34 #include <feel/feelpoly/geomap.hpp>
39 #include <boost/assign/list_of.hpp>
40 #include <boost/assign/std/vector.hpp>
44 template<
class Convex,
47 class PointSetWarpBlend;
49 template<
class Convex,
52 class PointSetGaussLobatto;
54 template<
class Convex,
57 class PointSetFeketeSimplex :
public PointSetInterpolation<Convex::nDim, Order, T, Simplex>
62 typedef PointSetWarpBlend<Convex, Order, T> super;
66 static const uint32_type Dim = Convex::nDim;
67 static const uint16_type nPoints1D = Order+1;
69 static const size_type Shape = Convex::Shape;
71 static const bool is_simplex = Convex::is_simplex;
72 static const bool is_hypercube = Convex::is_hypercube;
74 typedef typename super::return_type return_type;
76 typedef ublas::vector<value_type> vector_type;
78 static const uint32_type topological_dimension = Convex::topological_dimension;
79 static const uint32_type numPoints = super::numPoints;
81 typedef Reference<Convex, Dim, Convex::nOrder, Dim, value_type> reference_convex_type;
83 typedef typename reference_convex_type::points_type points_type;
85 static const uint32_type nbPtsPerFace = super::nbPtsPerFace;
87 typedef std::vector<uint16_type> orbits_type;
89 reference_convex_type RefConv;
91 PointSetFeketeSimplex(
int interior = 0 )
93 PointSetWarpBlend<Convex, Order, T> G( interior );
95 points_type final_pts = G.points();
98 this->setEid( G.getEid() );
99 this->setPtE( G.getPtE() );
103 points_type Gt( Dim, nbPtsPerFace );
105 Gt = innerFeketePoints();
106 Gt = orderInteriorFace( Gt );
112 final_pts = putInPointset ( final_pts, Gt, G.interiorRangeById( 2, 0 ) );
118 this->setName(
"fekete", Order );
121 ~PointSetFeketeSimplex() {}
125 points_type innerFeketePoints()
127 points_type inner_pts ( Dim, nbPtsPerFace );
129 std::vector< std::vector<double> > pts ( nbPtsPerFace );
131 using namespace boost::assign;
137 pts[0] += -double( 1.0 )/double( 3.0 ), -double( 1.0 )/double( 3.0 );
143 pts[0] += -0.566915270681781, -0.566915270681781;
144 pts[1] += -0.566915270681781, 0.133830541363562;
145 pts[2] += 0.133830541363562, -0.566915270681781;
152 pts[0] += -0.703961057369349, -0.703961057370137;
153 pts[1] += -0.683302157170358, -0.158348921415476;
154 pts[2] += -0.703961057370137, 0.407922114739486;
155 pts[3] += -0.158348921414166, -0.683302157170358;
156 pts[4] += -0.158348921415476, -0.158348921414166;
157 pts[5] += 0.407922114739486, -0.703961057369349;
163 pts[0] += -0.333333333333333, -0.333333333333333;
164 pts[1] += -0.367460408129093, -0.765638165744237;
165 pts[2] += -0.787329063247951, -0.787329063247952;
166 pts[3] += -0.765638165744237, -0.367460408129093;
167 pts[4] += 0.133098573873330, -0.765638165744237;
168 pts[5] += -0.367460408129093, 0.133098573873330;
169 pts[6] += -0.765638165744237, 0.133098573873330;
170 pts[7] += 0.133098573873330, -0.367460408129093;
171 pts[8] += -0.787329063247952, 0.574658126495903;
172 pts[9] += 0.574658126495903, -0.787329063247951;
179 pts[0] += -0.473581790085882, -0.473581790086410;
180 pts[1] += -0.092029311878152, -0.815941376243689;
181 pts[2] += -0.513270713769908, -0.822113905089151;
182 pts[3] += -0.840822986239630, -0.840822986239633;
183 pts[4] += -0.473581790086410, -0.052836419827708;
184 pts[5] += -0.052836419827708, -0.473581790085882;
185 pts[6] += -0.815941376243689, -0.092029311878159;
186 pts[7] += -0.092029311878159, -0.092029311878152;
187 pts[8] += -0.822113905089151, -0.513270713769908;
188 pts[9] += 0.335384618859059, -0.822113905089151;
189 pts[10] += -0.513270713769908, 0.335384618859059;
190 pts[11] += -0.822113905089151, 0.335384618859059;
191 pts[12] += 0.335384618859059, -0.513270713769908;
192 pts[13] += -0.840822986239633, 0.681645972479263;
193 pts[14] += 0.681645972479263, -0.840822986239630;
199 pts[0] += -0.216365666632575, -0.567268666734080;
200 pts[1] += -0.579556771293157, -0.579556771293783;
201 pts[2] += -0.265519472998560, -0.853908185662976;
202 pts[3] += -0.616451325376556, -0.861487487652122;
203 pts[4] += -0.876851564079131, -0.876851564079171;
204 pts[5] += -0.567268666733596, -0.216365666633543;
205 pts[6] += -0.216365666634537, -0.216365666631639;
206 pts[7] += -0.579556771294394, 0.159113542587640;
207 pts[8] += 0.159113542586342, -0.579556771292601;
208 pts[9] += -0.853908185662855, -0.265519472998911;
209 pts[10] += 0.119427658661863, -0.853908185662948;
210 pts[11] += -0.265519472998830, 0.119427658661806;
211 pts[12] += -0.853908185662892, 0.119427658661475;
212 pts[13] += 0.119427658661483, -0.265519472998638;
213 pts[14] += -0.861487487652025, -0.616451325376726;
214 pts[15] += 0.477938813028659, -0.861487487651878;
215 pts[16] += -0.616451325376719, 0.477938813028829;
216 pts[17] += -0.861487487652288, 0.477938813028806;
217 pts[18] += 0.477938813028602, -0.616451325376548;
218 pts[19] += -0.876851564079185, 0.753703128158331;
219 pts[20] += 0.753703128158281, -0.876851564079116;
225 pts[0] += -0.333333333333333, -0.333333333333333;
226 pts[1] += -0.349513020087187, -0.643132482384194;
227 pts[2] += -0.659136359813528, -0.659136359813511;
228 pts[3] += -0.060082471166027, -0.879835057667481;
229 pts[4] += -0.397951578026397, -0.882287024211335;
230 pts[5] += -0.691219611179607, -0.889648384166848;
231 pts[6] += -0.902130860890619, -0.902130860890625;
232 pts[7] += -0.643132482384194, -0.349513020087187;
233 pts[8] += -0.007354497528619, -0.643132482384194;
234 pts[9] += -0.349513020087187, -0.007354497528619;
235 pts[10] += -0.643132482384194, -0.007354497528619;
236 pts[11] += -0.007354497528619, -0.349513020087187;
237 pts[12] += -0.659136359813511, 0.318272719627039;
238 pts[13] += 0.318272719627039, -0.659136359813528;
239 pts[14] += -0.879835057667481, -0.060082471166492;
240 pts[15] += -0.060082471166492, -0.060082471166027;
241 pts[16] += -0.882287024211335, -0.397951578026397;
242 pts[17] += 0.280238602237732, -0.882287024211335;
243 pts[18] += -0.397951578026397, 0.280238602237732;
244 pts[19] += -0.882287024211335, 0.280238602237732;
245 pts[20] += 0.280238602237732, -0.397951578026397;
246 pts[21] += -0.889648384166848, -0.691219611179607;
247 pts[22] += 0.580867995346455, -0.889648384166848;
248 pts[23] += -0.691219611179607, 0.580867995346455;
249 pts[24] += -0.889648384166848, 0.580867995346455;
250 pts[25] += 0.580867995346455, -0.691219611179607;
251 pts[26] += -0.902130860890625, 0.804261721781244;
252 pts[27] += 0.804261721781244, -0.902130860890619;
258 pts[0] += -0.239750033297594, -0.520499933404811;
259 pts[1] += -0.516800012629008, -0.516800012629009;
260 pts[2] += -0.257946265874160, -0.790148650478844;
261 pts[3] += -0.553131324174815, -0.752415268984459;
262 pts[4] += -0.781465283043698, -0.781465283043698;
263 pts[5] += -0.033736396065064, -0.932527207869870;
264 pts[6] += -0.484262543101076, -0.925302995602205;
265 pts[7] += -0.818984113526921, -0.931063288077205;
266 pts[8] += -0.520499933404811, -0.239750033297595;
267 pts[9] += -0.239750033297595, -0.239750033297594;
268 pts[10] += -0.516800012629009, 0.033600025258018;
269 pts[11] += 0.033600025258018, -0.516800012629008;
270 pts[12] += -0.790148650478844, -0.257946265874160;
271 pts[13] += 0.048094916353004, -0.790148650478844;
272 pts[14] += -0.257946265874160, 0.048094916353004;
273 pts[15] += -0.790148650478844, 0.048094916353004;
274 pts[16] += 0.048094916353004, -0.257946265874160;
275 pts[17] += -0.752415268984459, -0.553131324174815;
276 pts[18] += 0.305546593159274, -0.752415268984459;
277 pts[19] += -0.553131324174815, 0.305546593159274;
278 pts[20] += -0.752415268984459, 0.305546593159274;
279 pts[21] += 0.305546593159274, -0.553131324174815;
280 pts[22] += -0.781465283043698, 0.562930566087395;
281 pts[23] += 0.562930566087395, -0.781465283043698;
282 pts[24] += -0.932527207869870, -0.033736396065066;
283 pts[25] += -0.033736396065066, -0.033736396065064;
284 pts[26] += -0.925302995602205, -0.484262543101076;
285 pts[27] += 0.409565538703281, -0.925302995602205;
286 pts[28] += -0.484262543101076, 0.409565538703281;
287 pts[29] += -0.925302995602205, 0.409565538703281;
288 pts[30] += 0.409565538703281, -0.484262543101076;
289 pts[31] += -0.931063288077205, -0.818984113526921;
290 pts[32] += 0.750047401604126, -0.931063288077205;
291 pts[33] += -0.818984113526921, 0.750047401604126;
292 pts[34] += -0.931063288077205, 0.750047401604126;
293 pts[35] += 0.750047401604126, -0.818984113526921;
299 pts[0] += -0.426288429164565, -0.426288429164564;
300 pts[1] += -0.184095969280423, -0.631808061439155;
301 pts[2] += -0.586974557425838, -0.586974557425838;
302 pts[3] += -0.377399646207547, -0.775153413812684;
303 pts[4] += -0.776324974302030, -0.908258463253342;
304 pts[5] += -0.086138932580443, -0.827722134839114;
305 pts[6] += -0.633345990227640, -0.798648875634472;
306 pts[7] += -0.908258463253342, -0.776324974302030;
307 pts[8] += -0.218515810917888, -0.935838462756195;
308 pts[9] += -0.535040235101238, -0.937261747926706;
309 pts[10] += -0.928290828736822, -0.928290828736822;
310 pts[11] += -0.426288429164564, -0.147423141670871;
311 pts[12] += -0.147423141670871, -0.426288429164565;
312 pts[13] += -0.631808061439155, -0.184095969280421;
313 pts[14] += -0.184095969280421, -0.184095969280423;
314 pts[15] += -0.586974557425838, 0.173949114851675;
315 pts[16] += 0.173949114851675, -0.586974557425838;
316 pts[17] += -0.775153413812684, -0.377399646207547;
317 pts[18] += 0.152553060020230, -0.775153413812684;
318 pts[19] += -0.377399646207547, 0.152553060020230;
319 pts[20] += -0.775153413812684, 0.152553060020230;
320 pts[21] += 0.152553060020230, -0.377399646207547;
321 pts[22] += -0.908258463253342, 0.684583437555372;
322 pts[23] += 0.684583437555372, -0.776324974302030;
323 pts[24] += -0.827722134839114, -0.086138932580443;
324 pts[25] += -0.086138932580443, -0.086138932580443;
325 pts[26] += -0.798648875634472, -0.633345990227640;
326 pts[27] += 0.431994865862111, -0.798648875634472;
327 pts[28] += -0.633345990227640, 0.431994865862111;
328 pts[29] += -0.798648875634472, 0.431994865862111;
329 pts[30] += 0.431994865862111, -0.633345990227640;
330 pts[31] += -0.776324974302030, 0.684583437555372;
331 pts[32] += 0.684583437555372, -0.908258463253342;
332 pts[33] += -0.935838462756195, -0.218515810917888;
333 pts[34] += 0.154354273674083, -0.935838462756195;
334 pts[35] += -0.218515810917888, 0.154354273674083;
335 pts[36] += -0.935838462756195, 0.154354273674083;
336 pts[37] += 0.154354273674083, -0.218515810917888;
337 pts[38] += -0.937261747926706, -0.535040235101238;
338 pts[39] += 0.472301983027943, -0.937261747926706;
339 pts[40] += -0.535040235101238, 0.472301983027943;
340 pts[41] += -0.937261747926706, 0.472301983027943;
341 pts[42] += 0.472301983027943, -0.535040235101238;
342 pts[43] += -0.928290828736822, 0.856581657473645;
343 pts[44] += 0.856581657473645, -0.928290828736822;
349 pts[0] += -0.333333333333333, -0.333333333333333;
350 pts[1] += -0.366118633733524, -0.559725774975652;
351 pts[2] += -0.074155591290824, -0.559725774975640;
352 pts[3] += -0.624565774148092, -0.624565774148093;
353 pts[4] += -0.140340214413457, -0.719319571173060;
354 pts[5] += -0.431536181329258, -0.768507319183628;
355 pts[6] += -0.833349444442592, -0.833349444442587;
356 pts[7] += -0.205647119941729, -0.865429878796984;
357 pts[8] += -0.644199866452571, -0.818032093757191;
358 pts[9] += -0.949540550694726, -0.867065080338688;
359 pts[10] += -0.021888401958102, -0.956223196083790;
360 pts[11] += -0.394807319693724, -0.936337673359307;
361 pts[12] += -0.653266898894878, -0.945296284206355;
362 pts[13] += -0.867065080338677, -0.949540550694725;
363 pts[14] += -0.559725774975652, -0.074155591290824;
364 pts[15] += -0.074155591290824, -0.366118633733524;
365 pts[16] += -0.559725774975640, -0.366118633733536;
366 pts[17] += -0.366118633733536, -0.074155591290824;
367 pts[18] += -0.624565774148093, 0.249131548296185;
368 pts[19] += 0.249131548296185, -0.624565774148092;
369 pts[20] += -0.719319571173060, -0.140340214413483;
370 pts[21] += -0.140340214413483, -0.140340214413457;
371 pts[22] += -0.768507319183628, -0.431536181329258;
372 pts[23] += 0.200043500512886, -0.768507319183628;
373 pts[24] += -0.431536181329258, 0.200043500512886;
374 pts[25] += -0.768507319183628, 0.200043500512886;
375 pts[26] += 0.200043500512886, -0.431536181329258;
376 pts[27] += -0.833349444442587, 0.666698888885179;
377 pts[28] += 0.666698888885179, -0.833349444442592;
378 pts[29] += -0.865429878796984, -0.205647119941729;
379 pts[30] += 0.071076998738713, -0.865429878796984;
380 pts[31] += -0.205647119941729, 0.071076998738713;
381 pts[32] += -0.865429878796984, 0.071076998738713;
382 pts[33] += 0.071076998738713, -0.205647119941729;
383 pts[34] += -0.818032093757191, -0.644199866452571;
384 pts[35] += 0.462231960209762, -0.818032093757191;
385 pts[36] += -0.644199866452571, 0.462231960209762;
386 pts[37] += -0.818032093757191, 0.462231960209762;
387 pts[38] += 0.462231960209762, -0.644199866452571;
388 pts[39] += -0.867065080338688, 0.816605631033414;
389 pts[40] += 0.816605631033414, -0.949540550694726;
390 pts[41] += -0.956223196083790, -0.021888401958108;
391 pts[42] += -0.021888401958108, -0.021888401958102;
392 pts[43] += -0.936337673359307, -0.394807319693724;
393 pts[44] += 0.331144993053031, -0.936337673359307;
394 pts[45] += -0.394807319693724, 0.331144993053031;
395 pts[46] += -0.936337673359307, 0.331144993053031;
396 pts[47] += 0.331144993053031, -0.394807319693724;
397 pts[48] += -0.945296284206355, -0.653266898894878;
398 pts[49] += 0.598563183101232, -0.945296284206355;
399 pts[50] += -0.653266898894878, 0.598563183101232;
400 pts[51] += -0.945296284206355, 0.598563183101232;
401 pts[52] += 0.598563183101232, -0.653266898894878;
402 pts[53] += -0.949540550694725, 0.816605631033402;
403 pts[54] += 0.816605631033402, -0.867065080338677;
410 pts[0] += -0.411407513886432, -0.411407513886432;
411 pts[1] += -0.214052183872017, -0.571895632255967;
412 pts[2] += -0.539573883106313, -0.539573883106313;
413 pts[3] += -0.287868553838811, -0.717902048140164;
414 pts[4] += -0.540297218250118, -0.732989588419528;
415 pts[5] += -0.743226499430370, -0.743226499430370;
416 pts[6] += -0.071171195753188, -0.857657608493625;
417 pts[7] += -0.335863001538683, -0.859363917043220;
418 pts[8] += -0.623056409518609, -0.862030029517440;
419 pts[9] += -0.852002455492610, -0.852002455492610;
420 pts[10] +=-0.178334191212880, -0.954817865487350;
421 pts[11] +=-0.464674822424600, -0.950458941099439;
422 pts[12] +=-0.701942332364525, -0.951956806119627;
423 pts[13] +=-0.883949040041051, -0.955838523904429;
424 pts[14] +=-0.411407513886432, -0.177184972227137;
425 pts[15] +=-0.177184972227137, -0.411407513886432;
426 pts[16] +=-0.571895632255967, -0.214052183872017;
427 pts[17] +=-0.214052183872017, -0.214052183872017;
428 pts[18] +=-0.539573883106313, 0.079147766212627;
429 pts[19] += 0.079147766212627, -0.539573883106313;
430 pts[20] +=-0.717902048140164, -0.287868553838811;
431 pts[21] += 0.005770601978975, -0.717902048140164;
432 pts[22] +=-0.287868553838811, 0.005770601978975;
433 pts[23] +=-0.717902048140164, 0.005770601978975;
434 pts[24] += 0.005770601978975, -0.287868553838811;
435 pts[25] +=-0.732989588419528, -0.540297218250118;
436 pts[26] += 0.273286806669646, -0.732989588419528;
437 pts[27] +=-0.540297218250118, 0.273286806669646;
438 pts[28] +=-0.732989588419528, 0.273286806669646;
439 pts[29] += 0.273286806669646, -0.540297218250118;
440 pts[30] +=-0.743226499430370, 0.486452998860741;
441 pts[31] += 0.486452998860741, -0.743226499430370;
442 pts[32] +=-0.857657608493625, -0.071171195753188;
443 pts[33] +=-0.071171195753188, -0.071171195753188;
444 pts[34] +=-0.859363917043220, -0.335863001538683;
445 pts[35] += 0.195226918581903, -0.859363917043220;
446 pts[36] +=-0.335863001538683, 0.195226918581903;
447 pts[37] +=-0.859363917043220, 0.195226918581903;
448 pts[38] += 0.195226918581903, -0.335863001538683;
449 pts[39] +=-0.862030029517440, -0.623056409518609;
450 pts[40] += 0.485086439036049, -0.862030029517440;
451 pts[41] +=-0.623056409518609, 0.485086439036049;
452 pts[42] +=-0.862030029517440, 0.485086439036049;
453 pts[43] += 0.485086439036049, -0.623056409518609;
454 pts[44] +=-0.852002455492610, 0.704004910985221;
455 pts[45] += 0.704004910985221, -0.852002455492610;
456 pts[46] +=-0.954817865487350, -0.178334191212880;
457 pts[47] += 0.133152056700230, -0.954817865487350;
458 pts[48] +=-0.178334191212880, 0.133152056700230;
459 pts[49] +=-0.954817865487350, 0.133152056700230;
460 pts[50] += 0.133152056700230, -0.178334191212880;
461 pts[51] +=-0.950458941099439, -0.464674822424600;
462 pts[52] += 0.415133763524038, -0.950458941099439;
463 pts[53] +=-0.464674822424600, 0.415133763524038;
464 pts[54] +=-0.950458941099439, 0.415133763524038;
465 pts[55] += 0.415133763524038, -0.464674822424600;
466 pts[56] +=-0.951956806119627, -0.701942332364525;
467 pts[57] += 0.653899138484151, -0.951956806119627;
468 pts[58] +=-0.701942332364525, 0.653899138484151;
469 pts[59] +=-0.951956806119627, 0.653899138484151;
470 pts[60] += 0.653899138484151, -0.701942332364525;
471 pts[61] +=-0.955838523904429, -0.883949040041051;
472 pts[62] += 0.839787563945479, -0.955838523904429;
473 pts[63] +=-0.883949040041051, 0.839787563945479;
474 pts[64] +=-0.955838523904429, 0.839787563945479;
475 pts[65] += 0.839787563945479, -0.883949040041051;
484 pts[0] += -0.210489388870677, -0.579021222258655;
485 pts[1] += -0.183849077476319, -0.408075461261843;
486 pts[2] += -0.127347936150219, -0.745304127699574;
487 pts[3] += -0.540572408690582, -0.540572408690580;
488 pts[4] += -0.364367592015457, -0.689962524023234;
489 pts[5] += -0.736068596037139, -0.736068596037137;
490 pts[6] += 0.038332201767425, -0.861626855061358;
491 pts[7] += -0.554243348588859, -0.727059313582804;
492 pts[8] += -0.871281426433905, -0.769687425283662;
493 pts[9] += -0.176705346706054, -0.861626855061365;
494 pts[10] +=-0.382367340313839, -0.872946396511865;
495 pts[11] +=-0.584327224183587, -0.875713493198755;
496 pts[12] +=-0.769687425283663, -0.871281426433905;
497 pts[13] +=-0.173252532533942, -0.957943978206850;
498 pts[14] +=-0.459441974333255, -0.960810947366647;
499 pts[15] +=-0.697211314708751, -0.958833352267252;
500 pts[16] +=-0.858673547396615, -0.945197866913093;
501 pts[17] +=-0.955761107477727, -0.955761107477727;
502 pts[18] +=-0.579021222258655, -0.210489388870668;
503 pts[19] +=-0.210489388870668, -0.210489388870677;
504 pts[20] +=-0.408075461261843, -0.408075461261838;
505 pts[21] +=-0.408075461261838, -0.183849077476319;
506 pts[22] +=-0.745304127699574, -0.127347936150206;
507 pts[23] +=-0.127347936150206, -0.127347936150219;
508 pts[24] +=-0.540572408690580, 0.081144817381162;
509 pts[25] += 0.081144817381162, -0.540572408690582;
510 pts[26] +=-0.689962524023234, -0.364367592015457;
511 pts[27] += 0.054330116038691, -0.689962524023234;
512 pts[28] +=-0.364367592015457, 0.054330116038691;
513 pts[29] +=-0.689962524023234, 0.054330116038691;
514 pts[30] += 0.054330116038691, -0.364367592015457;
515 pts[31] +=-0.736068596037137, 0.472137192074276;
516 pts[32] += 0.472137192074276, -0.736068596037139;
517 pts[33] +=-0.861626855061358, -0.176705346706066;
518 pts[34] +=-0.176705346706066, 0.038332201767425;
519 pts[35] +=-0.727059313582804, -0.554243348588859;
520 pts[36] += 0.281302662171663, -0.727059313582804;
521 pts[37] +=-0.554243348588859, 0.281302662171663;
522 pts[38] +=-0.727059313582804, 0.281302662171663;
523 pts[39] += 0.281302662171663, -0.554243348588859;
524 pts[40] +=-0.769687425283662, 0.640968851717568;
525 pts[41] += 0.640968851717568, -0.871281426433905;
526 pts[42] +=-0.861626855061365, 0.038332201767419;
527 pts[43] += 0.038332201767419, -0.176705346706054;
528 pts[44] +=-0.872946396511865, -0.382367340313839;
529 pts[45] += 0.255313736825704, -0.872946396511865;
530 pts[46] +=-0.382367340313839, 0.255313736825704;
531 pts[47] +=-0.872946396511865, 0.255313736825704;
532 pts[48] += 0.255313736825704, -0.382367340313839;
533 pts[49] +=-0.875713493198755, -0.584327224183587;
534 pts[50] += 0.460040717382342, -0.875713493198755;
535 pts[51] +=-0.584327224183587, 0.460040717382342;
536 pts[52] +=-0.875713493198755, 0.460040717382342;
537 pts[53] += 0.460040717382342, -0.584327224183587;
538 pts[54] +=-0.871281426433905, 0.640968851717568;
539 pts[55] += 0.640968851717568, -0.769687425283663;
540 pts[56] +=-0.957943978206850, -0.173252532533942;
541 pts[57] += 0.131196510740792, -0.957943978206850;
542 pts[58] +=-0.173252532533942, 0.131196510740792;
543 pts[59] +=-0.957943978206850, 0.131196510740792;
544 pts[60] += 0.131196510740792, -0.173252532533942;
545 pts[61] +=-0.960810947366647, -0.459441974333255;
546 pts[62] += 0.420252921699902, -0.960810947366647;
547 pts[63] +=-0.459441974333255, 0.420252921699902;
548 pts[64] +=-0.960810947366647, 0.420252921699902;
549 pts[65] += 0.420252921699902, -0.459441974333255;
550 pts[66] +=-0.958833352267252, -0.697211314708751;
551 pts[67] += 0.656044666976003, -0.958833352267252;
552 pts[68] +=-0.697211314708751, 0.656044666976003;
553 pts[69] +=-0.958833352267252, 0.656044666976003;
554 pts[70] += 0.656044666976003, -0.697211314708751;
555 pts[71] +=-0.945197866913093, -0.858673547396615;
556 pts[72] += 0.803871414309708, -0.945197866913093;
557 pts[73] +=-0.858673547396615, 0.803871414309708;
558 pts[74] +=-0.945197866913093, 0.803871414309708;
559 pts[75] += 0.803871414309708, -0.858673547396615;
560 pts[76] +=-0.955761107477727, 0.911522214955453;
561 pts[77] += 0.911522214955453, -0.955761107477727;
567 pts[0] += -0.333333333333333, -0.333333333333333;
568 pts[1] += -0.345919243961035, -0.524125896411661;
569 pts[2] += -0.524125896411661, -0.345919243961035;
570 pts[3] += -0.158607804822441, -0.682784390355118;
571 pts[4] += -0.397236169198181, -0.682930809798947;
572 pts[5] += -0.547891729121480, -0.547891729121479;
573 pts[6] += -0.229298471311900, -0.805494870290821;
574 pts[7] += -0.450017853162840, -0.824969972041269;
575 pts[8] += -0.604881786728350, -0.732090458434108;
576 pts[9] += -0.762668477812969, -0.762668477812969;
577 pts[10] +=-0.047709572520027, -0.904580854959946;
578 pts[11] +=-0.295197559068932, -0.904875474507678;
579 pts[12] +=-0.604222488756960, -0.880761064604909;
580 pts[13] +=-0.767507099479299, -0.893012043623240;
581 pts[14] +=-0.893765292435529, -0.893765292435529;
582 pts[15] +=-0.164799653568441, -0.968562022370700;
583 pts[16] +=-0.431133449666801, -0.960622535118110;
584 pts[17] +=-0.648097761351901, -0.963860302249784;
585 pts[18] +=-0.836672115891999, -0.965611696960525;
586 pts[19] +=-0.956100831729230, -0.956100831729230;
587 pts[20] +=-0.524125896411661, -0.129954859627304;
588 pts[21] +=-0.129954859627304, -0.345919243961035;
589 pts[22] +=-0.345919243961035, -0.129954859627304;
590 pts[23] +=-0.129954859627304, -0.524125896411661;
591 pts[24] +=-0.682784390355118, -0.158607804822441;
592 pts[25] +=-0.158607804822441, -0.158607804822441;
593 pts[26] +=-0.682930809798947, -0.397236169198181;
594 pts[27] += 0.080166978997128, -0.682930809798947;
595 pts[28] +=-0.397236169198181, 0.080166978997128;
596 pts[29] +=-0.682930809798947, 0.080166978997128;
597 pts[30] += 0.080166978997128, -0.397236169198181;
598 pts[31] +=-0.547891729121479, 0.095783458242960;
599 pts[32] += 0.095783458242960, -0.547891729121480;
600 pts[33] +=-0.805494870290821, -0.229298471311900;
601 pts[34] += 0.034793341602721, -0.805494870290821;
602 pts[35] +=-0.229298471311900, 0.034793341602721;
603 pts[36] +=-0.805494870290821, 0.034793341602721;
604 pts[37] += 0.034793341602721, -0.229298471311900;
605 pts[38] +=-0.824969972041269, -0.450017853162840;
606 pts[39] += 0.274987825204109, -0.824969972041269;
607 pts[40] +=-0.450017853162840, 0.274987825204109;
608 pts[41] +=-0.824969972041269, 0.274987825204109;
609 pts[42] += 0.274987825204109, -0.450017853162840;
610 pts[43] +=-0.732090458434108, -0.604881786728350;
611 pts[44] += 0.336972245162458, -0.732090458434108;
612 pts[45] +=-0.604881786728350, 0.336972245162458;
613 pts[46] +=-0.732090458434108, 0.336972245162458;
614 pts[47] += 0.336972245162458, -0.604881786728350;
615 pts[48] +=-0.762668477812969, 0.525336955625937;
616 pts[49] += 0.525336955625937, -0.762668477812969;
617 pts[50] +=-0.904580854959946, -0.047709572520027;
618 pts[51] +=-0.047709572520027, -0.047709572520027;
619 pts[52] +=-0.904875474507678, -0.295197559068932;
620 pts[53] += 0.200073033576611, -0.904875474507678;
621 pts[54] +=-0.295197559068932, 0.200073033576611;
622 pts[55] +=-0.904875474507678, 0.200073033576611;
623 pts[56] += 0.200073033576611, -0.295197559068932;
624 pts[57] +=-0.880761064604909, -0.604222488756960;
625 pts[58] += 0.484983553361869, -0.880761064604909;
626 pts[59] +=-0.604222488756960, 0.484983553361869;
627 pts[60] +=-0.880761064604909, 0.484983553361869;
628 pts[61] += 0.484983553361869, -0.604222488756960;
629 pts[62] +=-0.893012043623240, -0.767507099479299;
630 pts[63] += 0.660519143102539, -0.893012043623240;
631 pts[64] +=-0.767507099479299, 0.660519143102539;
632 pts[65] +=-0.893012043623240, 0.660519143102539;
633 pts[66] += 0.660519143102539, -0.767507099479299;
634 pts[67] +=-0.893765292435529, 0.787530584871058;
635 pts[68] += 0.787530584871058, -0.893765292435529;
636 pts[69] +=-0.968562022370700, -0.164799653568441;
637 pts[70] += 0.133361675939142, -0.968562022370700;
638 pts[71] +=-0.164799653568441, 0.133361675939142;
639 pts[72] +=-0.968562022370700, 0.133361675939142;
640 pts[73] += 0.133361675939142, -0.164799653568441;
641 pts[74] +=-0.960622535118110, -0.431133449666801;
642 pts[75] += 0.391755984784911, -0.960622535118110;
643 pts[76] +=-0.431133449666801, 0.391755984784911;
644 pts[77] +=-0.960622535118110, 0.391755984784911;
645 pts[78] += 0.391755984784911, -0.431133449666801;
646 pts[79] +=-0.963860302249784, -0.648097761351901;
647 pts[80] += 0.611958063601684, -0.963860302249784;
648 pts[81] +=-0.648097761351901, 0.611958063601684;
649 pts[82] +=-0.963860302249784, 0.611958063601684;
650 pts[83] += 0.611958063601684, -0.648097761351901;
651 pts[84] +=-0.965611696960525, -0.836672115891999;
652 pts[85] += 0.802283812852524, -0.965611696960525;
653 pts[86] +=-0.836672115891999, 0.802283812852524;
654 pts[87] +=-0.965611696960525, 0.802283812852524;
655 pts[88] += 0.802283812852524, -0.836672115891999;
656 pts[89] +=-0.956100831729230, 0.912201663458459;
657 pts[90] += 0.912201663458459, -0.956100831729230;
663 pts[0] +=-0.205820142532107, -0.397089928733963;
664 pts[1] +=-0.226704334870422, -0.546591330259216;
665 pts[2] +=-0.147053788408309, -0.705892423183383;
666 pts[3] +=-0.347803355325610, -0.660885382368244;
667 pts[4] +=-0.506158324630743, -0.506158324630741;
668 pts[5] +=-0.221123161795997, -0.810980203769963;
669 pts[6] +=-0.533571481527389, -0.668243726484405;
670 pts[7] +=-0.636973186435847, -0.764734627714721;
671 pts[8] +=-0.781455865395765, -0.781455865395762;
672 pts[9] +=-0.049575040474585, -0.900849919050827;
673 pts[10] +=-0.301249843385144, -0.900753138395183;
674 pts[11] +=-0.444218443770085, -0.801617084992224;
675 pts[12] +=-0.672144704736634, -0.893074100698409;
676 pts[13] +=-0.808077031149289, -0.894419861496723;
677 pts[14] +=-0.908273312282669, -0.908273312282669;
678 pts[15] +=-0.130478222056322, -0.965904946909586;
679 pts[16] +=-0.360416071313197, -0.968507402379088;
680 pts[17] +=-0.504672216906210, -0.904515816522186;
681 pts[18] +=-0.589971542834612, -0.968078774774457;
682 pts[19] +=-0.780437138124852, -0.968331431821818;
683 pts[20] +=-0.925378007505782, -0.971660798597053;
684 pts[21] +=-0.397089928733963, -0.397089928733930;
685 pts[22] +=-0.397089928733930, -0.205820142532107;
686 pts[23] +=-0.546591330259216, -0.226704334870362;
687 pts[24] +=-0.226704334870362, -0.226704334870422;
688 pts[25] +=-0.705892423183383, -0.147053788408308;
689 pts[26] +=-0.147053788408308, -0.147053788408309;
690 pts[27] +=-0.660885382368244, -0.347803355325610;
691 pts[28] += 0.008688737693854, -0.660885382368244;
692 pts[29] +=-0.347803355325610, 0.008688737693854;
693 pts[30] +=-0.660885382368244, 0.008688737693854;
694 pts[31] += 0.008688737693854, -0.347803355325610;
695 pts[32] +=-0.506158324630741, 0.012316649261484;
696 pts[33] += 0.012316649261484, -0.506158324630743;
697 pts[34] +=-0.810980203769963, -0.221123161795997;
698 pts[35] += 0.032103365565961, -0.810980203769963;
699 pts[36] +=-0.221123161795997, 0.032103365565961;
700 pts[37] +=-0.810980203769963, 0.032103365565961;
701 pts[38] += 0.032103365565961, -0.221123161795997;
702 pts[39] +=-0.668243726484405, -0.533571481527389;
703 pts[40] += 0.201815208011793, -0.668243726484405;
704 pts[41] +=-0.533571481527389, 0.201815208011793;
705 pts[42] +=-0.668243726484405, 0.201815208011793;
706 pts[43] += 0.201815208011793, -0.533571481527389;
707 pts[44] +=-0.764734627714721, -0.636973186435847;
708 pts[45] += 0.401707814150568, -0.764734627714721;
709 pts[46] +=-0.636973186435847, 0.401707814150568;
710 pts[47] +=-0.764734627714721, 0.401707814150568;
711 pts[48] += 0.401707814150568, -0.636973186435847;
712 pts[49] +=-0.781455865395762, 0.562911730791527;
713 pts[50] += 0.562911730791527, -0.781455865395765;
714 pts[51] +=-0.900849919050827, -0.049575040474587;
715 pts[52] +=-0.049575040474587, -0.049575040474585;
716 pts[53] +=-0.900753138395183, -0.301249843385144;
717 pts[54] += 0.202002981780326, -0.900753138395183;
718 pts[55] +=-0.301249843385144, 0.202002981780326;
719 pts[56] +=-0.900753138395183, 0.202002981780326;
720 pts[57] += 0.202002981780326, -0.301249843385144;
721 pts[58] +=-0.801617084992224, -0.444218443770085;
722 pts[59] += 0.245835528762309, -0.801617084992224;
723 pts[60] +=-0.444218443770085, 0.245835528762309;
724 pts[61] +=-0.801617084992224, 0.245835528762309;
725 pts[62] += 0.245835528762309, -0.444218443770085;
726 pts[63] +=-0.893074100698409, -0.672144704736634;
727 pts[64] += 0.565218805435043, -0.893074100698409;
728 pts[65] +=-0.672144704736634, 0.565218805435043;
729 pts[66] +=-0.893074100698409, 0.565218805435043;
730 pts[67] += 0.565218805435043, -0.672144704736634;
731 pts[68] +=-0.894419861496723, -0.808077031149289;
732 pts[69] += 0.702496892646012, -0.894419861496723;
733 pts[70] +=-0.808077031149289, 0.702496892646012;
734 pts[71] +=-0.894419861496723, 0.702496892646012;
735 pts[72] += 0.702496892646012, -0.808077031149289;
736 pts[73] +=-0.908273312282669, 0.816546624565338;
737 pts[74] += 0.816546624565338, -0.908273312282669;
738 pts[75] +=-0.965904946909586, -0.130478222056322;
739 pts[76] += 0.096383168965909, -0.965904946909586;
740 pts[77] +=-0.130478222056322, 0.096383168965909;
741 pts[78] +=-0.965904946909586, 0.096383168965909;
742 pts[79] += 0.096383168965909, -0.130478222056322;
743 pts[80] +=-0.968507402379088, -0.360416071313197;
744 pts[81] += 0.328923473692285, -0.968507402379088;
745 pts[82] +=-0.360416071313197, 0.328923473692285;
746 pts[83] +=-0.968507402379088, 0.328923473692285;
747 pts[84] += 0.328923473692285, -0.360416071313197;
748 pts[85] +=-0.904515816522186, -0.504672216906210;
749 pts[86] += 0.409188033428395, -0.904515816522186;
750 pts[87] +=-0.504672216906210, 0.409188033428395;
751 pts[88] +=-0.904515816522186, 0.409188033428395;
752 pts[89] += 0.409188033428395, -0.504672216906210;
753 pts[90] +=-0.968078774774457, -0.589971542834612;
754 pts[91] += 0.558050317609069, -0.968078774774457;
755 pts[92] +=-0.589971542834612, 0.558050317609069;
756 pts[93] +=-0.968078774774457, 0.558050317609069;
757 pts[94] += 0.558050317609069, -0.589971542834612;
758 pts[95] +=-0.968331431821818, -0.780437138124852;
759 pts[96] += 0.748768569946670, -0.968331431821818;
760 pts[97] +=-0.780437138124852, 0.748768569946670;
761 pts[98] +=-0.968331431821818, 0.748768569946670;
762 pts[99] += 0.748768569946670, -0.780437138124852;
763 pts[100] +=-0.971660798597053, -0.925378007505782;
764 pts[101] += 0.897038806102834, -0.971660798597053;
765 pts[102] +=-0.925378007505782, 0.897038806102834;
766 pts[103] +=-0.971660798597053, 0.897038806102834;
767 pts[104] += 0.897038806102834, -0.925378007505782;
773 pts[0] +=-0.274418069203627, -0.451163861592915;
774 pts[1] +=-0.454542715481369, -0.454542715481372;
775 pts[2] +=-0.304432262743245, -0.603457916280128;
776 pts[3] +=-0.494494713443969, -0.621442380901352;
777 pts[4] +=-0.658725522099670, -0.658725522099675;
778 pts[5] +=-0.135472335404057, -0.729055329191558;
779 pts[6] +=-0.352087942349477, -0.733502615179034;
780 pts[7] +=-0.390991263418732, -0.850467523022011;
781 pts[8] +=-0.538875562890167, -0.776709531025512;
782 pts[9] +=-0.814453782144371, -0.814453782144367;
783 pts[10] +=-0.195103212265680, -0.834191333597611;
784 pts[11] +=-0.252286838337513, -0.919078757215168;
785 pts[12] +=-0.526146769703608, -0.899421376980804;
786 pts[13] +=-0.684707100047466, -0.799915944717937;
787 pts[14] +=-0.817800237901515, -0.916958697330690;
788 pts[15] +=-0.916944777907565, -0.916944777907568;
789 pts[16] +=-0.040450078409046, -0.919099843181106;
790 pts[17] +=-0.139681499859092, -0.973704822173568;
791 pts[18] +=-0.365272864060711, -0.966341745722431;
792 pts[19] +=-0.553244326836927, -0.969305591113758;
793 pts[20] +=-0.687104081104119, -0.907603260148529;
794 pts[21] +=-0.727794870234229, -0.972100556591935;
795 pts[22] +=-0.874388356916094, -0.973207851954675;
796 pts[23] +=-0.966114906224907, -0.966114906224907;
797 pts[24] +=-0.451163861592915, -0.274418069203458;
798 pts[25] +=-0.274418069203458, -0.274418069203627;
799 pts[26] +=-0.454542715481372, -0.090914569037259;
800 pts[27] +=-0.090914569037259, -0.454542715481369;
801 pts[28] +=-0.603457916280128, -0.304432262743245;
802 pts[29] +=-0.092109820976628, -0.603457916280128;
803 pts[30] +=-0.304432262743245, -0.092109820976628;
804 pts[31] +=-0.603457916280128, -0.092109820976628;
805 pts[32] +=-0.092109820976628, -0.304432262743245;
806 pts[33] +=-0.621442380901352, -0.494494713443969;
807 pts[34] += 0.115937094345321, -0.621442380901352;
808 pts[35] +=-0.494494713443969, 0.115937094345321;
809 pts[36] +=-0.621442380901352, 0.115937094345321;
810 pts[37] += 0.115937094345321, -0.494494713443969;
811 pts[38] +=-0.658725522099675, 0.317451044199345;
812 pts[39] += 0.317451044199345, -0.658725522099670;
813 pts[40] +=-0.729055329191558, -0.135472335404385;
814 pts[41] +=-0.135472335404385, -0.135472335404057;
815 pts[42] +=-0.733502615179034, -0.352087942349477;
816 pts[43] += 0.085590557528511, -0.733502615179034;
817 pts[44] +=-0.352087942349477, 0.085590557528511;
818 pts[45] +=-0.733502615179034, 0.085590557528511;
819 pts[46] += 0.085590557528511, -0.352087942349477;
820 pts[47] +=-0.850467523022011, -0.390991263418732;
821 pts[48] += 0.241458786440742, -0.850467523022011;
822 pts[49] +=-0.390991263418732, 0.241458786440742;
823 pts[50] +=-0.850467523022011, 0.241458786440742;
824 pts[51] += 0.241458786440742, -0.390991263418732;
825 pts[52] +=-0.776709531025512, -0.538875562890167;
826 pts[53] += 0.315585093915678, -0.776709531025512;
827 pts[54] +=-0.538875562890167, 0.315585093915678;
828 pts[55] +=-0.776709531025512, 0.315585093915678;
829 pts[56] += 0.315585093915678, -0.538875562890167;
830 pts[57] +=-0.814453782144367, 0.628907564288738;
831 pts[58] += 0.628907564288738, -0.814453782144371;
832 pts[59] +=-0.834191333597611, -0.195103212265680;
833 pts[60] += 0.029294545863291, -0.834191333597611;
834 pts[61] +=-0.195103212265680, 0.029294545863291;
835 pts[62] +=-0.834191333597611, 0.029294545863291;
836 pts[63] += 0.029294545863291, -0.195103212265680;
837 pts[64] +=-0.919078757215168, -0.252286838337513;
838 pts[65] += 0.171365595552681, -0.919078757215168;
839 pts[66] +=-0.252286838337513, 0.171365595552681;
840 pts[67] +=-0.919078757215168, 0.171365595552681;
841 pts[68] += 0.171365595552681, -0.252286838337513;
842 pts[69] +=-0.899421376980804, -0.526146769703608;
843 pts[70] += 0.425568146684412, -0.899421376980804;
844 pts[71] +=-0.526146769703608, 0.425568146684412;
845 pts[72] +=-0.899421376980804, 0.425568146684412;
846 pts[73] += 0.425568146684412, -0.526146769703608;
847 pts[74] +=-0.799915944717937, -0.684707100047466;
848 pts[75] += 0.484623044765403, -0.799915944717937;
849 pts[76] +=-0.684707100047466, 0.484623044765403;
850 pts[77] +=-0.799915944717937, 0.484623044765403;
851 pts[78] += 0.484623044765403, -0.684707100047466;
852 pts[79] +=-0.916958697330690, -0.817800237901515;
853 pts[80] += 0.734758935232205, -0.916958697330690;
854 pts[81] +=-0.817800237901515, 0.734758935232205;
855 pts[82] +=-0.916958697330690, 0.734758935232205;
856 pts[83] += 0.734758935232205, -0.817800237901515;
857 pts[84] +=-0.916944777907568, 0.833889555815133;
858 pts[85] += 0.833889555815133, -0.916944777907565;
859 pts[86] +=-0.919099843181106, -0.040450078409849;
860 pts[87] +=-0.040450078409849, -0.040450078409046;
861 pts[88] +=-0.973704822173568, -0.139681499859092;
862 pts[89] += 0.113386322032660, -0.973704822173568;
863 pts[90] +=-0.139681499859092, 0.113386322032660;
864 pts[91] +=-0.973704822173568, 0.113386322032660;
865 pts[92] += 0.113386322032660, -0.139681499859092;
866 pts[93] +=-0.966341745722431, -0.365272864060711;
867 pts[94] += 0.331614609783141, -0.966341745722431;
868 pts[95] +=-0.365272864060711, 0.331614609783141;
869 pts[96] +=-0.966341745722431, 0.331614609783141;
870 pts[97] += 0.331614609783141, -0.365272864060711;
871 pts[98] +=-0.969305591113758, -0.553244326836927;
872 pts[99] += 0.522549917950685, -0.969305591113758;
873 pts[100] +=-0.553244326836927, 0.522549917950685;
874 pts[101] +=-0.969305591113758, 0.522549917950685;
875 pts[102] += 0.522549917950685, -0.553244326836927;
876 pts[103] +=-0.907603260148529, -0.687104081104119;
877 pts[104] += 0.594707341252649, -0.907603260148529;
878 pts[105] +=-0.687104081104119, 0.594707341252649;
879 pts[106] +=-0.907603260148529, 0.594707341252649;
880 pts[107] += 0.594707341252649, -0.687104081104119;
881 pts[108] +=-0.972100556591935, -0.727794870234229;
882 pts[109] += 0.699895426826163, -0.972100556591935;
883 pts[110] +=-0.727794870234229, 0.699895426826163;
884 pts[111] +=-0.972100556591935, 0.699895426826163;
885 pts[112] += 0.699895426826163, -0.727794870234229;
886 pts[113] +=-0.973207851954675, -0.874388356916094;
887 pts[114] += 0.847596208870770, -0.973207851954675;
888 pts[115] +=-0.874388356916094, 0.847596208870770;
889 pts[116] +=-0.973207851954675, 0.847596208870770;
890 pts[117] += 0.847596208870770, -0.874388356916094;
891 pts[118] +=-0.966114906224907, 0.932229812449814;
892 pts[119] += 0.932229812449814, -0.966114906224907;
898 pts[0] +=-0.333333333333333, -0.333333333333333;
899 pts[1] +=-0.341403167501697, -0.496889379374577;
900 pts[2] +=-0.496889379374577, -0.341403167501698;
901 pts[3] +=-0.180193099610473, -0.639613800779053;
902 pts[4] +=-0.380906991836065, -0.635706815999634;
903 pts[5] +=-0.512270446598166, -0.512270446598166;
904 pts[6] +=-0.242142213764944, -0.750619748986711;
905 pts[7] +=-0.426216871527756, -0.764111722863127;
906 pts[8] +=-0.559026266119071, -0.672116309193513;
907 pts[9] +=-0.697487089299080, -0.697487089299080;
908 pts[10] +=-0.081068949345966, -0.837862101308069;
909 pts[11] +=-0.293493269298788, -0.851490067387505;
910 pts[12] +=-0.561603804138562, -0.812436645793173;
911 pts[13] +=-0.710745308672525, -0.821809722624405;
912 pts[14] +=-0.833448470288251, -0.833448470288251;
913 pts[15] +=-0.127891272883473, -0.918186951448195;
914 pts[16] +=-0.440803029204592, -0.902264822053879;
915 pts[17] +=-0.593157770542283, -0.907931574540618;
916 pts[18] +=-0.728191943973380, -0.915862562521078;
917 pts[19] +=-0.926186882686440, -0.926186882686440;
918 pts[20] +=-0.132621542700647, -0.976724412008478;
919 pts[21] +=-0.282882435206159, -0.940187562507177;
920 pts[22] +=-0.406379266660819, -0.973537374255463;
921 pts[23] +=-0.589944148624057, -0.972780306197722;
922 pts[24] +=-0.753570755371218, -0.975026063234546;
923 pts[25] +=-0.838829021310763, -0.926960440578635;
924 pts[26] +=-0.889023739684485, -0.976272446974781;
925 pts[27] +=-0.970085029900325, -0.970085029900325;
926 pts[28] +=-0.496889379374577, -0.161707453123726;
927 pts[29] +=-0.161707453123726, -0.341403167501697;
928 pts[30] +=-0.341403167501698, -0.161707453123726;
929 pts[31] +=-0.161707453123726, -0.496889379374577;
930 pts[32] +=-0.639613800779053, -0.180193099610473;
931 pts[33] +=-0.180193099610473, -0.180193099610473;
932 pts[34] +=-0.635706815999634, -0.380906991836065;
933 pts[35] += 0.016613807835700, -0.635706815999634;
934 pts[36] +=-0.380906991836065, 0.016613807835700;
935 pts[37] +=-0.635706815999634, 0.016613807835700;
936 pts[38] += 0.016613807835700, -0.380906991836065;
937 pts[39] +=-0.512270446598166, 0.024540893196332;
938 pts[40] += 0.024540893196332, -0.512270446598166;
939 pts[41] +=-0.750619748986711, -0.242142213764944;
940 pts[42] +=-0.007238037248346, -0.750619748986711;
941 pts[43] +=-0.242142213764944, -0.007238037248346;
942 pts[44] +=-0.750619748986711, -0.007238037248346;
943 pts[45] +=-0.007238037248346, -0.242142213764944;
944 pts[46] +=-0.764111722863127, -0.426216871527756;
945 pts[47] += 0.190328594390883, -0.764111722863127;
946 pts[48] +=-0.426216871527756, 0.190328594390883;
947 pts[49] +=-0.764111722863127, 0.190328594390883;
948 pts[50] += 0.190328594390883, -0.426216871527756;
949 pts[51] +=-0.672116309193513, -0.559026266119071;
950 pts[52] += 0.231142575312584, -0.672116309193513;
951 pts[53] +=-0.559026266119071, 0.231142575312584;
952 pts[54] +=-0.672116309193513, 0.231142575312584;
953 pts[55] += 0.231142575312584, -0.559026266119071;
954 pts[56] +=-0.697487089299080, 0.394974178598160;
955 pts[57] += 0.394974178598160, -0.697487089299080;
956 pts[58] +=-0.837862101308069, -0.081068949345966;
957 pts[59] +=-0.081068949345966, -0.081068949345966;
958 pts[60] +=-0.851490067387505, -0.293493269298788;
959 pts[61] += 0.144983336686293, -0.851490067387505;
960 pts[62] +=-0.293493269298788, 0.144983336686293;
961 pts[63] +=-0.851490067387505, 0.144983336686293;
962 pts[64] += 0.144983336686293, -0.293493269298788;
963 pts[65] +=-0.812436645793173, -0.561603804138562;
964 pts[66] += 0.374040449931736, -0.812436645793173;
965 pts[67] +=-0.561603804138562, 0.374040449931736;
966 pts[68] +=-0.812436645793173, 0.374040449931736;
967 pts[69] += 0.374040449931736, -0.561603804138562;
968 pts[70] +=-0.821809722624405, -0.710745308672525;
969 pts[71] += 0.532555031296929, -0.821809722624405;
970 pts[72] +=-0.710745308672525, 0.532555031296929;
971 pts[73] +=-0.821809722624405, 0.532555031296929;
972 pts[74] += 0.532555031296929, -0.710745308672525;
973 pts[75] +=-0.833448470288251, 0.666896940576502;
974 pts[76] += 0.666896940576502, -0.833448470288251;
975 pts[77] +=-0.918186951448195, -0.127891272883473;
976 pts[78] += 0.046078224331668, -0.918186951448195;
977 pts[79] +=-0.127891272883473, 0.046078224331668;
978 pts[80] +=-0.918186951448195, 0.046078224331668;
979 pts[81] += 0.046078224331668, -0.127891272883473;
980 pts[82] +=-0.902264822053879, -0.440803029204592;
981 pts[83] += 0.343067851258471, -0.902264822053879;
982 pts[84] +=-0.440803029204592, 0.343067851258471;
983 pts[85] +=-0.902264822053879, 0.343067851258471;
984 pts[86] += 0.343067851258471, -0.440803029204592;
985 pts[87] +=-0.907931574540618, -0.593157770542283;
986 pts[88] += 0.501089345082902, -0.907931574540618;
987 pts[89] +=-0.593157770542283, 0.501089345082902;
988 pts[90] +=-0.907931574540618, 0.501089345082902;
989 pts[91] += 0.501089345082902, -0.593157770542283;
990 pts[92] +=-0.915862562521078, -0.728191943973380;
991 pts[93] += 0.644054506494458, -0.915862562521078;
992 pts[94] +=-0.728191943973380, 0.644054506494458;
993 pts[95] +=-0.915862562521078, 0.644054506494458;
994 pts[96] += 0.644054506494458, -0.728191943973380;
995 pts[97] +=-0.926186882686440, 0.852373765372881;
996 pts[98] += 0.852373765372881, -0.926186882686440;
997 pts[99] +=-0.976724412008478, -0.132621542700647;
998 pts[100] += 0.109345954709125, -0.976724412008478;
999 pts[101] +=-0.132621542700647, 0.109345954709125;
1000 pts[102] +=-0.976724412008478, 0.109345954709125;
1001 pts[103] += 0.109345954709125, -0.132621542700647;
1002 pts[104] +=-0.940187562507177, -0.282882435206159;
1003 pts[105] += 0.223069997713336, -0.940187562507177;
1004 pts[106] +=-0.282882435206159, 0.223069997713336;
1005 pts[107] +=-0.940187562507177, 0.223069997713336;
1006 pts[108] += 0.223069997713336, -0.282882435206159;
1007 pts[109] +=-0.973537374255463, -0.406379266660819;
1008 pts[110] += 0.379916640916282, -0.973537374255463;
1009 pts[111] +=-0.406379266660819, 0.379916640916282;
1010 pts[112] +=-0.973537374255463, 0.379916640916282;
1011 pts[113] += 0.379916640916282, -0.406379266660819;
1012 pts[114] +=-0.972780306197722, -0.589944148624057;
1013 pts[115] += 0.562724454821779, -0.972780306197722;
1014 pts[116] +=-0.589944148624057, 0.562724454821779;
1015 pts[117] +=-0.972780306197722, 0.562724454821779;
1016 pts[118] += 0.562724454821779, -0.589944148624057;
1017 pts[119] +=-0.975026063234546, -0.753570755371218;
1018 pts[120] += 0.728596818605764, -0.975026063234546;
1019 pts[121] +=-0.753570755371218, 0.728596818605764;
1020 pts[122] +=-0.975026063234546, 0.728596818605764;
1021 pts[123] += 0.728596818605764, -0.753570755371218;
1022 pts[124] +=-0.926960440578635, -0.838829021310763;
1023 pts[125] += 0.765789461889398, -0.926960440578635;
1024 pts[126] +=-0.838829021310763, 0.765789461889398;
1025 pts[127] +=-0.926960440578635, 0.765789461889398;
1026 pts[128] += 0.765789461889398, -0.838829021310763;
1027 pts[129] +=-0.976272446974781, -0.889023739684485;
1028 pts[130] += 0.865296186659265, -0.976272446974781;
1029 pts[131] +=-0.889023739684485, 0.865296186659265;
1030 pts[132] +=-0.976272446974781, 0.865296186659265;
1031 pts[133] += 0.865296186659265, -0.889023739684485;
1032 pts[134] +=-0.970085029900325, 0.940170059800650;
1033 pts[135] += 0.940170059800650, -0.970085029900325;
1039 pts[0] +=-0.287000355881118, -0.425999288237764;
1040 pts[1] +=-0.206758293148238, -0.586483413703523;
1041 pts[2] +=-0.389224594690171, -0.516424689183957;
1042 pts[3] +=-0.310764541061254, -0.657966548675822;
1043 pts[4] +=-0.480302382494788, -0.613218952389985;
1044 pts[5] +=-0.624981326354916, -0.624981326354917;
1045 pts[6] +=-0.128321805315155, -0.743356389369689;
1046 pts[7] +=-0.323351460920740, -0.766969030527911;
1047 pts[8] +=-0.497244231750085, -0.746567934356032;
1048 pts[9] +=-0.643816871049108, -0.758951147831367;
1049 pts[10] +=-0.770126681161834, -0.770126681161834;
1050 pts[11] +=-0.170097600290176, -0.844942783021920;
1051 pts[12] +=-0.357925049990872, -0.857114592267436;
1052 pts[13] +=-0.533042015447951, -0.851309640748108;
1053 pts[14] +=-0.699217252744167, -0.856334228586824;
1054 pts[15] +=-0.841136978797186, -0.841136978797186;
1055 pts[16] +=-0.037328752151830, -0.925342495696341;
1056 pts[17] +=-0.222195753165427, -0.925717377197022;
1057 pts[18] +=-0.420154075742092, -0.925542373085800;
1058 pts[19] +=-0.603685694381808, -0.923025153620202;
1059 pts[20] +=-0.747149943107145, -0.927211175398458;
1060 pts[21] +=-0.854489586141069, -0.927618164018200;
1061 pts[22] +=-0.933895989466742, -0.933895989466742;
1062 pts[23] +=-0.114781279448575, -0.976416029994295;
1063 pts[24] +=-0.310533830593028, -0.974760850589475;
1064 pts[25] +=-0.485753632927623, -0.974389077853428;
1065 pts[26] +=-0.642843887255066, -0.975894779040898;
1066 pts[27] +=-0.783926073185151, -0.977387818113720;
1067 pts[28] +=-0.897917737079264, -0.978019404606716;
1068 pts[29] +=-0.972658489043534, -0.972658489043534;
1069 pts[30] +=-0.425999288237764, -0.287000355881118;
1070 pts[31] +=-0.287000355881118, -0.287000355881118;
1071 pts[32] +=-0.586483413703523, -0.206758293148238;
1072 pts[33] +=-0.206758293148238, -0.206758293148238;
1073 pts[34] +=-0.516424689183957, -0.389224594690171;
1074 pts[35] +=-0.094350716125871, -0.516424689183957;
1075 pts[36] +=-0.389224594690171, -0.094350716125871;
1076 pts[37] +=-0.516424689183957, -0.094350716125871;
1077 pts[38] +=-0.094350716125871, -0.389224594690171;
1078 pts[39] +=-0.657966548675822, -0.310764541061254;
1079 pts[40] +=-0.031268910262925, -0.657966548675822;
1080 pts[41] +=-0.310764541061254, -0.031268910262925;
1081 pts[42] +=-0.657966548675822, -0.031268910262925;
1082 pts[43] +=-0.031268910262925, -0.310764541061254;
1083 pts[44] +=-0.613218952389985, -0.480302382494788;
1084 pts[45] += 0.093521334884772, -0.613218952389985;
1085 pts[46] +=-0.480302382494788, 0.093521334884772;
1086 pts[47] +=-0.613218952389985, 0.093521334884772;
1087 pts[48] += 0.093521334884772, -0.480302382494788;
1088 pts[49] +=-0.624981326354917, 0.249962652709833;
1089 pts[50] += 0.249962652709833, -0.624981326354916;
1090 pts[51] +=-0.743356389369689, -0.128321805315155;
1091 pts[52] +=-0.128321805315155, -0.128321805315155;
1092 pts[53] +=-0.766969030527911, -0.323351460920740;
1093 pts[54] += 0.090320491448651, -0.766969030527911;
1094 pts[55] +=-0.323351460920740, 0.090320491448651;
1095 pts[56] +=-0.766969030527911, 0.090320491448651;
1096 pts[57] += 0.090320491448651, -0.323351460920740;
1097 pts[58] +=-0.746567934356032, -0.497244231750085;
1098 pts[59] += 0.243812166106117, -0.746567934356032;
1099 pts[60] +=-0.497244231750085, 0.243812166106117;
1100 pts[61] +=-0.746567934356032, 0.243812166106117;
1101 pts[62] += 0.243812166106117, -0.497244231750085;
1102 pts[63] +=-0.758951147831367, -0.643816871049108;
1103 pts[64] += 0.402768018880476, -0.758951147831367;
1104 pts[65] +=-0.643816871049108, 0.402768018880476;
1105 pts[66] +=-0.758951147831367, 0.402768018880476;
1106 pts[67] += 0.402768018880476, -0.643816871049108;
1107 pts[68] +=-0.770126681161834, 0.540253362323669;
1108 pts[69] += 0.540253362323669, -0.770126681161834;
1109 pts[70] +=-0.844942783021920, -0.170097600290176;
1110 pts[71] += 0.015040383312096, -0.844942783021920;
1111 pts[72] +=-0.170097600290176, 0.015040383312096;
1112 pts[73] +=-0.844942783021920, 0.015040383312096;
1113 pts[74] += 0.015040383312096, -0.170097600290176;
1114 pts[75] +=-0.857114592267436, -0.357925049990872;
1115 pts[76] += 0.215039642258308, -0.857114592267436;
1116 pts[77] +=-0.357925049990872, 0.215039642258308;
1117 pts[78] +=-0.857114592267436, 0.215039642258308;
1118 pts[79] += 0.215039642258308, -0.357925049990872;
1119 pts[80] +=-0.851309640748108, -0.533042015447951;
1120 pts[81] += 0.384351656196059, -0.851309640748108;
1121 pts[82] +=-0.533042015447951, 0.384351656196059;
1122 pts[83] +=-0.851309640748108, 0.384351656196059;
1123 pts[84] += 0.384351656196059, -0.533042015447951;
1124 pts[85] +=-0.856334228586824, -0.699217252744167;
1125 pts[86] += 0.555551481330991, -0.856334228586824;
1126 pts[87] +=-0.699217252744167, 0.555551481330991;
1127 pts[88] +=-0.856334228586824, 0.555551481330991;
1128 pts[89] += 0.555551481330991, -0.699217252744167;
1129 pts[90] +=-0.841136978797186, 0.682273957594371;
1130 pts[91] += 0.682273957594371, -0.841136978797186;
1131 pts[92] +=-0.925342495696341, -0.037328752151830;
1132 pts[93] +=-0.037328752151830, -0.037328752151830;
1133 pts[94] +=-0.925717377197022, -0.222195753165427;
1134 pts[95] += 0.147913130362450, -0.925717377197022;
1135 pts[96] +=-0.222195753165427, 0.147913130362450;
1136 pts[97] +=-0.925717377197022, 0.147913130362450;
1137 pts[98] += 0.147913130362450, -0.222195753165427;
1138 pts[99] +=-0.925542373085800, -0.420154075742092;
1139 pts[100] += 0.345696448827892, -0.925542373085800;
1140 pts[101] +=-0.420154075742092, 0.345696448827892;
1141 pts[102] +=-0.925542373085800, 0.345696448827892;
1142 pts[103] += 0.345696448827892, -0.420154075742092;
1143 pts[104] +=-0.923025153620202, -0.603685694381808;
1144 pts[105] += 0.526710848002010, -0.923025153620202;
1145 pts[106] +=-0.603685694381808, 0.526710848002010;
1146 pts[107] +=-0.923025153620202, 0.526710848002010;
1147 pts[108] += 0.526710848002010, -0.603685694381808;
1148 pts[109] +=-0.927211175398458, -0.747149943107145;
1149 pts[110] += 0.674361118505603, -0.927211175398458;
1150 pts[111] +=-0.747149943107145, 0.674361118505603;
1151 pts[112] +=-0.927211175398458, 0.674361118505603;
1152 pts[113] += 0.674361118505603, -0.747149943107145;
1153 pts[114] +=-0.927618164018200, -0.854489586141069;
1154 pts[115] += 0.782107750159270, -0.927618164018200;
1155 pts[116] +=-0.854489586141069, 0.782107750159270;
1156 pts[117] +=-0.927618164018200, 0.782107750159270;
1157 pts[118] += 0.782107750159270, -0.854489586141069;
1158 pts[119] +=-0.933895989466742, 0.867791978933485;
1159 pts[120] += 0.867791978933485, -0.933895989466742;
1160 pts[121] +=-0.976416029994295, -0.114781279448575;
1161 pts[122] += 0.091197309442870, -0.976416029994295;
1162 pts[123] +=-0.114781279448575, 0.091197309442870;
1163 pts[124] +=-0.976416029994295, 0.091197309442870;
1164 pts[125] += 0.091197309442870, -0.114781279448575;
1165 pts[126] +=-0.974760850589475, -0.310533830593028;
1166 pts[127] += 0.285294681182503, -0.974760850589475;
1167 pts[128] +=-0.310533830593028, 0.285294681182503;
1168 pts[129] +=-0.974760850589475, 0.285294681182503;
1169 pts[130] += 0.285294681182503, -0.310533830593028;
1170 pts[131] +=-0.974389077853428, -0.485753632927623;
1171 pts[132] += 0.460142710781051, -0.974389077853428;
1172 pts[133] +=-0.485753632927623, 0.460142710781051;
1173 pts[134] +=-0.974389077853428, 0.460142710781051;
1174 pts[135] += 0.460142710781051, -0.485753632927623;
1175 pts[136] +=-0.975894779040898, -0.642843887255066;
1176 pts[137] += 0.618738666295964, -0.975894779040898;
1177 pts[138] +=-0.642843887255066, 0.618738666295964;
1178 pts[139] +=-0.975894779040898, 0.618738666295964;
1179 pts[140] += 0.618738666295964, -0.642843887255066;
1180 pts[141] +=-0.977387818113720, -0.783926073185151;
1181 pts[142] += 0.761313891298871, -0.977387818113720;
1182 pts[143] +=-0.783926073185151, 0.761313891298871;
1183 pts[144] +=-0.977387818113720, 0.761313891298871;
1184 pts[145] += 0.761313891298871, -0.783926073185151;
1185 pts[146] +=-0.978019404606716, -0.897917737079264;
1186 pts[147] += 0.875937141685979, -0.978019404606716;
1187 pts[148] +=-0.897917737079264, 0.875937141685979;
1188 pts[149] +=-0.978019404606716, 0.875937141685979;
1189 pts[150] += 0.875937141685979, -0.897917737079264;
1190 pts[151] +=-0.972658489043534, 0.945316978087067;
1191 pts[152] += 0.945316978087067, -0.972658489043534;
1200 for ( int32_type i = 0; i<nbPtsPerFace; ++i )
1202 inner_pts( 0,i ) = pts[i][0];
1203 inner_pts( 1,i ) = pts[i][1];
1210 points_type putInPointset ( points_type final_pts, points_type pts, std::pair<uint16_type, uint16_type> position )
1212 ublas::subrange( final_pts, 0, 2, position.first, position.second ) = pts;
1218 static bool order( vector_type a, vector_type b )
1220 return a( n ) < b( n );
1223 points_type orderInteriorFace( points_type pts )
1225 std::vector<vector_type> aux( pts.size2() );
1227 for ( uint16_type i=0; i<pts.size2(); i++ )
1228 aux[i] = ublas::column( pts, i );
1230 std::sort( aux.begin(), aux.end(), &order<1> );
1232 for ( uint16_type p=0, i=Order-3; i>0; i-- )
1234 std::sort( aux.begin()+p, aux.begin()+p+i+1, &order<0> );
1238 for ( uint16_type i=0; i<pts.size2(); i++ )
1239 ublas::column( pts, i ) = aux[i];
1248 template<
class Convex,
1250 typename T =
double >
1251 class PointSetFekete :
public mpl::if_<mpl::or_<mpl::equal_to<mpl::bool_<Convex::is_hypercube>, mpl::bool_<true> >,
1252 mpl::equal_to<mpl::int_<Convex::nDim>, mpl::int_<1> > >,
1253 mpl::identity<PointSetGaussLobatto<Convex,Order,T> >,
1254 typename mpl::if_<mpl::equal_to<mpl::int_<Convex::nDim>, mpl::int_<3> >,
1255 mpl::identity<PointSetWarpBlend<Convex,Order,T> >,
1256 mpl::identity<PointSetFeketeSimplex<Convex,Order,T> > >::type >::type::type
1258 typedef typename mpl::if_<mpl::or_<mpl::equal_to<mpl::bool_<Convex::is_hypercube>, mpl::bool_<true> >,
1259 mpl::equal_to<mpl::int_<Convex::nDim>, mpl::int_<1> > >,
1260 mpl::identity<PointSetGaussLobatto<Convex,Order,T> >,
1261 typename mpl::if_<mpl::equal_to<mpl::int_<Convex::nDim>, mpl::int_<3> >,
1262 mpl::identity<PointSetWarpBlend<Convex,Order,T> >,
1263 mpl::identity<PointSetFeketeSimplex<Convex,Order,T> > >::type>::type::type super;
void setPoints(nodes_type const &pts)
Definition: pointset.hpp:267
Definition: fekete.hpp:1251
size_t size_type
Indices (starting from 0)
Definition: feelcore/feel.hpp:319