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