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// Copyright (c) 2015 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/fair_impl.h $
// $Id: include/CGAL/Polygon_mesh_processing/internal/fair_impl.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Jane Tournois
#ifndef CGAL_POLYGON_MESH_PROCESSING_FAIR_POLYHEDRON_3_H
#define CGAL_POLYGON_MESH_PROCESSING_FAIR_POLYHEDRON_3_H
#include <CGAL/license/Polygon_mesh_processing/meshing_hole_filling.h>
#include <map>
#include <set>
#include <CGAL/assertions.h>
#include <CGAL/boost/graph/helpers.h>
#ifdef CGAL_PMP_FAIR_DEBUG
#include <CGAL/Timer.h>
#endif
#include <iterator>
namespace CGAL {
namespace Polygon_mesh_processing {
namespace internal {
// [On Linear Variational Surface Deformation Methods-2008]
template<class PolygonMesh,
class SparseLinearSolver,
class WeightCalculator,
class VertexPointMap>
class Fair_Polyhedron_3 {
// typedefs
typedef typename VertexPointMap::value_type Point_3;
typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor vertex_descriptor;
typedef Halfedge_around_target_circulator<PolygonMesh> Halfedge_around_vertex_circulator;
typedef SparseLinearSolver Sparse_linear_solver;
typedef typename Sparse_linear_solver::Matrix Solver_matrix;
typedef typename Sparse_linear_solver::Vector Solver_vector;
// members
PolygonMesh& pmesh;
WeightCalculator weight_calculator;
VertexPointMap ppmap;
public:
Fair_Polyhedron_3(PolygonMesh& pmesh
, VertexPointMap vpmap
, WeightCalculator weight_calculator)
: pmesh(pmesh)
, weight_calculator(weight_calculator)
, ppmap(vpmap)
{ }
private:
double sum_weight(vertex_descriptor v) {
double weight = 0;
Halfedge_around_vertex_circulator circ(halfedge(v,pmesh),pmesh), done(circ);
do {
weight += CGAL::to_double(weight_calculator.w_ij(*circ));
} while(++circ != done);
return weight;
}
// recursively computes a row (use depth parameter to compute L, L^2, L^3)
// Equation 6 in [On Linear Variational Surface Deformation Methods]
void compute_row(
vertex_descriptor v,
int row_id, // which row to insert in [ frees stay left-hand side ]
Solver_matrix& matrix,
double& x, double& y, double& z, // constants transferred to right-hand side
double multiplier,
const std::map<vertex_descriptor, std::size_t>& vertex_id_map,
unsigned int depth)
{
if(depth == 0) {
typename std::map<vertex_descriptor, std::size_t>::const_iterator vertex_id_it = vertex_id_map.find(v);
if(vertex_id_it != vertex_id_map.end()) {
int col_id = static_cast<int>(vertex_id_it->second);
matrix.add_coef(row_id, col_id, multiplier);
}
else {
typename boost::property_traits<VertexPointMap>::reference p = get(ppmap, v);
x += multiplier * - to_double(p.x());
y += multiplier * - to_double(p.y());
z += multiplier * - to_double(p.z());
}
}
else {
double w_i = CGAL::to_double(weight_calculator.w_i(v));
Halfedge_around_vertex_circulator circ(halfedge(v,pmesh),pmesh), done(circ);
do {
double w_i_w_ij = w_i * CGAL::to_double(weight_calculator.w_ij(*circ)) ;
vertex_descriptor nv = target(opposite(*circ,pmesh),pmesh);
compute_row(nv, row_id, matrix, x, y, z, -w_i_w_ij*multiplier, vertex_id_map, depth-1);
} while(++circ != done);
double w_i_w_ij_sum = w_i * sum_weight(v);
compute_row(v, row_id, matrix, x, y, z, w_i_w_ij_sum*multiplier, vertex_id_map, depth-1);
}
}
public:
template<class VertexRange>
bool fair(const VertexRange& vertices
, SparseLinearSolver solver
, unsigned int fc)
{
int depth = static_cast<int>(fc) + 1;
if(depth < 0 || depth > 3) {
CGAL_warning_msg(false, "Continuity should be between 0 and 2 inclusively!");
return false;
}
std::set<vertex_descriptor> interior_vertices(std::begin(vertices),
std::end(vertices));
if(interior_vertices.empty()) { return true; }
#ifdef CGAL_PMP_FAIR_DEBUG
CGAL::Timer timer; timer.start();
#endif
const std::size_t nb_vertices = interior_vertices.size();
Solver_vector X(nb_vertices), Bx(nb_vertices);
Solver_vector Y(nb_vertices), By(nb_vertices);
Solver_vector Z(nb_vertices), Bz(nb_vertices);
std::map<vertex_descriptor, std::size_t> vertex_id_map;
std::size_t id = 0;
for(vertex_descriptor vd : interior_vertices)
{
if( !vertex_id_map.insert(std::make_pair(vd, id)).second ) {
CGAL_warning_msg(false, "Duplicate vertex is found!");
return false;
}
++id;
}
Solver_matrix A(nb_vertices);
for(vertex_descriptor vd : interior_vertices)
{
int v_id = static_cast<int>(vertex_id_map[vd]);
compute_row(vd, v_id, A, Bx[v_id], By[v_id], Bz[v_id], 1, vertex_id_map, depth);
}
#ifdef CGAL_PMP_FAIR_DEBUG
std::cerr << "**Timer** System construction: " << timer.time() << std::endl; timer.reset();
#endif
// factorize
double D;
bool prefactor_ok = solver.factor(A, D);
if(!prefactor_ok) {
CGAL_warning_msg(false, "pre_factor failed!");
return false;
}
#ifdef CGAL_PMP_FAIR_DEBUG
std::cerr << "**Timer** System factorization: " << timer.time() << std::endl; timer.reset();
#endif
// solve
bool is_all_solved = solver.linear_solver(Bx, X) && solver.linear_solver(By, Y) && solver.linear_solver(Bz, Z);
if(!is_all_solved) {
CGAL_warning_msg(false, "linear_solver failed!");
return false;
}
#ifdef CGAL_PMP_FAIR_DEBUG
std::cerr << "**Timer** System solver: " << timer.time() << std::endl; timer.reset();
#endif
/* This relative error is to large for cases that the results are not good */
/*
double rel_err_x = (A.eigen_object()*X - Bx).norm() / Bx.norm();
double rel_err_y = (A.eigen_object()*Y - By).norm() / By.norm();
double rel_err_z = (A.eigen_object()*Z - Bz).norm() / Bz.norm();
CGAL_TRACE_STREAM << "rel error: " << rel_err_x
<< " " << rel_err_y
<< " " << rel_err_z << std::endl;
*/
// update
id = 0;
for(vertex_descriptor vd : interior_vertices)
{
put(ppmap, vd, Point_3(X[id], Y[id], Z[id]));
++id;
}
return true;
}
};
}//namespace internal
}//namespace Polygon_mesh_processing
}//namespace CGAL
#endif //CGAL_POLYGON_MESH_PROCESSING_FAIR_POLYHEDRON_3_H
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