\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 5.0 - 3D Mesh Generation
CGAL/Mesh_3/initialize_triangulation_from_labeled_image.h
// Copyright (c) 2015,2016 GeometryFactory
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/releases/CGAL-5.0-I-190/Mesh_3/include/CGAL/Mesh_3/initialize_triangulation_from_labeled_image.h $
// $Id: initialize_triangulation_from_labeled_image.h 254d60f 2019-10-19T15:23:19+02:00 S├ębastien Loriot
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Laurent Rineau
#ifndef CGAL_MESH_3_INITIALIZE_TRIANGULATION_FROM_LABELED_IMAGE_H
#define CGAL_MESH_3_INITIALIZE_TRIANGULATION_FROM_LABELED_IMAGE_H
#include <CGAL/license/Mesh_3.h>
#include <CGAL/Mesh_3/search_for_connected_components_in_labeled_image.h>
#include <CGAL/Mesh_3/squared_distance_Point_3_Triangle_3.h>
#include <CGAL/make_mesh_3.h>
#include <CGAL/enum.h>
#include <CGAL/iterator.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/Image_3.h>
#include <iostream>
#include <queue>
template <typename Point>
struct Get_point
{
const double vx, vy, vz;
Get_point(const CGAL::Image_3* image)
: vx(image->vx())
, vy(image->vy())
, vz(image->vz())
{}
Point operator()(const std::size_t i,
const std::size_t j,
const std::size_t k) const
{
return Point(double(i) * vx, double(j) * vy, double(k) * vz);
}
};
template<class C3T3, class MeshDomain, class MeshCriteria>
void init_tr_from_labeled_image_call_init_features(C3T3&,
const MeshDomain&,
const MeshCriteria&,
{
}
template<class C3T3, class MeshDomain, class MeshCriteria>
void init_tr_from_labeled_image_call_init_features(C3T3& c3t3,
const MeshDomain& domain,
const MeshCriteria& criteria,
{
CGAL::Mesh_3::internal::init_c3t3_with_features(c3t3,
domain,
criteria);
std::cout << c3t3.triangulation().number_of_vertices()
<< " initial points on 1D-features" << std::endl;
}
template<class C3T3, class MeshDomain, class MeshCriteria,
typename Image_word_type>
void initialize_triangulation_from_labeled_image(C3T3& c3t3,
const MeshDomain& domain,
const CGAL::Image_3& image,
const MeshCriteria& criteria,
Image_word_type,
bool protect_features = false
)
{
typedef typename C3T3::Triangulation Tr;
typedef typename Tr::Geom_traits Gt;
typedef typename Gt::FT FT;
typedef typename Tr::Weighted_point Weighted_point;
typedef typename Tr::Bare_point Bare_point;
typedef typename Tr::Segment Segment_3;
typedef typename Tr::Vertex_handle Vertex_handle;
typedef typename Tr::Cell_handle Cell_handle;
typedef typename Gt::Vector_3 Vector_3;
typedef MeshDomain Mesh_domain;
Tr& tr = c3t3.triangulation();
typename Gt::Compare_weighted_squared_radius_3 cwsr =
tr.geom_traits().compare_weighted_squared_radius_3_object();
typename Gt::Construct_point_3 cp =
tr.geom_traits().construct_point_3_object();
typename Gt::Construct_weighted_point_3 cwp =
tr.geom_traits().construct_weighted_point_3_object();
if(protect_features) {
init_tr_from_labeled_image_call_init_features
(c3t3, domain, criteria,
CGAL::Mesh_3::internal::Has_features<Mesh_domain>());
}
const double max_v = (std::max)((std::max)(image.vx(),
image.vy()),
image.vz());
typedef std::vector<std::pair<Bare_point, std::size_t> > Seeds;
Seeds seeds;
Get_point<Bare_point> get_point(&image);
std::cout << "Searching for connected components..." << std::endl;
search_for_connected_components_in_labeled_image(image,
std::back_inserter(seeds),
no_transformation,
get_point,
Image_word_type());
std::cout << " " << seeds.size() << " components were found." << std::endl;
std::cout << "Construct initial points..." << std::endl;
for(typename Seeds::const_iterator it = seeds.begin(), end = seeds.end();
it != end; ++it)
{
const double radius = double(it->second + 1)* max_v;
CGAL::Random_points_on_sphere_3<Bare_point> points_on_sphere_3(radius);
typename Mesh_domain::Construct_intersection construct_intersection =
domain.construct_intersection_object();
std::vector<Vector_3> directions;
if(it->second < 2) {
// shoot in six directions
directions.push_back(Vector_3(-radius, 0, 0));
directions.push_back(Vector_3(+radius, 0, 0));
directions.push_back(Vector_3(0, -radius, 0));
directions.push_back(Vector_3(0, +radius, 0));
directions.push_back(Vector_3(0, 0, -radius));
directions.push_back(Vector_3(0, 0, +radius));
} else {
for(int i = 0; i < 20; ++i)
{
// shoot 20 random directions
directions.push_back(*points_on_sphere_3++ - CGAL::ORIGIN);
}
}
for(const Vector_3& v : directions)
{
const Bare_point test = it->first + v;
const typename Mesh_domain::Intersection intersect =
construct_intersection(Segment_3(it->first, test));
if (std::get<2>(intersect) != 0)
{
const Bare_point& bpi = std::get<0>(intersect);
Weighted_point pi = cwp(bpi);
// This would cause trouble to optimizers
// check pi will not be hidden
typename Tr::Locate_type lt;
int li, lj;
Cell_handle pi_cell = tr.locate(pi, lt, li, lj);
if(lt != Tr::OUTSIDE_AFFINE_HULL) {
switch (tr.dimension())
{ //skip dimension 0
case 1:
if (tr.side_of_power_segment(pi_cell, pi, true) != CGAL::ON_BOUNDED_SIDE)
continue;
break;
case 2:
if (tr.side_of_power_circle(pi_cell, 3, pi, true) != CGAL::ON_BOUNDED_SIDE)
continue;
break;
case 3:
if (tr.side_of_power_sphere(pi_cell, pi, true) != CGAL::ON_BOUNDED_SIDE)
continue;
}
}
//check pi is not inside a protecting ball
std::vector<Vertex_handle> conflict_vertices;
if (tr.dimension() == 3)
{
tr.vertices_on_conflict_zone_boundary(pi, pi_cell
, std::back_inserter(conflict_vertices));
}
else
{
for (typename Tr::Finite_vertices_iterator vit = tr.finite_vertices_begin();
vit != tr.finite_vertices_end(); ++vit)
{
const Weighted_point& wp = tr.point(vit);
if (cwsr(wp, FT(0)) == CGAL::SMALLER) // 0 < wp's weight
conflict_vertices.push_back(vit);
}
}
bool pi_inside_protecting_sphere = false;
for(Vertex_handle cv : conflict_vertices)
{
if(tr.is_infinite(cv))
continue;
const Weighted_point& cv_wp = tr.point(cv);
if (cwsr(cv_wp, FT(0)) == CGAL::EQUAL) // 0 == wp's weight
continue;
// if the (squared) distance between bpi and cv is smaller or equal than cv's weight
if (cwsr(cv_wp, - tr.min_squared_distance(bpi, cp(cv_wp))) != CGAL::LARGER)
{
pi_inside_protecting_sphere = true;
break;
}
}
if (pi_inside_protecting_sphere)
continue;
const typename Mesh_domain::Index index = std::get<1>(intersect);
Vertex_handle v = tr.insert(pi);
// `v` could be null if `pi` is hidden by other vertices of `tr`.
CGAL_assertion(v != Vertex_handle());
c3t3.set_dimension(v, 2); // by construction, points are on surface
c3t3.set_index(v, index);
}
// else
// {
// std::cerr <<
// boost::format("Error. Segment (%1%, %2%) does not intersect the surface!\n")
// % it->first % test;
// }
}
}
std::cout << " " << tr.number_of_vertices() << " initial points." << std::endl;
if ( c3t3.triangulation().dimension() != 3 )
{
std::cout << " not enough points: triangulation.dimension() == "
<< c3t3.triangulation().dimension() << std::endl;
CGAL::Mesh_3::internal::init_c3t3(c3t3, domain, criteria, 20);
std::cout << " -> " << tr.number_of_vertices() << " initial points." << std::endl;
}
}
#endif // CGAL_MESH_3_INITIALIZE_TRIANGULATION_FROM_LABELED_IMAGE_H