curvature.hpp 25.7 KB
Newer Older
Pierre Kraemer's avatar
Pierre Kraemer committed
1
2
3
/*******************************************************************************
 * CGoGN: Combinatorial and Geometric modeling with Generic N-dimensional Maps  *
 * version 0.1                                                                  *
4
 * Copyright (C) 2009-2012, IGG Team, LSIIT, University of Strasbourg           *
Pierre Kraemer's avatar
Pierre Kraemer committed
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
 *                                                                              *
 * This library is free software; you can redistribute it and/or modify it      *
 * under the terms of the GNU Lesser General Public License as published by the *
 * Free Software Foundation; either version 2.1 of the License, or (at your     *
 * option) any later version.                                                   *
 *                                                                              *
 * This library is distributed in the hope that it will be useful, but WITHOUT  *
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or        *
 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License  *
 * for more details.                                                            *
 *                                                                              *
 * You should have received a copy of the GNU Lesser General Public License     *
 * along with this library; if not, write to the Free Software Foundation,      *
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301 USA.           *
 *                                                                              *
20
 * Web site: http://cgogn.unistra.fr/                                           *
Pierre Kraemer's avatar
Pierre Kraemer committed
21
22
23
24
25
26
 * Contact information: cgogn@unistra.fr                                        *
 *                                                                              *
 *******************************************************************************/

#include "Algo/Geometry/localFrame.h"
#include "Geometry/matrix.h"
27
28
#include "Topology/generic/traversorCell.h"
#include "Topology/generic/traversor2.h"
Pierre Kraemer's avatar
Pierre Kraemer committed
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43

extern "C"
{
	#include "C_BLAS_LAPACK/INCLUDE/f2c.h"
	#include "C_BLAS_LAPACK/INCLUDE/clapack.h"
}
#undef max
#undef min

namespace CGoGN
{

namespace Algo
{

44
45
46
namespace Surface
{

Pierre Kraemer's avatar
Pierre Kraemer committed
47
48
49
50
namespace Geometry
{

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
51
52
void computeCurvatureVertices_QuadraticFitting(
	typename PFP::MAP& map,
53
54
55
56
57
58
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
Pierre Kraemer's avatar
Pierre Kraemer committed
59
	const FunctorSelect& select)
Pierre Kraemer's avatar
Pierre Kraemer committed
60
{
Pierre Kraemer's avatar
Pierre Kraemer committed
61
	TraversorV<typename PFP::MAP> t(map, select) ;
62
	for(Dart d = t.begin(); d != t.end(); d = t.next())
Pierre Kraemer's avatar
Pierre Kraemer committed
63
		computeCurvatureVertex_QuadraticFitting<PFP>(map, d, position, normal, kmax, kmin, Kmax, Kmin) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
64
65
66
}

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
67
68
69
void computeCurvatureVertex_QuadraticFitting(
	typename PFP::MAP& map,
	Dart dart,
70
71
72
73
74
75
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin)
Pierre Kraemer's avatar
Pierre Kraemer committed
76
77
78
79
80
81
{
	typedef typename PFP::REAL REAL ;
	typedef typename PFP::VEC3 VEC3 ;
	typedef typename PFP::MATRIX33 MATRIX33 ;

	VEC3 n = normal[dart] ;
Pierre Kraemer's avatar
Pierre Kraemer committed
82

83
	MATRIX33 localFrame = Algo::Geometry::vertexLocalFrame<PFP>(map, dart, position, n) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
84
85
86
87
88
	MATRIX33 invLocalFrame ;
	localFrame.invert(invLocalFrame) ;

	REAL a, b, c, d, e;
	//vertexCubicFitting(map,dart,localFrame,a,b,c,d,e,f,g,h,i) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
89
	vertexQuadraticFitting<PFP>(map, dart, localFrame, position, normal, a, b, c, d, e) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
90

Pierre Kraemer's avatar
Pierre Kraemer committed
91
	REAL kmax_v, kmin_v, Kmax_x, Kmax_y ;
Pierre Kraemer's avatar
Pierre Kraemer committed
92
	//int res = slaev2_(&e, &f, &g, &maxC, &minC, &dirX, &dirY) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
93
	/*int res = */slaev2_(&a, &b, &c, &kmax_v, &kmin_v, &Kmax_x, &Kmax_y) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
94

Pierre Kraemer's avatar
Pierre Kraemer committed
95
96
97
	VEC3 Kmax_v(Kmax_x, Kmax_y, 0.0f) ;
	Kmax_v = invLocalFrame * Kmax_v ;
	VEC3 Kmin_v = n ^ Kmax_v ;
Pierre Kraemer's avatar
Pierre Kraemer committed
98

Pierre Kraemer's avatar
Pierre Kraemer committed
99
	if (kmax_v < kmin_v)
100
	{
Pierre Kraemer's avatar
Pierre Kraemer committed
101
102
103
104
		kmax[dart] = -kmax_v ;
		kmin[dart] = -kmin_v ;
		Kmax[dart] = Kmax_v ;
		Kmin[dart] = Kmin_v ;
105
106
107
	}
	else
	{
Pierre Kraemer's avatar
Pierre Kraemer committed
108
109
110
111
		kmax[dart] = -kmin_v ;
		kmin[dart] = -kmax_v ;
		Kmax[dart] = Kmin_v ;
		Kmin[dart] = Kmax_v ;
112
	}
Pierre Kraemer's avatar
Pierre Kraemer committed
113
114
115
}

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
116
void vertexQuadraticFitting(
Pierre Kraemer's avatar
Pierre Kraemer committed
117
118
119
	typename PFP::MAP& map,
	Dart dart,
	typename PFP::MATRIX33& localFrame,
120
121
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
Pierre Kraemer's avatar
Pierre Kraemer committed
122
	float& a, float& b, float& c, float& d, float& e)
Pierre Kraemer's avatar
Pierre Kraemer committed
123
{
Pierre Kraemer's avatar
Pierre Kraemer committed
124
	typename PFP::VEC3 p = position[dart] ;
Pierre Kraemer's avatar
Pierre Kraemer committed
125
126
127
128

	LinearSolver<CPUSolverTraits> solver(5) ;
	solver.set_least_squares(true) ;
	solver.begin_system() ;
129
130
	Traversor2VVaE<typename PFP::MAP> tav(map, dart) ;
	for(Dart it = tav.begin(); it != tav.end(); it = tav.next())
Pierre Kraemer's avatar
Pierre Kraemer committed
131
	{
132
		typename PFP::VEC3 v = position[it] ;
Pierre Kraemer's avatar
Pierre Kraemer committed
133
		quadraticFittingAddVertexPos<PFP>(v, p, localFrame, solver) ;
134
		typename PFP::VEC3 n = normal[it] ;
Pierre Kraemer's avatar
Pierre Kraemer committed
135
		quadraticFittingAddVertexNormal<PFP>(v, n, p, localFrame, solver) ;
136
	}
Pierre Kraemer's avatar
Pierre Kraemer committed
137
138
139
140
141
142
143
144
145
146
147
	solver.end_system() ;
	solver.solve() ;

	a = solver.variable(0).value() ;
	b = solver.variable(1).value() ;
	c = solver.variable(2).value() ;
	d = solver.variable(3).value() ;
	e = solver.variable(4).value() ;
}

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
148
void quadraticFittingAddVertexPos(typename PFP::VEC3& v, typename PFP::VEC3& p, typename PFP::MATRIX33& localFrame, LinearSolver<CPUSolverTraits>& solver)
Pierre Kraemer's avatar
Pierre Kraemer committed
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
{
	typename PFP::VEC3 vec = v - p ;
	vec = localFrame * vec ;
	solver.begin_row() ;

	solver.add_coefficient(0, vec[0]*vec[0]) ;
	solver.add_coefficient(1, vec[0]*vec[1]) ;
	solver.add_coefficient(2, vec[1]*vec[1]) ;
	solver.add_coefficient(3, vec[0]) ;
	solver.add_coefficient(4, vec[1]) ;

	solver.set_right_hand_side(vec[2]) ;
	solver.end_row() ;
}

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
165
void quadraticFittingAddVertexNormal(typename PFP::VEC3& v, typename PFP::VEC3& n, typename PFP::VEC3& p, typename PFP::MATRIX33& localFrame, LinearSolver<CPUSolverTraits>& solver)
Pierre Kraemer's avatar
Pierre Kraemer committed
166
167
168
169
170
171
{
	typename PFP::VEC3 vec = v - p ;
	vec = localFrame * vec ;
	typename PFP::VEC3 norm = localFrame * n ;
	solver.begin_row() ;

Pierre Kraemer's avatar
Pierre Kraemer committed
172
	solver.add_coefficient(0, 2.0f * vec[0]) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
173
174
175
176
	solver.add_coefficient(1, vec[1]) ;
	solver.add_coefficient(2, 0) ;
	solver.add_coefficient(3, 1.0f) ;
	solver.add_coefficient(4, 0) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
177
	solver.set_right_hand_side(-1.0f * norm[0] / norm[2]) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
178
179
180
181
182
	solver.end_row() ;

	solver.begin_row() ;
	solver.add_coefficient(0, 0) ;
	solver.add_coefficient(1, vec[0]) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
183
	solver.add_coefficient(2, 2.0f * vec[1]) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
184
185
	solver.add_coefficient(3, 0) ;
	solver.add_coefficient(4, 1.0f) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
186
	solver.set_right_hand_side(-1.0f * norm[1] / norm[2]) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
187
188
189
190
	solver.end_row() ;
}
/*
template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
191
void vertexCubicFitting(Dart dart, gmtl::Vec3f& normal, float& a, float& b, float& c, float& d, float& e, float& f, float& g, float& h, float& i)
Pierre Kraemer's avatar
Pierre Kraemer committed
192
193
{
	gmtl::Matrix33f localFrame, invLocalFrame ;
194
	Geometry::vertexLocalFrame<PFP>(m_map,dart,normal,localFrame) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
195
196
197
198
199
	gmtl::invertFull(invLocalFrame, localFrame) ;
	gmtl::Vec3f p = m_map.getVertexEmb(dart)->getPosition() ;
	solverC->reset(false) ;
	solverC->set_least_squares(true) ;
	solverC->begin_system() ;
200
201
	Traversor2VVaE<typename PFP::MAP> tav(map, dart) ;
	for(Dart it = tav.begin(); it != tav.end(); it = tav.next())
Pierre Kraemer's avatar
Pierre Kraemer committed
202
203
	{
		// 1-ring vertices
204
		gmtl::Vec3f v = m_map.getVertexEmb(it)->getPosition() ;
Pierre Kraemer's avatar
Pierre Kraemer committed
205
		cubicFittingAddVertexPos(v,p,localFrame) ;
206
		gmtl::Vec3f n = m_normalsV[m_map.getVertexEmb(it)->getLabel()] ;
Pierre Kraemer's avatar
Pierre Kraemer committed
207
		cubicFittingAddVertexNormal(v,n,p,localFrame) ;
208
	}
Pierre Kraemer's avatar
Pierre Kraemer committed
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
	solverC->end_system() ;
	solverC->solve() ;
	a = solverC->variable(0).value() ;
	b = solverC->variable(1).value() ;
	c = solverC->variable(2).value() ;
	d = solverC->variable(3).value() ;
	e = solverC->variable(4).value() ;
	f = solverC->variable(5).value() ;
	g = solverC->variable(6).value() ;
	h = solverC->variable(7).value() ;
	i = solverC->variable(8).value() ;

//	normal = gmtl::Vec3f(-h, -i, 1.0f) ;
//	gmtl::normalize(normal) ;
//	normal = invLocalFrame * normal ;
}

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
227
void cubicFittingAddVertexPos(gmtl::Vec3f& v, gmtl::Vec3f& p, gmtl::Matrix33f& localFrame)
Pierre Kraemer's avatar
Pierre Kraemer committed
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
{
	gmtl::Vec3f vec = v - p ;
	vec = localFrame * vec ;
	solverC->begin_row() ;

	solverC->add_coefficient(0, vec[0]*vec[0]*vec[0]) ;
	solverC->add_coefficient(1, vec[0]*vec[0]*vec[1]) ;
	solverC->add_coefficient(2, vec[0]*vec[1]*vec[1]) ;
	solverC->add_coefficient(3, vec[1]*vec[1]*vec[1]) ;
	solverC->add_coefficient(4, vec[0]*vec[0]) ;
	solverC->add_coefficient(5, vec[0]*vec[1]) ;
	solverC->add_coefficient(6, vec[1]*vec[1]) ;
	solverC->add_coefficient(7, vec[0]) ;
	solverC->add_coefficient(8, vec[1]) ;

	solverC->set_right_hand_side(vec[2]) ;
	solverC->end_row() ;
}

template <typename PFP>
Pierre Kraemer's avatar
Pierre Kraemer committed
248
void cubicFittingAddVertexNormal(gmtl::Vec3f& v, gmtl::Vec3f& n, gmtl::Vec3f& p, gmtl::Matrix33f& localFrame)
Pierre Kraemer's avatar
Pierre Kraemer committed
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
{
	gmtl::Vec3f vec = v - p ;
	vec = localFrame * vec ;
	gmtl::Vec3f norm = localFrame * n ;
	solverC->begin_row() ;

	solverC->add_coefficient(0, 3.0f*vec[0]*vec[0]) ;
	solverC->add_coefficient(1, 2.0f*vec[0]*vec[1]) ;
	solverC->add_coefficient(2, vec[1]*vec[1]) ;
	solverC->add_coefficient(3, 0) ;
	solverC->add_coefficient(4, 2.0f*vec[0]) ;
	solverC->add_coefficient(5, vec[1]) ;
	solverC->add_coefficient(6, 0) ;
	solverC->add_coefficient(7, 1.0f) ;
	solverC->add_coefficient(8, 0) ;
	solverC->set_right_hand_side(-1.0f*norm[0]/norm[2]) ;
	solverC->end_row() ;

	solverC->begin_row() ;
	solverC->add_coefficient(0, 0) ;
	solverC->add_coefficient(1, vec[0]*vec[0]) ;
	solverC->add_coefficient(2, 2.0f*vec[0]*vec[1]) ;
	solverC->add_coefficient(3, 3.0f*vec[1]*vec[1]) ;
	solverC->add_coefficient(4, 0) ;
	solverC->add_coefficient(5, vec[0]) ;
	solverC->add_coefficient(6, 2.0f*vec[1]) ;
	solverC->add_coefficient(7, 0) ;
	solverC->add_coefficient(8, 1.0f) ;
	solverC->set_right_hand_side(-1.0f*norm[1]/norm[2]) ;
	solverC->end_row() ;
}
*/
Pierre Kraemer's avatar
Pierre Kraemer committed
281
282
283
284
285

template <typename PFP>
void computeCurvatureVertices_NormalCycles(
	typename PFP::MAP& map,
	typename PFP::REAL radius,
286
287
288
289
290
291
292
293
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal,
294
	const FunctorSelect& select, unsigned int thread)
Pierre Kraemer's avatar
Pierre Kraemer committed
295
{
Pierre Kraemer's avatar
Pierre Kraemer committed
296
	TraversorV<typename PFP::MAP> t(map, select) ;
297
	for(Dart d = t.begin(); d != t.end(); d = t.next())
298
		computeCurvatureVertex_NormalCycles<PFP>(map, d, radius, position, normal, edgeangle, kmax, kmin, Kmax, Kmin, Knormal,thread) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
299
300
301
302
303
304
305
}

template <typename PFP>
void computeCurvatureVertex_NormalCycles(
	typename PFP::MAP& map,
	Dart dart,
	typename PFP::REAL radius,
306
307
308
309
310
311
312
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
313
	VertexAttribute<typename PFP::VEC3>& Knormal, unsigned int thread)
Pierre Kraemer's avatar
Pierre Kraemer committed
314
{
315
316
	typedef typename PFP::REAL REAL ;
	typedef typename PFP::VEC3 VEC3 ;
317
318
	typedef Geom::Matrix<3,3,REAL> MATRIX;
	typedef Eigen::Matrix<REAL,3,1> E_VEC3;
Sauvage's avatar
Sauvage committed
319
	typedef Eigen::Matrix<REAL,3,3,Eigen::RowMajor> E_MATRIX;
320

321
	// collect the normal cycle tensor
322
	Selection::Collector_WithinSphere<PFP> neigh(map, position, radius, thread) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
323
	neigh.collectAll(dart) ;
324

325
	MATRIX tensor(0) ;
326
	neigh.computeNormalCyclesTensor(position, edgeangle,tensor);
327

328
	// solve eigen problem
329
330
331
	Eigen::SelfAdjointEigenSolver<E_MATRIX> solver (Utils::convertRef<E_MATRIX>(tensor));
	const VEC3& ev = Utils::convertRef<VEC3>(solver.eigenvalues());
	const MATRIX& evec = Utils::convertRef<MATRIX>(solver.eigenvectors());
332

333
	normalCycles_SortAndSetEigenComponents<PFP>(ev,evec,kmax[dart],kmin[dart],Kmax[dart],Kmin[dart],Knormal[dart],normal[dart],thread);
Sauvage's avatar
Sauvage committed
334
335
336
337
338
339
340
341
342
343

//	if (dart.index % 15000 == 0)
//	{
//		CGoGNout << solver.eigenvalues() << CGoGNendl;
//		CGoGNout << solver.eigenvectors() << CGoGNendl;
//		normalCycles_SortTensor<PFP>(tensor);
//		solver.compute(Utils::convertRef<E_MATRIX>(tensor));
//		CGoGNout << solver.eigenvalues() << CGoGNendl;
//		CGoGNout << solver.eigenvectors() << CGoGNendl;
//	}
344
345
}

Sauvage's avatar
Sauvage committed
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
template <typename PFP>
void computeCurvatureVertices_NormalCycles_Projected(
	typename PFP::MAP& map,
	typename PFP::REAL radius,
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal,
	const FunctorSelect& select, unsigned int thread)
{
	TraversorV<typename PFP::MAP> t(map, select) ;
	for(Dart d = t.begin(); d != t.end(); d = t.next())
		computeCurvatureVertex_NormalCycles_Projected<PFP>(map, d, radius, position, normal, edgeangle, kmax, kmin, Kmax, Kmin, Knormal,thread) ;
}

template <typename PFP>
void computeCurvatureVertex_NormalCycles_Projected(
	typename PFP::MAP& map,
	Dart dart,
	typename PFP::REAL radius,
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal, unsigned int thread)
{
379
	typedef typename PFP::REAL REAL ;
Sauvage's avatar
Sauvage committed
380
381
382
383
	typedef typename PFP::VEC3 VEC3 ;
	typedef Geom::Matrix<3,3,REAL> MATRIX;
	typedef Eigen::Matrix<REAL,3,1> E_VEC3;
	typedef Eigen::Matrix<REAL,3,3,Eigen::RowMajor> E_MATRIX;
384

385
	// collect the normal cycle tensor
386
	Selection::Collector_WithinSphere<PFP> neigh(map, position, radius, thread) ;
Pierre Kraemer's avatar
Pierre Kraemer committed
387
	neigh.collectAll(dart) ;
388

Sauvage's avatar
Sauvage committed
389
390
	MATRIX tensor(0) ;
	neigh.computeNormalCyclesTensor(position, edgeangle,tensor);
391

Sauvage's avatar
Sauvage committed
392
393
	// project the tensor
	normalCycles_ProjectTensor<PFP>(tensor,normal[dart],thread);
394

Sauvage's avatar
Sauvage committed
395
396
397
398
399
400
401
402
	// solve eigen problem
	Eigen::SelfAdjointEigenSolver<E_MATRIX> solver (Utils::convertRef<E_MATRIX>(tensor));
	const VEC3& ev = Utils::convertRef<VEC3>(solver.eigenvalues());
	const MATRIX& evec = Utils::convertRef<MATRIX>(solver.eigenvectors());

	normalCycles_SortAndSetEigenComponents<PFP>(ev,evec,kmax[dart],kmin[dart],Kmax[dart],Kmin[dart],Knormal[dart],normal[dart],thread);
}

403
404
405
template <typename PFP>
void computeCurvatureVertices_NormalCycles(
	typename PFP::MAP& map,
406
	Selection::Collector<PFP> & neigh,
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal,
	const FunctorSelect& select, unsigned int thread)
{
	TraversorV<typename PFP::MAP> t(map, select) ;
	for(Dart d = t.begin(); d != t.end(); d = t.next())
		computeCurvatureVertex_NormalCycles<PFP>(map, d, neigh, position, normal, edgeangle, kmax, kmin, Kmax, Kmin, Knormal,thread) ;
}

template <typename PFP>
void computeCurvatureVertex_NormalCycles(
	typename PFP::MAP& map,
	Dart dart,
426
	Selection::Collector<PFP> & neigh,
427
428
429
430
431
432
433
434
435
436
437
438
439
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal, unsigned int thread)
{
	typedef typename PFP::REAL REAL ;
	typedef typename PFP::VEC3 VEC3 ;
	typedef Geom::Matrix<3,3,REAL> MATRIX;
	typedef Eigen::Matrix<REAL,3,1> E_VEC3;
Sauvage's avatar
Sauvage committed
440
	typedef Eigen::Matrix<REAL,3,3,Eigen::RowMajor> E_MATRIX;
441
442
443

	// collect the normal cycle tensor
	neigh.collectAll(dart) ;
444

445
446
	MATRIX tensor(0) ;
	neigh.computeNormalCyclesTensor(position, edgeangle,tensor);
447

448
	// solve eigen problem
449
450
451
452
453
454
455
	Eigen::SelfAdjointEigenSolver<E_MATRIX> solver (Utils::convertRef<E_MATRIX>(tensor));
	const VEC3& ev = Utils::convertRef<VEC3>(solver.eigenvalues());
	const MATRIX& evec = Utils::convertRef<MATRIX>(solver.eigenvectors());

	normalCycles_SortAndSetEigenComponents<PFP>(ev,evec,kmax[dart],kmin[dart],Kmax[dart],Kmin[dart],Knormal[dart],normal[dart],thread);
}

Sauvage's avatar
Sauvage committed
456
457
458
template <typename PFP>
void computeCurvatureVertices_NormalCycles_Projected(
	typename PFP::MAP& map,
459
	Selection::Collector<PFP> & neigh,
Sauvage's avatar
Sauvage committed
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal,
	const FunctorSelect& select, unsigned int thread)
{
	TraversorV<typename PFP::MAP> t(map, select) ;
	for(Dart d = t.begin(); d != t.end(); d = t.next())
		computeCurvatureVertex_NormalCycles_Projected<PFP>(map, d, neigh, position, normal, edgeangle, kmax, kmin, Kmax, Kmin, Knormal,thread) ;
}

template <typename PFP>
void computeCurvatureVertex_NormalCycles_Projected(
	typename PFP::MAP& map,
	Dart dart,
479
	Selection::Collector<PFP> & neigh,
Sauvage's avatar
Sauvage committed
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal, unsigned int thread)
{
	typedef typename PFP::REAL REAL ;
	typedef typename PFP::VEC3 VEC3 ;
	typedef Geom::Matrix<3,3,REAL> MATRIX;
	typedef Eigen::Matrix<REAL,3,1> E_VEC3;
	typedef Eigen::Matrix<REAL,3,3,Eigen::RowMajor> E_MATRIX;

	// collect the normal cycle tensor
	neigh.collectAll(dart) ;

	MATRIX tensor(0) ;
	neigh.computeNormalCyclesTensor(position, edgeangle,tensor);

	// project the tensor
	normalCycles_ProjectTensor<PFP>(tensor,normal[dart],thread);

	// solve eigen problem
	Eigen::SelfAdjointEigenSolver<E_MATRIX> solver (Utils::convertRef<E_MATRIX>(tensor));
	const VEC3& ev = Utils::convertRef<VEC3>(solver.eigenvalues());
	const MATRIX& evec = Utils::convertRef<MATRIX>(solver.eigenvectors());

	normalCycles_SortAndSetEigenComponents<PFP>(ev,evec,kmax[dart],kmin[dart],Kmax[dart],Kmin[dart],Knormal[dart],normal[dart],thread);
}
511

512
513
514
515
516
517
518
519
520
521
522
523
template <typename PFP>
void normalCycles_SortAndSetEigenComponents(
	const typename PFP::VEC3& e_val,
	const Geom::Matrix<3,3,typename PFP::REAL> & e_vec,
	typename PFP::REAL& kmax,
	typename PFP::REAL& kmin,
	typename PFP::VEC3& Kmax,
	typename PFP::VEC3& Kmin,
	typename PFP::VEC3& Knormal,
	const typename PFP::VEC3& normal,
	unsigned int thread=0)
{
Sauvage's avatar
Sauvage committed
524
	// sort eigen components : ev[inormal] has minimal absolute value ; kmin = ev[imin] <= ev[imax] = kmax
Sauvage's avatar
Sauvage committed
525
	int inormal=0, imin, imax ;
Sauvage's avatar
Sauvage committed
526
527
528
529
	if (abs(e_val[1]) < abs(e_val[inormal])) inormal = 1;
	if (abs(e_val[2]) < abs(e_val[inormal])) inormal = 2;
	imin = (inormal + 1) % 3;
	imax = (inormal + 2) % 3;
Sauvage's avatar
Sauvage committed
530
	if (e_val[imax] < e_val[imin]) { int tmp = imin ; imin = imax ; imax = tmp ; }
531

532
	// set curvatures from sorted eigen components
533
534
	// warning : Kmin and Kmax are switched w.r.t. kmin and kmax
	// normal direction : minimal absolute eigen value
Sauvage's avatar
Sauvage committed
535
536
537
	Knormal[0] = e_vec(0,inormal);
	Knormal[1] = e_vec(1,inormal);
	Knormal[2] = e_vec(2,inormal);
538
	if (Knormal * normal < 0) Knormal *= -1; // change orientation
539
	// min curvature
Sauvage's avatar
Sauvage committed
540
541
542
543
	kmin = e_val[imin] ;
	Kmin[0] = e_vec(0,imax);
	Kmin[1] = e_vec(1,imax);
	Kmin[2] = e_vec(2,imax);
544
	// max curvature
Sauvage's avatar
Sauvage committed
545
546
547
548
	kmax = e_val[imax] ;
	Kmax[0] = e_vec(0,imin);
	Kmax[1] = e_vec(1,imin);
	Kmax[2] = e_vec(2,imin);
Pierre Kraemer's avatar
Pierre Kraemer committed
549
550
}

Sauvage's avatar
Sauvage committed
551
552
553
554
555
556
557
558
559
560
561
template <typename PFP>
void normalCycles_SortTensor( Geom::Matrix<3,3,typename PFP::REAL> & tensor, unsigned int thread=0)
{
	typedef typename PFP::REAL REAL ;
	typedef typename PFP::VEC3 VEC3 ;
	typedef Geom::Matrix<3,3,REAL> MATRIX;
	typedef Eigen::Matrix<REAL,3,1> E_VEC3;
	typedef Eigen::Matrix<REAL,3,3,Eigen::RowMajor> E_MATRIX;

	// compute eigen components
	Eigen::SelfAdjointEigenSolver<E_MATRIX> solver (Utils::convertRef<E_MATRIX>(tensor));
Sauvage's avatar
Sauvage committed
562
563
	const VEC3& e_val = Utils::convertRef<VEC3>(solver.eigenvalues());
	const MATRIX& e_vec = Utils::convertRef<MATRIX>(solver.eigenvectors());
Sauvage's avatar
Sauvage committed
564

Sauvage's avatar
Sauvage committed
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
	// switch kmin and kmax w.r.t. Kmin and Kmax
	int inormal=0, imin, imax ;
	if (abs(e_val[1]) < abs(e_val[inormal])) inormal = 1;
	if (abs(e_val[2]) < abs(e_val[inormal])) inormal = 2;
	imin = (inormal + 1) % 3;
	imax = (inormal + 2) % 3;
	if (e_val[imax] < e_val[imin]) { int tmp = imin ; imin = imax ; imax = tmp ; }

	tensor = e_vec;
	int i; REAL v;
	i = inormal; v = e_val[inormal];
	tensor(0,i) *= v; tensor(1,i) *= v; tensor(2,i) *= v;
	i = imin; v = e_val[imax];
	tensor(0,i) *= v; tensor(1,i) *= v; tensor(2,i) *= v;
	i = imax; v = e_val[imin];
	tensor(0,i) *= v; tensor(1,i) *= v; tensor(2,i) *= v;
	tensor = tensor*e_vec.transposed();
Sauvage's avatar
Sauvage committed
582
583
}

Sauvage's avatar
Sauvage committed
584
585
586
587
588
589
590
template <typename PFP>
void normalCycles_ProjectTensor( Geom::Matrix<3,3,typename PFP::REAL> & tensor, const typename PFP::VEC3& normal_vector, unsigned int thread=0)
{
	Geom::Matrix<3,3,typename PFP::REAL> proj;
	proj.identity();
	proj -= Geom::transposed_vectors_mult(normal_vector,normal_vector);
	tensor = proj * tensor * proj;
Pierre Kraemer's avatar
Pierre Kraemer committed
591
592
}

593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628

namespace Parallel
{

template <typename PFP>
class FunctorComputeCurvatureVertices_NormalCycles: public FunctorMapThreaded<typename PFP::MAP >
{
	typename PFP::REAL m_radius;
	const VertexAttribute<typename PFP::VEC3>& m_position;
	const VertexAttribute<typename PFP::VEC3>& m_normal;
	const EdgeAttribute<typename PFP::REAL>& m_edgeangle;
	VertexAttribute<typename PFP::REAL>& m_kmax;
	VertexAttribute<typename PFP::REAL>& m_kmin;
	VertexAttribute<typename PFP::VEC3>& m_Kmax;
	VertexAttribute<typename PFP::VEC3>& m_Kmin;
	VertexAttribute<typename PFP::VEC3>& m_Knormal;
public:
	 FunctorComputeCurvatureVertices_NormalCycles( typename PFP::MAP& map,
		typename PFP::REAL radius,
		const VertexAttribute<typename PFP::VEC3>& position,
		const VertexAttribute<typename PFP::VEC3>& normal,
		const EdgeAttribute<typename PFP::REAL>& edgeangle,
		VertexAttribute<typename PFP::REAL>& kmax,
		VertexAttribute<typename PFP::REAL>& kmin,
		VertexAttribute<typename PFP::VEC3>& Kmax,
		VertexAttribute<typename PFP::VEC3>& Kmin,
		VertexAttribute<typename PFP::VEC3>& Knormal):
	  FunctorMapThreaded<typename PFP::MAP>(map),
	  m_radius(radius),
	  m_position(position),
	  m_normal(normal),
	  m_edgeangle(edgeangle),
	  m_kmax(kmax),
	  m_kmin(kmin),
	  m_Kmax(Kmax),
	  m_Kmin(Kmin),
Sylvain Thery's avatar
Sylvain Thery committed
629
	  m_Knormal(Knormal)
630
631
	 { }

632
	void run(Dart d, unsigned int threadID)
633
	{
Sylvain Thery's avatar
Sylvain Thery committed
634
		computeCurvatureVertex_NormalCycles<PFP>(this->m_map, d, m_radius, m_position, m_normal, m_edgeangle, m_kmax, m_kmin, m_Kmax, m_Kmin, m_Knormal, threadID) ;
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
	}
};

template <typename PFP>
void computeCurvatureVertices_NormalCycles(
	typename PFP::MAP& map,
	typename PFP::REAL radius,
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	const EdgeAttribute<typename PFP::REAL>& edgeangle,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
	VertexAttribute<typename PFP::VEC3>& Knormal,
650
	const FunctorSelect& select, unsigned int nbth)
651
{
Sylvain Thery's avatar
Sylvain Thery committed
652
653
654
655
	// WAHOO BIG PROBLEM WITH LAZZY EMBEDDING !!!
	if (!map. template isOrbitEmbedded<VERTEX>())
	{
		CellMarkerNoUnmark<VERTEX> cm(map);
656
		map. template initAllOrbitsEmbedding<VERTEX>();
Sylvain Thery's avatar
Sylvain Thery committed
657
658
659
660
	}
	if (!map. template isOrbitEmbedded<EDGE>())
	{
		CellMarkerNoUnmark<EDGE> cm(map);
661
		map. template initAllOrbitsEmbedding<EDGE>();
Sylvain Thery's avatar
Sylvain Thery committed
662
663
664
665
	}
	if (!map. template isOrbitEmbedded<FACE>())
	{
		CellMarkerNoUnmark<FACE> cm(map);
666
		map. template initAllOrbitsEmbedding<FACE>();
Sylvain Thery's avatar
Sylvain Thery committed
667
668
	}

669
	FunctorComputeCurvatureVertices_NormalCycles<PFP> funct(map, radius, position, normal, edgeangle, kmax, kmin, Kmax, Kmin, Knormal);
670
	Algo::Parallel::foreach_cell<typename PFP::MAP,VERTEX>(map, funct, nbth, true, select);
671
672
}

Sylvain Thery's avatar
Sylvain Thery committed
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716


template <typename PFP>
class FunctorComputeCurvatureVertices_QuadraticFitting: public FunctorMapThreaded<typename PFP::MAP >
{
	const VertexAttribute<typename PFP::VEC3>& m_position;
	const VertexAttribute<typename PFP::VEC3>& m_normal;
	VertexAttribute<typename PFP::REAL>& m_kmax;
	VertexAttribute<typename PFP::REAL>& m_kmin;
	VertexAttribute<typename PFP::VEC3>& m_Kmax;
	VertexAttribute<typename PFP::VEC3>& m_Kmin;
public:
	 FunctorComputeCurvatureVertices_QuadraticFitting( typename PFP::MAP& map,
		const VertexAttribute<typename PFP::VEC3>& position,
		const VertexAttribute<typename PFP::VEC3>& normal,
		VertexAttribute<typename PFP::REAL>& kmax,
		VertexAttribute<typename PFP::REAL>& kmin,
		VertexAttribute<typename PFP::VEC3>& Kmax,
		VertexAttribute<typename PFP::VEC3>& Kmin):
	  FunctorMapThreaded<typename PFP::MAP>(map),
	  m_position(position),
	  m_normal(normal),
	  m_kmax(kmax),
	  m_kmin(kmin),
	  m_Kmax(Kmax),
	  m_Kmin(Kmin)
	 { }

	void run(Dart d, unsigned int threadID)
	{
		computeCurvatureVertex_QuadraticFitting<PFP>(this->m_map, d, m_position, m_normal, m_kmax, m_kmin, m_Kmax, m_Kmin) ;
	}
};


template <typename PFP>
void computeCurvatureVertices_QuadraticFitting(
	typename PFP::MAP& map,
	const VertexAttribute<typename PFP::VEC3>& position,
	const VertexAttribute<typename PFP::VEC3>& normal,
	VertexAttribute<typename PFP::REAL>& kmax,
	VertexAttribute<typename PFP::REAL>& kmin,
	VertexAttribute<typename PFP::VEC3>& Kmax,
	VertexAttribute<typename PFP::VEC3>& Kmin,
717
	const FunctorSelect& select, unsigned int nbth)
Sylvain Thery's avatar
Sylvain Thery committed
718
719
{
	FunctorComputeCurvatureVertices_QuadraticFitting<PFP> funct(map, position, normal, kmax, kmin, Kmax, Kmin);
720
	Algo::Parallel::foreach_cell<typename PFP::MAP,VERTEX>(map, funct, nbth, true, select);
721
722
}

Sylvain Thery's avatar
Sylvain Thery committed
723
} // namespace Parallel
724
725


Pierre Kraemer's avatar
Pierre Kraemer committed
726
727
} // namespace Geometry

728
729
}

Pierre Kraemer's avatar
Pierre Kraemer committed
730
731
732
} // namespace Algo

} // namespace CGoGN