GCC Code Coverage Report

Line	Branch	Exec	Source
1			/*
2			* Copyright (c) 2000-2022 Inria
3			* All rights reserved.
4			*
5			* Redistribution and use in source and binary forms, with or without
6			* modification, are permitted provided that the following conditions are met:
7			*
8			* * Redistributions of source code must retain the above copyright notice,
9			* this list of conditions and the following disclaimer.
10			* * Redistributions in binary form must reproduce the above copyright notice,
11			* this list of conditions and the following disclaimer in the documentation
12			* and/or other materials provided with the distribution.
13			* * Neither the name of the ALICE Project-Team nor the names of its
14			* contributors may be used to endorse or promote products derived from this
15			* software without specific prior written permission.
16			*
17			* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18			* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19			* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20			* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
21			* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22			* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23			* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24			* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25			* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26			* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27			* POSSIBILITY OF SUCH DAMAGE.
28			*
29			* Contact: Bruno Levy
30			*
31			* https://www.inria.fr/fr/bruno-levy
32			*
33			* Inria,
34			* Domaine de Voluceau,
35			* 78150 Le Chesnay - Rocquencourt
36			* FRANCE
37			*
38			*/
39
40			#include <geogram/parameterization/mesh_LSCM.h>
41			#include <geogram/mesh/mesh.h>
42			#include <geogram/mesh/mesh_geometry.h>
43			#include <geogram/bibliography/bibliography.h>
44			#include <geogram/NL/nl.h>
45			#include <geogram/NL/nl_ext.h>
46			#include <algorithm>
47
48			namespace {
49			using namespace GEO;
50
51
52			/**
53			* \brief Computes Least Squares Conformal Maps in least squares or
54			* spectral mode.
55			* \details The method is described in the following references:
56			* - Least Squares Conformal Maps, Levy, Petitjean, Ray, Maillot, ACM
57			* SIGGRAPH, 2002
58			* - Spectral Conformal Parameterization, Mullen, Tong, Alliez, Desbrun,
59			* Computer Graphics Forum (SGP conf. proc.), 2008
60			*/
61			class LSCM {
62			public:
63
64			/**
65			* \brief LSCM constructor
66			* \param[in] M a reference to the mesh. It needs to correspond to a
67			* topological disk (open surface with one border and no handle).
68			* \param[in] tex_coord a vector property of dimension 2 where to
69			* store the texture coordinates.
70			*/
71		✗	LSCM(Mesh& M, Attribute<double>& tex_coord, Attribute<double>& angle) :
72		✗	mesh_(M), tex_coord_(tex_coord), angle_(angle), eigen_(0) {
73		✗	geo_assert(tex_coord.dimension() == 2);
74		✗	locked_1_ = NO_INDEX;
75		✗	locked_2_ = NO_INDEX;
76		✗	verbose_ = false;
77		✗	}
78
79			/**
80			* \brief Enables or disables messages.
81			* \param[in] x if true, messages are displayed on the console
82			* with statistics. Default is non-verbose.
83			*/
84			void set_verbose(bool x) {
85		✗	verbose_ = x;
86			}
87
88			/**
89			* \brief Sets whether spectral mode is used.
90			* \details In default mode, the trivial solution (all vertices to zero)
91			* is avoided by locking two vertices (that are as "extremal"
92			* as possible). In spectral mode, the trivial solution is avoided by
93			* finding the first minimizer that is orthogonal to it (more elegant,
94			* but more costly).
95			*/
96			void set_spectral(bool x) {
97		✗	spectral_ = x;
98			}
99
100			/**
101			* \brief Computes the least squares conformal map and stores it in
102			* the texture coordinates of the mesh.
103			* \details Outline of the algorithm (steps 1,2,3 are not used
104			* in spectral mode):
105			* - 1) Find an initial solution by projecting on a plane
106			* - 2) Lock two vertices of the mesh
107			* - 3) Copy the initial u,v coordinates to OpenNL
108			* - 4) Construct the LSCM equation with OpenNL
109			* - 5) Solve the equation with OpenNL
110			* - 6) Copy OpenNL solution to the u,v coordinates
111			*/
112
113		✗	void apply() {
114
115		✗	geo_cite("DBLP:journals/tog/LevyPRM02");
116		✗	if(spectral_) {
117		✗	geo_cite("DBLP:journals/cgf/MullenTAD08");
118			}
119
120			const int nb_eigens = 10;
121		✗	nlNewContext();
122		✗	NLuint nb_vertices = NLuint(mesh_.vertices.nb());
123
124		✗	if(spectral_) {
125		✗	if(nlInitExtension("ARPACK")) {
126		✗	if(verbose_) {
127		✗	Logger::out("LSCM") << "ARPACK extension initialized"
128			<< std::endl;
129			}
130		✗	nlEigenSolverParameteri(NL_EIGEN_SOLVER, NL_ARPACK_EXT);
131		✗	nlEigenSolverParameteri(NL_NB_EIGENS, nb_eigens);
132		✗	if(verbose_) {
133		✗	nlEnable(NL_VERBOSE);
134			}
135			} else {
136		✗	if(verbose_) {
137		✗	Logger::out("LSCM")
138			<< "Could not initialize ARPACK extension"
139			<< std::endl;
140		✗	Logger::out("LSCM")
141			<< "Falling back to least squares mode"
142			<< std::endl;
143			}
144		✗	spectral_ = false;
145			}
146			} else {
147			#ifndef GEO_OS_ANDROID
148			if(
149		✗	nb_vertices <= 200000 && (
150		✗	nlExtensionIsInitialized("SUPERLU") ||
151		✗	nlInitExtension("SUPERLU")
152			)
153			) {
154		✗	if(verbose_) {
155		✗	Logger::out("LSCM") << "using SUPERLU"
156			<< std::endl;
157			}
158		✗	nlSolverParameteri(NL_SOLVER, NL_PERM_SUPERLU_EXT);
159			} else if(
160		✗	nlExtensionIsInitialized("AMGCL") ||
161		✗	nlInitExtension("AMGCL")
162			) {
163		✗	if(verbose_) {
164		✗	nlEnable(NL_VERBOSE);
165		✗	Logger::out("LSCM") << "using AMGCL"
166			<< std::endl;
167			}
168		✗	nlSolverParameteri(NL_SOLVER, NL_AMGCL_EXT);
169			} else
170			#endif
171			{
172		✗	if(verbose_) {
173		✗	nlEnable(NL_VERBOSE);
174		✗	Logger::out("LSCM") << "using JacobiCG"
175			<< std::endl;
176			}
177			}
178			}
179		✗	if(!spectral_) {
180		✗	project();
181			}
182		✗	nlSolverParameteri(NL_NB_VARIABLES, NLint(2*nb_vertices));
183		✗	nlSolverParameteri(NL_LEAST_SQUARES, NL_TRUE);
184		✗	nlSolverParameteri(NL_MAX_ITERATIONS, NLint(5*nb_vertices));
185		✗	if(spectral_) {
186		✗	nlSolverParameterd(NL_THRESHOLD, 0.0);
187			} else {
188		✗	nlSolverParameterd(NL_THRESHOLD, 1e-10);
189			}
190		✗	nlBegin(NL_SYSTEM);
191		✗	mesh_to_solver();
192		✗	nlBegin(NL_MATRIX);
193			setup_lscm();
194		✗	nlEnd(NL_MATRIX);
195		✗	nlEnd(NL_SYSTEM);
196		✗	if(verbose_) {
197		✗	Logger::out("LSCM") << "Solving ..." << std::endl;
198			}
199
200		✗	if(spectral_) {
201		✗	nlEigenSolve();
202		✗	if(verbose_) {
203		✗	for(NLuint i=0; i<nb_eigens; ++i) {
204		✗	Logger::out("LSCM") << "[" << i << "] "
205		✗	<< nlGetEigenValue(i) << std::endl;
206			}
207			}
208
209			// Find first "non-zero" eigenvalue
210		✗	double small_eigen = ::fabs(nlGetEigenValue(0)) ;
211		✗	eigen_ = 1;
212		✗	for(NLuint i=1; i<nb_eigens; ++i) {
213		✗	if(::fabs(nlGetEigenValue(i)) / small_eigen > 1e3) {
214		✗	eigen_ = i ;
215		✗	break ;
216			}
217			}
218			} else{
219		✗	nlSolve();
220			}
221
222		✗	solver_to_mesh();
223		✗	normalize_uv();
224
225		✗	if(!spectral_) {
226		✗	if(verbose_) {
227			double time;
228			NLint iterations;
229		✗	nlGetDoublev(NL_ELAPSED_TIME, &time);
230		✗	nlGetIntegerv(NL_USED_ITERATIONS, &iterations);
231		✗	Logger::out("LSCM") << "Solver time: " << time << std::endl;
232		✗	Logger::out("LSCM") << "Used iterations: "
233		✗	<< iterations << std::endl;
234			}
235			}
236		✗	nlDeleteContext(nlGetCurrent());
237		✗	}
238
239			protected:
240
241			/**
242			* \brief Creates the LSCM equations in OpenNL.
243			*/
244			void setup_lscm() {
245		✗	for(NLuint f=0; f<mesh_.facets.nb(); ++f) {
246		✗	setup_lscm(f);
247			}
248			}
249
250			/**
251			* \brief Creates the LSCM equations in OpenNL, related
252			* with a given facet.
253			* \param[in] f the index of the facet.
254			* \details no-need to triangulate the facet,
255			* we do that "virtually", by creating triangles
256			* radiating around vertex 0 of the facet.
257			* (however, this may be invalid for concave facets)
258			*/
259		✗	void setup_lscm(NLuint f) {
260		✗	NLuint nv = NLuint(mesh_.facets.nb_vertices(f));
261		✗	if(angle_.is_bound()) {
262			index_t c0 = mesh_.facets.corners_begin(f);
263		✗	double a0 = angle_[c0];
264		✗	for(NLuint i=1; i<nv-1; ++i) {
265		✗	double ai = angle_[c0+i];
266		✗	double aip1 = angle_[c0+1+1];
267		✗	setup_conformal_map_relations(
268			NLuint(mesh_.facets.vertex(f,0)),
269			NLuint(mesh_.facets.vertex(f,i)),
270		✗	NLuint(mesh_.facets.vertex(f,i+1)),
271			a0, ai, aip1
272			);
273			}
274			} else {
275		✗	for(NLuint i=1; i<nv-1; ++i) {
276		✗	setup_conformal_map_relations(
277			NLuint(mesh_.facets.vertex(f,0)),
278		✗	NLuint(mesh_.facets.vertex(f,i)),
279		✗	NLuint(mesh_.facets.vertex(f,i+1))
280			);
281			}
282			}
283		✗	}
284
285			/**
286			* \brief Computes the coordinates of the vertices of a triangle
287			* in a local 2D orthonormal basis of the triangle's plane.
288			* \param[in] p0 , p1 , p2 the 3D coordinates of the vertices of
289			* the triangle
290			* \param[out] z0 , z1 , z2 the 2D coordinates of the vertices of
291			* the triangle
292			*/
293		✗	static void project_triangle(
294			const vec3& p0,
295			const vec3& p1,
296			const vec3& p2,
297			vec2& z0,
298			vec2& z1,
299			vec2& z2
300			) {
301			vec3 X = p1 - p0;
302		✗	X = normalize(X);
303			vec3 Z = cross(X,(p2 - p0));
304		✗	Z = normalize(Z);
305			vec3 Y = cross(Z,X);
306			const vec3& O = p0;
307
308			double x0 = 0;
309			double y0 = 0;
310			double x1 = (p1 - O).length();
311			double y1 = 0;
312			double x2 = dot((p2 - O),X);
313			double y2 = dot((p2 - O),Y);
314
315		✗	z0 = vec2(x0,y0);
316		✗	z1 = vec2(x1,y1);
317		✗	z2 = vec2(x2,y2);
318		✗	}
319
320			/**
321			* \brief Creates the LSCM equation in OpenNL, related with
322			* a given triangle, specified by vertex indices.
323			* \param[in] v0 , v1 , v2 the indices of the three vertices of
324			* the triangle.
325			* \details Uses the geometric form of LSCM equation:
326			* (Z1 - Z0)(U2 - U0) = (Z2 - Z0)(U1 - U0)
327			* Where Uk = uk + i.vk is the complex number
328			* corresponding to (u,v) coords
329			* Zk = xk + i.yk is the complex number
330			* corresponding to local (x,y) coords
331			* There is no divide with this expression,
332			* this makes it more numerically stable in
333			* the presence of degenerate triangles.
334			*/
335		✗	void setup_conformal_map_relations(
336			NLuint v0, NLuint v1, NLuint v2
337			) {
338
339		✗	const vec3& p0 = mesh_.vertices.point(v0);
340		✗	const vec3& p1 = mesh_.vertices.point(v1);
341		✗	const vec3& p2 = mesh_.vertices.point(v2);
342
343			vec2 z0,z1,z2;
344		✗	project_triangle(p0,p1,p2,z0,z1,z2);
345			vec2 z01 = z1 - z0;
346			vec2 z02 = z2 - z0;
347			double a = z01.x;
348			double b = z01.y;
349			double c = z02.x;
350			double d = z02.y;
351		✗	geo_assert(b == 0.0);
352
353			// Note : 2*id + 0 --> u
354			// 2*id + 1 --> v
355		✗	NLuint u0_id = 2*v0 ;
356		✗	NLuint v0_id = 2*v0 + 1;
357		✗	NLuint u1_id = 2*v1 ;
358		✗	NLuint v1_id = 2*v1 + 1;
359		✗	NLuint u2_id = 2*v2 ;
360		✗	NLuint v2_id = 2*v2 + 1;
361
362			// Note : rhs = 0
363
364			// Real part
365		✗	nlBegin(NL_ROW);
366		✗	nlCoefficient(u0_id, -a+c) ;
367		✗	nlCoefficient(v0_id, b-d) ;
368		✗	nlCoefficient(u1_id, -c) ;
369		✗	nlCoefficient(v1_id, d) ;
370		✗	nlCoefficient(u2_id, a);
371		✗	nlEnd(NL_ROW);
372
373			// Imaginary part
374		✗	nlBegin(NL_ROW);
375		✗	nlCoefficient(u0_id, -b+d);
376		✗	nlCoefficient(v0_id, -a+c);
377		✗	nlCoefficient(u1_id, -d);
378		✗	nlCoefficient(v1_id, -c);
379		✗	nlCoefficient(v2_id, a);
380		✗	nlEnd(NL_ROW);
381		✗	}
382
383			/**
384			* \brief Creates the LSCM equation in OpenNL, related with
385			* a given triangle, specified by vertex indices, and with
386			* specified desired angles.
387			* \details This version is used to recoved the u,v coordinates
388			* from the angles computed by ABF++.
389			* \param[in] v0 , v1 , v2 the indices of the three vertices of
390			* the triangle.
391			* \param[in] alpha0 , alpha1 , alpha2 the desired angles at the
392			* three vertices of the triangle
393			*/
394		✗	void setup_conformal_map_relations(
395			NLuint v0, NLuint v1, NLuint v2,
396			double alpha0, double alpha1, double alpha2
397			) {
398		✗	const vec3& p0 = mesh_.vertices.point(v0);
399		✗	const vec3& p1 = mesh_.vertices.point(v1);
400		✗	const vec3& p2 = mesh_.vertices.point(v2);
401
402		✗	double scaling = ::sin(alpha1) / ::sin(alpha2) ;
403		✗	double a = scaling * ::cos(alpha0);
404		✗	double b = scaling * ::sin(alpha0);
405
406			double area = Geom::triangle_area(p0,p1,p2) ;
407		✗	double s = ::sqrt(area) ;
408
409			// Note : 2*id + 0 --> u
410			// 2*id + 1 --> v
411		✗	NLuint u0_id = 2*v0 ;
412		✗	NLuint v0_id = 2*v0 + 1;
413		✗	NLuint u1_id = 2*v1 ;
414		✗	NLuint v1_id = 2*v1 + 1;
415		✗	NLuint u2_id = 2*v2 ;
416		✗	NLuint v2_id = 2*v2 + 1;
417
418			// Note : rhs = 0
419
420			// Real part
421		✗	nlRowScaling(s);
422		✗	nlBegin(NL_ROW);
423		✗	nlCoefficient(u0_id, 1.0 - a) ;
424		✗	nlCoefficient(v0_id, b) ;
425		✗	nlCoefficient(u1_id, a) ;
426		✗	nlCoefficient(v1_id, -b) ;
427		✗	nlCoefficient(u2_id, -1.0);
428		✗	nlEnd(NL_ROW);
429
430			// Imaginary part
431		✗	nlRowScaling(s);
432		✗	nlBegin(NL_ROW);
433		✗	nlCoefficient(u0_id, -b);
434		✗	nlCoefficient(v0_id, 1.0-a);
435		✗	nlCoefficient(u1_id, b);
436		✗	nlCoefficient(v1_id, a);
437		✗	nlCoefficient(v2_id, -1.0);
438		✗	nlEnd(NL_ROW);
439		✗	}
440
441			/**
442			* \brief Copies u,v coordinates from OpenNL solver to the mesh.
443			*/
444		✗	void solver_to_mesh() {
445		✗	for(index_t i: mesh_.vertices) {
446		✗	double u = spectral_ ? nlMultiGetVariable(NLuint(2*i),eigen_)
447		✗	: nlGetVariable(2*i);
448		✗	double v = spectral_ ? nlMultiGetVariable(NLuint(2*i+1),eigen_)
449		✗	: nlGetVariable(2*i+1);
450		✗	tex_coord_[2*i] = u;
451		✗	tex_coord_[2*i+1] = v;
452			}
453		✗	}
454
455			/**
456			* \brief Translates and scales tex coords in such a way that they fit
457			* within the unit square.
458			*/
459		✗	void normalize_uv() {
460		✗	double u_min= Numeric::max_float64();
461		✗	double v_min= Numeric::max_float64();
462		✗	double u_max= -Numeric::max_float64();
463		✗	double v_max= -Numeric::max_float64();
464		✗	for(NLuint i=0; i<mesh_.vertices.nb(); ++i) {
465		✗	double u = tex_coord_[2*i];
466		✗	double v = tex_coord_[2*i+1];
467		✗	u_min = std::min(u_min, u);
468		✗	v_min = std::min(v_min, v);
469		✗	u_max = std::max(u_max, u);
470		✗	v_max = std::max(v_max, v);
471			}
472		✗	double l = std::max(u_max-u_min,v_max-v_min);
473		✗	for(NLuint i=0; i<mesh_.vertices.nb(); ++i) {
474		✗	tex_coord_[2*i] -= u_min;
475		✗	tex_coord_[2*i] /= l;
476		✗	tex_coord_[2*i+1] -= v_min;
477		✗	tex_coord_[2*i+1] /= l;
478			}
479		✗	}
480
481			/**
482			* \brief Tests whether a vertex is locked.
483			* \param[in] v the index of the vertex
484			* \retval true if the vertex is locked
485			* \retval false otherwise
486			*/
487			bool is_locked(index_t v) {
488		✗	return (v==locked_1_ || v==locked_2_);
489			}
490
491			/**
492			* \brief Copies u,v coordinates from the mesh to OpenNL solver.
493			*/
494		✗	void mesh_to_solver() {
495		✗	for(NLuint i=0; i<mesh_.vertices.nb(); ++i) {
496		✗	double u = tex_coord_[2*i];
497		✗	double v = tex_coord_[2*i+1];
498		✗	nlSetVariable(2 * i , u);
499		✗	nlSetVariable(2 * i + 1, v);
500		✗	if(!spectral_ && is_locked(i)) {
501		✗	nlLockVariable(2 * i );
502		✗	nlLockVariable(2 * i + 1);
503			}
504			}
505		✗	}
506
507			/**
508			* \brief Chooses an initial solution, and locks two vertices.
509			*/
510		✗	void project() {
511			// Get bbox
512		✗	double xmin = 1e30;
513		✗	double ymin = 1e30;
514		✗	double zmin = 1e30;
515		✗	double xmax = -1e30;
516		✗	double ymax = -1e30;
517		✗	double zmax = -1e30;
518
519		✗	for(index_t i: mesh_.vertices) {
520			const vec3& p = mesh_.vertices.point(i);
521		✗	xmin = std::min(p.x, xmin);
522		✗	ymin = std::min(p.y, ymin);
523		✗	zmin = std::min(p.z, zmin);
524
525		✗	xmax = std::max(p.x, xmax);
526		✗	ymax = std::max(p.y, ymax);
527		✗	zmax = std::max(p.z, zmax);
528			}
529
530		✗	double dx = xmax - xmin;
531		✗	double dy = ymax - ymin;
532		✗	double dz = zmax - zmin;
533
534			vec3 V1,V2;
535
536			// Find shortest bbox axis
537		✗	if(dx <= dy && dx <= dz) {
538		✗	if(dy > dz) {
539			V1 = vec3(0,1,0);
540			V2 = vec3(0,0,1);
541			} else {
542			V2 = vec3(0,1,0);
543			V1 = vec3(0,0,1);
544			}
545		✗	} else if(dy <= dx && dy <= dz) {
546		✗	if(dx > dz) {
547			V1 = vec3(1,0,0);
548			V2 = vec3(0,0,1);
549			} else {
550			V2 = vec3(1,0,0);
551			V1 = vec3(0,0,1);
552			}
553		✗	} else if(dz <= dx && dz <= dy) {
554		✗	if(dx > dy) {
555			V1 = vec3(1,0,0);
556			V2 = vec3(0,1,0);
557			} else {
558			V2 = vec3(1,0,0);
559			V1 = vec3(0,1,0);
560			}
561			}
562
563			// Project onto shortest bbox axis,
564			// and lock extrema vertices
565
566			double umin = 1e30;
567			double umax = -1e30;
568
569		✗	for(index_t i: mesh_.vertices) {
570			const vec3& p = mesh_.vertices.point(i);
571			double u = dot(p,V1);
572			double v = dot(p,V2);
573		✗	tex_coord_[2*i] = u;
574		✗	tex_coord_[2*i+1] = v;
575		✗	if(u < umin) {
576		✗	locked_1_ = i;
577			umin = u;
578			}
579		✗	if(u > umax) {
580		✗	locked_2_ = i;
581			umax = u;
582			}
583			}
584		✗	}
585
586			Mesh& mesh_;
587
588			Attribute<double>& tex_coord_;
589
590			Attribute<double>& angle_;
591			/**
592			* \brief true if spectral mode is used,
593			* false if locked least squares mode is used.
594			*/
595			bool spectral_;
596
597			/**
598			* \brief In spectral mode, the index of the first
599			* non-zero eigenvalue.
600			*/
601			NLuint eigen_;
602
603			/**
604			* \brief The indices of the two locked vertices.
605			*/
606			index_t locked_1_, locked_2_;
607
608			bool verbose_;
609			};
610
611			}
612
613			namespace GEO {
614
615		✗	void mesh_compute_LSCM(
616			Mesh& M, const std::string& attribute_name, bool spectral,
617			const std::string& angle_attribute_name,
618			bool verbose
619			) {
620			Attribute<double> tex_coord;
621		✗	tex_coord.bind_if_is_defined(M.vertices.attributes(), attribute_name);
622		✗	if(tex_coord.is_bound() && tex_coord.dimension() != 2) {
623		✗	Logger::err("LSCM") << "Attribute " << attribute_name
624			<< " already exists in mesh with dimension "
625			<< tex_coord.dimension()
626			<< " (expected 2)"
627			<< std::endl;
628			return;
629			}
630			if(!tex_coord.is_bound()) {
631		✗	tex_coord.create_vector_attribute(
632			M.vertices.attributes(),attribute_name,2
633			);
634			}
635			Attribute<double> angle;
636		✗	angle.bind_if_is_defined(
637			M.facet_corners.attributes(), angle_attribute_name
638			);
639		✗	LSCM lscm(M,tex_coord,angle);
640			lscm.set_spectral(spectral);
641			lscm.set_verbose(verbose);
642		✗	lscm.apply();
643			}
644			}
645