\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Planar Parameterization of Triangulated Surface Meshes

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Surface_mesh_parameterization/polyhedron_ex_parameterization.cpp
// ----------------------------------------------------------------------------
// USAGE EXAMPLES
// ----------------------------------------------------------------------------
//----------------------------------------------------------
// Discrete Conformal Map parameterization
// circle border
// OpenNL solver
// output is a eps map
// input file is mesh.off
//----------------------------------------------------------
// polyhedron_ex_parameterization -t conformal -b circle mesh.off mesh.eps
//----------------------------------------------------------
// Least Squares Conformal Maps parameterization
// two pinned vertices (automatically picked)
// OpenNL solver
// output is a .obj
// input file is mesh.off
//----------------------------------------------------------
// polyhedron_ex_parameterization -t lscm -b 2pts mesh.off mesh.obj
#include <CGAL/Timer.h>
#include <CGAL/parameterize.h>
#include <CGAL/Parameterization_mesh_patch_3.h>
#include <CGAL/Circular_border_parameterizer_3.h>
#include <CGAL/Square_border_parameterizer_3.h>
#include <CGAL/Two_vertices_parameterizer_3.h>
#include <CGAL/Barycentric_mapping_parameterizer_3.h>
#include <CGAL/Discrete_conformal_map_parameterizer_3.h>
#include <CGAL/Discrete_authalic_parameterizer_3.h>
#include <CGAL/Mean_value_coordinates_parameterizer_3.h>
#include <CGAL/LSCM_parameterizer_3.h>
#include <CGAL/Parameterization_mesh_feature_extractor.h>
#include <CGAL/OpenNL/linear_solver.h>
#include "Polyhedron_ex.h"
#include "Mesh_cutter.h"
#include "Parameterization_polyhedron_adaptor_ex.h"
#include <iostream>
#include <string.h>
#include <ctype.h>
#include <fstream>
#include <cassert>
#if defined(CGAL_USE_BOOST_PROGRAM_OPTIONS) && ! defined(DONT_USE_BOOST_PROGRAM_OPTIONS)
#include <boost/program_options.hpp>
namespace po = boost::program_options;
#endif
// ----------------------------------------------------------------------------
// Private types
// ----------------------------------------------------------------------------
typedef Polyhedron_ex Polyhedron;
// Mesh adaptors
typedef Parameterization_polyhedron_adaptor_ex Parameterization_polyhedron_adaptor;
typedef CGAL::Parameterization_mesh_patch_3<Parameterization_polyhedron_adaptor>
Mesh_patch_polyhedron;
// Type describing a border or seam as a vertex list
typedef std::list<Parameterization_polyhedron_adaptor::Vertex_handle>
Seam;
// ----------------------------------------------------------------------------
// Private functions
// ----------------------------------------------------------------------------
// Cut the mesh to make it homeomorphic to a disk
// or extract a region homeomorphic to a disc.
// Return the border of this region (empty on error)
//
// CAUTION:
// This method is provided "as is". It is very buggy and simply part of this example.
// Developers using this package should implement a more robust cut algorithm!
static Seam cut_mesh(Parameterization_polyhedron_adaptor& mesh_adaptor)
{
// Helper class to compute genus or extract borders
typedef CGAL::Parameterization_mesh_feature_extractor<Parameterization_polyhedron_adaptor_ex>
Mesh_feature_extractor;
typedef Mesh_cutter::Backbone Backbone;
Seam seam; // returned list
// Get refererence to Polyhedron_3 mesh
Polyhedron& mesh = mesh_adaptor.get_adapted_mesh();
// Extract mesh borders and compute genus
Mesh_feature_extractor feature_extractor(mesh_adaptor);
int nb_borders = feature_extractor.get_nb_borders();
int genus = feature_extractor.get_genus();
// If mesh is a topological disk
if (genus == 0 && nb_borders > 0)
{
// Pick the longest border
seam = feature_extractor.get_longest_border();
}
else // if mesh is *not* a topological disk, create a virtual cut
{
Backbone seamingBackbone; // result of cutting
Backbone::iterator he;
// Compute a cutting path that makes the mesh a "virtual" topological disk
mesh.compute_facet_centers();
Mesh_cutter cutter(mesh);
if (genus == 0)
{
// no border, we need to cut the mesh
assert (nb_borders == 0);
cutter.cut(seamingBackbone); // simple cut
}
else // genus > 0 -> cut the mesh
{
cutter.cut_genus(seamingBackbone);
}
// The Mesh_cutter class is quite buggy
// => we check that seamingBackbone is valid
//
// 1) Check that seamingBackbone is not empty
if (seamingBackbone.begin() == seamingBackbone.end())
return seam; // return empty list
//
// 2) Check that seamingBackbone is a loop and
// count occurences of seam halfedges
mesh.tag_halfedges(0); // Reset counters
for (he = seamingBackbone.begin(); he != seamingBackbone.end(); he++)
{
// Get next halfedge iterator (looping)
Backbone::iterator next_he = he;
next_he++;
if (next_he == seamingBackbone.end())
next_he = seamingBackbone.begin();
// Check that seamingBackbone is a loop: check that
// end of current HE == start of next one
if ((*he)->vertex() != (*next_he)->opposite()->vertex())
return seam; // return empty list
// Increment counter (in "tag" field) of seam halfedges
(*he)->tag( (*he)->tag()+1 );
}
//
// 3) check that the seamingBackbone is a two-way list
for (he = seamingBackbone.begin(); he != seamingBackbone.end(); he++)
{
// Counter of halfedge and opposite halfedge must be 1
if ((*he)->tag() != 1 || (*he)->opposite()->tag() != 1)
return seam; // return empty list
}
// Convert list of halfedges to a list of vertices
for (he = seamingBackbone.begin(); he != seamingBackbone.end(); he++)
seam.push_back((*he)->vertex());
}
return seam;
}
// Call appropriate parameterization method based on command line parameters
template<
class ParameterizationMesh_3, // 3D surface
class GeneralSparseLinearAlgebraTraits_d,
// Traits class to solve a general sparse linear system
class SymmetricSparseLinearAlgebraTraits_d
// Traits class to solve a symmetric sparse linear system
>
typename CGAL::Parameterizer_traits_3<ParameterizationMesh_3>::Error_code
parameterize(ParameterizationMesh_3& mesh, // Mesh parameterization adaptor
const std::string& type, // type of parameterization (see usage)
const std::string& border) // type of border parameterization (see usage)
{
typename CGAL::Parameterizer_traits_3<ParameterizationMesh_3>::Error_code err;
if ( (type == std::string("floater")) && (border == std::string("circle")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Mean_value_coordinates_parameterizer_3<
ParameterizationMesh_3,
CGAL::Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("floater")) && (border == std::string("square")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Mean_value_coordinates_parameterizer_3<
ParameterizationMesh_3,
CGAL::Square_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("barycentric")) && (border == std::string("circle")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Barycentric_mapping_parameterizer_3<
ParameterizationMesh_3,
CGAL::Circular_border_uniform_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("barycentric")) && (border == std::string("square")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Barycentric_mapping_parameterizer_3<
ParameterizationMesh_3,
CGAL::Square_border_uniform_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("conformal")) && (border == std::string("circle")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Discrete_conformal_map_parameterizer_3<
ParameterizationMesh_3,
CGAL::Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("conformal")) && (border == std::string("square")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Discrete_conformal_map_parameterizer_3<
ParameterizationMesh_3,
CGAL::Square_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("authalic")) && (border == std::string("circle")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Discrete_authalic_parameterizer_3<
ParameterizationMesh_3,
CGAL::Circular_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("authalic")) && (border == std::string("square")) )
{
err = CGAL::parameterize(
mesh,
CGAL::Discrete_authalic_parameterizer_3<
ParameterizationMesh_3,
CGAL::Square_border_arc_length_parameterizer_3<ParameterizationMesh_3>,
GeneralSparseLinearAlgebraTraits_d
>());
}
else if ( (type == std::string("lscm")) && (border == std::string("2pts")) )
{
err = CGAL::parameterize(
mesh,
CGAL::LSCM_parameterizer_3<
ParameterizationMesh_3,
CGAL::Two_vertices_parameterizer_3<ParameterizationMesh_3>,
SymmetricSparseLinearAlgebraTraits_d
>());
}
else
{
std::cerr << "Error: invalid parameters combination " << type << " + " << border << std::endl;
err = CGAL::Parameterizer_traits_3<ParameterizationMesh_3>::ERROR_WRONG_PARAMETER;
}
return err;
}
// ----------------------------------------------------------------------------
// main()
// ----------------------------------------------------------------------------
#if defined(CGAL_USE_BOOST_PROGRAM_OPTIONS) && ! defined(DONT_USE_BOOST_PROGRAM_OPTIONS)
int main(int argc, char * argv[])
#else
int main()
#endif
{
CGAL::Timer total_timer;
total_timer.start();
std::cerr << "PARAMETERIZATION" << std::endl;
//***************************************
// Read options on the command line
//***************************************
std::string type; // default: Floater param
std::string border; // default: circular border param.
std::string solver; // default: OpenNL solver
std::string input; // required
std::string output; // default: out.eps
try
{
#if defined(CGAL_USE_BOOST_PROGRAM_OPTIONS) && ! defined(DONT_USE_BOOST_PROGRAM_OPTIONS)
po::options_description desc("Allowed options");
desc.add_options()
("help,h", "prints this help message")
("type,t", po::value<std::string>(&type)->default_value("floater"),
"parameterization method: floater, conformal, barycentric, authalic or lscm")
("border,b", po::value<std::string>(&border)->default_value("circle"),
"border shape: circle, square or 2pts (lscm only)")
("solver,s", po::value<std::string>(&solver)->default_value("opennl"),
"solver: opennl")
("input,i", po::value<std::string>(&input)->default_value(""),
"input mesh (OFF)")
("output,o", po::value<std::string>(&output)->default_value("out.eps"),
"output file (EPS or OBJ)")
;
po::positional_options_description p;
p.add("input", 1);
p.add("output", 1);
po::variables_map vm;
po::store(po::command_line_parser(argc, argv).options(desc).positional(p).run(), vm);
po::notify(vm);
if (vm.count("help")) {
std::cout << desc << "\n";
return 1;
}
#else
std::cerr << "Command-line options require Boost.ProgramOptions" << std::endl;
std::cerr << "Use hard-coded options" << std::endl;
border = "square";
type = "floater";
solver = "opennl";
input = "data/rotor.off";
output = "rotor_floater_square_opennl_parameterized.obj";
#endif
}
catch(std::exception& e) {
std::cerr << "error: " << e.what() << "\n";
return 1;
}
catch(...) {
std::cerr << "Exception of unknown type!\n";
throw;
}
//***************************************
// Read the mesh
//***************************************
CGAL::Timer task_timer;
task_timer.start();
// Read the mesh
std::ifstream stream(input.c_str());
Polyhedron mesh;
stream >> mesh;
if(!stream || !mesh.is_valid() || mesh.empty())
{
std::cerr << "Error: cannot read OFF file " << input << std::endl;
return EXIT_FAILURE;
}
std::cerr << "Read file " << input << ": "
<< task_timer.time() << " seconds "
<< "(" << mesh.size_of_facets() << " facets, "
<< mesh.size_of_vertices() << " vertices)" << std::endl;
task_timer.reset();
//***************************************
// Create mesh adaptor
//***************************************
// The Surface_mesh_parameterization package needs an adaptor to handle Polyhedron_ex meshes
Parameterization_polyhedron_adaptor mesh_adaptor(mesh);
// The parameterization methods support only meshes that
// are topological disks => we need to compute a cutting path
// that makes the mesh a "virtual" topological disk
//
// 1) Cut the mesh
Seam seam = cut_mesh(mesh_adaptor);
if (seam.empty())
{
std::cerr << "Input mesh not supported: the example cutting algorithm is too simple to cut this shape" << std::endl;
return EXIT_FAILURE;
}
//
// 2) Create adaptor that virtually "cuts" a patch in a Polyhedron_ex mesh
Mesh_patch_polyhedron mesh_patch(mesh_adaptor, seam.begin(), seam.end());
if (!mesh_patch.is_valid())
{
std::cerr << "Input mesh not supported: non manifold shape or invalid cutting" << std::endl;
return EXIT_FAILURE;
}
std::cerr << "Mesh cutting: " << task_timer.time() << " seconds." << std::endl;
task_timer.reset();
//***************************************
// switch parameterization
//***************************************
std::cerr << "Parameterization..." << std::endl;
// Defines the error codes
typedef CGAL::Parameterizer_traits_3<Mesh_patch_polyhedron> Parameterizer;
Parameterizer::Error_code err;
if (solver == std::string("opennl"))
{
err = parameterize<Mesh_patch_polyhedron,
OpenNL::DefaultLinearSolverTraits<double>,
OpenNL::SymmetricLinearSolverTraits<double>
>(mesh_patch, type, border);
}
else
{
std::cerr << "Error: invalid solver parameter " << solver << std::endl;
err = Parameterizer::ERROR_WRONG_PARAMETER;
}
// Report errors
switch(err) {
case Parameterizer::OK: // Success
break;
case Parameterizer::ERROR_EMPTY_MESH: // Input mesh not supported
case Parameterizer::ERROR_NON_TRIANGULAR_MESH:
case Parameterizer::ERROR_NO_TOPOLOGICAL_DISC:
case Parameterizer::ERROR_BORDER_TOO_SHORT:
std::cerr << "Input mesh not supported: " << Parameterizer::get_error_message(err) << std::endl;
return EXIT_FAILURE;
break;
default: // Error
std::cerr << "Error: " << Parameterizer::get_error_message(err) << std::endl;
return EXIT_FAILURE;
break;
};
std::cerr << "Parameterization: " << task_timer.time() << " seconds." << std::endl;
task_timer.reset();
//***************************************
// Output
//***************************************
// get output file's extension
std::string extension = output.substr(output.find_last_of('.'));
// Save mesh
if (extension == ".eps" || extension == ".EPS")
{
// write Postscript file
if ( ! mesh.write_file_eps(output.c_str()) )
{
std::cerr << "Error: cannot write file " << output << std::endl;
return EXIT_FAILURE;
}
}
else if (extension == ".obj" || extension == ".OBJ")
{
// write Wavefront obj file
if ( ! mesh.write_file_obj(output.c_str()) )
{
std::cerr << "Error: cannot write file " << output << std::endl;
return EXIT_FAILURE;
}
}
else
{
std::cerr << "Error: output format not supported" << output << std::endl;
err = Parameterizer::ERROR_WRONG_PARAMETER;
return EXIT_FAILURE;
}
std::cerr << "Write file " << output << ": "
<< task_timer.time() << " seconds " << std::endl;
return EXIT_SUCCESS;
}