6; | |
1110 | resVuvv = result + dim2 + 6; | |
1111 | } | |
1112 | resVuv = result + (d2 << 1) + d2 + 6; | |
1113 | if (UDegree <= 2) resVuuu = BSplSLib_zero; | |
1114 | else resVuuu = result + (dim2 << 1) + dim2; | |
1115 | if (VDegree <= 2) resVvvv = BSplSLib_zero; | |
1116 | else resVvvv = result + 9; | |
1117 | } | |
1118 | } | |
1119 | else { | |
1120 | if (rational) { | |
1121 | dim = 4; | |
1122 | dim2 = (d2 + 1) << 2; | |
1123 | BSplCLib::Bohm (u1,d1,3,*dc.knots1,dim2,*dc.poles); | |
1124 | BSplCLib::Bohm (u2,d2,3,*dc.knots2,dim ,*dc.poles); | |
1125 | BSplCLib::Bohm (u2,d2,2,*dc.knots2,dim ,*(dc.poles + dim2)); | |
1126 | if (d1 > 1) | |
1127 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
1128 | if (d1 > 2) | |
1129 | BSplCLib::Eval(u2,d2 ,*dc.knots2,dim ,*(dc.poles + (dim2 << 1) + dim2)); | |
1130 | BSplSLib::RationalDerivative(d1,d2,3,3,*dc.poles,*dc.ders); | |
1131 | result = dc.ders; | |
1132 | resVu = result + 3; | |
1133 | resVv = result + 12; | |
1134 | resVuu = result + 6; | |
1135 | resVvv = result + 24; | |
1136 | resVuv = result + 15; | |
1137 | resVuuu = result + 9; | |
1138 | resVvvv = result + 36; | |
1139 | resVuuv = result + 18; | |
1140 | resVuvv = result + 27; | |
1141 | } | |
1142 | else { | |
1143 | dim = 3; | |
1144 | dim2 = (d2 + 1); | |
1145 | dim2 = (dim2 << 1) + dim2; | |
1146 | BSplCLib::Bohm (u1,d1,3,*dc.knots1,dim2,*dc.poles); | |
1147 | BSplCLib::Bohm (u2,d2,3,*dc.knots2,dim ,*dc.poles); | |
1148 | BSplCLib::Bohm (u2,d2,2,*dc.knots2,dim ,*(dc.poles + dim2)); | |
1149 | if (d1 > 1) | |
1150 | BSplCLib::Bohm(u2,d2,1,*dc.knots2,dim ,*(dc.poles + (dim2 << 1))); | |
1151 | if (d1 > 2) | |
1152 | BSplCLib::Eval(u2,d2 ,*dc.knots2,dim ,*(dc.poles + (dim2 << 1) + dim2)); | |
1153 | result = dc.poles; | |
1154 | resVu = result + 3; | |
1155 | resVv = result + dim2; | |
1156 | if (UDegree <= 1) { | |
1157 | resVuu = BSplSLib_zero; | |
1158 | resVuuv = BSplSLib_zero; | |
1159 | } | |
1160 | else { | |
1161 | resVuu = result + 6; | |
1162 | resVuuv = result + dim2 + 6; | |
1163 | } | |
1164 | if (VDegree <= 1) { | |
1165 | resVvv = BSplSLib_zero; | |
1166 | resVuvv = BSplSLib_zero; | |
1167 | } | |
1168 | else { | |
1169 | resVvv = result + (dim2 << 1); | |
1170 | resVuvv = result + (dim2 << 1) + 3; | |
1171 | } | |
1172 | resVuv = result + (d2 << 1) + d2 + 6; | |
1173 | if (UDegree <= 2) resVuuu = BSplSLib_zero; | |
1174 | else resVuuu = result + 9; | |
1175 | if (VDegree <= 2) resVvvv = BSplSLib_zero; | |
1176 | else resVvvv = result + (dim2 << 1) + dim2; | |
1177 | } | |
1178 | } | |
1179 | ||
1180 | P .SetX(result [0]); | |
1181 | Vu .SetX(resVu [0]); | |
1182 | Vv .SetX(resVv [0]); | |
1183 | Vuu .SetX(resVuu [0]); | |
1184 | Vvv .SetX(resVvv [0]); | |
1185 | Vuv .SetX(resVuv [0]); | |
1186 | Vuuu.SetX(resVuuu[0]); | |
1187 | Vvvv.SetX(resVvvv[0]); | |
1188 | Vuuv.SetX(resVuuv[0]); | |
1189 | Vuvv.SetX(resVuvv[0]); | |
1190 | ||
1191 | P .SetY(result [1]); | |
1192 | Vu .SetY(resVu [1]); | |
1193 | Vv .SetY(resVv [1]); | |
1194 | Vuu .SetY(resVuu [1]); | |
1195 | Vvv .SetY(resVvv [1]); | |
1196 | Vuv .SetY(resVuv [1]); | |
1197 | Vuuu.SetY(resVuuu[1]); | |
1198 | Vvvv.SetY(resVvvv[1]); | |
1199 | Vuuv.SetY(resVuuv[1]); | |
1200 | Vuvv.SetY(resVuvv[1]); | |
1201 | ||
1202 | P .SetZ(result [2]); | |
1203 | Vu .SetZ(resVu [2]); | |
1204 | Vv .SetZ(resVv [2]); | |
1205 | Vuu .SetZ(resVuu [2]); | |
1206 | Vvv .SetZ(resVvv [2]); | |
1207 | Vuv .SetZ(resVuv [2]); | |
1208 | Vuuu.SetZ(resVuuu[2]); | |
1209 | Vvvv.SetZ(resVvvv[2]); | |
1210 | Vuuv.SetZ(resVuuv[2]); | |
1211 | Vuvv.SetZ(resVuvv[2]); | |
1212 | } | |
1213 | ||
1214 | //======================================================================= | |
1215 | //function : DN | |
1216 | //purpose : | |
1217 | //======================================================================= | |
1218 | ||
1219 | void BSplSLib::DN | |
1220 | (const Standard_Real U, | |
1221 | const Standard_Real V, | |
1222 | const Standard_Integer Nu, | |
1223 | const Standard_Integer Nv, | |
1224 | const Standard_Integer UIndex, | |
1225 | const Standard_Integer VIndex, | |
1226 | const TColgp_Array2OfPnt& Poles, | |
1227 | const TColStd_Array2OfReal& Weights, | |
1228 | const TColStd_Array1OfReal& UKnots, | |
1229 | const TColStd_Array1OfReal& VKnots, | |
1230 | const TColStd_Array1OfInteger& UMults, | |
1231 | const TColStd_Array1OfInteger& VMults, | |
1232 | const Standard_Integer UDegree, | |
1233 | const Standard_Integer VDegree, | |
1234 | const Standard_Boolean URat, | |
1235 | const Standard_Boolean VRat, | |
1236 | const Standard_Boolean UPer, | |
1237 | const Standard_Boolean VPer, | |
1238 | gp_Vec& Vn) | |
1239 | { | |
1240 | Standard_Boolean rational; | |
1241 | Standard_Integer k,dim; | |
1242 | Standard_Real u1,u2; | |
1243 | Standard_Integer d1,d2; | |
1244 | ||
1245 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
1246 | Standard_Boolean ufirst = PrepareEval | |
1247 | (U,V,UIndex,VIndex,UDegree,VDegree,URat,VRat,UPer,VPer, | |
1248 | Poles,Weights,UKnots,VKnots,UMults,VMults, | |
1249 | u1,u2,d1,d2,rational,dc); | |
1250 | dim = rational ? 4 : 3; | |
1251 | ||
1252 | if (!rational) { | |
1253 | if ((Nu > UDegree) || (Nv > VDegree)) { | |
1254 | Vn.SetX(0.); | |
1255 | Vn.SetY(0.); | |
1256 | Vn.SetZ(0.); | |
1257 | return; | |
1258 | } | |
1259 | } | |
1260 | ||
1261 | Standard_Integer n1 = ufirst ? Nu : Nv; | |
1262 | Standard_Integer n2 = ufirst ? Nv : Nu; | |
1263 | ||
1264 | BSplCLib::Bohm(u1,d1,n1,*dc.knots1,dim * (d2 + 1),*dc.poles); | |
1265 | ||
1266 | for (k = 0; k <= Min(n1,d1); k++) | |
1267 | BSplCLib::Bohm(u2,d2,n2,*dc.knots2,dim,*(dc.poles+k*dim*(d2+1))); | |
1268 | ||
1269 | Standard_Real *result; | |
1270 | if (rational) { | |
1271 | BSplSLib::RationalDerivative(d1,d2,n1,n2,*dc.poles,*dc.ders,Standard_False); | |
1272 | result = dc.ders; // because Standard_False ci-dessus. | |
1273 | ||
1274 | } | |
1275 | else { | |
1276 | result = dc.poles + (n1 * (d2+1) + n2) * dim ; | |
1277 | } | |
1278 | ||
1279 | Vn.SetX(result[0]); | |
1280 | Vn.SetY(result[1]); | |
1281 | Vn.SetZ(result[2]); | |
1282 | } | |
1283 | ||
1284 | // | |
1285 | // Surface modifications | |
1286 | // | |
1287 | // a surface is processed as a curve of curves. | |
1288 | // i.e : a curve of parameter u where the current point is the set of poles | |
1289 | // of the iso. | |
1290 | // | |
1291 | ||
1292 | //======================================================================= | |
1293 | //function : Iso | |
1294 | //purpose : | |
1295 | //======================================================================= | |
1296 | ||
1297 | void BSplSLib::Iso(const Standard_Real Param, | |
1298 | const Standard_Boolean IsU, | |
1299 | const TColgp_Array2OfPnt& Poles, | |
1300 | const TColStd_Array2OfReal& Weights, | |
1301 | const TColStd_Array1OfReal& Knots, | |
1302 | const TColStd_Array1OfInteger& Mults, | |
1303 | const Standard_Integer Degree, | |
1304 | const Standard_Boolean Periodic, | |
1305 | TColgp_Array1OfPnt& CPoles, | |
1306 | TColStd_Array1OfReal& CWeights) | |
1307 | { | |
1308 | Standard_Integer index = 0; | |
1309 | Standard_Real u = Param; | |
1310 | Standard_Boolean rational = &Weights != NULL; | |
1311 | Standard_Integer dim = rational ? 4 : 3; | |
1312 | ||
1313 | // compute local knots | |
1314 | ||
f7b4312f | 1315 | NCollection_LocalArray<Standard_Real> locknots1 (2*Degree); |
7fd59977 | 1316 | BSplCLib::LocateParameter(Degree,Knots,Mults,u,Periodic,index,u); |
1317 | BSplCLib::BuildKnots(Degree,index,Periodic,Knots,Mults,*locknots1); | |
1318 | if (&Mults == NULL) | |
1319 | index -= Knots.Lower() + Degree; | |
1320 | else | |
1321 | index = BSplCLib::PoleIndex(Degree,index,Periodic,Mults); | |
1322 | ||
1323 | ||
1324 | // copy the local poles | |
1325 | ||
1326 | // Standard_Integer f1,l1,f2,l2,i,j,k; | |
1327 | Standard_Integer f1,l1,f2,l2,i,j; | |
1328 | ||
1329 | if (IsU) { | |
1330 | f1 = Poles.LowerRow(); | |
1331 | l1 = Poles.UpperRow(); | |
1332 | f2 = Poles.LowerCol(); | |
1333 | l2 = Poles.UpperCol(); | |
1334 | } | |
1335 | else { | |
1336 | f1 = Poles.LowerCol(); | |
1337 | l1 = Poles.UpperCol(); | |
1338 | f2 = Poles.LowerRow(); | |
1339 | l2 = Poles.UpperRow(); | |
1340 | } | |
1341 | ||
f7b4312f | 1342 | NCollection_LocalArray<Standard_Real> locpoles ((Degree+1) * (l2-f2+1) * dim); |
7fd59977 | 1343 | |
1344 | Standard_Real w, *pole = locpoles; | |
1345 | index += f1; | |
1346 | ||
1347 | for (i = 0; i <= Degree; i++) { | |
1348 | ||
1349 | for (j = f2; j <= l2; j++) { | |
1350 | ||
1351 | const gp_Pnt& P = IsU ? Poles(index,j) : Poles(j,index); | |
1352 | if (rational) { | |
1353 | pole[3] = w = IsU ? Weights(index,j) : Weights(j,index); | |
1354 | pole[0] = P.X() * w; | |
1355 | pole[1] = P.Y() * w; | |
1356 | pole[2] = P.Z() * w; | |
1357 | } | |
1358 | else { | |
1359 | pole[0] = P.X(); | |
1360 | pole[1] = P.Y(); | |
1361 | pole[2] = P.Z(); | |
1362 | } | |
1363 | pole += dim; | |
1364 | } | |
1365 | index++; | |
1366 | if (index > l1) index = f1; | |
1367 | } | |
1368 | ||
1369 | // compute the iso | |
1370 | BSplCLib::Eval(u,Degree,*locknots1,(l2-f2+1)*dim,*locpoles); | |
1371 | ||
1372 | // get the result | |
1373 | pole = locpoles; | |
1374 | ||
1375 | for (i = CPoles.Lower(); i <= CPoles.Upper(); i++) { | |
1376 | gp_Pnt& P = CPoles(i); | |
1377 | if (rational) { | |
1378 | CWeights(i) = w = pole[3]; | |
1379 | P.SetX( pole[0] / w); | |
1380 | P.SetY( pole[1] / w); | |
1381 | P.SetZ( pole[2] / w); | |
1382 | } | |
1383 | else { | |
1384 | P.SetX( pole[0]); | |
1385 | P.SetY( pole[1]); | |
1386 | P.SetZ( pole[2]); | |
1387 | } | |
1388 | pole += dim; | |
1389 | } | |
1390 | ||
1391 | // if the input is not rational but weights are wanted | |
1392 | if (!rational && (&CWeights != NULL)) { | |
1393 | ||
1394 | for (i = CWeights.Lower(); i <= CWeights.Upper(); i++) | |
1395 | CWeights(i) = 1.; | |
1396 | } | |
1397 | } | |
1398 | ||
1399 | //======================================================================= | |
1400 | //function : Reverse | |
1401 | //purpose : | |
1402 | //======================================================================= | |
1403 | ||
1404 | void BSplSLib::Reverse( TColgp_Array2OfPnt& Poles, | |
1405 | const Standard_Integer Last, | |
1406 | const Standard_Boolean UDirection) | |
1407 | { | |
1408 | Standard_Integer i,j, l = Last; | |
1409 | if ( UDirection) { | |
1410 | l = Poles.LowerRow() + | |
1411 | (l - Poles.LowerRow())%(Poles.ColLength()); | |
1412 | TColgp_Array2OfPnt temp(0, Poles.ColLength()-1, | |
1413 | Poles.LowerCol(), Poles.UpperCol()); | |
1414 | ||
1415 | for (i = Poles.LowerRow(); i <= l; i++) { | |
1416 | ||
1417 | for (j = Poles.LowerCol(); j <= Poles.UpperCol(); j++) { | |
1418 | temp(l-i,j) = Poles(i,j); | |
1419 | } | |
1420 | } | |
1421 | ||
1422 | for (i = l+1; i <= Poles.UpperRow(); i++) { | |
1423 | ||
1424 | for (j = Poles.LowerCol(); j <= Poles.UpperCol(); j++) { | |
1425 | temp(l+Poles.ColLength()-i,j) = Poles(i,j); | |
1426 | } | |
1427 | } | |
1428 | ||
1429 | for (i = Poles.LowerRow(); i <= Poles.UpperRow(); i++) { | |
1430 | ||
1431 | for (j = Poles.LowerCol(); j <= Poles.UpperCol(); j++) { | |
1432 | Poles(i,j) = temp (i-Poles.LowerRow(),j); | |
1433 | } | |
1434 | } | |
1435 | } | |
1436 | else { | |
1437 | l = Poles.LowerCol() + | |
1438 | (l - Poles.LowerCol())%(Poles.RowLength()); | |
1439 | TColgp_Array2OfPnt temp(Poles.LowerRow(), Poles.UpperRow(), | |
1440 | 0, Poles.RowLength()-1); | |
1441 | ||
1442 | for (j = Poles.LowerCol(); j <= l; j++) { | |
1443 | ||
1444 | for (i = Poles.LowerRow(); i <= Poles.UpperRow(); i++) { | |
1445 | temp(i,l-j) = Poles(i,j); | |
1446 | } | |
1447 | } | |
1448 | ||
1449 | for (j = l+1; j <= Poles.UpperCol(); j++) { | |
1450 | ||
1451 | for (i = Poles.LowerRow(); i <= Poles.UpperRow(); i++) { | |
1452 | temp(i,l+Poles.RowLength()-j) = Poles(i,j); | |
1453 | } | |
1454 | } | |
1455 | ||
1456 | for (i = Poles.LowerRow(); i <= Poles.UpperRow(); i++) { | |
1457 | ||
1458 | for (j = Poles.LowerCol(); j <= Poles.UpperCol(); j++) { | |
1459 | Poles(i,j) = temp (i,j-Poles.LowerCol()); | |
1460 | } | |
1461 | } | |
1462 | } | |
1463 | } | |
1464 | ||
1465 | //======================================================================= | |
1466 | //function : Reverse | |
1467 | //purpose : | |
1468 | //======================================================================= | |
1469 | ||
1470 | void BSplSLib::Reverse( TColStd_Array2OfReal& Weights, | |
1471 | const Standard_Integer Last, | |
1472 | const Standard_Boolean UDirection) | |
1473 | { | |
1474 | Standard_Integer i,j, l = Last; | |
1475 | if ( UDirection) { | |
1476 | l = Weights.LowerRow() + | |
1477 | (l - Weights.LowerRow())%(Weights.ColLength()); | |
1478 | TColStd_Array2OfReal temp(0, Weights.ColLength()-1, | |
1479 | Weights.LowerCol(), Weights.UpperCol()); | |
1480 | ||
1481 | for (i = Weights.LowerRow(); i <= l; i++) { | |
1482 | ||
1483 | for (j = Weights.LowerCol(); j <= Weights.UpperCol(); j++) { | |
1484 | temp(l-i,j) = Weights(i,j); | |
1485 | } | |
1486 | } | |
1487 | ||
1488 | for (i = l+1; i <= Weights.UpperRow(); i++) { | |
1489 | ||
1490 | for (j = Weights.LowerCol(); j <= Weights.UpperCol(); j++) { | |
1491 | temp(l+Weights.ColLength()-i,j) = Weights(i,j); | |
1492 | } | |
1493 | } | |
1494 | ||
1495 | for (i = Weights.LowerRow(); i <= Weights.UpperRow(); i++) { | |
1496 | ||
1497 | for (j = Weights.LowerCol(); j <= Weights.UpperCol(); j++) { | |
1498 | Weights(i,j) = temp (i-Weights.LowerRow(),j); | |
1499 | } | |
1500 | } | |
1501 | } | |
1502 | else { | |
1503 | l = Weights.LowerCol() + | |
1504 | (l - Weights.LowerCol())%(Weights.RowLength()); | |
1505 | TColStd_Array2OfReal temp(Weights.LowerRow(), Weights.UpperRow(), | |
1506 | 0, Weights.RowLength()-1); | |
1507 | ||
1508 | for (j = Weights.LowerCol(); j <= l; j++) { | |
1509 | ||
1510 | for (i = Weights.LowerRow(); i <= Weights.UpperRow(); i++) { | |
1511 | temp(i,l-j) = Weights(i,j); | |
1512 | } | |
1513 | } | |
1514 | ||
1515 | for (j = l+1; j <= Weights.UpperCol(); j++) { | |
1516 | ||
1517 | for (i = Weights.LowerRow(); i <= Weights.UpperRow(); i++) { | |
1518 | temp(i,l+Weights.RowLength()-j) = Weights(i,j); | |
1519 | } | |
1520 | } | |
1521 | ||
1522 | for (i = Weights.LowerRow(); i <= Weights.UpperRow(); i++) { | |
1523 | ||
1524 | for (j = Weights.LowerCol(); j <= Weights.UpperCol(); j++) { | |
1525 | Weights(i,j) = temp (i,j-Weights.LowerCol()); | |
1526 | } | |
1527 | } | |
1528 | } | |
1529 | } | |
1530 | ||
1531 | //======================================================================= | |
1532 | //function : IsRational | |
1533 | //purpose : | |
1534 | //======================================================================= | |
1535 | ||
1536 | Standard_Boolean BSplSLib::IsRational | |
1537 | (const TColStd_Array2OfReal& Weights, | |
1538 | const Standard_Integer I1, | |
1539 | const Standard_Integer I2, | |
1540 | const Standard_Integer J1, | |
1541 | const Standard_Integer J2, | |
1542 | const Standard_Real Epsi) | |
1543 | { | |
1544 | Standard_Real eps = (Epsi > 0.0) ? Epsi : Epsilon(Weights(I1,I2)); | |
1545 | Standard_Integer i,j; | |
1546 | Standard_Integer fi = Weights.LowerRow(), li = Weights.ColLength(); | |
1547 | Standard_Integer fj = Weights.LowerCol(), lj = Weights.RowLength(); | |
1548 | ||
1549 | for (i = I1 - fi; i < I2 - fi; i++) { | |
1550 | ||
1551 | for (j = J1 - fj; j < J2 - fj; j++) { | |
1552 | if (Abs(Weights(fi+i%li,fj+j%lj)-Weights(fi+(i+1)%li,fj+j%lj))>eps) | |
1553 | return Standard_True; | |
1554 | } | |
1555 | } | |
1556 | return Standard_False; | |
1557 | } | |
1558 | ||
1559 | //======================================================================= | |
1560 | //function : SetPoles | |
1561 | //purpose : | |
1562 | //======================================================================= | |
1563 | ||
1564 | void BSplSLib::SetPoles(const TColgp_Array2OfPnt& Poles, | |
1565 | TColStd_Array1OfReal& FP, | |
1566 | const Standard_Boolean UDirection) | |
1567 | { | |
1568 | Standard_Integer i, j, l = FP.Lower(); | |
1569 | Standard_Integer PLowerRow = Poles.LowerRow(); | |
1570 | Standard_Integer PUpperRow = Poles.UpperRow(); | |
1571 | Standard_Integer PLowerCol = Poles.LowerCol(); | |
1572 | Standard_Integer PUpperCol = Poles.UpperCol(); | |
1573 | if (UDirection) { | |
1574 | ||
1575 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1576 | ||
1577 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1578 | const gp_Pnt& P = Poles.Value(i,j); | |
1579 | FP(l) = P.X(); l++; | |
1580 | FP(l) = P.Y(); l++; | |
1581 | FP(l) = P.Z(); l++; | |
1582 | } | |
1583 | } | |
1584 | } | |
1585 | else { | |
1586 | ||
1587 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1588 | ||
1589 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1590 | const gp_Pnt& P = Poles.Value(i,j); | |
1591 | FP(l) = P.X(); l++; | |
1592 | FP(l) = P.Y(); l++; | |
1593 | FP(l) = P.Z(); l++; | |
1594 | } | |
1595 | } | |
1596 | } | |
1597 | } | |
1598 | ||
1599 | //======================================================================= | |
1600 | //function : SetPoles | |
1601 | //purpose : | |
1602 | //======================================================================= | |
1603 | ||
1604 | void BSplSLib::SetPoles(const TColgp_Array2OfPnt& Poles, | |
1605 | const TColStd_Array2OfReal& Weights, | |
1606 | TColStd_Array1OfReal& FP, | |
1607 | const Standard_Boolean UDirection) | |
1608 | { | |
1609 | Standard_Integer i, j, l = FP.Lower(); | |
1610 | Standard_Integer PLowerRow = Poles.LowerRow(); | |
1611 | Standard_Integer PUpperRow = Poles.UpperRow(); | |
1612 | Standard_Integer PLowerCol = Poles.LowerCol(); | |
1613 | Standard_Integer PUpperCol = Poles.UpperCol(); | |
1614 | if (UDirection) { | |
1615 | ||
1616 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1617 | ||
1618 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1619 | const gp_Pnt& P = Poles .Value(i,j); | |
1620 | Standard_Real w = Weights.Value(i,j); | |
1621 | FP(l) = P.X() * w; l++; | |
1622 | FP(l) = P.Y() * w; l++; | |
1623 | FP(l) = P.Z() * w; l++; | |
1624 | FP(l) = w; l++; | |
1625 | } | |
1626 | } | |
1627 | } | |
1628 | else { | |
1629 | ||
1630 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1631 | ||
1632 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1633 | const gp_Pnt& P = Poles .Value(i,j); | |
1634 | Standard_Real w = Weights.Value(i,j); | |
1635 | FP(l) = P.X() * w; l++; | |
1636 | FP(l) = P.Y() * w; l++; | |
1637 | FP(l) = P.Z() * w; l++; | |
1638 | FP(l) = w; l++; | |
1639 | } | |
1640 | } | |
1641 | } | |
1642 | } | |
1643 | ||
1644 | //======================================================================= | |
1645 | //function : GetPoles | |
1646 | //purpose : | |
1647 | //======================================================================= | |
1648 | ||
1649 | void BSplSLib::GetPoles(const TColStd_Array1OfReal& FP, | |
1650 | TColgp_Array2OfPnt& Poles, | |
1651 | const Standard_Boolean UDirection) | |
1652 | { | |
1653 | Standard_Integer i, j, l = FP.Lower(); | |
1654 | Standard_Integer PLowerRow = Poles.LowerRow(); | |
1655 | Standard_Integer PUpperRow = Poles.UpperRow(); | |
1656 | Standard_Integer PLowerCol = Poles.LowerCol(); | |
1657 | Standard_Integer PUpperCol = Poles.UpperCol(); | |
1658 | if (UDirection) { | |
1659 | ||
1660 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1661 | ||
1662 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1663 | gp_Pnt& P = Poles.ChangeValue(i,j); | |
1664 | P.SetX(FP(l)); l++; | |
1665 | P.SetY(FP(l)); l++; | |
1666 | P.SetZ(FP(l)); l++; | |
1667 | } | |
1668 | } | |
1669 | } | |
1670 | else { | |
1671 | ||
1672 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1673 | ||
1674 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1675 | gp_Pnt& P = Poles.ChangeValue(i,j); | |
1676 | P.SetX(FP(l)); l++; | |
1677 | P.SetY(FP(l)); l++; | |
1678 | P.SetZ(FP(l)); l++; | |
1679 | } | |
1680 | } | |
1681 | } | |
1682 | } | |
1683 | ||
1684 | //======================================================================= | |
1685 | //function : GetPoles | |
1686 | //purpose : | |
1687 | //======================================================================= | |
1688 | ||
1689 | void BSplSLib::GetPoles(const TColStd_Array1OfReal& FP, | |
1690 | TColgp_Array2OfPnt& Poles, | |
1691 | TColStd_Array2OfReal& Weights, | |
1692 | const Standard_Boolean UDirection) | |
1693 | { | |
1694 | Standard_Integer i, j, l = FP.Lower(); | |
1695 | Standard_Integer PLowerRow = Poles.LowerRow(); | |
1696 | Standard_Integer PUpperRow = Poles.UpperRow(); | |
1697 | Standard_Integer PLowerCol = Poles.LowerCol(); | |
1698 | Standard_Integer PUpperCol = Poles.UpperCol(); | |
1699 | if (UDirection) { | |
1700 | ||
1701 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1702 | ||
1703 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1704 | Standard_Real w = FP( l + 3); | |
1705 | Weights(i,j) = w; | |
1706 | gp_Pnt& P = Poles.ChangeValue(i,j); | |
1707 | P.SetX(FP(l) / w); l++; | |
1708 | P.SetY(FP(l) / w); l++; | |
1709 | P.SetZ(FP(l) / w); l++; | |
1710 | l++; | |
1711 | } | |
1712 | } | |
1713 | } | |
1714 | else { | |
1715 | ||
1716 | for ( j = PLowerCol; j <= PUpperCol; j++) { | |
1717 | ||
1718 | for ( i = PLowerRow; i <= PUpperRow; i++) { | |
1719 | Standard_Real w = FP( l + 3); | |
1720 | Weights(i,j) = w; | |
1721 | gp_Pnt& P = Poles.ChangeValue(i,j); | |
1722 | P.SetX(FP(l) / w); l++; | |
1723 | P.SetY(FP(l) / w); l++; | |
1724 | P.SetZ(FP(l) / w); l++; | |
1725 | l++; | |
1726 | } | |
1727 | } | |
1728 | } | |
1729 | } | |
1730 | ||
1731 | //======================================================================= | |
1732 | //function : InsertKnots | |
1733 | //purpose : | |
1734 | //======================================================================= | |
1735 | ||
1736 | void BSplSLib::InsertKnots(const Standard_Boolean UDirection, | |
1737 | const Standard_Integer Degree, | |
1738 | const Standard_Boolean Periodic, | |
1739 | const TColgp_Array2OfPnt& Poles, | |
1740 | const TColStd_Array2OfReal& Weights, | |
1741 | const TColStd_Array1OfReal& Knots, | |
1742 | const TColStd_Array1OfInteger& Mults, | |
1743 | const TColStd_Array1OfReal& AddKnots, | |
1744 | const TColStd_Array1OfInteger& AddMults, | |
1745 | TColgp_Array2OfPnt& NewPoles, | |
1746 | TColStd_Array2OfReal& NewWeights, | |
1747 | TColStd_Array1OfReal& NewKnots, | |
1748 | TColStd_Array1OfInteger& NewMults, | |
1749 | const Standard_Real Epsilon, | |
1750 | const Standard_Boolean Add ) | |
1751 | { | |
1752 | Standard_Boolean rational = &Weights != NULL; | |
1753 | Standard_Integer dim = 3; | |
1754 | if (rational) dim++; | |
1755 | ||
1756 | TColStd_Array1OfReal poles( 1, dim*Poles.RowLength()*Poles.ColLength()); | |
1757 | TColStd_Array1OfReal | |
1758 | newpoles( 1, dim*NewPoles.RowLength()*NewPoles.ColLength()); | |
1759 | ||
1760 | if (rational) SetPoles(Poles,Weights,poles,UDirection); | |
1761 | else SetPoles(Poles,poles,UDirection); | |
1762 | ||
1763 | if (UDirection) { | |
1764 | dim *= Poles.RowLength(); | |
1765 | } | |
1766 | else { | |
1767 | dim *= Poles.ColLength(); | |
1768 | } | |
1769 | BSplCLib::InsertKnots(Degree,Periodic,dim,poles,Knots,Mults, | |
1770 | AddKnots,AddMults,newpoles,NewKnots,NewMults, | |
1771 | Epsilon,Add); | |
1772 | ||
1773 | if (rational) GetPoles(newpoles,NewPoles,NewWeights,UDirection); | |
1774 | else GetPoles(newpoles,NewPoles,UDirection); | |
1775 | } | |
1776 | ||
1777 | //======================================================================= | |
1778 | //function : RemoveKnot | |
1779 | //purpose : | |
1780 | //======================================================================= | |
1781 | ||
1782 | Standard_Boolean BSplSLib::RemoveKnot | |
1783 | (const Standard_Boolean UDirection, | |
1784 | const Standard_Integer Index, | |
1785 | const Standard_Integer Mult, | |
1786 | const Standard_Integer Degree, | |
1787 | const Standard_Boolean Periodic, | |
1788 | const TColgp_Array2OfPnt& Poles, | |
1789 | const TColStd_Array2OfReal& Weights, | |
1790 | const TColStd_Array1OfReal& Knots, | |
1791 | const TColStd_Array1OfInteger& Mults, | |
1792 | TColgp_Array2OfPnt& NewPoles, | |
1793 | TColStd_Array2OfReal& NewWeights, | |
1794 | TColStd_Array1OfReal& NewKnots, | |
1795 | TColStd_Array1OfInteger& NewMults, | |
1796 | const Standard_Real Tolerance) | |
1797 | { | |
1798 | Standard_Boolean rational = &Weights != NULL; | |
1799 | Standard_Integer dim = 3; | |
1800 | if (rational) dim++; | |
1801 | ||
1802 | TColStd_Array1OfReal poles( 1, dim*Poles.RowLength()*Poles.ColLength()); | |
1803 | TColStd_Array1OfReal | |
1804 | newpoles( 1, dim*NewPoles.RowLength()*NewPoles.ColLength()); | |
1805 | ||
1806 | if (rational) SetPoles(Poles,Weights,poles,UDirection); | |
1807 | else SetPoles(Poles,poles,UDirection); | |
1808 | ||
1809 | if (UDirection) { | |
1810 | dim *= Poles.RowLength(); | |
1811 | } | |
1812 | else { | |
1813 | dim *= Poles.ColLength(); | |
1814 | } | |
1815 | ||
1816 | if ( !BSplCLib::RemoveKnot(Index,Mult,Degree,Periodic,dim, | |
1817 | poles,Knots,Mults,newpoles,NewKnots,NewMults, | |
1818 | Tolerance)) | |
1819 | return Standard_False; | |
1820 | ||
1821 | if (rational) GetPoles(newpoles,NewPoles,NewWeights,UDirection); | |
1822 | else GetPoles(newpoles,NewPoles,UDirection); | |
1823 | return Standard_True; | |
1824 | } | |
1825 | ||
1826 | //======================================================================= | |
1827 | //function : IncreaseDegree | |
1828 | //purpose : | |
1829 | //======================================================================= | |
1830 | ||
1831 | void BSplSLib::IncreaseDegree | |
1832 | (const Standard_Boolean UDirection, | |
1833 | const Standard_Integer Degree, | |
1834 | const Standard_Integer NewDegree, | |
1835 | const Standard_Boolean Periodic, | |
1836 | const TColgp_Array2OfPnt& Poles, | |
1837 | const TColStd_Array2OfReal& Weights, | |
1838 | const TColStd_Array1OfReal& Knots, | |
1839 | const TColStd_Array1OfInteger& Mults, | |
1840 | TColgp_Array2OfPnt& NewPoles, | |
1841 | TColStd_Array2OfReal& NewWeights, | |
1842 | TColStd_Array1OfReal& NewKnots, | |
1843 | TColStd_Array1OfInteger& NewMults) | |
1844 | { | |
1845 | Standard_Boolean rational = &Weights != NULL; | |
1846 | Standard_Integer dim = 3; | |
1847 | if (rational) dim++; | |
1848 | ||
1849 | TColStd_Array1OfReal poles( 1, dim*Poles.RowLength()*Poles.ColLength()); | |
1850 | TColStd_Array1OfReal | |
1851 | newpoles( 1, dim*NewPoles.RowLength()*NewPoles.ColLength()); | |
1852 | ||
1853 | if (rational) SetPoles(Poles,Weights,poles,UDirection); | |
1854 | else SetPoles(Poles,poles,UDirection); | |
1855 | ||
1856 | if (UDirection) { | |
1857 | dim *= Poles.RowLength(); | |
1858 | } | |
1859 | else { | |
1860 | dim *= Poles.ColLength(); | |
1861 | } | |
1862 | ||
1863 | BSplCLib::IncreaseDegree(Degree,NewDegree,Periodic,dim,poles,Knots,Mults, | |
1864 | newpoles,NewKnots,NewMults); | |
1865 | ||
1866 | if (rational) GetPoles(newpoles,NewPoles,NewWeights,UDirection); | |
1867 | else GetPoles(newpoles,NewPoles,UDirection); | |
1868 | } | |
1869 | ||
1870 | //======================================================================= | |
1871 | //function : Unperiodize | |
1872 | //purpose : | |
1873 | //======================================================================= | |
1874 | ||
1875 | void BSplSLib::Unperiodize | |
1876 | (const Standard_Boolean UDirection, | |
1877 | const Standard_Integer Degree, | |
1878 | const TColStd_Array1OfInteger& Mults, | |
1879 | const TColStd_Array1OfReal& Knots, | |
1880 | const TColgp_Array2OfPnt& Poles, | |
1881 | const TColStd_Array2OfReal& Weights, | |
1882 | TColStd_Array1OfInteger& NewMults, | |
1883 | TColStd_Array1OfReal& NewKnots, | |
1884 | TColgp_Array2OfPnt& NewPoles, | |
1885 | TColStd_Array2OfReal& NewWeights) | |
1886 | { | |
1887 | Standard_Boolean rational = &Weights != NULL; | |
1888 | Standard_Integer dim = 3; | |
1889 | if (rational) dim++; | |
1890 | ||
1891 | TColStd_Array1OfReal poles( 1, dim*Poles.RowLength()*Poles.ColLength()); | |
1892 | TColStd_Array1OfReal | |
1893 | newpoles( 1, dim*NewPoles.RowLength()*NewPoles.ColLength()); | |
1894 | ||
1895 | if (rational) SetPoles(Poles,Weights,poles,UDirection); | |
1896 | else SetPoles(Poles,poles,UDirection); | |
1897 | ||
1898 | if (UDirection) { | |
1899 | dim *= Poles.RowLength(); | |
1900 | } | |
1901 | else { | |
1902 | dim *= Poles.ColLength(); | |
1903 | } | |
1904 | ||
1905 | BSplCLib::Unperiodize(Degree, dim, Mults, Knots, poles, | |
1906 | NewMults, NewKnots, newpoles); | |
1907 | ||
1908 | if (rational) GetPoles(newpoles,NewPoles,NewWeights,UDirection); | |
1909 | else GetPoles(newpoles,NewPoles,UDirection); | |
1910 | } | |
1911 | ||
1912 | //======================================================================= | |
1913 | //function : BuildCache | |
1914 | //purpose : Stores theTaylor expansion normalized between 0,1 in the | |
1915 | // Cache : in case of a rational function the Poles are | |
1916 | // stored in homogeneous form | |
1917 | //======================================================================= | |
1918 | ||
1919 | void BSplSLib::BuildCache | |
1920 | (const Standard_Real U, | |
1921 | const Standard_Real V, | |
1922 | const Standard_Real USpanDomain, | |
1923 | const Standard_Real VSpanDomain, | |
1924 | const Standard_Boolean UPeriodic, | |
1925 | const Standard_Boolean VPeriodic, | |
1926 | const Standard_Integer UDegree, | |
1927 | const Standard_Integer VDegree, | |
1928 | const Standard_Integer UIndex, | |
1929 | const Standard_Integer VIndex, | |
1930 | const TColStd_Array1OfReal& UFlatKnots, | |
1931 | const TColStd_Array1OfReal& VFlatKnots, | |
1932 | const TColgp_Array2OfPnt& Poles, | |
1933 | const TColStd_Array2OfReal& Weights, | |
1934 | TColgp_Array2OfPnt& CachePoles, | |
1935 | TColStd_Array2OfReal& CacheWeights) | |
1936 | { | |
1937 | Standard_Boolean rational,rational_u,rational_v,flag_u_or_v; | |
1938 | Standard_Integer kk,d1,d1p1,d2,d2p1,ii,jj,iii,jjj,Index; | |
1939 | Standard_Real u1,min_degree_domain,max_degree_domain,f,factor[2],u2; | |
1940 | if (&Weights != NULL) | |
1941 | rational_u = rational_v = Standard_True; | |
1942 | else | |
1943 | rational_u = rational_v = Standard_False; | |
1944 | BSplSLib_DataContainer dc (UDegree, VDegree); | |
1945 | flag_u_or_v = | |
1946 | PrepareEval (U, | |
1947 | V, | |
1948 | UIndex, | |
1949 | VIndex, | |
1950 | UDegree, | |
1951 | VDegree, | |
1952 | rational_u, | |
1953 | rational_v, | |
1954 | UPeriodic, | |
1955 | VPeriodic, | |
1956 | Poles, | |
1957 | Weights, | |
1958 | UFlatKnots, | |
1959 | VFlatKnots, | |
1960 | (BSplCLib::NoMults()), | |
1961 | (BSplCLib::NoMults()), | |
1962 | u1, | |
1963 | u2, | |
1964 | d1, | |
1965 | d2, | |
1966 | rational, | |
1967 | dc); | |
1968 | d1p1 = d1 + 1; | |
1969 | d2p1 = d2 + 1; | |
1970 | if (rational) { | |
1971 | BSplCLib::Bohm(u1,d1,d1,*dc.knots1,4 * d2p1,*dc.poles); | |
1972 | ||
1973 | for (kk = 0; kk <= d1 ; kk++) | |
1974 | BSplCLib::Bohm(u2,d2,d2,*dc.knots2,4,*(dc.poles + kk * 4 * d2p1)); | |
1975 | if (flag_u_or_v) { | |
1976 | min_degree_domain = USpanDomain ; | |
1977 | max_degree_domain = VSpanDomain ; | |
1978 | } | |
1979 | else { | |
1980 | min_degree_domain = VSpanDomain ; | |
1981 | max_degree_domain = USpanDomain ; | |
1982 | } | |
1983 | factor[0] = 1.0e0 ; | |
1984 | ||
1985 | for (ii = 0 ; ii <= d2 ; ii++) { | |
1986 | iii = ii + 1; | |
1987 | factor[1] = 1.0e0 ; | |
1988 | ||
1989 | for (jj = 0 ; jj <= d1 ; jj++) { | |
1990 | jjj = jj + 1; | |
1991 | Index = jj * d2p1 + ii ; | |
1992 | Index = Index << 2; | |
1993 | gp_Pnt& P = CachePoles(iii,jjj); | |
1994 | f = factor[0] * factor[1]; | |
1995 | P.SetX( f * dc.poles[Index]); Index++; | |
1996 | P.SetY( f * dc.poles[Index]); Index++; | |
1997 | P.SetZ( f * dc.poles[Index]); Index++; | |
1998 | CacheWeights(iii ,jjj) = f * dc.poles[Index] ; | |
1999 | factor[1] *= min_degree_domain / (Standard_Real) (jjj) ; | |
2000 | } | |
2001 | factor[0] *= max_degree_domain / (Standard_Real) (iii) ; | |
2002 | } | |
2003 | } | |
2004 | else { | |
2005 | BSplCLib::Bohm(u1,d1,d1,*dc.knots1,3 * d2p1,*dc.poles); | |
2006 | ||
2007 | for (kk = 0; kk <= d1 ; kk++) | |
2008 | BSplCLib::Bohm(u2,d2,d2,*dc.knots2,3,*(dc.poles + kk * 3 * d2p1)); | |
2009 | if (flag_u_or_v) { | |
2010 | min_degree_domain = USpanDomain ; | |
2011 | max_degree_domain = VSpanDomain ; | |
2012 | } | |
2013 | else { | |
2014 | min_degree_domain = VSpanDomain ; | |
2015 | max_degree_domain = USpanDomain ; | |
2016 | } | |
2017 | factor[0] = 1.0e0 ; | |
2018 | ||
2019 | for (ii = 0 ; ii <= d2 ; ii++) { | |
2020 | iii = ii + 1; | |
2021 | factor[1] = 1.0e0 ; | |
2022 | ||
2023 | for (jj = 0 ; jj <= d1 ; jj++) { | |
2024 | jjj = jj + 1; | |
2025 | Index = jj * d2p1 + ii ; | |
2026 | Index = (Index << 1) + Index; | |
2027 | gp_Pnt& P = CachePoles(iii,jjj); | |
2028 | f = factor[0] * factor[1]; | |
2029 | P.SetX( f * dc.poles[Index]); Index++; | |
2030 | P.SetY( f * dc.poles[Index]); Index++; | |
2031 | P.SetZ( f * dc.poles[Index]); | |
2032 | factor[1] *= min_degree_domain / (Standard_Real) (jjj) ; | |
2033 | } | |
2034 | factor[0] *= max_degree_domain / (Standard_Real) (iii) ; | |
2035 | } | |
2036 | if (&Weights != NULL) { | |
2037 | // | |
2038 | // means that PrepareEval did found out that the surface was | |
2039 | // locally polynomial but since the surface is constructed | |
2040 | // with some weights we need to set the weight polynomial to constant | |
2041 | // | |
2042 | ||
2043 | for (ii = 1 ; ii <= d2p1 ; ii++) { | |
2044 | ||
2045 | for (jj = 1 ; jj <= d1p1 ; jj++) { | |
2046 | CacheWeights(ii,jj) = 0.0e0 ; | |
2047 | } | |
2048 | } | |
2049 | CacheWeights(1,1) = 1.0e0 ; | |
2050 | } | |
2051 | } | |
2052 | } | |
2053 | ||
2054 | //======================================================================= | |
2055 | //function : CacheD0 | |
2056 | //purpose : Evaluates the polynomial cache of the Bspline Curve | |
2057 | // | |
2058 | //======================================================================= | |
2059 | ||
2060 | void BSplSLib::CacheD0(const Standard_Real UParameter, | |
2061 | const Standard_Real VParameter, | |
2062 | const Standard_Integer UDegree, | |
2063 | const Standard_Integer VDegree, | |
2064 | const Standard_Real UCacheParameter, | |
2065 | const Standard_Real VCacheParameter, | |
2066 | const Standard_Real USpanLenght, | |
2067 | const Standard_Real VSpanLenght, | |
2068 | const TColgp_Array2OfPnt& PolesArray, | |
2069 | const TColStd_Array2OfReal& WeightsArray, | |
2070 | gp_Pnt& aPoint) | |
2071 | { | |
2072 | // | |
2073 | // the CacheParameter is where the cache polynomial was evaluated in homogeneous | |
2074 | // form | |
2075 | // the SpanLenght is the normalizing factor so that the polynomial is between | |
2076 | // 0 and 1 | |
2077 | Standard_Integer | |
2078 | // ii, | |
2079 | dimension, | |
2080 | min_degree, | |
2081 | max_degree ; | |
2082 | ||
2083 | Standard_Real | |
2084 | new_parameter[2] , | |
2085 | inverse ; | |
2086 | ||
2087 | Standard_Real * | |
2088 | PArray = (Standard_Real *) | |
2089 | &(PolesArray(PolesArray.LowerCol(), PolesArray.LowerRow())) ; | |
2090 | Standard_Real * | |
2091 | myPoint = (Standard_Real *) &aPoint ; | |
2092 | if (UDegree <= VDegree) { | |
2093 | min_degree = UDegree ; | |
2094 | max_degree = VDegree ; | |
2095 | new_parameter[1] = (UParameter - UCacheParameter) / USpanLenght ; | |
2096 | new_parameter[0] = (VParameter - VCacheParameter) / VSpanLenght ; | |
2097 | dimension = 3 * (UDegree + 1) ; | |
2098 | } | |
2099 | else { | |
2100 | min_degree = VDegree ; | |
2101 | max_degree = UDegree ; | |
2102 | new_parameter[0] = (UParameter - UCacheParameter) / USpanLenght ; | |
2103 | new_parameter[1] = (VParameter - VCacheParameter) / VSpanLenght ; | |
2104 | dimension = 3 * (VDegree + 1) ; | |
2105 | } | |
f7b4312f | 2106 | NCollection_LocalArray<Standard_Real> locpoles(dimension); |
7fd59977 | 2107 | |
2108 | PLib::NoDerivativeEvalPolynomial(new_parameter[0], | |
2109 | max_degree, | |
2110 | dimension, | |
2111 | max_degree*dimension, | |
2112 | PArray[0], | |
2113 | locpoles[0]) ; | |
2114 | ||
2115 | PLib::NoDerivativeEvalPolynomial(new_parameter[1], | |
2116 | min_degree, | |
2117 | 3, | |
2118 | (min_degree << 1) + min_degree, | |
2119 | locpoles[0], | |
2120 | myPoint[0]) ; | |
2121 | if (&WeightsArray != NULL) { | |
2122 | dimension = min_degree + 1 ; | |
2123 | Standard_Real * | |
2124 | WArray = (Standard_Real *) | |
2125 | &WeightsArray(WeightsArray.LowerCol(),WeightsArray.LowerRow()) ; | |
2126 | PLib::NoDerivativeEvalPolynomial(new_parameter[0], | |
2127 | max_degree, | |
2128 | dimension, | |
2129 | max_degree*dimension, | |
2130 | WArray[0], | |
2131 | locpoles[0]) ; | |
2132 | ||
2133 | PLib::NoDerivativeEvalPolynomial(new_parameter[1], | |
2134 | min_degree, | |
2135 | 1, | |
2136 | min_degree, | |
2137 | locpoles[0], | |
2138 | inverse) ; | |
2139 | inverse = 1.0e0/ inverse ; | |
2140 | ||
2141 | myPoint[0] *= inverse ; | |
2142 | myPoint[1] *= inverse ; | |
2143 | myPoint[2] *= inverse ; | |
2144 | } | |
2145 | } | |
2146 | ||
2147 | //======================================================================= | |
2148 | //function : CacheD1 | |
2149 | //purpose : Evaluates the polynomial cache of the Bspline Curve | |
2150 | // | |
2151 | //======================================================================= | |
2152 | ||
2153 | void BSplSLib::CacheD1(const Standard_Real UParameter, | |
2154 | const Standard_Real VParameter, | |
2155 | const Standard_Integer UDegree, | |
2156 | const Standard_Integer VDegree, | |
2157 | const Standard_Real UCacheParameter, | |
2158 | const Standard_Real VCacheParameter, | |
2159 | const Standard_Real USpanLenght, | |
2160 | const Standard_Real VSpanLenght, | |
2161 | const TColgp_Array2OfPnt& PolesArray, | |
2162 | const TColStd_Array2OfReal& WeightsArray, | |
2163 | gp_Pnt& aPoint, | |
2164 | gp_Vec& aVecU, | |
2165 | gp_Vec& aVecV) | |
2166 | { | |
2167 | // | |
2168 | // the CacheParameter is where the cache polynomial was evaluated in homogeneous | |
2169 | // form | |
2170 | // the SpanLenght is the normalizing factor so that the polynomial is between | |
2171 | // 0 and 1 | |
2172 | Standard_Integer | |
2173 | // ii, | |
2174 | // jj, | |
2175 | // kk, | |
2176 | dimension, | |
2177 | min_degree, | |
2178 | max_degree ; | |
2179 | ||
2180 | Standard_Real | |
2181 | inverse_min, | |
2182 | inverse_max, | |
2183 | new_parameter[2] ; | |
2184 | ||
2185 | Standard_Real * | |
2186 | PArray = (Standard_Real *) | |
2187 | &(PolesArray(PolesArray.LowerCol(), PolesArray.LowerRow())) ; | |
2188 | Standard_Real local_poles_array[2][2][3], | |
2189 | local_poles_and_weights_array[2][2][4], | |
2190 | local_weights_array[2][2] ; | |
2191 | Standard_Real * my_vec_min, | |
2192 | * my_vec_max, | |
2193 | * my_point ; | |
2194 | my_point = (Standard_Real *) &aPoint ; | |
2195 | // | |
2196 | // initialize in case of rational evaluation | |
2197 | // because RationalDerivative will use all | |
2198 | // the coefficients | |
2199 | // | |
2200 | // | |
2201 | if (&WeightsArray != NULL) { | |
2202 | ||
2203 | local_poles_array [0][0][0] = 0.0e0 ; | |
2204 | local_poles_array [0][0][1] = 0.0e0 ; | |
2205 | local_poles_array [0][0][2] = 0.0e0 ; | |
2206 | local_weights_array [0][0] = 0.0e0 ; | |
2207 | local_poles_and_weights_array[0][0][0] = 0.0e0 ; | |
2208 | local_poles_and_weights_array[0][0][1] = 0.0e0 ; | |
2209 | local_poles_and_weights_array[0][0][2] = 0.0e0 ; | |
2210 | local_poles_and_weights_array[0][0][3] = 0.0e0 ; | |
2211 | ||
2212 | local_poles_array [0][1][0] = 0.0e0 ; | |
2213 | local_poles_array [0][1][1] = 0.0e0 ; | |
2214 | local_poles_array [0][1][2] = 0.0e0 ; | |
2215 | local_weights_array [0][1] = 0.0e0 ; | |
2216 | local_poles_and_weights_array[0][1][0] = 0.0e0 ; | |
2217 | local_poles_and_weights_array[0][1][1] = 0.0e0 ; | |
2218 | local_poles_and_weights_array[0][1][2] = 0.0e0 ; | |
2219 | local_poles_and_weights_array[0][1][3] = 0.0e0 ; | |
2220 | ||
2221 | local_poles_array [1][0][0] = 0.0e0 ; | |
2222 | local_poles_array [1][0][1] = 0.0e0 ; | |
2223 | local_poles_array [1][0][2] = 0.0e0 ; | |
2224 | local_weights_array [1][0] = 0.0e0 ; | |
2225 | local_poles_and_weights_array[1][0][0] = 0.0e0 ; | |
2226 | local_poles_and_weights_array[1][0][1] = 0.0e0 ; | |
2227 | local_poles_and_weights_array[1][0][2] = 0.0e0 ; | |
2228 | local_poles_and_weights_array[1][0][3] = 0.0e0 ; | |
2229 | ||
2230 | local_poles_array [1][1][0] = 0.0e0 ; | |
2231 | local_poles_array [1][1][1] = 0.0e0 ; | |
2232 | local_poles_array [1][1][2] = 0.0e0 ; | |
2233 | local_weights_array [1][1] = 0.0e0 ; | |
2234 | local_poles_and_weights_array[1][1][0] = 0.0e0 ; | |
2235 | local_poles_and_weights_array[1][1][1] = 0.0e0 ; | |
2236 | local_poles_and_weights_array[1][1][2] = 0.0e0 ; | |
2237 | local_poles_and_weights_array[1][1][3] = 0.0e0 ; | |
2238 | } | |
2239 | ||
2240 | if (UDegree <= VDegree) { | |
2241 | min_degree = UDegree ; | |
2242 | max_degree = VDegree ; | |
2243 | inverse_min = 1.0e0/USpanLenght ; | |
2244 | inverse_max = 1.0e0/VSpanLenght ; | |
2245 | new_parameter[0] = (VParameter - VCacheParameter) * inverse_max ; | |
2246 | new_parameter[1] = (UParameter - UCacheParameter) * inverse_min ; | |
2247 | ||
2248 | dimension = 3 * (UDegree + 1) ; | |
2249 | my_vec_min = (Standard_Real *) &aVecU ; | |
2250 | my_vec_max = (Standard_Real *) &aVecV ; | |
2251 | } | |
2252 | else { | |
2253 | min_degree = VDegree ; | |
2254 | max_degree = UDegree ; | |
2255 | inverse_min = 1.0e0/VSpanLenght ; | |
2256 | inverse_max = 1.0e0/USpanLenght ; | |
2257 | new_parameter[0] = (UParameter - UCacheParameter) * inverse_max ; | |
2258 | new_parameter[1] = (VParameter - VCacheParameter) * inverse_min ; | |
2259 | dimension = 3 * (VDegree + 1) ; | |
2260 | my_vec_min = (Standard_Real *) &aVecV ; | |
2261 | my_vec_max = (Standard_Real *) &aVecU ; | |
2262 | } | |
2263 | ||
f7b4312f | 2264 | NCollection_LocalArray<Standard_Real> locpoles (2 * dimension); |
7fd59977 | 2265 | |
2266 | PLib::EvalPolynomial(new_parameter[0], | |
2267 | 1, | |
2268 | max_degree, | |
2269 | dimension, | |
2270 | PArray[0], | |
2271 | locpoles[0]) ; | |
2272 | ||
2273 | PLib::EvalPolynomial(new_parameter[1], | |
2274 | 1, | |
2275 | min_degree, | |
2276 | 3, | |
2277 | locpoles[0], | |
2278 | local_poles_array[0][0][0]) ; | |
2279 | PLib::NoDerivativeEvalPolynomial(new_parameter[1], | |
2280 | min_degree, | |
2281 | 3, | |
2282 | (min_degree << 1) + min_degree, | |
2283 | locpoles[dimension], | |
2284 | local_poles_array[1][0][0]) ; | |
2285 | ||
2286 | if (&WeightsArray != NULL) { | |
2287 | dimension = min_degree + 1 ; | |
2288 | Standard_Real * | |
2289 | WArray = (Standard_Real *) | |
2290 | &WeightsArray(WeightsArray.LowerCol(),WeightsArray.LowerRow()) ; | |
2291 | PLib::EvalPolynomial(new_parameter[0], | |
2292 | 1, | |
2293 | max_degree, | |
2294 | dimension, | |
2295 | WArray[0], | |
2296 | locpoles[0]) ; | |
2297 | ||
2298 | PLib::EvalPolynomial(new_parameter[1], | |
2299 | 1, | |
2300 | min_degree, | |
2301 | 1, | |
2302 | locpoles[0], | |
2303 | local_weights_array[0][0]) ; | |
2304 | PLib::NoDerivativeEvalPolynomial(new_parameter[1], | |
2305 | min_degree, | |
2306 | 1, | |
2307 | min_degree, | |
2308 | locpoles[dimension], | |
2309 | local_weights_array[1][0]) ; | |
2310 | ||
2311 | local_poles_and_weights_array[0][0][0] = local_poles_array [0][0][0] ; | |
2312 | local_poles_and_weights_array[0][0][1] = local_poles_array [0][0][1] ; | |
2313 | local_poles_and_weights_array[0][0][2] = local_poles_array [0][0][2] ; | |
2314 | local_poles_and_weights_array[0][0][3] = local_weights_array[0][0] ; | |
2315 | ||
2316 | local_poles_and_weights_array[0][1][0] = local_poles_array [0][1][0] ; | |
2317 | local_poles_and_weights_array[0][1][1] = local_poles_array [0][1][1] ; | |
2318 | local_poles_and_weights_array[0][1][2] = local_poles_array [0][1][2] ; | |
2319 | local_poles_and_weights_array[0][1][3] = local_weights_array[0][1] ; | |
2320 | ||
2321 | local_poles_and_weights_array[1][0][0] = local_poles_array [1][0][0] ; | |
2322 | local_poles_and_weights_array[1][0][1] = local_poles_array [1][0][1] ; | |
2323 | local_poles_and_weights_array[1][0][2] = local_poles_array [1][0][2] ; | |
2324 | local_poles_and_weights_array[1][0][3] = local_weights_array[1][0] ; | |
2325 | ||
2326 | local_poles_and_weights_array[1][1][0] = local_poles_array [1][1][0] ; | |
2327 | local_poles_and_weights_array[1][1][1] = local_poles_array [1][1][1] ; | |
2328 | local_poles_and_weights_array[1][1][2] = local_poles_array [1][1][2] ; | |
2329 | local_poles_and_weights_array[1][1][3] = local_weights_array[1][1] ; | |
2330 | ||
2331 | BSplSLib::RationalDerivative(1, | |
2332 | 1, | |
2333 | 1, | |
2334 | 1, | |
2335 | local_poles_and_weights_array[0][0][0], | |
2336 | local_poles_array[0][0][0]) ; | |
2337 | } | |
2338 | ||
2339 | my_point [0] = local_poles_array [0][0][0] ; | |
2340 | my_vec_min[0] = inverse_min * local_poles_array[0][1][0] ; | |
2341 | my_vec_max[0] = inverse_max * local_poles_array[1][0][0] ; | |
2342 | ||
2343 | my_point [1] = local_poles_array [0][0][1] ; | |
2344 | my_vec_min[1] = inverse_min * local_poles_array[0][1][1] ; | |
2345 | my_vec_max[1] = inverse_max * local_poles_array[1][0][1] ; | |
2346 | ||
2347 | my_point [2] = local_poles_array [0][0][2] ; | |
2348 | my_vec_min[2] = inverse_min * local_poles_array[0][1][2] ; | |
2349 | my_vec_max[2] = inverse_max * local_poles_array[1][0][2] ; | |
2350 | } | |
2351 | ||
2352 | //======================================================================= | |
2353 | //function : CacheD2 | |
2354 | //purpose : Evaluates the polynomial cache of the Bspline Curve | |
2355 | // | |
2356 | //======================================================================= | |
2357 | ||
2358 | void BSplSLib::CacheD2(const Standard_Real UParameter, | |
2359 | const Standard_Real VParameter, | |
2360 | const Standard_Integer UDegree, | |
2361 | const Standard_Integer VDegree, | |
2362 | const Standard_Real UCacheParameter, | |
2363 | const Standard_Real VCacheParameter, | |
2364 | const Standard_Real USpanLenght, | |
2365 | const Standard_Real VSpanLenght, | |
2366 | const TColgp_Array2OfPnt& PolesArray, | |
2367 | const TColStd_Array2OfReal& WeightsArray, | |
2368 | gp_Pnt& aPoint, | |
2369 | gp_Vec& aVecU, | |
2370 | gp_Vec& aVecV, | |
2371 | gp_Vec& aVecUU, | |
2372 | gp_Vec& aVecUV, | |
2373 | gp_Vec& aVecVV) | |
2374 | { | |
2375 | // | |
2376 | // the CacheParameter is where the cache polynomial was evaluated in homogeneous | |
2377 | // form | |
2378 | // the SpanLenght is the normalizing factor so that the polynomial is between | |
2379 | // 0 and 1 | |
2380 | Standard_Integer | |
2381 | ii, | |
2382 | // jj, | |
2383 | kk, | |
2384 | index, | |
2385 | dimension, | |
2386 | min_degree, | |
2387 | max_degree ; | |
2388 | ||
2389 | Standard_Real | |
2390 | inverse_min, | |
2391 | inverse_max, | |
2392 | new_parameter[2] ; | |
2393 | ||
2394 | Standard_Real * | |
2395 | PArray = (Standard_Real *) | |
2396 | &(PolesArray(PolesArray.LowerCol(), PolesArray.LowerRow())) ; | |
2397 | Standard_Real local_poles_array[3][3][3], | |
2398 | local_poles_and_weights_array[3][3][4], | |
2399 | local_weights_array[3][3] ; | |
2400 | Standard_Real * my_vec_min, | |
2401 | * my_vec_max, | |
2402 | * my_vec_min_min, | |
2403 | * my_vec_max_max, | |
2404 | * my_vec_min_max, | |
2405 | * my_point ; | |
2406 | my_point = (Standard_Real *) &aPoint ; | |
2407 | ||
2408 | // | |
2409 | // initialize in case the min and max degree are less than 2 | |
2410 | // | |
2411 | local_poles_array[0][0][0] = 0.0e0 ; | |
2412 | local_poles_array[0][0][1] = 0.0e0 ; | |
2413 | local_poles_array[0][0][2] = 0.0e0 ; | |
2414 | local_poles_array[0][1][0] = 0.0e0 ; | |
2415 | local_poles_array[0][1][1] = 0.0e0 ; | |
2416 | local_poles_array[0][1][2] = 0.0e0 ; | |
2417 | local_poles_array[0][2][0] = 0.0e0 ; | |
2418 | local_poles_array[0][2][1] = 0.0e0 ; | |
2419 | local_poles_array[0][2][2] = 0.0e0 ; | |
2420 | ||
2421 | local_poles_array[1][0][0] = 0.0e0 ; | |
2422 | local_poles_array[1][0][1] = 0.0e0 ; | |
2423 | local_poles_array[1][0][2] = 0.0e0 ; | |
2424 | local_poles_array[1][1][0] = 0.0e0 ; | |
2425 | local_poles_array[1][1][1] = 0.0e0 ; | |
2426 | local_poles_array[1][1][2] = 0.0e0 ; | |
2427 | local_poles_array[1][2][0] = 0.0e0 ; | |
2428 | local_poles_array[1][2][1] = 0.0e0 ; | |
2429 | local_poles_array[1][2][2] = 0.0e0 ; | |
2430 | ||
2431 | local_poles_array[2][0][0] = 0.0e0 ; | |
2432 | local_poles_array[2][0][1] = 0.0e0 ; | |
2433 | local_poles_array[2][0][2] = 0.0e0 ; | |
2434 | local_poles_array[2][1][0] = 0.0e0 ; | |
2435 | local_poles_array[2][1][1] = 0.0e0 ; | |
2436 | local_poles_array[2][1][2] = 0.0e0 ; | |
2437 | local_poles_array[2][2][0] = 0.0e0 ; | |
2438 | local_poles_array[2][2][1] = 0.0e0 ; | |
2439 | local_poles_array[2][2][2] = 0.0e0 ; | |
2440 | // | |
2441 | // initialize in case of rational evaluation | |
2442 | // because RationalDerivative will use all | |
2443 | // the coefficients | |
2444 | // | |
2445 | // | |
2446 | if (&WeightsArray != NULL) { | |
2447 | ||
2448 | local_poles_and_weights_array[0][0][0] = 0.0e0 ; | |
2449 | local_poles_and_weights_array[0][0][1] = 0.0e0 ; | |
2450 | local_poles_and_weights_array[0][0][2] = 0.0e0 ; | |
2451 | local_poles_and_weights_array[0][1][0] = 0.0e0 ; | |
2452 | local_poles_and_weights_array[0][1][1] = 0.0e0 ; | |
2453 | local_poles_and_weights_array[0][1][2] = 0.0e0 ; | |
2454 | local_poles_and_weights_array[0][2][0] = 0.0e0 ; | |
2455 | local_poles_and_weights_array[0][2][1] = 0.0e0 ; | |
2456 | local_poles_and_weights_array[0][2][2] = 0.0e0 ; | |
2457 | ||
2458 | local_poles_and_weights_array[1][0][0] = 0.0e0 ; | |
2459 | local_poles_and_weights_array[1][0][1] = 0.0e0 ; | |
2460 | local_poles_and_weights_array[1][0][2] = 0.0e0 ; | |
2461 | local_poles_and_weights_array[1][1][0] = 0.0e0 ; | |
2462 | local_poles_and_weights_array[1][1][1] = 0.0e0 ; | |
2463 | local_poles_and_weights_array[1][1][2] = 0.0e0 ; | |
2464 | local_poles_and_weights_array[1][2][0] = 0.0e0 ; | |
2465 | local_poles_and_weights_array[1][2][1] = 0.0e0 ; | |
2466 | local_poles_and_weights_array[1][2][2] = 0.0e0 ; | |
2467 | ||
2468 | local_poles_and_weights_array[2][0][0] = 0.0e0 ; | |
2469 | local_poles_and_weights_array[2][0][1] = 0.0e0 ; | |
2470 | local_poles_and_weights_array[2][0][2] = 0.0e0 ; | |
2471 | local_poles_and_weights_array[2][1][0] = 0.0e0 ; | |
2472 | local_poles_and_weights_array[2][1][1] = 0.0e0 ; | |
2473 | local_poles_and_weights_array[2][1][2] = 0.0e0 ; | |
2474 | local_poles_and_weights_array[2][2][0] = 0.0e0 ; | |
2475 | local_poles_and_weights_array[2][2][1] = 0.0e0 ; | |
2476 | local_poles_and_weights_array[2][2][2] = 0.0e0 ; | |
2477 | ||
2478 | local_poles_and_weights_array[0][0][3] = | |
2479 | local_weights_array[0][0] = 0.0e0 ; | |
2480 | local_poles_and_weights_array[0][1][3] = | |
2481 | local_weights_array[0][1] = 0.0e0 ; | |
2482 | local_poles_and_weights_array[0][2][3] = | |
2483 | local_weights_array[0][2] = 0.0e0 ; | |
2484 | local_poles_and_weights_array[1][0][3] = | |
2485 | local_weights_array[1][0] = 0.0e0 ; | |
2486 | local_poles_and_weights_array[1][1][3] = | |
2487 | local_weights_array[1][1] = 0.0e0 ; | |
2488 | local_poles_and_weights_array[1][2][3] = | |
2489 | local_weights_array[1][2] = 0.0e0 ; | |
2490 | local_poles_and_weights_array[2][0][3] = | |
2491 | local_weights_array[2][0] = 0.0e0 ; | |
2492 | local_poles_and_weights_array[2][1][3] = | |
2493 | local_weights_array[2][1] = 0.0e0 ; | |
2494 | local_poles_and_weights_array[2][2][3] = | |
2495 | local_weights_array[2][2] = 0.0e0 ; | |
2496 | } | |
2497 | ||
2498 | if (UDegree <= VDegree) { | |
2499 | min_degree = UDegree ; | |
2500 | max_degree = VDegree ; | |
2501 | inverse_min = 1.0e0/USpanLenght ; | |
2502 | inverse_max = 1.0e0/VSpanLenght ; | |
2503 | new_parameter[0] = (VParameter - VCacheParameter) * inverse_max ; | |
2504 | new_parameter[1] = (UParameter - UCacheParameter) * inverse_min ; | |
2505 | ||
2506 | dimension = 3 * (UDegree + 1) ; | |
2507 | my_vec_min = (Standard_Real *) &aVecU ; | |
2508 | my_vec_max = (Standard_Real *) &aVecV ; | |
2509 | my_vec_min_min = (Standard_Real *) &aVecUU ; | |
2510 | my_vec_min_max = (Standard_Real *) &aVecUV ; | |
2511 | my_vec_max_max = (Standard_Real *) &aVecVV ; | |
2512 | } | |
2513 | else { | |
2514 | min_degree = VDegree ; | |
2515 | max_degree = UDegree ; | |
2516 | inverse_min = 1.0e0/VSpanLenght ; | |
2517 | inverse_max = 1.0e0/USpanLenght ; | |
2518 | new_parameter[0] = (UParameter - UCacheParameter) * inverse_max ; | |
2519 | new_parameter[1] = (VParameter - VCacheParameter) * inverse_min ; | |
2520 | dimension = 3 * (VDegree + 1) ; | |
2521 | my_vec_min = (Standard_Real *) &aVecV ; | |
2522 | my_vec_max = (Standard_Real *) &aVecU ; | |
2523 | my_vec_min_min = (Standard_Real *) &aVecVV ; | |
2524 | my_vec_min_max = (Standard_Real *) &aVecUV ; | |
2525 | my_vec_max_max = (Standard_Real *) &aVecUU ; | |
2526 | } | |
2527 | ||
f7b4312f | 2528 | NCollection_LocalArray<Standard_Real> locpoles (3 * dimension); |
7fd59977 | 2529 | |
2530 | // | |
2531 | // initialize in case min or max degree are less than 2 | |
2532 | // | |
2533 | Standard_Integer MinIndMax = 2; | |
2534 | if ( max_degree < 2) MinIndMax = max_degree; | |
2535 | Standard_Integer MinIndMin = 2; | |
2536 | if ( min_degree < 2) MinIndMin = min_degree; | |
2537 | ||
2538 | index = MinIndMax * dimension ; | |
2539 | ||
2540 | for (ii = MinIndMax ; ii < 3 ; ii++) { | |
2541 | ||
2542 | for (kk = 0 ; kk < dimension ; kk++) { | |
2543 | locpoles[index] = 0.0e0 ; | |
2544 | index += 1 ; | |
2545 | } | |
2546 | } | |
2547 | ||
2548 | PLib::EvalPolynomial(new_parameter[0], | |
2549 | MinIndMax, | |
2550 | max_degree, | |
2551 | dimension, | |
2552 | PArray[0], | |
2553 | locpoles[0]) ; | |
2554 | ||
2555 | PLib::EvalPolynomial(new_parameter[1], | |
2556 | MinIndMin, | |
2557 | min_degree, | |
2558 | 3, | |
2559 | locpoles[0], | |
2560 | local_poles_array[0][0][0]) ; | |
2561 | PLib::EvalPolynomial(new_parameter[1], | |
2562 | 1, | |
2563 | min_degree, | |
2564 | 3, | |
2565 | locpoles[dimension], | |
2566 | local_poles_array[1][0][0]) ; | |
2567 | ||
2568 | PLib::NoDerivativeEvalPolynomial(new_parameter[1], | |
2569 | min_degree, | |
2570 | 3, | |
2571 | (min_degree << 1) + min_degree, | |
2572 | locpoles[dimension + dimension], | |
2573 | local_poles_array[2][0][0]) ; | |
2574 | ||
2575 | if (&WeightsArray != NULL) { | |
2576 | dimension = min_degree + 1 ; | |
2577 | Standard_Real * | |
2578 | WArray = (Standard_Real *) | |
2579 | &WeightsArray(WeightsArray.LowerCol(),WeightsArray.LowerRow()) ; | |
2580 | PLib::EvalPolynomial(new_parameter[0], | |
2581 | MinIndMax, | |
2582 | max_degree, | |
2583 | dimension, | |
2584 | WArray[0], | |
2585 | locpoles[0]) ; | |
2586 | ||
2587 | PLib::EvalPolynomial(new_parameter[1], | |
2588 | MinIndMin, | |
2589 | min_degree, | |
2590 | 1, | |
2591 | locpoles[0], | |
2592 | local_weights_array[0][0]) ; | |
2593 | PLib::EvalPolynomial(new_parameter[1], | |
2594 | 1, | |
2595 | min_degree, | |
2596 | 1, | |
2597 | locpoles[dimension], | |
2598 | local_weights_array[1][0]) ; | |
2599 | PLib::NoDerivativeEvalPolynomial(new_parameter[1], | |
2600 | min_degree, | |
2601 | 1, | |
2602 | min_degree, | |
2603 | locpoles[dimension + dimension], | |
2604 | local_weights_array[2][0]) ; | |
2605 | ||
2606 | ||
2607 | local_poles_and_weights_array[0][0][0] = local_poles_array[0][0][0]; | |
2608 | local_poles_and_weights_array[0][0][1] = local_poles_array[0][0][1]; | |
2609 | local_poles_and_weights_array[0][0][2] = local_poles_array[0][0][2]; | |
2610 | local_poles_and_weights_array[0][1][0] = local_poles_array[0][1][0]; | |
2611 | local_poles_and_weights_array[0][1][1] = local_poles_array[0][1][1]; | |
2612 | local_poles_and_weights_array[0][1][2] = local_poles_array[0][1][2]; | |
2613 | local_poles_and_weights_array[0][2][0] = local_poles_array[0][2][0]; | |
2614 | local_poles_and_weights_array[0][2][1] = local_poles_array[0][2][1]; | |
2615 | local_poles_and_weights_array[0][2][2] = local_poles_array[0][2][2]; | |
2616 | ||
2617 | local_poles_and_weights_array[1][0][0] = local_poles_array[1][0][0]; | |
2618 | local_poles_and_weights_array[1][0][1] = local_poles_array[1][0][1]; | |
2619 | local_poles_and_weights_array[1][0][2] = local_poles_array[1][0][2]; | |
2620 | local_poles_and_weights_array[1][1][0] = local_poles_array[1][1][0]; | |
2621 | local_poles_and_weights_array[1][1][1] = local_poles_array[1][1][1]; | |
2622 | local_poles_and_weights_array[1][1][2] = local_poles_array[1][1][2]; | |
2623 | local_poles_and_weights_array[1][2][0] = local_poles_array[1][2][0]; | |
2624 | local_poles_and_weights_array[1][2][1] = local_poles_array[1][2][1]; | |
2625 | local_poles_and_weights_array[1][2][2] = local_poles_array[1][2][2]; | |
2626 | ||
2627 | local_poles_and_weights_array[2][0][0] = local_poles_array[2][0][0]; | |
2628 | local_poles_and_weights_array[2][0][1] = local_poles_array[2][0][1]; | |
2629 | local_poles_and_weights_array[2][0][2] = local_poles_array[2][0][2]; | |
2630 | local_poles_and_weights_array[2][1][0] = local_poles_array[2][1][0]; | |
2631 | local_poles_and_weights_array[2][1][1] = local_poles_array[2][1][1]; | |
2632 | local_poles_and_weights_array[2][1][2] = local_poles_array[2][1][2]; | |
2633 | local_poles_and_weights_array[2][2][0] = local_poles_array[2][2][0]; | |
2634 | local_poles_and_weights_array[2][2][1] = local_poles_array[2][2][1]; | |
2635 | local_poles_and_weights_array[2][2][2] = local_poles_array[2][2][2]; | |
2636 | ||
2637 | ||
2638 | local_poles_and_weights_array[0][0][3] = local_weights_array[0][0]; | |
2639 | local_poles_and_weights_array[0][1][3] = local_weights_array[0][1]; | |
2640 | local_poles_and_weights_array[0][2][3] = local_weights_array[0][2]; | |
2641 | local_poles_and_weights_array[1][0][3] = local_weights_array[1][0]; | |
2642 | local_poles_and_weights_array[1][1][3] = local_weights_array[1][1]; | |
2643 | local_poles_and_weights_array[1][2][3] = local_weights_array[1][2]; | |
2644 | local_poles_and_weights_array[2][0][3] = local_weights_array[2][0]; | |
2645 | local_poles_and_weights_array[2][1][3] = local_weights_array[2][1]; | |
2646 | local_poles_and_weights_array[2][2][3] = local_weights_array[2][2]; | |
2647 | ||
2648 | BSplSLib::RationalDerivative(2, | |
2649 | 2, | |
2650 | 2, | |
2651 | 2, | |
2652 | local_poles_and_weights_array[0][0][0], | |
2653 | local_poles_array[0][0][0]) ; | |
2654 | } | |
2655 | ||
2656 | ||
2657 | Standard_Real minmin = inverse_min * inverse_min; | |
2658 | Standard_Real minmax = inverse_min * inverse_max; | |
2659 | Standard_Real maxmax = inverse_max * inverse_max; | |
2660 | ||
2661 | my_point [0] = local_poles_array [0][0][0] ; | |
2662 | my_vec_min [0] = inverse_min * local_poles_array[0][1][0] ; | |
2663 | my_vec_max [0] = inverse_max * local_poles_array[1][0][0] ; | |
2664 | my_vec_min_min[0] = minmin * local_poles_array [0][2][0] ; | |
2665 | my_vec_min_max[0] = minmax * local_poles_array [1][1][0] ; | |
2666 | my_vec_max_max[0] = maxmax * local_poles_array [2][0][0] ; | |
2667 | ||
2668 | my_point [1] = local_poles_array [0][0][1] ; | |
2669 | my_vec_min [1] = inverse_min * local_poles_array[0][1][1] ; | |
2670 | my_vec_max [1] = inverse_max * local_poles_array[1][0][1] ; | |
2671 | my_vec_min_min[1] = minmin * local_poles_array [0][2][1] ; | |
2672 | my_vec_min_max[1] = minmax * local_poles_array [1][1][1] ; | |
2673 | my_vec_max_max[1] = maxmax * local_poles_array [2][0][1] ; | |
2674 | ||
2675 | my_point [2] = local_poles_array [0][0][2] ; | |
2676 | my_vec_min [2] = inverse_min * local_poles_array[0][1][2] ; | |
2677 | my_vec_max [2] = inverse_max * local_poles_array[1][0][2] ; | |
2678 | my_vec_min_min[2] = minmin * local_poles_array [0][2][2] ; | |
2679 | my_vec_min_max[2] = minmax * local_poles_array [1][1][2] ; | |
2680 | my_vec_max_max[2] = maxmax * local_poles_array [2][0][2] ; | |
2681 | } | |
2682 | ||
2683 | //======================================================================= | |
2684 | //function : MovePoint | |
2685 | //purpose : Find the new poles which allows an old point (with a | |
2686 | // given u and v as parameters) to reach a new position | |
2687 | //======================================================================= | |
2688 | ||
2689 | void BSplSLib::MovePoint (const Standard_Real U, | |
2690 | const Standard_Real V, | |
2691 | const gp_Vec& Displ, | |
2692 | const Standard_Integer UIndex1, | |
2693 | const Standard_Integer UIndex2, | |
2694 | const Standard_Integer VIndex1, | |
2695 | const Standard_Integer VIndex2, | |
2696 | const Standard_Integer UDegree, | |
2697 | const Standard_Integer VDegree, | |
2698 | const Standard_Boolean Rational, | |
2699 | const TColgp_Array2OfPnt& Poles, | |
2700 | const TColStd_Array2OfReal& Weights, | |
2701 | const TColStd_Array1OfReal& UFlatKnots, | |
2702 | const TColStd_Array1OfReal& VFlatKnots, | |
2703 | Standard_Integer& UFirstIndex, | |
2704 | Standard_Integer& ULastIndex, | |
2705 | Standard_Integer& VFirstIndex, | |
2706 | Standard_Integer& VLastIndex, | |
2707 | TColgp_Array2OfPnt& NewPoles) | |
2708 | { | |
2709 | // calculate the UBSplineBasis in the parameter U | |
2710 | Standard_Integer UFirstNonZeroBsplineIndex; | |
2711 | math_Matrix UBSplineBasis(1, 1, | |
2712 | 1, UDegree+1); | |
2713 | Standard_Integer ErrorCod1 = BSplCLib::EvalBsplineBasis(1, | |
2714 | 0, | |
2715 | UDegree+1, | |
2716 | UFlatKnots, | |
2717 | U, | |
2718 | UFirstNonZeroBsplineIndex, | |
2719 | UBSplineBasis); | |
2720 | // calculate the VBSplineBasis in the parameter V | |
2721 | Standard_Integer VFirstNonZeroBsplineIndex; | |
2722 | math_Matrix VBSplineBasis(1, 1, | |
2723 | 1, VDegree+1); | |
2724 | Standard_Integer ErrorCod2 = BSplCLib::EvalBsplineBasis(1, | |
2725 | 0, | |
2726 | VDegree+1, | |
2727 | VFlatKnots, | |
2728 | V, | |
2729 | VFirstNonZeroBsplineIndex, | |
2730 | VBSplineBasis); | |
2731 | if (ErrorCod1 || ErrorCod2) { | |
2732 | UFirstIndex = 0; | |
2733 | ULastIndex = 0; | |
2734 | VFirstIndex = 0; | |
2735 | VLastIndex = 0; | |
2736 | return; | |
2737 | } | |
2738 | ||
2739 | // find the span which is predominant for parameter U | |
2740 | UFirstIndex = UFirstNonZeroBsplineIndex; | |
2741 | ULastIndex = UFirstNonZeroBsplineIndex + UDegree ; | |
2742 | if (UFirstIndex < UIndex1) UFirstIndex = UIndex1; | |
2743 | if (ULastIndex > UIndex2) ULastIndex = UIndex2; | |
2744 | ||
2745 | Standard_Real maxValue = 0.0; | |
2746 | Standard_Integer i, ukk1=0, ukk2; | |
2747 | ||
2748 | for (i = UFirstIndex-UFirstNonZeroBsplineIndex+1; i <= ULastIndex-UFirstNonZeroBsplineIndex+1; i++) { | |
2749 | if (UBSplineBasis(1,i) > maxValue) { | |
2750 | ukk1 = i + UFirstNonZeroBsplineIndex - 1; | |
2751 | maxValue = UBSplineBasis(1,i); | |
2752 | } | |
2753 | } | |
2754 | ||
2755 | // find a ukk2 if symetriy | |
2756 | ukk2 = ukk1; | |
2757 | i = ukk1 - UFirstNonZeroBsplineIndex + 2; | |
2758 | if ((ukk1+1) <= ULastIndex) { | |
2759 | if (Abs(UBSplineBasis(1, ukk1-UFirstNonZeroBsplineIndex+2) - maxValue) < 1.e-10) { | |
2760 | ukk2 = ukk1+1; | |
2761 | } | |
2762 | } | |
2763 | ||
2764 | // find the span which is predominant for parameter V | |
2765 | VFirstIndex = VFirstNonZeroBsplineIndex; | |
2766 | VLastIndex = VFirstNonZeroBsplineIndex + VDegree ; | |
2767 | ||
2768 | if (VFirstIndex < VIndex1) VFirstIndex = VIndex1; | |
2769 | if (VLastIndex > VIndex2) VLastIndex = VIndex2; | |
2770 | ||
2771 | maxValue = 0.0; | |
2772 | Standard_Integer j, vkk1=0, vkk2; | |
2773 | ||
2774 | for (j = VFirstIndex-VFirstNonZeroBsplineIndex+1; j <= VLastIndex-VFirstNonZeroBsplineIndex+1; j++) { | |
2775 | if (VBSplineBasis(1,j) > maxValue) { | |
2776 | vkk1 = j + VFirstNonZeroBsplineIndex - 1; | |
2777 | maxValue = VBSplineBasis(1,j); | |
2778 | } | |
2779 | } | |
2780 | ||
2781 | // find a vkk2 if symetriy | |
2782 | vkk2 = vkk1; | |
2783 | j = vkk1 - VFirstNonZeroBsplineIndex + 2; | |
2784 | if ((vkk1+1) <= VLastIndex) { | |
2785 | if (Abs(VBSplineBasis(1, vkk1-VFirstNonZeroBsplineIndex+2) - maxValue) < 1.e-10) { | |
2786 | vkk2 = vkk1+1; | |
2787 | } | |
2788 | } | |
2789 | ||
2790 | // compute the vector of displacement | |
2791 | Standard_Real D1 = 0.0; | |
2792 | Standard_Real D2 = 0.0; | |
2793 | Standard_Real hN, Coef, DvalU, DvalV; | |
2794 | ||
2795 | Standard_Integer ii, jj; | |
2796 | ||
2797 | for (i = 1; i <= UDegree+1; i++) { | |
2798 | ii = i + UFirstNonZeroBsplineIndex - 1; | |
2799 | if (ii < ukk1) { | |
2800 | DvalU = ukk1-ii; | |
2801 | } | |
2802 | else if (ii > ukk2) { | |
2803 | DvalU = ii - ukk2; | |
2804 | } | |
2805 | else { | |
2806 | DvalU = 0.0; | |
2807 | } | |
2808 | ||
2809 | for (j = 1; j <= VDegree+1; j++) { | |
2810 | jj = j + VFirstNonZeroBsplineIndex - 1; | |
2811 | if (Rational) { | |
2812 | hN = Weights(ii, jj)*UBSplineBasis(1, i)*VBSplineBasis(1,j); | |
2813 | D2 += hN; | |
2814 | } | |
2815 | else { | |
2816 | hN = UBSplineBasis(1, i)*VBSplineBasis(1,j); | |
2817 | } | |
2818 | if (ii >= UFirstIndex && ii <= ULastIndex && jj >= VFirstIndex && jj <= VLastIndex) { | |
2819 | if (jj < vkk1) { | |
2820 | DvalV = vkk1-jj; | |
2821 | } | |
2822 | else if (jj > vkk2) { | |
2823 | DvalV = jj - vkk2; | |
2824 | } | |
2825 | else { | |
2826 | DvalV = 0.0; | |
2827 | } | |
2828 | D1 += 1./(DvalU + DvalV + 1.) * hN; | |
2829 | } | |
2830 | } | |
2831 | } | |
2832 | ||
2833 | if (Rational) { | |
2834 | Coef = D2/D1; | |
2835 | } | |
2836 | else { | |
2837 | Coef = 1./D1; | |
2838 | } | |
2839 | ||
2840 | // compute the new poles | |
2841 | ||
2842 | for (i=Poles.LowerRow(); i<=Poles.UpperRow(); i++) { | |
2843 | if (i < ukk1) { | |
2844 | DvalU = ukk1-i; | |
2845 | } | |
2846 | else if (i > ukk2) { | |
2847 | DvalU = i - ukk2; | |
2848 | } | |
2849 | else { | |
2850 | DvalU = 0.0; | |
2851 | } | |
2852 | ||
2853 | for (j=Poles.LowerCol(); j<=Poles.UpperCol(); j++) { | |
2854 | if (i >= UFirstIndex && i <= ULastIndex && j >= VFirstIndex && j <= VLastIndex) { | |
2855 | if (j < vkk1) { | |
2856 | DvalV = vkk1-j; | |
2857 | } | |
2858 | else if (j > vkk2) { | |
2859 | DvalV = j - vkk2; | |
2860 | } | |
2861 | else { | |
2862 | DvalV = 0.0; | |
2863 | } | |
2864 | NewPoles(i,j) = Poles(i,j).Translated((Coef/(DvalU + DvalV + 1.))*Displ); | |
2865 | } | |
2866 | else { | |
2867 | NewPoles(i,j) = Poles(i,j); | |
2868 | } | |
2869 | } | |
2870 | } | |
2871 | } | |
2872 | ||
2873 | //======================================================================= | |
0d969553 Y |
2874 | // function : Resolution |
2875 | // purpose : this computes an estimate for the maximum of the | |
7fd59977 | 2876 | // partial derivatives both in U and in V |
2877 | // | |
2878 | // | |
0d969553 Y |
2879 | // The calculation resembles at the calculation of curves with |
2880 | // additional index for the control point. Let Si,j be the | |
2881 | // control points for ls surface and Di,j the weights. | |
2882 | // The checking of upper bounds for the partial derivatives | |
2883 | // will be omitted and Su is the next upper bound in the polynomial case : | |
7fd59977 | 2884 | // |
2885 | // | |
2886 | // | |
2887 | // | Si,j - Si-1,j | | |
2888 | // d * Max | ------------- | | |
2889 | // i = 2,n | ti+d - ti | | |
2890 | // i=1.m | |
2891 | // | |
2892 | // | |
0d969553 | 2893 | // and in the rational case : |
7fd59977 | 2894 | // |
2895 | // | |
2896 | // | |
2897 | // Di,j * (Si,j - Sk,j) - Di-1,j * (Si-1,j - Sk,j) | |
2898 | // Max Max d * ----------------------------------------------- | |
2899 | // k=1,n i dans Rj ti+d - ti | |
2900 | // j=1,m | |
2901 | // ---------------------------------------------------------------------- | |
2902 | // | |
2903 | // Min Di,j | |
2904 | // i=1,n | |
2905 | // j=1,m | |
2906 | // | |
2907 | // | |
2908 | // | |
0d969553 | 2909 | // with Rj = {j-d, ...., j+d+d+1}. |
7fd59977 | 2910 | // |
2911 | // | |
2912 | //======================================================================= | |
2913 | ||
2914 | void BSplSLib::Resolution(const TColgp_Array2OfPnt& Poles, | |
2915 | const TColStd_Array2OfReal& Weights, | |
2916 | const TColStd_Array1OfReal& UKnots, | |
2917 | const TColStd_Array1OfReal& VKnots, | |
2918 | const TColStd_Array1OfInteger& UMults, | |
2919 | const TColStd_Array1OfInteger& VMults, | |
2920 | const Standard_Integer UDegree, | |
2921 | const Standard_Integer VDegree, | |
2922 | const Standard_Boolean URational, | |
2923 | const Standard_Boolean VRational, | |
2924 | const Standard_Boolean UPeriodic, | |
2925 | const Standard_Boolean VPeriodic, | |
2926 | const Standard_Real Tolerance3D, | |
2927 | Standard_Real& UTolerance, | |
2928 | Standard_Real& VTolerance) | |
2929 | { | |
2930 | Standard_Real Wij,Wmj,Wji,Wjm; | |
2931 | Standard_Real Xij,Xmj,Xji,Xjm,Xpq,Xqp; | |
2932 | Standard_Real Yij,Ymj,Yji,Yjm,Ypq,Yqp; | |
2933 | Standard_Real Zij,Zmj,Zji,Zjm,Zpq,Zqp; | |
2934 | Standard_Real factor,value,min,min_weights=0,inverse,max_derivative[2]; | |
2935 | ||
2936 | max_derivative[0] = max_derivative[1] = 0.0e0 ; | |
2937 | ||
2938 | Standard_Integer PRowLength, PColLength; | |
2939 | Standard_Integer ii,jj,pp,qq,ii_index,jj_index,pp_index,qq_index; | |
2940 | Standard_Integer ii_minus,upper[2],lower[2],poles_length[2]; | |
2941 | Standard_Integer num_poles[2],num_flat_knots[2]; | |
2942 | ||
2943 | num_flat_knots[0] = | |
2944 | BSplCLib::KnotSequenceLength(UMults, | |
2945 | UDegree, | |
2946 | UPeriodic) ; | |
2947 | num_flat_knots[1] = | |
2948 | BSplCLib::KnotSequenceLength(VMults, | |
2949 | VDegree, | |
2950 | VPeriodic) ; | |
2951 | TColStd_Array1OfReal flat_knots_in_u(1,num_flat_knots[0]) ; | |
2952 | TColStd_Array1OfReal flat_knots_in_v(1,num_flat_knots[1]) ; | |
2953 | BSplCLib::KnotSequence(UKnots, | |
2954 | UMults, | |
2955 | UDegree, | |
2956 | UPeriodic, | |
2957 | flat_knots_in_u) ; | |
2958 | BSplCLib::KnotSequence(VKnots, | |
2959 | VMults, | |
2960 | VDegree, | |
2961 | VPeriodic, | |
2962 | flat_knots_in_v) ; | |
2963 | PRowLength = Poles.RowLength(); | |
2964 | PColLength = Poles.ColLength(); | |
2965 | if (URational || VRational) { | |
2966 | Standard_Integer Wsize = PRowLength * PColLength; | |
2967 | const Standard_Real * WG = &Weights(Weights.LowerRow(),Weights.LowerCol()); | |
2968 | min_weights = WG[0]; | |
2969 | ||
2970 | for (ii = 1 ; ii < Wsize ; ii++) { | |
2971 | min = WG[ii]; | |
2972 | if (min_weights > min) min_weights = min; | |
2973 | } | |
2974 | } | |
2975 | Standard_Integer UD1 = UDegree + 1; | |
2976 | Standard_Integer VD1 = VDegree + 1; | |
2977 | num_poles[0] = num_flat_knots[0] - UD1; | |
2978 | num_poles[1] = num_flat_knots[1] - VD1; | |
2979 | poles_length[0] = PColLength; | |
2980 | poles_length[1] = PRowLength; | |
2981 | if(URational) { | |
2982 | Standard_Integer UD2 = UDegree << 1; | |
2983 | Standard_Integer VD2 = VDegree << 1; | |
2984 | ||
2985 | for (ii = 2 ; ii <= num_poles[0] ; ii++) { | |
2986 | ii_index = (ii - 1) % poles_length[0] + 1 ; | |
2987 | ii_minus = (ii - 2) % poles_length[0] + 1 ; | |
2988 | inverse = flat_knots_in_u(ii + UDegree) - flat_knots_in_u(ii) ; | |
2989 | inverse = 1.0e0 / inverse ; | |
2990 | lower[0] = ii - UD1; | |
2991 | if (lower[0] < 1) lower[0] = 1; | |
2992 | upper[0] = ii + UD2 + 1; | |
2993 | if (upper[0] > num_poles[0]) upper[0] = num_poles[0]; | |
2994 | ||
2995 | for ( jj = 1 ; jj <= num_poles[1] ; jj++) { | |
2996 | jj_index = (jj - 1) % poles_length[1] + 1 ; | |
2997 | lower[1] = jj - VD1; | |
2998 | if (lower[1] < 1) lower[1] = 1; | |
2999 | upper[1] = jj + VD2 + 1; | |
3000 | if (upper[1] > num_poles[1]) upper[1] = num_poles[1]; | |
3001 | const gp_Pnt& Pij = Poles .Value(ii_index,jj_index); | |
3002 | Wij = Weights.Value(ii_index,jj_index); | |
3003 | const gp_Pnt& Pmj = Poles .Value(ii_minus,jj_index); | |
3004 | Wmj = Weights.Value(ii_minus,jj_index); | |
3005 | Xij = Pij.X(); | |
3006 | Yij = Pij.Y(); | |
3007 | Zij = Pij.Z(); | |
3008 | Xmj = Pmj.X(); | |
3009 | Ymj = Pmj.Y(); | |
3010 | Zmj = Pmj.Z(); | |
3011 | ||
3012 | for (pp = lower[0] ; pp <= upper[0] ; pp++) { | |
3013 | pp_index = (pp - 1) % poles_length[0] + 1 ; | |
3014 | ||
3015 | for (qq = lower[1] ; qq <= upper[1] ; qq++) { | |
3016 | value = 0.0e0 ; | |
3017 | qq_index = (qq - 1) % poles_length[1] + 1 ; | |
3018 | const gp_Pnt& Ppq = Poles.Value(pp_index,qq_index); | |
3019 | Xpq = Ppq.X(); | |
3020 | Ypq = Ppq.Y(); | |
3021 | Zpq = Ppq.Z(); | |
3022 | factor = (Xpq - Xij) * Wij; | |
3023 | factor -= (Xpq - Xmj) * Wmj; | |
3024 | if (factor < 0) factor = - factor; | |
3025 | value += factor ; | |
3026 | factor = (Ypq - Yij) * Wij; | |
3027 | factor -= (Ypq - Ymj) * Wmj; | |
3028 | if (factor < 0) factor = - factor; | |
3029 | value += factor ; | |
3030 | factor = (Zpq - Zij) * Wij; | |
3031 | factor -= (Zpq - Zmj) * Wmj; | |
3032 | if (factor < 0) factor = - factor; | |
3033 | value += factor ; | |
3034 | value *= inverse ; | |
3035 | if (max_derivative[0] < value) max_derivative[0] = value ; | |
3036 | } | |
3037 | } | |
3038 | } | |
3039 | } | |
3040 | max_derivative[0] /= min_weights ; | |
3041 | } | |
3042 | else { | |
3043 | ||
3044 | for (ii = 2 ; ii <= num_poles[0] ; ii++) { | |
3045 | ii_index = (ii - 1) % poles_length[0] + 1 ; | |
3046 | ii_minus = (ii - 2) % poles_length[0] + 1 ; | |
3047 | inverse = flat_knots_in_u(ii + UDegree) - flat_knots_in_u(ii) ; | |
3048 | inverse = 1.0e0 / inverse ; | |
3049 | ||
3050 | for ( jj = 1 ; jj <= num_poles[1] ; jj++) { | |
3051 | jj_index = (jj - 1) % poles_length[1] + 1 ; | |
3052 | value = 0.0e0 ; | |
3053 | const gp_Pnt& Pij = Poles.Value(ii_index,jj_index); | |
3054 | const gp_Pnt& Pmj = Poles.Value(ii_minus,jj_index); | |
3055 | factor = Pij.X() - Pmj.X(); | |
3056 | if (factor < 0) factor = - factor; | |
3057 | value += factor; | |
3058 | factor = Pij.Y() - Pmj.Y(); | |
3059 | if (factor < 0) factor = - factor; | |
3060 | value += factor; | |
3061 | factor = Pij.Z() - Pmj.Z(); | |
3062 | if (factor < 0) factor = - factor; | |
3063 | value += factor; | |
3064 | value *= inverse ; | |
3065 | if (max_derivative[0] < value) max_derivative[0] = value ; | |
3066 | } | |
3067 | } | |
3068 | } | |
3069 | max_derivative[0] *= UDegree ; | |
3070 | if(VRational) { | |
3071 | Standard_Integer UD2 = UDegree << 1; | |
3072 | Standard_Integer VD2 = VDegree << 1; | |
3073 | ||
3074 | for (ii = 2 ; ii <= num_poles[1] ; ii++) { | |
3075 | ii_index = (ii - 1) % poles_length[1] + 1 ; | |
3076 | ii_minus = (ii - 2) % poles_length[1] + 1 ; | |
3077 | inverse = flat_knots_in_v(ii + VDegree) - flat_knots_in_v(ii) ; | |
3078 | inverse = 1.0e0 / inverse ; | |
3079 | lower[0] = ii - VD1; | |
3080 | if (lower[0] < 1) lower[0] = 1; | |
3081 | upper[0] = ii + VD2 + 1; | |
3082 | if (upper[0] > num_poles[1]) upper[0] = num_poles[1]; | |
3083 | ||
3084 | for ( jj = 1 ; jj <= num_poles[0] ; jj++) { | |
3085 | jj_index = (jj - 1) % poles_length[0] + 1 ; | |
3086 | lower[1] = jj - UD1; | |
3087 | if (lower[1] < 1) lower[1] = 1; | |
3088 | upper[1] = jj + UD2 + 1; | |
3089 | if (upper[1] > num_poles[0]) upper[1] = num_poles[0]; | |
3090 | const gp_Pnt& Pji = Poles .Value(jj_index,ii_index); | |
3091 | Wji = Weights.Value(jj_index,ii_index); | |
3092 | const gp_Pnt& Pjm = Poles .Value(jj_index,ii_minus); | |
3093 | Wjm = Weights.Value(jj_index,ii_minus); | |
3094 | Xji = Pji.X(); | |
3095 | Yji = Pji.Y(); | |
3096 | Zji = Pji.Z(); | |
3097 | Xjm = Pjm.X(); | |
3098 | Yjm = Pjm.Y(); | |
3099 | Zjm = Pjm.Z(); | |
3100 | ||
3101 | for (pp = lower[1] ; pp <= upper[1] ; pp++) { | |
3102 | pp_index = (pp - 1) % poles_length[1] + 1 ; | |
3103 | ||
3104 | for (qq = lower[0] ; qq <= upper[0] ; qq++) { | |
3105 | value = 0.0e0 ; | |
3106 | qq_index = (qq - 1) % poles_length[0] + 1 ; | |
3107 | const gp_Pnt& Pqp = Poles.Value(qq_index,pp_index); | |
3108 | Xqp = Pqp.X(); | |
3109 | Yqp = Pqp.Y(); | |
3110 | Zqp = Pqp.Z(); | |
3111 | factor = (Xqp - Xji) * Wji; | |
3112 | factor -= (Xqp - Xjm) * Wjm; | |
3113 | if (factor < 0) factor = - factor; | |
3114 | value += factor ; | |
3115 | factor = (Yqp - Yji) * Wji; | |
3116 | factor -= (Yqp - Yjm) * Wjm; | |
3117 | if (factor < 0) factor = - factor; | |
3118 | value += factor ; | |
3119 | factor = (Zqp - Zji) * Wji; | |
3120 | factor -= (Zqp - Zjm) * Wjm; | |
3121 | if (factor < 0) factor = - factor; | |
3122 | value += factor ; | |
3123 | value *= inverse ; | |
3124 | if (max_derivative[1] < value) max_derivative[1] = value ; | |
3125 | } | |
3126 | } | |
3127 | } | |
3128 | } | |
3129 | max_derivative[1] /= min_weights ; | |
3130 | } | |
3131 | else { | |
3132 | ||
3133 | for (ii = 2 ; ii <= num_poles[1] ; ii++) { | |
3134 | ii_index = (ii - 1) % poles_length[1] + 1 ; | |
3135 | ii_minus = (ii - 2) % poles_length[1] + 1 ; | |
3136 | inverse = flat_knots_in_v(ii + VDegree) - flat_knots_in_v(ii) ; | |
3137 | inverse = 1.0e0 / inverse ; | |
3138 | ||
3139 | for ( jj = 1 ; jj <= num_poles[0] ; jj++) { | |
3140 | jj_index = (jj - 1) % poles_length[0] + 1 ; | |
3141 | value = 0.0e0 ; | |
3142 | const gp_Pnt& Pji = Poles.Value(jj_index,ii_index); | |
3143 | const gp_Pnt& Pjm = Poles.Value(jj_index,ii_minus); | |
3144 | factor = Pji.X() - Pjm.X() ; | |
3145 | if (factor < 0) factor = - factor; | |
3146 | value += factor; | |
3147 | factor = Pji.Y() - Pjm.Y() ; | |
3148 | if (factor < 0) factor = - factor; | |
3149 | value += factor; | |
3150 | factor = Pji.Z() - Pjm.Z() ; | |
3151 | if (factor < 0) factor = - factor; | |
3152 | value += factor; | |
3153 | value *= inverse ; | |
3154 | if (max_derivative[1] < value) max_derivative[1] = value ; | |
3155 | } | |
3156 | } | |
3157 | } | |
3158 | max_derivative[1] *= VDegree ; | |
3159 | max_derivative[0] *= M_SQRT2 ; | |
3160 | max_derivative[1] *= M_SQRT2 ; | |
3161 | if(max_derivative[0] && max_derivative[1]) { | |
3162 | UTolerance = Tolerance3D / max_derivative[0] ; | |
3163 | VTolerance = Tolerance3D / max_derivative[1] ; | |
3164 | } | |
3165 | else { | |
3166 | UTolerance=VTolerance=0.0; | |
3167 | #ifdef DEB | |
3168 | cout<<"ElSLib.cxx : maxderivative = 0.0 "<<endl; | |
3169 | #endif | |
3170 | } | |
3171 | } | |
3172 | ||
3173 | //======================================================================= | |
3174 | //function : Interpolate | |
3175 | //purpose : | |
3176 | //======================================================================= | |
3177 | ||
3178 | void BSplSLib::Interpolate(const Standard_Integer UDegree, | |
3179 | const Standard_Integer VDegree, | |
3180 | const TColStd_Array1OfReal& UFlatKnots, | |
3181 | const TColStd_Array1OfReal& VFlatKnots, | |
3182 | const TColStd_Array1OfReal& UParameters, | |
3183 | const TColStd_Array1OfReal& VParameters, | |
3184 | TColgp_Array2OfPnt& Poles, | |
3185 | TColStd_Array2OfReal& Weights, | |
3186 | Standard_Integer& InversionProblem) | |
3187 | { | |
3188 | Standard_Integer ii, jj, ll, kk, dimension; | |
3189 | Standard_Integer ULength = UParameters.Length(); | |
3190 | Standard_Integer VLength = VParameters.Length(); | |
3191 | Standard_Real * poles_array; | |
3192 | ||
0d969553 | 3193 | // extraction of iso u |
7fd59977 | 3194 | dimension = 4*ULength; |
3195 | TColStd_Array2OfReal Points(1, VLength, | |
3196 | 1, dimension); | |
3197 | ||
3198 | Handle(TColStd_HArray1OfInteger) ContactOrder = | |
3199 | new (TColStd_HArray1OfInteger)(1, VLength); | |
3200 | ContactOrder->Init(0); | |
3201 | ||
3202 | for (ii=1; ii <= VLength; ii++) { | |
3203 | ||
3204 | for (jj=1, ll=1; jj<= ULength; jj++, ll+=4) { | |
3205 | Points(ii,ll) = Poles(jj, ii).X(); | |
3206 | Points(ii,ll+1) = Poles(jj, ii).Y(); | |
3207 | Points(ii,ll+2) = Poles(jj, ii).Z(); | |
3208 | Points(ii,ll+3) = Weights(jj,ii) ; | |
3209 | } | |
3210 | } | |
3211 | ||
0d969553 | 3212 | // interpolation of iso u |
7fd59977 | 3213 | poles_array = (Standard_Real *) &Points.ChangeValue(1,1) ; |
3214 | BSplCLib::Interpolate(VDegree, | |
3215 | VFlatKnots, | |
3216 | VParameters, | |
3217 | ContactOrder->Array1(), | |
3218 | dimension, | |
3219 | poles_array[0], | |
3220 | InversionProblem) ; | |
3221 | if (InversionProblem != 0) return; | |
3222 | ||
0d969553 | 3223 | // extraction of iso v |
7fd59977 | 3224 | |
3225 | dimension = VLength*4; | |
3226 | TColStd_Array2OfReal IsoPoles(1, ULength, | |
3227 | 1, dimension); | |
3228 | ||
3229 | ContactOrder = new (TColStd_HArray1OfInteger)(1, ULength); | |
3230 | ContactOrder->Init(0); | |
3231 | poles_array = (Standard_Real *) &IsoPoles.ChangeValue(1,1) ; | |
3232 | ||
3233 | for (ii=1, kk=1; ii <= ULength; ii++, kk+=4) { | |
3234 | ||
3235 | for (jj=1, ll=1; jj<= VLength; jj++, ll+=4) { | |
3236 | IsoPoles (ii,ll) = Points(jj, kk); | |
3237 | IsoPoles (ii,ll+1) = Points(jj, kk+1); | |
3238 | IsoPoles (ii,ll+2) = Points(jj, kk+2); | |
3239 | IsoPoles (ii,ll+3) = Points(jj, kk+3); | |
3240 | } | |
3241 | } | |
0d969553 | 3242 | // interpolation of iso v |
7fd59977 | 3243 | BSplCLib::Interpolate(UDegree, |
3244 | UFlatKnots, | |
3245 | UParameters, | |
3246 | ContactOrder->Array1(), | |
3247 | dimension, | |
3248 | poles_array[0], | |
3249 | InversionProblem); | |
3250 | ||
0d969553 | 3251 | // return results |
7fd59977 | 3252 | |
3253 | for (ii=1; ii <= ULength; ii++) { | |
3254 | ||
3255 | for (jj=1, ll=1; jj<= VLength; jj++, ll+=4) { | |
3256 | gp_Pnt Pnt(IsoPoles(ii,ll), IsoPoles(ii,ll+1), IsoPoles(ii,ll+2)); | |
3257 | Poles.SetValue(ii, jj, Pnt); | |
3258 | Weights.SetValue(ii,jj,IsoPoles(ii,ll+3)) ; | |
3259 | } | |
3260 | } | |
3261 | } | |
3262 | ||
3263 | //======================================================================= | |
3264 | //function : Interpolate | |
3265 | //purpose : | |
3266 | //======================================================================= | |
3267 | ||
3268 | void BSplSLib::Interpolate(const Standard_Integer UDegree, | |
3269 | const Standard_Integer VDegree, | |
3270 | const TColStd_Array1OfReal& UFlatKnots, | |
3271 | const TColStd_Array1OfReal& VFlatKnots, | |
3272 | const TColStd_Array1OfReal& UParameters, | |
3273 | const TColStd_Array1OfReal& VParameters, | |
3274 | TColgp_Array2OfPnt& Poles, | |
3275 | Standard_Integer& InversionProblem) | |
3276 | { | |
3277 | Standard_Integer ii, jj, ll, kk, dimension; | |
3278 | Standard_Integer ULength = UParameters.Length(); | |
3279 | Standard_Integer VLength = VParameters.Length(); | |
3280 | Standard_Real * poles_array; | |
3281 | ||
0d969553 | 3282 | // extraction of iso u |
7fd59977 | 3283 | dimension = 3*ULength; |
3284 | TColStd_Array2OfReal Points(1, VLength, | |
3285 | 1, dimension); | |
3286 | ||
3287 | Handle(TColStd_HArray1OfInteger) ContactOrder = | |
3288 | new (TColStd_HArray1OfInteger)(1, VLength); | |
3289 | ContactOrder->Init(0); | |
3290 | ||
3291 | for (ii=1; ii <= VLength; ii++) { | |
3292 | ||
3293 | for (jj=1, ll=1; jj<= ULength; jj++, ll+=3) { | |
3294 | Points(ii,ll) = Poles(jj, ii).X(); | |
3295 | Points(ii,ll+1) = Poles(jj, ii).Y(); | |
3296 | Points(ii,ll+2) = Poles(jj, ii).Z(); | |
3297 | } | |
3298 | } | |
3299 | ||
0d969553 | 3300 | // interpolation of iso u |
7fd59977 | 3301 | poles_array = (Standard_Real *) &Points.ChangeValue(1,1) ; |
3302 | BSplCLib::Interpolate(VDegree, | |
3303 | VFlatKnots, | |
3304 | VParameters, | |
3305 | ContactOrder->Array1(), | |
3306 | dimension, | |
3307 | poles_array[0], | |
3308 | InversionProblem) ; | |
3309 | if (InversionProblem != 0) return; | |
3310 | ||
0d969553 | 3311 | // extraction of iso v |
7fd59977 | 3312 | |
3313 | dimension = VLength*3; | |
3314 | TColStd_Array2OfReal IsoPoles(1, ULength, | |
3315 | 1, dimension); | |
3316 | ||
3317 | ContactOrder = new (TColStd_HArray1OfInteger)(1, ULength); | |
3318 | ContactOrder->Init(0); | |
3319 | poles_array = (Standard_Real *) &IsoPoles.ChangeValue(1,1) ; | |
3320 | ||
3321 | for (ii=1, kk=1; ii <= ULength; ii++, kk+=3) { | |
3322 | ||
3323 | for (jj=1, ll=1; jj<= VLength; jj++, ll+=3) { | |
3324 | IsoPoles (ii,ll) = Points(jj, kk); | |
3325 | IsoPoles (ii,ll+1) = Points(jj, kk+1); | |
3326 | IsoPoles (ii,ll+2) = Points(jj, kk+2); | |
3327 | } | |
3328 | } | |
0d969553 | 3329 | // interpolation of iso v |
7fd59977 | 3330 | BSplCLib::Interpolate(UDegree, |
3331 | UFlatKnots, | |
3332 | UParameters, | |
3333 | ContactOrder->Array1(), | |
3334 | dimension, | |
3335 | poles_array[0], | |
3336 | InversionProblem); | |
3337 | ||
0d969553 | 3338 | // return results |
7fd59977 | 3339 | |
3340 | for (ii=1; ii <= ULength; ii++) { | |
3341 | ||
3342 | for (jj=1, ll=1; jj<= VLength; jj++, ll+=3) { | |
3343 | gp_Pnt Pnt(IsoPoles(ii,ll), IsoPoles(ii,ll+1), IsoPoles(ii,ll+2)); | |
3344 | Poles.SetValue(ii, jj, Pnt); | |
3345 | } | |
3346 | } | |
3347 | } | |
3348 | ||
3349 | //======================================================================= | |
3350 | //function : FunctionMultiply | |
3351 | //purpose : | |
3352 | //======================================================================= | |
3353 | ||
3354 | void BSplSLib::FunctionMultiply | |
3355 | (const BSplSLib_EvaluatorFunction& Function, | |
3356 | const Standard_Integer UBSplineDegree, | |
3357 | const Standard_Integer VBSplineDegree, | |
3358 | const TColStd_Array1OfReal& UBSplineKnots, | |
3359 | const TColStd_Array1OfReal& VBSplineKnots, | |
3360 | const TColStd_Array1OfInteger & UMults, | |
3361 | const TColStd_Array1OfInteger & VMults, | |
3362 | const TColgp_Array2OfPnt& Poles, | |
3363 | const TColStd_Array2OfReal& Weights, | |
3364 | const TColStd_Array1OfReal& UFlatKnots, | |
3365 | const TColStd_Array1OfReal& VFlatKnots, | |
3366 | const Standard_Integer UNewDegree, | |
3367 | const Standard_Integer VNewDegree, | |
3368 | TColgp_Array2OfPnt& NewNumerator, | |
3369 | TColStd_Array2OfReal& NewDenominator, | |
3370 | Standard_Integer& Status) | |
3371 | { | |
3372 | Standard_Integer num_uparameters, | |
3373 | // ii,jj,kk, | |
3374 | ii,jj, | |
3375 | error_code, | |
3376 | num_vparameters ; | |
3377 | Standard_Real result ; | |
3378 | ||
3379 | num_uparameters = UFlatKnots.Length() - UNewDegree - 1 ; | |
3380 | num_vparameters = VFlatKnots.Length() - VNewDegree - 1 ; | |
3381 | TColStd_Array1OfReal UParameters(1,num_uparameters) ; | |
3382 | TColStd_Array1OfReal VParameters(1,num_vparameters) ; | |
3383 | ||
3384 | if ((NewNumerator.ColLength() == num_uparameters) && | |
3385 | (NewNumerator.RowLength() == num_vparameters) && | |
3386 | (NewDenominator.ColLength() == num_uparameters) && | |
3387 | (NewDenominator.RowLength() == num_vparameters)) { | |
3388 | ||
3389 | ||
3390 | BSplCLib::BuildSchoenbergPoints(UNewDegree, | |
3391 | UFlatKnots, | |
3392 | UParameters) ; | |
3393 | ||
3394 | BSplCLib::BuildSchoenbergPoints(VNewDegree, | |
3395 | VFlatKnots, | |
3396 | VParameters) ; | |
3397 | ||
3398 | for (ii = 1 ; ii <= num_uparameters ; ii++) { | |
3399 | ||
3400 | for (jj = 1 ; jj <= num_vparameters ; jj++) { | |
3401 | HomogeneousD0(UParameters(ii), | |
3402 | VParameters(jj), | |
3403 | 0, | |
3404 | 0, | |
3405 | Poles, | |
3406 | Weights, | |
3407 | UBSplineKnots, | |
3408 | VBSplineKnots, | |
3409 | UMults, | |
3410 | VMults, | |
3411 | UBSplineDegree, | |
3412 | VBSplineDegree, | |
3413 | Standard_True, | |
3414 | Standard_True, | |
3415 | Standard_False, | |
3416 | Standard_False, | |
3417 | NewDenominator(ii,jj), | |
3418 | NewNumerator(ii,jj)) ; | |
3419 | ||
41194117 | 3420 | Function.Evaluate (0, |
7fd59977 | 3421 | UParameters(ii), |
3422 | VParameters(jj), | |
3423 | result, | |
3424 | error_code) ; | |
3425 | if (error_code) { | |
3426 | Standard_ConstructionError::Raise(); | |
3427 | } | |
3428 | gp_Pnt& P = NewNumerator(ii,jj); | |
3429 | P.SetX(P.X() * result); | |
3430 | P.SetY(P.Y() * result); | |
3431 | P.SetZ(P.Z() * result); | |
3432 | NewDenominator(ii,jj) *= result ; | |
3433 | } | |
3434 | } | |
3435 | Interpolate(UNewDegree, | |
3436 | VNewDegree, | |
3437 | UFlatKnots, | |
3438 | VFlatKnots, | |
3439 | UParameters, | |
3440 | VParameters, | |
3441 | NewNumerator, | |
3442 | NewDenominator, | |
3443 | Status) ; | |
3444 | } | |
3445 | else { | |
3446 | Standard_ConstructionError::Raise(); | |
3447 | } | |
3448 | } |