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cgal/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h

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// Copyright (c) 2015 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Maxime Gimeno, Sebastien Loriot, Martin Skrodzki, Dmitry Anisimov
#ifndef CGAL_POLYGON_MESH_PROCESSING_DISTANCE_H
#define CGAL_POLYGON_MESH_PROCESSING_DISTANCE_H
#include <CGAL/license/Polygon_mesh_processing/distance.h>
#include <CGAL/Polygon_mesh_processing/internal/mesh_to_point_set_hausdorff_distance.h>
#include <CGAL/Polygon_mesh_processing/internal/AABB_traversal_traits_with_Hausdorff_distance.h>
#include <CGAL/Polygon_mesh_processing/measure.h>
#include <CGAL/Polygon_mesh_processing/bbox.h>
#include <CGAL/AABB_tree.h>
#include <CGAL/AABB_traits_3.h>
#include <CGAL/AABB_triangle_primitive_3.h>
#include <CGAL/AABB_face_graph_triangle_primitive.h>
#include <CGAL/utility.h>
#include <CGAL/Named_function_parameters.h>
#include <CGAL/boost/graph/named_params_helper.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/Spatial_sort_traits_adapter_3.h>
#include <CGAL/spatial_sort.h>
#include <CGAL/Real_timer.h>
#include <CGAL/iterator.h>
#include <CGAL/boost/graph/Face_filtered_graph.h>
#if defined(CGAL_METIS_ENABLED)
#include <CGAL/boost/graph/partition.h>
#endif // CGAL_METIS_ENABLED
#ifdef CGAL_LINKED_WITH_TBB
#include <tbb/parallel_reduce.h>
#include <tbb/blocked_range.h>
#endif // CGAL_LINKED_WITH_TBB
#include <any>
#include <unordered_set>
#include <algorithm>
#include <array>
#include <cmath>
#include <limits>
#ifdef CGAL_HAUSDORFF_DEBUG_PP
#ifndef CGAL_HAUSDORFF_DEBUG
#define CGAL_HAUSDORFF_DEBUG
#endif
#endif
namespace CGAL {
namespace Polygon_mesh_processing {
namespace internal {
template <class Kernel, class PointOutputIterator>
PointOutputIterator
triangle_grid_sampling(const typename Kernel::Point_3& p0,
const typename Kernel::Point_3& p1,
const typename Kernel::Point_3& p2,
double distance,
PointOutputIterator out)
{
typename Kernel::Compute_squared_distance_3 squared_distance;
const double d_p0p1 = to_double(approximate_sqrt(squared_distance(p0, p1)));
const double d_p0p2 = to_double(approximate_sqrt(squared_distance(p0, p2)));
const double n = (std::max)(std::ceil(d_p0p1 / distance),
std::ceil(d_p0p2 / distance));
for(double i=1; i<n; ++i)
{
for(double j=1; j<n-i; ++j)
{
const double c0=(1-(i+j)/n), c1=i/n, c2=j/n;
*out++ = typename Kernel::Point_3(p0.x()*c0 + p1.x()*c1 + p2.x()*c2,
p0.y()*c0 + p1.y()*c1 + p2.y()*c2,
p0.z()*c0 + p1.z()*c1 + p2.z()*c2);
}
}
return out;
}
#if defined(CGAL_LINKED_WITH_TBB)
template <class Kernel, class AABB_tree, class PointRange>
struct Distance_computation
{
typedef typename Kernel::FT FT;
typedef typename PointRange::const_iterator::value_type Point_3;
const AABB_tree& tree;
const PointRange& sample_points;
Point_3 initial_hint;
FT sq_distance;
//constructor
Distance_computation(const AABB_tree& tree,
const Point_3& p,
const PointRange& sample_points)
: tree(tree),
sample_points(sample_points),
initial_hint(p),
sq_distance(-1)
{}
//split constructor
Distance_computation(Distance_computation& s, tbb::split)
: tree(s.tree),
sample_points(s.sample_points),
initial_hint(s.initial_hint),
sq_distance(-1)
{}
void operator()(const tbb::blocked_range<std::size_t>& range)
{
Point_3 hint = initial_hint;
FT sq_hdist = 0;
typename Kernel_traits<Point_3>::Kernel::Compute_squared_distance_3 squared_distance;
for(std::size_t i = range.begin(); i != range.end(); ++i)
{
hint = tree.closest_point(*(sample_points.begin() + i), hint);
FT sq_d = squared_distance(hint,*(sample_points.begin() + i));
if(sq_d > sq_hdist)
sq_hdist = sq_d;
}
if(sq_hdist > sq_distance)
sq_distance = sq_hdist;
}
void join(Distance_computation& rhs) { sq_distance = (std::max)(rhs.sq_distance, sq_distance); }
};
#endif
template <class Concurrency_tag,
class PointRange,
class AABBTree,
class Kernel>
double max_distance_to_mesh_impl(const PointRange& sample_points,
const AABBTree& tree,
typename Kernel::Point_3 hint, // intentional copy
const Kernel& k)
{
using FT = typename Kernel::FT;
#if !defined(CGAL_LINKED_WITH_TBB)
static_assert (!(std::is_convertible<Concurrency_tag, Parallel_tag>::value),
"Parallel_tag is enabled but TBB is unavailable.");
#else
if(std::is_convertible<Concurrency_tag,Parallel_tag>::value)
{
Distance_computation<Kernel, AABBTree, PointRange> f(tree, hint, sample_points);
tbb::parallel_reduce(tbb::blocked_range<std::size_t>(0, sample_points.size()), f);
return to_double(approximate_sqrt(f.sq_distance));
}
else
#endif
{
FT sq_hdist = 0;
typename Kernel::Compute_squared_distance_3 squared_distance = k.compute_squared_distance_3_object();
for(const typename Kernel::Point_3& pt : sample_points)
{
hint = tree.closest_point(pt, hint);
FT sq_d = squared_distance(hint, pt);
if(sq_d > sq_hdist)
sq_hdist = sq_d;
}
return to_double(approximate_sqrt(sq_hdist));
}
}
template<typename PointOutputIterator,
typename GeomTraits,
typename NamedParameters,
typename TriangleIterator,
typename Randomizer,
typename Creator,
typename Derived>
struct Triangle_structure_sampler_base
{
const NamedParameters np;
GeomTraits gt;
PointOutputIterator& out;
Triangle_structure_sampler_base(PointOutputIterator& out,
const NamedParameters& np)
: np(np), out(out)
{}
void sample_points();
double get_squared_minimum_edge_length();
template<typename Tr>
double get_tr_area(const Tr&);
template<typename Tr>
std::array<typename GeomTraits::Point_3, 3> get_tr_points(const Tr& tr);
void ms_edges_sample(const std::size_t& nb_points_per_edge,
const std::size_t& nb_pts_l_u);
void ru_edges_sample();
void internal_sample_triangles(double, bool, bool);
Randomizer get_randomizer();
std::pair<TriangleIterator, TriangleIterator> get_range();
std::size_t get_points_size();
void procede()
{
using parameters::choose_parameter;
using parameters::get_parameter;
using parameters::is_default_parameter;
gt = choose_parameter<GeomTraits>(get_parameter(np, internal_np::geom_traits));
bool use_rs = choose_parameter(get_parameter(np, internal_np::random_uniform_sampling), true);
bool use_gs = choose_parameter(get_parameter(np, internal_np::grid_sampling), false);
bool use_ms = choose_parameter(get_parameter(np, internal_np::monte_carlo_sampling), false);
if(use_gs || use_ms)
{
if(is_default_parameter<NamedParameters, internal_np::random_uniform_sampling_t>::value)
use_rs = false;
}
bool smpl_vrtcs = choose_parameter(get_parameter(np, internal_np::do_sample_vertices), true);
bool smpl_dgs = choose_parameter(get_parameter(np, internal_np::do_sample_edges), true);
bool smpl_fcs = choose_parameter(get_parameter(np, internal_np::do_sample_faces), true);
double nb_pts_a_u = choose_parameter(get_parameter(np, internal_np::nb_points_per_area_unit), 0.);
double nb_pts_l_u = choose_parameter(get_parameter(np, internal_np::nb_points_per_distance_unit), 0.);
// sample vertices
if(smpl_vrtcs)
static_cast<Derived*>(this)->sample_points();
// grid sampling
if(use_gs)
{
double grid_spacing_ = choose_parameter(get_parameter(np, internal_np::grid_spacing), 0.);
// set grid spacing to the shortest edge length
if(grid_spacing_ == 0.)
grid_spacing_ = std::sqrt(static_cast<Derived*>(this)->get_squared_minimum_edge_length());
static_cast<Derived*>(this)->internal_sample_triangles(grid_spacing_, smpl_fcs, smpl_dgs);
}
// monte carlo sampling
if(use_ms)
{
double min_sq_edge_length = (std::numeric_limits<double>::max)();
std::size_t nb_points_per_face =
choose_parameter(get_parameter(np, internal_np::number_of_points_per_face), 0);
std::size_t nb_points_per_edge =
choose_parameter(get_parameter(np, internal_np::number_of_points_per_edge), 0);
if((nb_points_per_face == 0 && nb_pts_a_u == 0.) ||
(nb_points_per_edge == 0 && nb_pts_l_u == 0.))
{
min_sq_edge_length = static_cast<Derived*>(this)->get_squared_minimum_edge_length();
}
// sample faces
if(smpl_fcs)
{
// set default value
if(nb_points_per_face == 0 && nb_pts_a_u == 0.)
nb_pts_a_u = 2. / min_sq_edge_length;
for(const auto& tr : make_range(static_cast<Derived*>(this)->get_range()))
{
std::size_t nb_points = nb_points_per_face;
if(nb_points == 0)
{
nb_points = (std::max)(
static_cast<std::size_t>(
std::ceil(static_cast<Derived*>(this)->get_tr_area(tr))
*nb_pts_a_u), std::size_t(1));
}
// extract triangle face points
std::array<typename GeomTraits::Point_3, 3> points = static_cast<Derived*>(this)->get_tr_points(tr);
Random_points_in_triangle_3<typename GeomTraits::Point_3, Creator> g(points[0], points[1], points[2]);
out = std::copy_n(g, nb_points, out);
}
}
// sample edges
if(smpl_dgs)
static_cast<Derived*>(this)->ms_edges_sample(nb_points_per_edge, nb_pts_l_u);
}
// random uniform sampling
if(use_rs)
{
// sample faces
if(smpl_fcs)
{
std::size_t nb_points
= choose_parameter(get_parameter(np, internal_np::number_of_points_on_faces), 0);
typename Derived::Randomizer g = static_cast<Derived*>(this)->get_randomizer();
if(nb_points == 0)
{
if(nb_pts_a_u == 0.)
nb_points = static_cast<Derived*>(this)->get_points_size();
else
nb_points = static_cast<std::size_t>(std::ceil(g.sum_of_weights()*nb_pts_a_u));
}
out = std::copy_n(g, nb_points, out);
}
// sample edges
if(smpl_dgs)
static_cast<Derived*>(this)->ru_edges_sample(nb_pts_l_u,nb_pts_a_u);
}
}
};
} // namespace internal
template <class Kernel,
class FaceRange,
class TriangleMesh,
class VertexPointMap,
class PointOutputIterator>
PointOutputIterator
sample_triangles(const FaceRange& triangles,
const TriangleMesh& tm,
VertexPointMap vpm,
double distance,
PointOutputIterator out,
bool sample_faces,
bool sample_edges,
bool add_vertices)
{
typedef typename boost::property_traits<VertexPointMap>::reference Point_ref;
typedef typename Kernel::Vector_3 Vector_3;
typedef typename boost::graph_traits<TriangleMesh>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::edge_descriptor edge_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
std::unordered_set<edge_descriptor> sampled_edges;
std::unordered_set<vertex_descriptor> endpoints;
for(face_descriptor fd : triangles)
{
// sample edges but skip endpoints
halfedge_descriptor hd = halfedge(fd, tm);
for(int i=0;i<3; ++i)
{
if(sample_edges && sampled_edges.insert(edge(hd, tm)).second)
{
Point_ref p0 = get(vpm, source(hd, tm));
Point_ref p1 = get(vpm, target(hd, tm));
typename Kernel::Compute_squared_distance_3 squared_distance;
const double d_p0p1 = to_double(approximate_sqrt(squared_distance(p0, p1)));
const double nb_pts = std::ceil(d_p0p1 / distance);
const Vector_3 step_vec = typename Kernel::Construct_scaled_vector_3()(
typename Kernel::Construct_vector_3()(p0, p1),
typename Kernel::FT(1)/typename Kernel::FT(nb_pts));
for(double i=1; i<nb_pts; ++i)
{
*out++=typename Kernel::Construct_translated_point_3()(p0,
typename Kernel::Construct_scaled_vector_3()(step_vec ,
typename Kernel::FT(i)));
}
}
//add endpoints once
if(add_vertices && endpoints.insert(target(hd, tm)).second)
*out++ = get(vpm, target(hd, tm));
hd = next(hd, tm);
}
// sample triangles
if(sample_faces)
{
Point_ref p0 = get(vpm, source(hd, tm));
Point_ref p1 = get(vpm, target(hd, tm));
Point_ref p2 = get(vpm, target(next(hd, tm), tm));
out = internal::triangle_grid_sampling<Kernel>(p0, p1, p2, distance, out);
}
}
return out;
}
namespace internal {
template<typename Mesh,
typename PointOutputIterator,
typename GeomTraits,
typename Creator,
typename Vpm,
typename NamedParameters>
struct Triangle_structure_sampler_for_triangle_mesh
: Triangle_structure_sampler_base<PointOutputIterator,
GeomTraits,
NamedParameters,
typename boost::graph_traits<Mesh>::face_iterator,
Random_points_in_triangle_mesh_3<Mesh, Vpm, Creator>,
Creator,
Triangle_structure_sampler_for_triangle_mesh<Mesh,
PointOutputIterator,
GeomTraits,
Creator,
Vpm,
NamedParameters> >
{
typedef Triangle_structure_sampler_for_triangle_mesh<Mesh,
PointOutputIterator,
GeomTraits,
Creator, Vpm,
NamedParameters> Self;
typedef Triangle_structure_sampler_base<PointOutputIterator,
GeomTraits,
NamedParameters,
typename boost::graph_traits<Mesh>::face_iterator,
Random_points_in_triangle_mesh_3<Mesh, Vpm, Creator>,
Creator,
Self> Base;
typedef typename boost::graph_traits<Mesh>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<Mesh>::edge_descriptor edge_descriptor;
typedef typename boost::graph_traits<Mesh>::face_descriptor face_descriptor;
typedef typename GeomTraits::FT FT;
typedef Random_points_in_triangle_mesh_3<Mesh, Vpm,Creator> Randomizer;
typedef typename boost::graph_traits<Mesh>::face_iterator TriangleIterator;
Vpm pmap;
double min_sq_edge_length;
const Mesh& tm;
CGAL::Random rnd;
Triangle_structure_sampler_for_triangle_mesh(const Mesh& m,
PointOutputIterator& out,
const NamedParameters& np)
: Base(out, np), tm(m)
{
using parameters::choose_parameter;
using parameters::get_parameter;
using parameters::is_default_parameter;
CGAL_assertion(!is_empty(tm));
pmap = choose_parameter(get_parameter(np, internal_np::vertex_point),
get_const_property_map(vertex_point, tm));
if(!(is_default_parameter<NamedParameters, internal_np::random_seed_t>::value))
rnd = CGAL::Random(choose_parameter(get_parameter(np, internal_np::random_seed),0));
min_sq_edge_length = (std::numeric_limits<double>::max)();
}
std::pair<TriangleIterator, TriangleIterator> get_range()
{
return std::make_pair(faces(tm).begin(), faces(tm).end());
}
void sample_points()
{
Property_map_to_unary_function<Vpm> unary(pmap);
this->out = std::copy(boost::make_transform_iterator(std::begin(vertices(tm)), unary),
boost::make_transform_iterator(std::end(vertices(tm)), unary),
this->out);
}
double get_squared_minimum_edge_length()
{
typedef typename boost::graph_traits<Mesh>::edge_descriptor edge_descriptor;
if(min_sq_edge_length != (std::numeric_limits<double>::max)())
return min_sq_edge_length;
FT m_sq_el = min_sq_edge_length;
for(edge_descriptor ed : edges(tm))
{
const FT sq_el = this->gt.compute_squared_distance_3_object()(get(pmap, source(ed, tm)),
get(pmap, target(ed, tm)));
if(sq_el < m_sq_el)
m_sq_el = sq_el;
}
min_sq_edge_length = to_double(m_sq_el);
return min_sq_edge_length;
}
double get_tr_area(const typename boost::graph_traits<Mesh>::face_descriptor& tr)
{
return to_double(face_area(tr, tm, parameters::geom_traits(this->gt)));
}
template<typename Tr>//tr = face_descriptor here
std::array<typename GeomTraits::Point_3, 3> get_tr_points(const Tr& tr)
{
std::array<typename GeomTraits::Point_3, 3> points;
halfedge_descriptor hd(halfedge(tr,tm));
for(int i=0; i<3; ++i)
{
points[i] = get(pmap, target(hd, tm));
hd = next(hd, tm);
}
return points;
}
void ms_edges_sample(std::size_t nb_points_per_edge,
double nb_pts_l_u)
{
typename GeomTraits::Compute_squared_distance_3 squared_distance = this->gt.compute_squared_distance_3_object();
if(nb_points_per_edge == 0 && nb_pts_l_u == 0.)
nb_pts_l_u = 1. / std::sqrt(min_sq_edge_length);
for(edge_descriptor ed : edges(tm))
{
std::size_t nb_points = nb_points_per_edge;
if(nb_points == 0)
{
nb_points = (std::max)(
static_cast<std::size_t>(std::ceil(std::sqrt(to_double(
squared_distance(get(pmap, source(ed, tm)),
get(pmap, target(ed, tm))))) * nb_pts_l_u)),
std::size_t(1));
}
// now do the sampling of the edge
Random_points_on_segment_3<typename GeomTraits::Point_3, Creator>
g(get(pmap, source(ed,tm)), get(pmap, target(ed, tm)));
this->out = std::copy_n(g, nb_points, this->out);
}
}
void ru_edges_sample(double nb_pts_l_u,
double nb_pts_a_u)
{
using parameters::choose_parameter;
using parameters::get_parameter;
std::size_t nb_points = choose_parameter(get_parameter(this->np, internal_np::number_of_points_on_edges), 0);
Random_points_on_edge_list_graph_3<Mesh, Vpm, Creator> g(tm, pmap);
if(nb_points == 0)
{
if(nb_pts_l_u == 0)
nb_points = num_vertices(tm);
else
nb_points = static_cast<std::size_t>(std::ceil(g.mesh_length() * nb_pts_a_u));
}
this->out = std::copy_n(g, nb_points, this->out);
}
Randomizer get_randomizer()
{
return Randomizer(tm, pmap, rnd);
}
void internal_sample_triangles(double grid_spacing_, bool smpl_fcs, bool smpl_dgs)
{
this->out = sample_triangles<GeomTraits>(faces(tm), tm, pmap, grid_spacing_,
this->out, smpl_fcs, smpl_dgs, false);
}
std::size_t get_points_size()
{
return num_vertices(tm);
}
};
template<typename PointRange,
typename TriangleRange,
typename PointOutputIterator,
typename GeomTraits,
typename Creator,
typename NamedParameters>
struct Triangle_structure_sampler_for_triangle_soup
: Triangle_structure_sampler_base<PointOutputIterator,
GeomTraits,
NamedParameters,
typename TriangleRange::const_iterator,
Random_points_in_triangle_soup<PointRange,
typename TriangleRange::value_type,
Creator>,
Creator,
Triangle_structure_sampler_for_triangle_soup<PointRange,
TriangleRange,
PointOutputIterator,
GeomTraits,
Creator,
NamedParameters> >
{
typedef typename TriangleRange::value_type TriangleType;
typedef Triangle_structure_sampler_for_triangle_soup<PointRange,
TriangleRange,
PointOutputIterator,
GeomTraits,
Creator,
NamedParameters> Self;
typedef Triangle_structure_sampler_base<PointOutputIterator,
GeomTraits,
NamedParameters,
typename TriangleRange::const_iterator,
Random_points_in_triangle_soup<PointRange, TriangleType, Creator>,
Creator,
Self> Base;
typedef typename GeomTraits::FT FT;
typedef typename GeomTraits::Point_3 Point_3;
typedef Random_points_in_triangle_soup<PointRange, TriangleType, Creator> Randomizer;
typedef typename TriangleRange::const_iterator TriangleIterator;
double min_sq_edge_length;
const PointRange& points;
const TriangleRange& triangles;
Random rnd;
Triangle_structure_sampler_for_triangle_soup(const PointRange& pts,
const TriangleRange& trs,
PointOutputIterator& out,
const NamedParameters& np)
: Base(out, np), points(pts), triangles(trs)
{
using parameters::choose_parameter;
using parameters::get_parameter;
using parameters::is_default_parameter;
min_sq_edge_length = (std::numeric_limits<double>::max)();
if(!(is_default_parameter<NamedParameters, internal_np::random_seed_t>::value))
rnd = CGAL::Random(choose_parameter(get_parameter(np, internal_np::random_seed),0));
}
std::pair<TriangleIterator, TriangleIterator> get_range()
{
return std::make_pair(triangles.begin(), triangles.end());
}
void sample_points()
{
this->out = std::copy(points.begin(), points.end(), this->out);
}
double get_squared_minimum_edge_length()
{
if(min_sq_edge_length != (std::numeric_limits<double>::max)())
return min_sq_edge_length;
FT m_sq_el = min_sq_edge_length;
for(const auto& tr : triangles)
{
for(std::size_t i = 0; i< 3; ++i)
{
const Point_3& a = points[tr[i]];
const Point_3& b = points[tr[(i+1)%3]];
const FT sq_el = this->gt.compute_squared_distance_3_object()(a, b);
if(sq_el < m_sq_el)
m_sq_el = sq_el;
}
}
min_sq_edge_length = to_double(m_sq_el);
return min_sq_edge_length;
}
template<typename Tr>
double get_tr_area(const Tr& tr)
{
// Kernel_3::Compute_area_3 uses `sqrt()`
return to_double(approximate_sqrt(
this->gt.compute_squared_area_3_object()(
points[tr[0]], points[tr[1]], points[tr[2]])));
}
template<typename Tr>
std::array<Point_3, 3> get_tr_points(const Tr& tr)
{
std::array<Point_3, 3> points;
for(int i=0; i<3; ++i)
points[i] = this->points[tr[i]];
return points;
}
void ms_edges_sample(std::size_t, double)
{
// don't sample edges in soup.
}
void ru_edges_sample(double, double)
{
// don't sample edges in soup.
}
Randomizer get_randomizer()
{
return Randomizer(triangles, points, rnd);
}
void internal_sample_triangles(double distance, bool, bool)
{
for(const auto& tr : triangles)
{
const Point_3& p0 = points[tr[0]];
const Point_3& p1 = points[tr[1]];
const Point_3& p2 = points[tr[2]];
this->out = internal::triangle_grid_sampling<GeomTraits>(p0, p1, p2, distance, this->out);
}
}
std::size_t get_points_size()
{
return points.size();
}
};
} // namespace internal
/** \ingroup PMP_distance_grp
*
* generates points on `tm` and outputs them to `out`; the sampling method
* is selected using named parameters.
*
* @tparam TriangleMesh a model of the concepts `EdgeListGraph` and `FaceListGraph`
* @tparam PointOutputIterator a model of `OutputIterator`
* holding objects of the same point type as
* the value type of the point type associated to the mesh `tm`, i.e., the value type of the vertex
* point map property map, if provided, or the value type of the internal point property map otherwise
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
*
* @param tm the triangle mesh to be sampled
* @param out output iterator to be filled with sample points
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{vertex_point_map}
* \cgalParamDescription{a property map associating points to the vertices of `tm`}
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
* as key type and `%Point_3` as value type}
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tm)`}
* \cgalParamExtra{If this parameter is omitted, an internal property map for `CGAL::vertex_point_t`
* must be available in `TriangleMesh`.}
* \cgalParamNEnd
*
* \cgalParamNBegin{geom_traits}
* \cgalParamDescription{an instance of a geometric traits class}
* \cgalParamType{a class model of `PMPDistanceTraits`}
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
* \cgalParamNEnd
*
* \cgalParamNBegin{random_seed}
* \cgalParamDescription{a value to seed the random number generator}
* \cgalParamType{unsigned int}
* \cgalParamDefault{a value generated with `std::time()`}
* \cgalParamNEnd
*
* \cgalParamNBegin{use_random_uniform_sampling}
* \cgalParamDescription{If `true` is passed, points are generated uniformly at random on faces and/or edges of `tm`.
If `do_sample_faces` is `true`, random points will be iteratively generated uniformly at random in the triangle of a face
selected with probability proportional to its area. If `do_sample_edges` is `true`, random points will be iteratively generated uniformly at random in the segment of an edge
selected with probability proportional to its length.}
* \cgalParamType{Boolean}
* \cgalParamType{`true`}
* \cgalParamExtra{For faces, the number of sample points is the value passed to the named
* parameter `number_of_points_on_faces`. If not set,
* the value passed to the named parameter `number_of_points_per_area_unit`
* is multiplied by the area of `tm` to get the number of sample points.
* If none of these parameters is set, the number of points sampled is `num_vertices(tm)`.
* For edges, the number of the number of sample points is the value passed to the named
* parameter `number_of_points_on_edges`. If not set,
* the value passed to the named parameter `number_of_points_per_distance_unit`
* is multiplied by the sum of the length of edges of `tm` to get the number of sample points.
* If none of these parameters is set, the number of points sampled is `num_vertices(tm)`.}
* \cgalParamNEnd
*
* \cgalParamNBegin{use_grid_sampling}
* \cgalParamDescription{If `true` is passed, points are generated on a grid in each triangle,
* with a minimum of one point per triangle.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`false`}
* \cgalParamExtra{The distance between two consecutive points in the grid is that of the length
* of the smallest non-null edge of `tm` or the value passed to the named parameter
* `grid_spacing`. Edges are also split using the same distance, if requested.}
* \cgalParamNEnd
*
* \cgalParamNBegin{use_monte_carlo_sampling}
* \cgalParamDescription{if `true` is passed, points are generated randomly in each triangle and/or on each edge.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`false`}
* \cgalParamExtra{For faces, the number of points per triangle is the value passed to the named
* parameter `number_of_points_per_face`. If not set, the value passed
* to the named parameter `number_of_points_per_area_unit` is
* used to pick a number of points per face proportional to the triangle
* area with a minimum of one point per face. If none of these parameters
* is set, 2 divided by the square of the length of the smallest non-null
* edge of `tm` is used as if it was passed to
* `number_of_points_per_area_unit`.
* For edges, the number of points per edge is the value passed to the named
* parameter `number_of_points_per_edge`. If not set, the value passed
* to the named parameter `number_of_points_per_distance_unit` is
* used to pick a number of points per edge proportional to the length of
* the edge with a minimum of one point per face. If none of these parameters
* is set, 1 divided by the length of the smallest non-null edge of `tm`
* is used as if it was passed to `number_of_points_per_distance_unit`.}
* \cgalParamNEnd
*
* \cgalParamNBegin{do_sample_vertices}
* \cgalParamDescription{If `true` is passed, the vertices of `tm` are part of the sample.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`true`}
* \cgalParamNEnd
*
* \cgalParamNBegin{do_sample_edges}
* \cgalParamDescription{If `true` is passed, edges of `tm` are sampled.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`true`}
* \cgalParamNEnd
*
* \cgalParamNBegin{do_sample_faces}
* \cgalParamDescription{If `true` is passed, faces of `tm` are sampled.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`true`}
* \cgalParamNEnd
*
* \cgalParamNBegin{grid_spacing}
* \cgalParamDescription{a value used as the grid spacing for the grid sampling method}
* \cgalParamType{double}
* \cgalParamDefault{the length of the shortest, non-degenerate edge of `tm`}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_on_edges}
* \cgalParamDescription{a value used for the random sampling method as the number of points to pick exclusively on edges}
* \cgalParamType{unsigned int}
* \cgalParamDefault{`num_vertices(tm)` or a value based on `nb_points_per_distance_unit`, if it is defined}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_on_faces}
* \cgalParamDescription{a value used for the random sampling method as the number of points to pick on the surface}
* \cgalParamType{unsigned int}
* \cgalParamDefault{`num_vertices(tm)` or a value based on `nb_points_per_area_unit`, if it is defined}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_per_distance_unit}
* \cgalParamDescription{a value used for the random sampling and the Monte Carlo sampling methods to
* respectively determine the total number of points on edges and the number of points per edge}
* \cgalParamType{double}
* \cgalParamDefault{`1` divided by the length of the shortest, non-degenerate edge of `tm`}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_per_edge}
* \cgalParamDescription{a value used by the Monte-Carlo sampling method as the number of points per edge to pick}
* \cgalParamType{unsigned int}
* \cgalParamDefault{`0`}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_per_area_unit}
* \cgalParamDescription{a value used for the random sampling and the Monte Carlo sampling methods to
* respectively determine the total number of points inside faces and the number of points per face}
* \cgalParamType{double}
* \cgalParamDefault{`2` divided by the squared length of the shortest, non-degenerate edge of `tm`}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_per_face}
* \cgalParamDescription{a value used by the Monte-Carlo sampling method as the number of points per face to pick}
* \cgalParamType{unsigned int}
* \cgalParamDefault{`0`}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* @see `CGAL::Polygon_mesh_processing::sample_triangle_soup()`
*/
template<class PointOutputIterator, class TriangleMesh,
class NamedParameters = parameters::Default_named_parameters>
PointOutputIterator
sample_triangle_mesh(const TriangleMesh& tm,
PointOutputIterator out,
const NamedParameters& np = parameters::default_values())
{
typedef typename GetGeomTraits<TriangleMesh, NamedParameters>::type GeomTraits;
typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::const_type Vpm;
CGAL_precondition(!is_empty(tm) && is_triangle_mesh(tm));
internal::Triangle_structure_sampler_for_triangle_mesh<
TriangleMesh,
PointOutputIterator,
GeomTraits,
Creator_uniform_3<typename GeomTraits::FT, typename GeomTraits::Point_3>,
Vpm,
NamedParameters> performer(tm, out, np);
performer.procede();
return performer.out;
}
/** \ingroup PMP_distance_grp
*
* generates points on a triangle soup and puts them to `out`; the sampling method
* is selected using named parameters.
*
* @tparam PointRange a model of the concept `RandomAccessContainer` whose value type is the point type.
* @tparam TriangleRange a model of the concept `RandomAccessContainer`
* whose `value_type` is itself a model of the concept `RandomAccessContainer`
* whose `value_type` is an unsigned integral value.
* @tparam PointOutputIterator a model of `OutputIterator` holding objects of the same type as `PointRange`'s value type
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
*
* @param points the points of the soup
* @param triangles a `TriangleRange` containing the triangles of the soup to be sampled
* @param out output iterator to be filled with sample points
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{geom_traits}
* \cgalParamDescription{an instance of a geometric traits class}
* \cgalParamType{a class model of `PMPDistanceTraits`}
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
* \cgalParamExtra{The geometric traits class must be compatible with the point range's point type.}
* \cgalParamNEnd
*
* \cgalParamNBegin{random_seed}
* \cgalParamDescription{a value to seed the random number generator}
* \cgalParamType{unsigned int}
* \cgalParamDefault{a value generated with `std::time()`}
* \cgalParamNEnd
*
* \cgalParamNBegin{use_random_uniform_sampling}
* \cgalParamDescription{If `true` is passed, points are generated in a random and uniform way
* over the triangles of the soup.}
* \cgalParamType{Boolean}
* \cgalParamType{`true`}
* \cgalParamExtra{The number of sample points is the value passed to the named
* parameter `number_of_points_on_faces`. If not set,
* the value passed to the named parameter `number_of_points_per_area_unit`
* is multiplied by the area of the soup to get the number of sample points.
* If none of these parameters is set, the number of points sampled is `points.size()`.}
* \cgalParamNEnd
*
* \cgalParamNBegin{use_grid_sampling}
* \cgalParamDescription{If `true` is passed, points are generated on a grid in each triangle,
* with a minimum of one point per triangle.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`false`}
* \cgalParamExtra{The distance between two consecutive points in the grid is that of the length
* of the smallest non-null edge of the soup or the value passed to the named parameter
* `grid_spacing`.}
* \cgalParamNEnd
* \cgalParamNBegin{use_monte_carlo_sampling}
* \cgalParamDescription{if `true` is passed, points are generated randomly in each triangle.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`false`}
* \cgalParamExtra{The number of points per triangle is the value passed to the named
* parameter `number_of_points_per_face`. If not set, the value passed
* to the named parameter `number_of_points_per_area_unit` is
* used to pick a number of points per face proportional to the triangle
* area with a minimum of one point per face. If none of these parameters
* is set, the number of points per area unit is set to 2 divided
* by the square of the length of the smallest non-null edge of the soup.}
* \cgalParamNEnd
*
* \cgalParamNBegin{do_sample_vertices}
* \cgalParamDescription{If `true` is passed, the points of `points` are part of the sample.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`true`}
* \cgalParamNEnd
*
* \cgalParamNBegin{do_sample_faces}
* \cgalParamDescription{If `true` is passed, faces of the soup are sampled.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`true`}
* \cgalParamNEnd
*
* \cgalParamNBegin{grid_spacing}
* \cgalParamDescription{a value used as the grid spacing for the grid sampling method}
* \cgalParamType{double}
* \cgalParamDefault{the length of the shortest, non-degenerate edge of the soup}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_on_faces}
* \cgalParamDescription{a value used for the random sampling method as the number of points to pick on the surface}
* \cgalParamType{unsigned int}
* \cgalParamDefault{`points.size()` or a value based on `nb_points_per_area_unit`, if it is defined}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_per_face}
* \cgalParamDescription{a value used by the Monte-Carlo sampling method as the number of points per face to pick}
* \cgalParamType{unsigned int}
* \cgalParamDefault{`0`}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_points_per_area_unit}
* \cgalParamDescription{a value used for the random sampling and the Monte Carlo sampling methods to
* respectively determine the total number of points inside faces and the number of points per face}
* \cgalParamType{double}
* \cgalParamDefault{`2` divided by the squared length of the shortest, non-degenerate edge of the soup}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* \attention Contrary to `sample_triangle_mesh()`, this method does not allow to sample edges.
*
* @see `CGAL::Polygon_mesh_processing::sample_triangle_mesh()`
*/
template<class PointOutputIterator,
class TriangleRange,
class PointRange,
class NamedParameters = parameters::Default_named_parameters>
PointOutputIterator
sample_triangle_soup(const PointRange& points,
const TriangleRange& triangles,
PointOutputIterator out,
const NamedParameters& np = parameters::default_values())
{
typedef typename PointRange::value_type Point_3;
typedef typename Kernel_traits<Point_3>::Kernel GeomTraits;
static_assert(std::is_same<Point_3, typename GeomTraits::Point_3>::value, "Wrong point type.");
CGAL_precondition(!triangles.empty());
internal::Triangle_structure_sampler_for_triangle_soup<
PointRange,
TriangleRange,
PointOutputIterator,
GeomTraits,
Creator_uniform_3<typename GeomTraits::FT, typename GeomTraits::Point_3>,
NamedParameters> performer(points, triangles, out, np);
performer.procede();
return performer.out;
}
/**
* \ingroup PMP_distance_grp
*
* returns the distance to `tm` of the point from `points` that is the furthest from `tm`.
*
* @tparam PointRange a range of `Point_3`, model of `Range`. Its iterator type is `RandomAccessIterator`.
* @tparam TriangleMesh a model of the concepts `EdgeListGraph` and `FaceListGraph`
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
*
* @param points the range of points of interest
* @param tm the triangle mesh to compute the distance to
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{vertex_point_map}
* \cgalParamDescription{a property map associating points to the vertices of `tm`}
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
* as key type and `%Point_3` as value type}
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tm)`}
* \cgalParamExtra{If this parameter is omitted, an internal property map for `CGAL::vertex_point_t`
* must be available in `TriangleMesh`.}
* \cgalParamNEnd
*
* \cgalParamNBegin{geom_traits}
* \cgalParamDescription{an instance of a geometric traits class}
* \cgalParamType{a class model of `PMPDistanceTraits`}
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* @pre `tm` is a non-empty triangle mesh and `points` is not empty.
*/
template< class Concurrency_tag,
class TriangleMesh,
class PointRange,
class NamedParameters = parameters::Default_named_parameters>
double max_distance_to_triangle_mesh(const PointRange& points,
const TriangleMesh& tm,
const NamedParameters& np = parameters::default_values())
{
CGAL_precondition(!is_empty(tm) && is_triangle_mesh(tm));
using parameters::choose_parameter;
using parameters::get_parameter;
typedef typename GetGeomTraits<TriangleMesh, NamedParameters>::type GeomTraits;
typedef typename GeomTraits::Point_3 Point_3;
GeomTraits gt = choose_parameter<GeomTraits>(get_parameter(np, internal_np::geom_traits));
typedef typename GetVertexPointMap<TriangleMesh, NamedParameters>::const_type VPM;
VPM vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
get_const_property_map(vertex_point, tm));
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "Nb sample points " << points.size() << "\n";
#endif
std::vector<Point_3> points_cpy(std::begin(points), std::end(points));
spatial_sort(points_cpy.begin(), points_cpy.end());
typedef AABB_face_graph_triangle_primitive<TriangleMesh, VPM> Primitive;
typedef AABB_traits_3<GeomTraits, Primitive> Tree_traits;
typedef AABB_tree<Tree_traits> Tree;
Tree_traits tgt/*(gt)*/;
Tree tree(tgt);
tree.insert(faces(tm).first, faces(tm).second, tm, vpm);
const Point_3& hint = get(vpm, *vertices(tm).first);
return internal::max_distance_to_mesh_impl<Concurrency_tag>(points_cpy, tree, hint, gt);
}
/**
* \ingroup PMP_distance_grp
*
* computes the approximate Hausdorff distance from `tm1` to `tm2` by returning
* the distance of the farthest point from `tm2` amongst a sampling of `tm1`
* generated with the function `sample_triangle_mesh()` with
* `tm1` and `np1` as parameter.
*
* A parallel version is provided and requires the executable to be
* linked against the <a href="https://github.com/oneapi-src/oneTBB">Intel TBB library</a>.
* To control the number of threads used, the user may use the `tbb::task_scheduler_init` class.
* See the <a href="https://software.intel.com/content/www/us/en/develop/documentation/onetbb-documentation/top.html">TBB documentation</a>
* for more details.
*
* @tparam Concurrency_tag enables sequential versus parallel algorithm.
* Possible values are `Sequential_tag`, `Parallel_tag`, and `Parallel_if_available_tag`.
* @tparam TriangleMesh a model of the concepts `EdgeListGraph` and `FaceListGraph`
* @tparam NamedParameters1 a sequence of \ref bgl_namedparameters "Named Parameters" for `tm1`
* @tparam NamedParameters2 a sequence of \ref bgl_namedparameters "Named Parameters" for `tm2`
*
* @param tm1 the triangle mesh that will be sampled
* @param tm2 the triangle mesh to compute the distance to
* @param np1 an optional sequence of \ref bgl_namedparameters "Named Parameters" forwarded to `sample_triangle_mesh()`
* @param np2 an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{vertex_point_map}
* \cgalParamDescription{a property map associating points to the vertices of `tm2`}
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
* as key type and `%Point_3` as value type}
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tm2)`}
* \cgalParamExtra{If this parameter is omitted, an internal property map for `CGAL::vertex_point_t`
* must be available in `TriangleMesh`.}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* @pre `tm1` and `tm2` are non-empty triangle meshes.
*/
template< class Concurrency_tag,
class TriangleMesh,
class NamedParameters1 = parameters::Default_named_parameters,
class NamedParameters2 = parameters::Default_named_parameters>
double approximate_Hausdorff_distance(const TriangleMesh& tm1,
const TriangleMesh& tm2,
const NamedParameters1& np1 = parameters::default_values(),
const NamedParameters2& np2 = parameters::default_values())
{
typedef typename GetGeomTraits<TriangleMesh, NamedParameters1>::type GeomTraits;
typedef typename GeomTraits::Point_3 Point_3;
CGAL_precondition(!is_empty(tm1) && is_triangle_mesh(tm1));
CGAL_precondition(!is_empty(tm2) && is_triangle_mesh(tm2));
std::vector<Point_3> sample_points;
sample_triangle_mesh(tm1, std::back_inserter(sample_points), np1);
return max_distance_to_triangle_mesh<Concurrency_tag>(sample_points, tm2, np2);
}
/**
* \ingroup PMP_distance_grp
*
* returns the approximate symmetric Hausdorff distance between `tm1` and `tm2`,
* that is the maximum of `approximate_Hausdorff_distance(tm1, tm2, np1, np2)`
* and `approximate_Hausdorff_distance(tm2, tm1, np2, np1)`.
*
* See the function `approximate_Hausdorff_distance()` for a complete description of the parameters
* and requirements.
*/
template <class Concurrency_tag,
class TriangleMesh,
class NamedParameters1 = parameters::Default_named_parameters,
class NamedParameters2 = parameters::Default_named_parameters>
double approximate_symmetric_Hausdorff_distance(const TriangleMesh& tm1,
const TriangleMesh& tm2,
const NamedParameters1& np1 = parameters::default_values(),
const NamedParameters2& np2 = parameters::default_values())
{
return (std::max)(approximate_Hausdorff_distance<Concurrency_tag>(tm1,tm2,np1,np2),
approximate_Hausdorff_distance<Concurrency_tag>(tm2,tm1,np2,np1));
}
/*!
*\ingroup PMP_distance_grp
*
* returns an approximation of the distance between `points` and the point lying on `tm` that is the farthest from `points`.
*
* @tparam PointRange a range of `Point_3`, model of `Range`
* @tparam TriangleMesh a model of the concept `FaceListGraph`
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
*
* @param tm a triangle mesh
* @param points a range of points
* @param precision for each triangle of `tm`, the distance of its farthest point from `points` is bounded.
* A triangle is subdivided into sub-triangles so that the difference of its distance bounds
* is smaller than `precision`. `precision` must be strictly positive to avoid infinite loops.
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{vertex_point_map}
* \cgalParamDescription{a property map associating points to the vertices of `tm`}
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
* as key type and `%Point_3` as value type}
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tm)`}
* \cgalParamExtra{If this parameter is omitted, an internal property map for `CGAL::vertex_point_t`
* must be available in `TriangleMesh`.}
* \cgalParamNEnd
*
* \cgalParamNBegin{geom_traits}
* \cgalParamDescription{an instance of a geometric traits class}
* \cgalParamType{a class model of `PMPDistanceTraits`}
* \cgalParamDefault{a \cgal Kernel deduced from the point type, using `CGAL::Kernel_traits`}
* \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* @pre `tm` is a non-empty triangle mesh and `points` is not empty.
*/
template< class TriangleMesh,
class PointRange,
class NamedParameters = parameters::Default_named_parameters>
double approximate_max_distance_to_point_set(const TriangleMesh& tm,
const PointRange& points,
const double precision,
const NamedParameters& np = parameters::default_values())
{
CGAL_precondition(!is_empty(tm) && is_triangle_mesh(tm));
CGAL_precondition(!points.empty());
typedef typename GetGeomTraits<TriangleMesh, NamedParameters>::type GeomTraits;
typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;
typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
typedef Orthogonal_k_neighbor_search<Search_traits_3<GeomTraits> > Knn;
typedef typename Knn::Tree Tree;
Tree tree(points.begin(), points.end());
CRefiner<GeomTraits> ref;
for(face_descriptor f : faces(tm))
{
typename GeomTraits::Point_3 points[3];
halfedge_descriptor hd(halfedge(f,tm));
for(int i=0; i<3; ++i)
{
points[i] = get(parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_point),
get_const_property_map(vertex_point, tm)),
target(hd, tm));
hd = next(hd, tm);
}
ref.add(points[0], points[1], points[2], tree);
}
return to_double(ref.refine(precision, tree));
}
////////////////////////////////////////////////////////////////////////
// Use this def in order to get back the parallel version of the one-sided Hausdorff code!
// #define USE_PARALLEL_BEHD
namespace internal {
template <class Kernel,
class TriangleMesh1,
class TriangleMesh2,
class VPM1,
class VPM2,
class NamedParameters1,
class NamedParameters2,
class TM1Tree,
class TM2Tree,
class FaceHandle1,
class FaceHandle2>
std::pair<typename Kernel::FT, bool>
preprocess_bounded_error_squared_Hausdorff_distance_impl(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const bool compare_meshes,
const VPM1 vpm1,
const VPM2 vpm2,
const bool is_one_sided_distance,
const NamedParameters1& np1,
const NamedParameters2& np2,
TM1Tree& tm1_tree,
TM2Tree& tm2_tree,
std::vector<FaceHandle1>& tm1_only,
std::vector<FaceHandle2>& tm2_only)
{
using FT = typename Kernel::FT;
#ifdef CGAL_HAUSDORFF_DEBUG
using Timer = CGAL::Real_timer;
Timer timer;
timer.start();
std::cout << "* preprocessing begin ...." << std::endl;
std::cout.precision(17);
#endif
// Compute the max value that is used as infinity value for the given meshes.
// In our case, it is twice the length of the diagonal of the bbox of two input meshes.
const Bbox_3 bbox1 = bbox(tm1);
const Bbox_3 bbox2 = bbox(tm2);
const Bbox_3 bb = bbox1 + bbox2;
const FT sq_dist = square(bb.xmax() - bb.xmin())
+ square(bb.ymax() - bb.ymin())
+ square(bb.zmax() - bb.zmin());
FT infinity_value = FT(4) * sq_dist;
CGAL_assertion(infinity_value >= FT(0));
// Compare meshes and build trees.
tm1_only.clear();
tm2_only.clear();
std::vector<std::pair<FaceHandle1, FaceHandle2> > common;
const auto faces1 = faces(tm1);
const auto faces2 = faces(tm2);
CGAL_precondition(faces1.size() > 0);
CGAL_precondition(faces2.size() > 0);
// Compare meshes.
bool rebuild = false;
if(compare_meshes) // exact check
{
match_faces(tm1, tm2, std::back_inserter(common),
std::back_inserter(tm1_only), std::back_inserter(tm2_only), np1, np2);
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "- common: " << common.size() << std::endl;
std::cout << "- tm1 only: " << tm1_only.size() << std::endl;
std::cout << "- tm2 only: " << tm2_only.size() << std::endl;
#endif
if(is_one_sided_distance) // one-sided distance
{
if(tm1_only.size() > 0) // create TM1 and and full TM2
{
tm1_tree.insert(tm1_only.begin(), tm1_only.end(), tm1, vpm1);
tm2_tree.insert(faces2.begin(), faces2.end(), tm2, vpm2);
}
else // do not create trees
{
CGAL_assertion(tm1_only.size() == 0);
infinity_value = FT(-1);
}
}
else // symmetric distance
{
if(tm1_only.size() == 0 && tm2_only.size() == 0) // do not create trees
{
infinity_value = FT(-1);
}
else if(common.size() == 0) // create full TM1 and TM2
{
tm1_tree.insert(faces1.begin(), faces1.end(), tm1, vpm1);
tm2_tree.insert(faces2.begin(), faces2.end(), tm2, vpm2);
}
else if(tm1_only.size() == 0) // create TM2 and full TM1
{
CGAL_assertion(tm2_only.size() > 0);
CGAL_assertion(tm2_only.size() < faces2.size());
tm1_tree.insert(faces1.begin(), faces1.end(), tm1, vpm1);
tm2_tree.insert(tm2_only.begin(), tm2_only.end(), tm2, vpm2);
}
else if(tm2_only.size() == 0) // create TM1 and full TM2
{
CGAL_assertion(tm1_only.size() > 0);
CGAL_assertion(tm1_only.size() < faces1.size());
tm1_tree.insert(tm1_only.begin(), tm1_only.end(), tm1, vpm1);
tm2_tree.insert(faces2.begin(), faces2.end(), tm2, vpm2);
}
else // create TM1 and full TM2 and set tag to rebuild them later
{
CGAL_assertion(tm1_only.size() > 0);
CGAL_assertion(tm1_only.size() < faces1.size());
tm1_tree.insert(tm1_only.begin(), tm1_only.end(), tm1, vpm1);
tm2_tree.insert(faces2.begin(), faces2.end(), tm2, vpm2);
rebuild = true;
}
}
}
else // create full TM1 and TM2
{
tm1_tree.insert(faces1.begin(), faces1.end(), tm1, vpm1);
tm2_tree.insert(faces2.begin(), faces2.end(), tm2, vpm2);
}
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
std::cout << "* .... end preprocessing" << std::endl;
std::cout << "* preprocessing time (sec.): " << timer.time() << std::endl;
#endif
return std::make_pair(infinity_value, rebuild);
}
template <class Kernel,
class TriangleMesh1,
class TriangleMesh2,
class VPM1,
class VPM2,
class TM1Tree,
class TM2Tree,
class OutputIterator>
typename Kernel::FT
bounded_error_squared_Hausdorff_distance_impl(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const VPM1 vpm1,
const VPM2 vpm2,
const TM1Tree& tm1_tree,
const TM2Tree& tm2_tree,
const typename Kernel::FT error_bound,
const typename Kernel::FT sq_initial_bound,
const typename Kernel::FT sq_distance_bound,
const typename Kernel::FT infinity_value,
OutputIterator& out)
{
using FT = typename Kernel::FT;
using Point_3 = typename Kernel::Point_3;
using Triangle_3 = typename Kernel::Triangle_3;
auto midpoint = Kernel().construct_midpoint_3_object();
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << " -- Bounded Hausdorff --" << std::endl;
std::cout << "error bound: " << error_bound << std::endl;
std::cout << "initial bound: " << sq_initial_bound << " (" << approximate_sqrt(sq_initial_bound) << ")" << std::endl;
std::cout << "distance bound: " << sq_distance_bound << " (" << approximate_sqrt(sq_distance_bound) << ")" << std::endl;
std::cout << "inf val: " << infinity_value << " (" << approximate_sqrt(infinity_value) << ")" << std::endl;
#endif
using TM1_hd_traits = Hausdorff_primitive_traits_tm1<Point_3, Kernel, TriangleMesh1, TriangleMesh2, VPM1, VPM2>;
using TM2_hd_traits = Hausdorff_primitive_traits_tm2<Triangle_3, Kernel, TriangleMesh1, TriangleMesh2, VPM2>;
using Face_handle_1 = typename boost::graph_traits<TriangleMesh1>::face_descriptor;
using Face_handle_2 = typename boost::graph_traits<TriangleMesh2>::face_descriptor;
using Candidate = Candidate_triangle<Kernel, Face_handle_1, Face_handle_2>;
CGAL_precondition(sq_initial_bound >= square(FT(error_bound)));
CGAL_precondition(sq_distance_bound != FT(0)); // value is -1 if unused
CGAL_precondition(tm1_tree.size() > 0);
CGAL_precondition(tm2_tree.size() > 0);
// First, we apply culling.
#ifdef CGAL_HAUSDORFF_DEBUG
using Timer = CGAL::Real_timer;
Timer timer;
timer.start();
std::cout << "- applying culling" << std::endl;
std::cout.precision(17);
#endif
// Build traversal traits for tm1_tree.
TM1_hd_traits traversal_traits_tm1(tm2_tree, tm1, tm2, vpm1, vpm2,
infinity_value, sq_initial_bound, sq_distance_bound);
// Find candidate triangles in TM1, which might realize the Hausdorff bound.
// We build a sorted structure while collecting the candidates.
const Point_3 stub(0, 0, 0); // dummy point given as query since it is not needed
tm1_tree.traversal_with_priority(stub, traversal_traits_tm1);
auto& candidate_triangles = traversal_traits_tm1.get_candidate_triangles();
Global_bounds<Kernel, Face_handle_1, Face_handle_2> global_bounds = traversal_traits_tm1.get_global_bounds();
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "- bounds post traversal: " << global_bounds.lower << " " << global_bounds.upper << std::endl;
std::cout << "- number of candidate triangles: " << candidate_triangles.size() << std::endl;
const FT culling_rate = FT(100) - (FT(candidate_triangles.size()) / FT(tm1_tree.size()) * FT(100));
std::cout << "- culling rate: " << culling_rate << "%" << std::endl;
timer.stop();
std::cout << "* culling (sec.): " << timer.time() << std::endl;
#endif
CGAL_assertion(global_bounds.lower >= FT(0));
CGAL_assertion(global_bounds.upper >= global_bounds.lower);
CGAL_assertion(global_bounds.lpair.first != boost::graph_traits<TriangleMesh1>::null_face());
CGAL_assertion(global_bounds.lpair.second != boost::graph_traits<TriangleMesh2>::null_face());
CGAL_assertion(global_bounds.upair.first != boost::graph_traits<TriangleMesh1>::null_face());
CGAL_assertion(global_bounds.upair.second != boost::graph_traits<TriangleMesh2>::null_face());
// If we already reached the user-defined max distance bound, we quit.
if(traversal_traits_tm1.early_exit())
{
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "Quitting early (TM1 traversal): temporary distance " << global_bounds.lower
<< " is already greater than user-defined bound " << sq_distance_bound << std::endl;
#endif
CGAL_assertion(global_bounds.lower > sq_distance_bound);
return global_bounds.lower;
}
// Second, we apply subdivision.
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
std::cout << "- applying subdivision" << std::endl;
timer.start();
std::size_t explored_candidates_count = 0;
#endif
// See Section 5.1 in the paper.
while(!candidate_triangles.empty())
{
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "===" << std::endl;
std::cout << candidate_triangles.size() << " candidates" << std::endl;
std::cout << "- infinity_value: " << infinity_value << std::endl;
std::cout << "- error_bound: " << error_bound << std::endl;
std::cout << "- sq_initial_bound: " << sq_initial_bound << std::endl;
std::cout << "- sq_distance_bound: " << sq_distance_bound << std::endl;
std::cout << "- global_bounds.lower: " << global_bounds.lower << std::endl;
std::cout << "- global_bounds.upper: " << global_bounds.upper << std::endl;
std::cout << "- diff = " << CGAL::approximate_sqrt(global_bounds.upper) -
CGAL::approximate_sqrt(global_bounds.lower) << ", below bound? "
<< ((CGAL::approximate_sqrt(global_bounds.upper) -
CGAL::approximate_sqrt(global_bounds.lower)) <= error_bound) << std::endl;
#endif
CGAL_assertion(global_bounds.lower >= FT(0));
CGAL_assertion(global_bounds.upper >= global_bounds.lower);
// @todo could cache those sqrts
if(CGAL::approximate_sqrt(global_bounds.upper) - CGAL::approximate_sqrt(global_bounds.lower) <= error_bound)
break;
// Check if we can early quit.
if(is_positive(sq_distance_bound)) // empty distance bound is FT(-1)
{
const bool early_quit = (sq_distance_bound <= global_bounds.lower);
if(early_quit)
{
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "Quitting early with lower bound: " << global_bounds.lower << std::endl;
#endif
break;
}
}
const Candidate triangle_and_bounds = candidate_triangles.top();
candidate_triangles.pop();
// Only process the triangle if it can contribute to the Hausdorff distance,
// i.e., if its upper bound is higher than the currently known best lower bound
// and the difference between the bounds to be obtained is larger than the
// user-given error.
const auto& triangle_bounds = triangle_and_bounds.bounds;
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Candidate:" << std::endl;
std::cout << triangle_and_bounds.triangle.vertex(0) << std::endl;
std::cout << triangle_and_bounds.triangle.vertex(1) << std::endl;
std::cout << triangle_and_bounds.triangle.vertex(2) << std::endl;
std::cout << "triangle_bounds.lower: " << triangle_bounds.lower << std::endl;
std::cout << "triangle_bounds.upper: " << triangle_bounds.upper << std::endl;
std::cout << "- diff = " << CGAL::approximate_sqrt(triangle_bounds.upper) -
CGAL::approximate_sqrt(triangle_bounds.lower) << ", below bound? "
<< ((CGAL::approximate_sqrt(triangle_bounds.upper) -
CGAL::approximate_sqrt(triangle_bounds.lower)) <= error_bound) << std::endl;
#endif
CGAL_assertion(triangle_bounds.lower >= FT(0));
CGAL_assertion(triangle_bounds.upper >= triangle_bounds.lower);
// @todo implement the enclosing-based end criterion (Section 5.1, optional step for TM1 & TM2 closed)
// Might have been a good candidate when added to the queue, but rendered useless by later insertions
if(triangle_bounds.upper < global_bounds.lower)
{
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Upper bound is lower than global.lower" << std::endl;
#endif
continue;
}
if((CGAL::approximate_sqrt(triangle_bounds.upper) - CGAL::approximate_sqrt(triangle_bounds.lower)) <= error_bound)
{
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Candidate triangle bounds are tight enough: " << triangle_bounds.lower << " " << triangle_bounds.upper << std::endl;
#endif
continue;
}
#ifdef CGAL_HAUSDORFF_DEBUG
++explored_candidates_count;
#endif
// Triangle to be subdivided
const Triangle_3& triangle_for_subdivision = triangle_and_bounds.triangle;
const Point_3& v0 = triangle_for_subdivision.vertex(0);
const Point_3& v1 = triangle_for_subdivision.vertex(1);
const Point_3& v2 = triangle_for_subdivision.vertex(2);
// Stopping condition: All three vertices of the triangle are projected onto the same triangle in TM2.
const auto closest_triangle_v0 = tm2_tree.closest_point_and_primitive(v0);
const auto closest_triangle_v1 = tm2_tree.closest_point_and_primitive(v1);
const auto closest_triangle_v2 = tm2_tree.closest_point_and_primitive(v2);
CGAL_assertion(closest_triangle_v0.second != boost::graph_traits<TriangleMesh2>::null_face());
CGAL_assertion(closest_triangle_v1.second != boost::graph_traits<TriangleMesh2>::null_face());
CGAL_assertion(closest_triangle_v2.second != boost::graph_traits<TriangleMesh2>::null_face());
if((closest_triangle_v0.second == closest_triangle_v1.second) &&
(closest_triangle_v1.second == closest_triangle_v2.second))
{
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Projects onto the same TM2 face" << std::endl;
#endif
// The upper bound of this triangle is the actual Hausdorff distance of
// the triangle to the second mesh. Use it as new global lower bound.
// Here, we update the reference to the realizing triangle as this is the best current guess.
global_bounds.lower = triangle_bounds.upper;
global_bounds.lpair.second = triangle_bounds.tm2_uface;
continue;
}
// Subdivide the triangle into four smaller triangles.
const Point_3 v01 = midpoint(v0, v1);
const Point_3 v02 = midpoint(v0, v2);
const Point_3 v12 = midpoint(v1, v2);
const std::array<Triangle_3, 4> sub_triangles = { Triangle_3(v0, v01, v02), Triangle_3(v1 , v01, v12),
Triangle_3(v2, v02, v12), Triangle_3(v01, v02, v12) };
// Send each of the four triangles to culling on B
for(std::size_t i=0; i<4; ++i)
{
// Call culling on B with the single triangle found.
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "\nSubface #" << i << "\n"
<< "Geometry: " << sub_triangles[i] << std::endl;
#endif
// Checking as in during TM1 culling is expensive
// @todo? For each sub-triangle `ts1` that has a vertex of `v` of the triangle `t1` being subdivided,
// we have a lower bound on `h(ts1, TM2)` because:
// h_t1_lower = max_{vi in t1} min_{t2 in TM2} d(vi, t2)
// and
// h_ts1_lower = max_{vi in ts1} min_{t2 in TM2} d(vi, t2) > min_{t2 in TM2} d(v, t2)
// But:
// - we don't keep that in memory (not very hard to change, simply put `m_hi_lower`
// from the TM2 traversal traits into the candidate
// - what's the point? TM2 culling is performed on the local upper bound, so is there
// a benefit from providing this value?
//
// (We also have that error_bound is a lower bound.)
const Bbox_3 sub_t1_bbox = sub_triangles[i].bbox();
// The lower bound is:
// h_lower(t1, TM2) := max_{v in t1} min_{t2 in TM2} d(v, t2)
// The upper bound is:
// h_upper(t1, TM2) := min_{t2 in TM2} max_{v in t1} d(v, t2)
// The value max_{p in t1} d(p, t2) is realized at a vertex of t1.
// Thus, when splitting t1 into four subtriangles, the distance at the three new vertices
// is smaller than max_{v in t1} d(v, t2)
// Thus, subdivision can only decrease the min, and the upper bound.
Local_bounds<Kernel, Face_handle_1, Face_handle_2> bounds(triangle_bounds.upper);
// Ensure 'uface' is initialized in case the upper bound is not changed by the subdivision
bounds.tm2_uface = triangle_bounds.tm2_uface;
TM2_hd_traits traversal_traits_tm2(sub_t1_bbox, tm2, vpm2, bounds, global_bounds, infinity_value);
tm2_tree.traversal_with_priority(sub_triangles[i], traversal_traits_tm2);
// Update global lower Hausdorff bound according to the obtained local bounds.
const auto& sub_triangle_bounds = traversal_traits_tm2.get_local_bounds();
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Subdivided triangle bounds: " << sub_triangle_bounds.lower << " " << sub_triangle_bounds.upper << std::endl;
#endif
CGAL_assertion(sub_triangle_bounds.lower >= FT(0));
CGAL_assertion(sub_triangle_bounds.upper >= sub_triangle_bounds.lower);
CGAL_assertion(sub_triangle_bounds.tm2_lface != boost::graph_traits<TriangleMesh2>::null_face());
CGAL_assertion(sub_triangle_bounds.tm2_uface != boost::graph_traits<TriangleMesh2>::null_face());
// The global lower bound is the max of the per-face lower bounds
if(sub_triangle_bounds.lower > global_bounds.lower)
{
global_bounds.lower = sub_triangle_bounds.lower;
global_bounds.lpair.first = triangle_and_bounds.tm1_face;
global_bounds.lpair.second = sub_triangle_bounds.tm2_lface;
}
// The global upper bound is:
// max_{query in TM1} min_{primitive in TM2} max_{v in query} (d(v, primitive))
// which can go down, so it is only recomputed once splitting is finished,
// using the top value of the PQ
candidate_triangles.emplace(sub_triangles[i], sub_triangle_bounds, triangle_and_bounds.tm1_face);
}
// Update global upper Hausdorff bound after subdivision.
const Candidate& top_candidate = candidate_triangles.top();
const FT current_upmost = top_candidate.bounds.upper;
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "global_bounds.lower = " << global_bounds.lower << std::endl;
std::cout << "global_bounds.upper = " << global_bounds.upper << std::endl;
std::cout << "current upper bound = " << current_upmost << std::endl;
#endif
CGAL_assertion(is_positive(current_upmost));
if(current_upmost < global_bounds.lower)
{
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Top of the queue is lower than the lowest!" << std::endl;
#endif
global_bounds.upper = global_bounds.lower; // not really needed since lower is returned but doesn't hurt
global_bounds.upair.first = global_bounds.lpair.first;
global_bounds.upair.second = global_bounds.lpair.second;
break;
}
CGAL_assertion(current_upmost >= global_bounds.lower);
global_bounds.upper = current_upmost;
global_bounds.upair.first = top_candidate.tm1_face;
global_bounds.upair.second = top_candidate.bounds.tm2_uface;
#ifdef CGAL_HAUSDORFF_DEBUG_PP
std::cout << "Global bounds post subdi: " << global_bounds.lower << " " << global_bounds.upper << std::endl;
#endif
CGAL_assertion(global_bounds.lower >= FT(0));
CGAL_assertion(global_bounds.upper >= global_bounds.lower);
}
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
std::cout << "* subdivision (sec.): " << timer.time() << std::endl;
std::cout << "Explored " << explored_candidates_count << " candidates" << std::endl;
std::cout << "Final global bounds: " << global_bounds.lower << " " << global_bounds.upper << std::endl;
std::cout << "Final global bounds (sqrt): " << CGAL::approximate_sqrt(global_bounds.lower) << " "
<< CGAL::approximate_sqrt(global_bounds.upper) << std::endl;
std::cout << "Difference: " << CGAL::approximate_sqrt(global_bounds.upper) -
CGAL::approximate_sqrt(global_bounds.lower) << std::endl;
#endif
CGAL_assertion(global_bounds.lower >= FT(0));
CGAL_assertion(global_bounds.upper >= global_bounds.lower);
CGAL_assertion(CGAL::approximate_sqrt(global_bounds.upper) - CGAL::approximate_sqrt(global_bounds.lower) <= error_bound);
// Get realizing triangles.
CGAL_assertion(global_bounds.lpair.first != boost::graph_traits<TriangleMesh1>::null_face());
CGAL_assertion(global_bounds.lpair.second != boost::graph_traits<TriangleMesh2>::null_face());
CGAL_assertion(global_bounds.upair.first != boost::graph_traits<TriangleMesh1>::null_face());
CGAL_assertion(global_bounds.upair.second != boost::graph_traits<TriangleMesh2>::null_face());
// Output face pairs, which realize the Hausdorff distance.
*out++ = global_bounds.lpair;
*out++ = global_bounds.upair;
// Return the lower bound because if the correct value is in [0; lower_bound[, the result
// must still be within the error bound (we have set lower_bound to error_bound initially)
return global_bounds.lower;
}
#if defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED) && defined(USE_PARALLEL_BEHD)
template<class TriangleMesh, class VPM, class TMTree>
struct Triangle_mesh_wrapper
{
const TriangleMesh& tm; const VPM& vpm;
const bool is_tm2; TMTree& tm_tree;
Triangle_mesh_wrapper(const TriangleMesh& tm, const VPM& vpm,
const bool is_tm2, TMTree& tm_tree)
: tm(tm), vpm(vpm), is_tm2(is_tm2), tm_tree(tm_tree)
{ }
void build_tree()
{
tm_tree.insert(faces(tm).begin(), faces(tm).end(), tm, vpm);
tm_tree.build();
if(is_tm2)
tm_tree.accelerate_distance_queries();
else
tm_tree.do_not_accelerate_distance_queries();
}
};
template<class TM1Wrapper, class TM2Wrapper>
struct Bounded_error_preprocessing
{
#ifdef CGAL_HAUSDORFF_DEBUG
using Timer = CGAL::Real_timer;
#endif
std::vector<std::any>& tm_wrappers;
// Constructor.
Bounded_error_preprocessing(std::vector<std::any>& tm_wrappers)
: tm_wrappers(tm_wrappers)
{ }
// Split constructor.
Bounded_error_preprocessing(Bounded_error_preprocessing& s, tbb::split)
: tm_wrappers(s.tm_wrappers)
{ }
bool is_tm1_wrapper(const std::any& operand) const { return operand.type() == typeid(TM1Wrapper); }
bool is_tm2_wrapper(const std::any& operand) const { return operand.type() == typeid(TM2Wrapper); }
// TODO: make AABB tree build parallel!
void operator()(const tbb::blocked_range<std::size_t>& range)
{
#ifdef CGAL_HAUSDORFF_DEBUG
Timer timer;
timer.reset();
timer.start();
std::cout.precision(17);
#endif
for(std::size_t i = range.begin(); i != range.end(); ++i)
{
CGAL_assertion(i < tm_wrappers.size());
auto& tm_wrapper = tm_wrappers[i];
if(is_tm1_wrapper(tm_wrapper))
{
TM1Wrapper& object = std::any_cast<TM1Wrapper&>(tm_wrapper);
object.build_tree();
}
else if(is_tm2_wrapper(tm_wrapper))
{
TM2Wrapper& object = std::any_cast<TM2Wrapper&>(tm_wrapper);
object.build_tree();
}
else
{
CGAL_assertion_msg(false, "Error: wrong boost any type!");
}
}
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
std::cout << "* time operator() preprocessing (sec.): " << timer.time() << std::endl;
#endif
}
void join(Bounded_error_preprocessing&) { }
};
template <class TriangleMesh1,
class TriangleMesh2,
class VPM1,
class VPM2,
class TM1Tree,
class TM2Tree,
class Kernel>
struct Bounded_error_squared_distance_computation
{
using FT = typename Kernel::FT;
#ifdef CGAL_HAUSDORFF_DEBUG
using Timer = CGAL::Real_timer;
#endif
const std::vector<TriangleMesh1>& tm1_parts;
const TriangleMesh2& tm2;
const double error_bound;
const VPM1 vpm1; const VPM2 vpm2;
const FT infinity_value;
const FT sq_initial_bound;
const std::vector<TM1Tree>& tm1_trees;
const TM2Tree& tm2_tree;
FT sq_hdist;
// Constructor.
Bounded_error_squared_distance_computation(const std::vector<TriangleMesh1>& tm1_parts,
const TriangleMesh2& tm2,
const double error_bound,
const VPM1 vpm1, const VPM2 vpm2,
const FT infinity_value,
const FT sq_initial_bound,
const std::vector<TM1Tree>& tm1_trees,
const TM2Tree& tm2_tree)
: tm1_parts(tm1_parts), tm2(tm2),
error_bound(error_bound),
vpm1(vpm1), vpm2(vpm2),
infinity_value(infinity_value), sq_initial_bound(sq_initial_bound),
tm1_trees(tm1_trees), tm2_tree(tm2_tree),
sq_hdist(-1)
{
CGAL_assertion(tm1_parts.size() == tm1_trees.size());
}
// Split constructor.
Bounded_error_squared_distance_computation(Bounded_error_squared_distance_computation& s, tbb::split)
: tm1_parts(s.tm1_parts), tm2(s.tm2),
error_bound(s.error_bound),
vpm1(s.vpm1), vpm2(s.vpm2),
infinity_value(s.infinity_value), sq_initial_bound(s.sq_initial_bound),
tm1_trees(s.tm1_trees), tm2_tree(s.tm2_tree),
sq_hdist(-1)
{
CGAL_assertion(tm1_parts.size() == tm1_trees.size());
}
void operator()(const tbb::blocked_range<std::size_t>& range)
{
#ifdef CGAL_HAUSDORFF_DEBUG
Timer timer;
timer.reset();
timer.start();
std::cout.precision(17);
#endif
FT sq_dist = FT(-1);
auto stub = CGAL::Emptyset_iterator();
for(std::size_t i = range.begin(); i != range.end(); ++i)
{
CGAL_assertion(i < tm1_parts.size());
CGAL_assertion(i < tm1_trees.size());
const auto& tm1 = tm1_parts[i];
const auto& tm1_tree = tm1_trees[i];
// TODO: add distance_bound (now it is FT(-1)) in case we use parallel
// for checking if two meshes are close.
const FT sqd = bounded_error_squared_Hausdorff_distance_impl<Kernel>(
tm1, tm2, vpm1, vpm2, tm1_tree, tm2_tree,
error_bound, sq_initial_bound, FT(-1) /*sq_distance_bound*/, infinity_value,
stub);
if(sqd > sq_dist)
sq_dist = sqd;
}
if(sq_dist > sq_hdist)
sq_hdist = sq_dist;
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
std::cout << "* time operator() computation (sec.): " << timer.time() << std::endl;
#endif
}
void join(Bounded_error_squared_distance_computation& rhs)
{
sq_hdist = (CGAL::max)(rhs.sq_hdist, sq_hdist);
}
};
#endif // defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED)
template <class Concurrency_tag,
class Kernel,
class TriangleMesh1,
class TriangleMesh2,
class VPM1,
class VPM2,
class NamedParameters1,
class NamedParameters2,
class OutputIterator>
typename Kernel::FT
bounded_error_squared_one_sided_Hausdorff_distance_impl(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const typename Kernel::FT error_bound,
const typename Kernel::FT sq_distance_bound,
const bool compare_meshes,
const VPM1 vpm1,
const VPM2 vpm2,
const NamedParameters1& np1,
const NamedParameters2& np2,
OutputIterator& out)
{
#if !defined(CGAL_LINKED_WITH_TBB) || !defined(CGAL_METIS_ENABLED)
static_assert(!std::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value,
"Parallel_tag is enabled but at least TBB or METIS is unavailable.");
#endif
using FT = typename Kernel::FT;
using TM1 = TriangleMesh1;
using TM2 = TriangleMesh2;
using TM1_primitive = AABB_face_graph_triangle_primitive<TM1, VPM1>;
using TM2_primitive = AABB_face_graph_triangle_primitive<TM2, VPM2>;
using TM1_traits = AABB_traits_3<Kernel, TM1_primitive>;
using TM2_traits = AABB_traits_3<Kernel, TM2_primitive>;
using TM1_tree = AABB_tree<TM1_traits>;
using TM2_tree = AABB_tree<TM2_traits>;
using Face_handle_1 = typename boost::graph_traits<TM1>::face_descriptor;
using Face_handle_2 = typename boost::graph_traits<TM2>::face_descriptor;
// This is parallel version: we split the tm1 into parts, build trees for all parts, and
// run in parallel all BHD computations. The final distance is obtained by taking the max
// between BHDs computed for these parts with respect to tm2.
// This is off by default because the parallel version does not show much of runtime improvement.
// The slowest part is building AABB trees and this is what should be accelerated in the future.
#if defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED) && defined(USE_PARALLEL_BEHD)
using TMF = CGAL::Face_filtered_graph<TM1>;
using TMF_primitive = AABB_face_graph_triangle_primitive<TMF, VPM1>;
using TMF_traits = AABB_traits_3<Kernel, TMF_primitive>;
using TMF_tree = AABB_tree<TMF_traits>;
using TM1_wrapper = Triangle_mesh_wrapper<TMF, VPM1, TMF_tree>;
using TM2_wrapper = Triangle_mesh_wrapper<TM2, VPM2, TM2_tree>;
std::vector<TMF> tm1_parts;
std::vector<TMF_tree> tm1_trees;
std::vector<std::any> tm_wrappers;
#endif // defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED)
#ifdef CGAL_HAUSDORFF_DEBUG
using Timer = CGAL::Real_timer;
Timer timer;
std::cout.precision(17);
#endif
TM1_tree tm1_tree;
TM2_tree tm2_tree;
FT infinity_value = FT(-1);
#if defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED) && defined(USE_PARALLEL_BEHD)
// TODO: add to NP!
const int nb_cores = 4;
const std::size_t min_nb_faces_to_split = 100; // TODO: increase this number?
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "* num cores: " << nb_cores << std::endl;
#endif
if(std::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value &&
nb_cores > 1 &&
faces(tm1).size() >= min_nb_faces_to_split)
{
// (0) -- Compute infinity value.
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
timer.start();
#endif
const Bbox_3 bbox1 = bbox(tm1);
const Bbox_3 bbox2 = bbox(tm2);
const Bbox_3 bb = bbox1 + bbox2;
const FT sq_dist = square(bb.xmax() - bb.xmin())
+ square(bb.ymax() - bb.ymin())
+ square(bb.zmax() - bb.zmin());
infinity_value = FT(4) * sq_dist;
CGAL_assertion(infinity_value >= FT(0));
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
const double time0 = timer.time();
std::cout << "- computing infinity (sec.): " << time0 << std::endl;
#endif
// (1) -- Create partition of tm1.
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
timer.start();
#endif
using Face_property_tag = CGAL::dynamic_face_property_t<int>;
auto face_pid_map = get(Face_property_tag(), tm1);
CGAL::METIS::partition_graph(tm1, nb_cores, CGAL::parameters::face_partition_id_map(face_pid_map));
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
const double time1 = timer.time();
std::cout << "- computing partition time (sec.): " << time1 << std::endl;
#endif
// (2) -- Create a filtered face graph for each part.
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
timer.start();
#endif
tm1_parts.reserve(nb_cores);
for(int i = 0; i < nb_cores; ++i)
{
tm1_parts.emplace_back(tm1, i, face_pid_map);
// TODO: why is it triggered sometimes?
// CGAL_assertion(tm1_parts.back().is_selection_valid());
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "- part " << i << " size: " << tm1_parts.back().number_of_faces() << std::endl;
#endif
}
CGAL_assertion(tm1_parts.size() == nb_cores);
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
const double time2 = timer.time();
std::cout << "- creating graphs time (sec.): " << time2 << std::endl;
#endif
// (3) -- Preprocess all input data.
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
timer.start();
#endif
tm1_trees.resize(tm1_parts.size());
tm_wrappers.reserve(tm1_parts.size() + 1);
for(std::size_t i = 0; i < tm1_parts.size(); ++i)
tm_wrappers.push_back(TM1_wrapper(tm1_parts[i], vpm1, false, tm1_trees[i]));
tm_wrappers.push_back(TM2_wrapper(tm2, vpm2, true, tm2_tree));
CGAL_assertion(tm_wrappers.size() == tm1_parts.size() + 1);
Bounded_error_preprocessing<TM1_wrapper, TM2_wrapper> bep(tm_wrappers);
tbb::parallel_reduce(tbb::blocked_range<std::size_t>(0, tm_wrappers.size()), bep);
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
const double time3 = timer.time();
std::cout << "- creating trees time (sec.) " << time3 << std::endl;
#endif
#ifdef CGAL_HAUSDORFF_DEBUG
// Final timing
std::cout << "* preprocessing parallel time (sec.) " << time0 + time1 + time2 + time3 << std::endl;
#endif
} else // sequential version
#endif // defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED)
{
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
timer.start();
std::cout << "* preprocessing sequential version " << std::endl;
#endif
bool rebuild = false;
std::vector<Face_handle_1> tm1_only;
std::vector<Face_handle_2> tm2_only;
std::tie(infinity_value, rebuild) =
preprocess_bounded_error_squared_Hausdorff_distance_impl<Kernel>(
tm1, tm2, compare_meshes, vpm1, vpm2, true /*is_one_sided_distance*/, np1, np2,
tm1_tree, tm2_tree, tm1_only, tm2_only);
CGAL_assertion(!rebuild);
if(infinity_value >= FT(0))
{
tm1_tree.build();
tm2_tree.build();
tm1_tree.do_not_accelerate_distance_queries();
tm2_tree.accelerate_distance_queries();
}
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
std::cout << "* preprocessing sequential time (sec.) " << timer.time() << std::endl;
#endif
}
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "* infinity_value: " << infinity_value << std::endl;
#endif
if(is_negative(infinity_value))
{
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "* culling rate: 100%" << std::endl;
#endif
const auto face1 = *(faces(tm1).begin());
const auto face2 = *(faces(tm2).begin());
*out++ = std::make_pair(face1, face2);
*out++ = std::make_pair(face1, face2);
return 0.; // TM1 is part of TM2 so the distance is zero
}
CGAL_assertion(infinity_value > FT(0));
CGAL_assertion(error_bound >= 0.);
const FT sq_initial_bound = square(FT(error_bound));
FT sq_hdist = FT(-1);
#ifdef CGAL_HAUSDORFF_DEBUG
timer.reset();
timer.start();
#endif
#if defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED) && defined(USE_PARALLEL_BEHD)
if(std::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value &&
nb_cores > 1 &&
faces(tm1).size() >= min_nb_faces_to_split)
{
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "* executing parallel version " << std::endl;
#endif
using Comp = Bounded_error_squared_distance_computation<TMF, TM2, VPM1, VPM2, TMF_tree, TM2_tree, Kernel>;
Comp bedc(tm1_parts, tm2, error_bound, vpm1, vpm2,
infinity_value, sq_initial_bound, tm1_trees, tm2_tree);
tbb::parallel_reduce(tbb::blocked_range<std::size_t>(0, tm1_parts.size()), bedc);
sq_hdist = bedc.sq_hdist;
}
else // sequential version
#endif // defined(CGAL_LINKED_WITH_TBB) && defined(CGAL_METIS_ENABLED)
{
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout << "* executing sequential version" << std::endl;
#endif
sq_hdist = bounded_error_squared_Hausdorff_distance_impl<Kernel>(
tm1, tm2, vpm1, vpm2, tm1_tree, tm2_tree,
error_bound, sq_initial_bound, sq_distance_bound, infinity_value, out);
}
#ifdef CGAL_HAUSDORFF_DEBUG
timer.stop();
std::cout << "* squared distance " << sq_hdist << std::endl;
std::cout << "* distance " << approximate_sqrt(sq_hdist) << std::endl;
std::cout << "* computation time (sec.) " << timer.time() << std::endl;
#endif
CGAL_postcondition(sq_hdist >= FT(0));
return sq_hdist;
}
template <class Concurrency_tag,
class Kernel,
class TriangleMesh1,
class TriangleMesh2,
class VPM1,
class VPM2,
class NamedParameters1,
class NamedParameters2,
class OutputIterator1,
class OutputIterator2>
typename Kernel::FT
bounded_error_squared_symmetric_Hausdorff_distance_impl(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const typename Kernel::FT error_bound,
const typename Kernel::FT sq_distance_bound,
const bool compare_meshes,
const VPM1 vpm1,
const VPM2 vpm2,
const NamedParameters1& np1,
const NamedParameters2& np2,
OutputIterator1& out1,
OutputIterator2& out2)
{
#if !defined(CGAL_LINKED_WITH_TBB) || !defined(CGAL_METIS_ENABLED)
static_assert(!std::is_convertible<Concurrency_tag, CGAL::Parallel_tag>::value,
"Parallel_tag is enabled but at least TBB or METIS is unavailable.");
#endif
// Optimized version.
// -- We compare meshes only if it is required.
// -- We first build trees and rebuild them only if it is required.
// -- We provide better initial lower bound in the second call to the Hausdorff distance.
using FT = typename Kernel::FT;
using TM1_primitive = AABB_face_graph_triangle_primitive<TriangleMesh1, VPM1>;
using TM2_primitive = AABB_face_graph_triangle_primitive<TriangleMesh2, VPM2>;
using TM1_traits = AABB_traits_3<Kernel, TM1_primitive>;
using TM2_traits = AABB_traits_3<Kernel, TM2_primitive>;
using TM1_tree = AABB_tree<TM1_traits>;
using TM2_tree = AABB_tree<TM2_traits>;
using Face_handle_1 = typename boost::graph_traits<TriangleMesh1>::face_descriptor;
using Face_handle_2 = typename boost::graph_traits<TriangleMesh2>::face_descriptor;
std::vector<Face_handle_1> tm1_only;
std::vector<Face_handle_2> tm2_only;
const FT sq_error_bound = square(FT(error_bound));
FT infinity_value = FT(-1);
// All trees below are built and/or accelerated lazily.
TM1_tree tm1_tree;
TM2_tree tm2_tree;
bool rebuild = false;
std::tie(infinity_value, rebuild) = preprocess_bounded_error_squared_Hausdorff_distance_impl<Kernel>(
tm1, tm2, compare_meshes, vpm1, vpm2, false /*is_one_sided_distance*/, np1, np2,
tm1_tree, tm2_tree, tm1_only, tm2_only);
if(is_negative(infinity_value))
{
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout.precision(17);
std::cout << "* culling rate: 100%" << std::endl;
#endif
const auto face1 = *(faces(tm1).begin());
const auto face2 = *(faces(tm2).begin());
*out1++ = std::make_pair(face1, face2);
*out1++ = std::make_pair(face1, face2);
*out2++ = std::make_pair(face2, face1);
*out2++ = std::make_pair(face2, face1);
return 0.; // TM1 and TM2 are equal so the distance is zero
}
CGAL_assertion(is_positive(infinity_value));
// Compute the first one-sided distance.
FT sq_initial_bound = sq_error_bound;
FT sq_dista = sq_error_bound;
if(!compare_meshes || (compare_meshes && tm1_only.size() > 0))
{
sq_dista = bounded_error_squared_Hausdorff_distance_impl<Kernel>(
tm1, tm2, vpm1, vpm2, tm1_tree, tm2_tree,
error_bound, sq_initial_bound, sq_distance_bound, infinity_value, out1);
}
// In case this is true, we need to rebuild trees in order to accelerate
// computations for the second call.
if(rebuild)
{
CGAL_assertion(compare_meshes);
tm1_tree.clear();
tm2_tree.clear();
CGAL_assertion(tm2_only.size() > 0);
CGAL_assertion(tm2_only.size() < faces(tm2).size());
tm1_tree.insert(faces(tm1).begin(), faces(tm1).end(), tm1, vpm1);
tm2_tree.insert(tm2_only.begin(), tm2_only.end(), tm2, vpm2);
}
// Compute the second one-sided distance.
sq_initial_bound = sq_dista; // @todo we should better test this optimization!
FT sq_distb = sq_error_bound;
if(!compare_meshes || (compare_meshes && tm2_only.size() > 0))
{
sq_distb = bounded_error_squared_Hausdorff_distance_impl<Kernel>(
tm2, tm1, vpm2, vpm1, tm2_tree, tm1_tree,
error_bound, sq_initial_bound, sq_distance_bound, infinity_value, out2);
}
return (CGAL::max)(sq_dista, sq_distb);
}
template<class Kernel, class TM2_tree>
typename Kernel::FT recursive_hausdorff_subdivision(const typename Kernel::Point_3& p0,
const typename Kernel::Point_3& p1,
const typename Kernel::Point_3& p2,
const TM2_tree& tm2_tree,
const typename Kernel::FT sq_error_bound)
{
using FT = typename Kernel::FT;
using Point_3 = typename Kernel::Point_3;
auto midpoint = Kernel().construct_midpoint_3_object();
auto squared_distance = Kernel().compute_squared_distance_3_object();
// If all edge lengths of the triangle are below the error bound,
// return the maximum of the distances of the three points to TM2 (via TM2_tree).
const FT max_squared_edge_length = (CGAL::max)((CGAL::max)(squared_distance(p0, p1),
squared_distance(p0, p2)),
squared_distance(p1, p2));
if(max_squared_edge_length < sq_error_bound)
{
return (CGAL::max)((CGAL::max)(squared_distance(p0, tm2_tree.closest_point(p0)),
squared_distance(p1, tm2_tree.closest_point(p1))),
squared_distance(p2, tm2_tree.closest_point(p2)));
}
// Else subdivide the triangle and proceed recursively.
const Point_3 p01 = midpoint(p0, p1);
const Point_3 p02 = midpoint(p0, p2);
const Point_3 p12 = midpoint(p1, p2);
return (CGAL::max)(
(CGAL::max)(recursive_hausdorff_subdivision<Kernel>( p0, p01, p02, tm2_tree, sq_error_bound),
recursive_hausdorff_subdivision<Kernel>( p1, p01, p12, tm2_tree, sq_error_bound)),
(CGAL::max)(recursive_hausdorff_subdivision<Kernel>( p2, p02, p12, tm2_tree, sq_error_bound),
recursive_hausdorff_subdivision<Kernel>(p01, p02, p12, tm2_tree, sq_error_bound)));
}
template <class Concurrency_tag,
class Kernel,
class TriangleMesh1,
class TriangleMesh2,
class VPM1,
class VPM2>
typename Kernel::FT
bounded_error_squared_Hausdorff_distance_naive_impl(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const typename Kernel::FT sq_error_bound,
const VPM1 vpm1,
const VPM2 vpm2)
{
using FT = typename Kernel::FT;
using Point_3 = typename Kernel::Point_3;
using Triangle_3 = typename Kernel::Triangle_3;
using TM2_primitive = AABB_face_graph_triangle_primitive<TriangleMesh2, VPM2>;
using TM2_traits = AABB_traits_3<Kernel, TM2_primitive>;
using TM2_tree = AABB_tree<TM2_traits>;
using TM1_face_to_triangle_map = Triangle_from_face_descriptor_map<TriangleMesh1, VPM1>;
FT sq_lower_bound = FT(0);
// Build an AABB tree on tm2.
TM2_tree tm2_tree(faces(tm2).begin(), faces(tm2).end(), tm2, vpm2);
tm2_tree.build();
tm2_tree.accelerate_distance_queries();
// Build a map to obtain actual triangles from the face descriptors of tm1.
const TM1_face_to_triangle_map face_to_triangle_map(&tm1, vpm1);
// Iterate over the faces of TM1.
for(const auto& face : faces(tm1))
{
// Get the vertices of the face and pass them on to a recursive method.
const Triangle_3 triangle = get(face_to_triangle_map, face);
const Point_3& v0 = triangle.vertex(0);
const Point_3& v1 = triangle.vertex(1);
const Point_3& v2 = triangle.vertex(2);
// Recursively process the current triangle to obtain a lower bound on its Hausdorff distance.
const FT sq_triangle_bound = recursive_hausdorff_subdivision<Kernel>(v0, v1, v2, tm2_tree, sq_error_bound);
// Store the largest lower bound.
if(sq_triangle_bound > sq_lower_bound)
sq_lower_bound = sq_triangle_bound;
}
return to_double(approximate_sqrt(sq_lower_bound));
}
} // namespace internal
/**
* \ingroup PMP_distance_grp
*
* returns an estimate on the Hausdorff distance from `tm1` to `tm2` that
* is at most `error_bound` away from the actual Hausdorff distance from `tm1` to `tm2`.
*
* @tparam Concurrency_tag enables sequential versus parallel algorithm.
* Possible values are `Sequential_tag` and `Parallel_tag`.
* Currently, the parallel version is not implemented and the
* sequential version is always used whatever tag is chosen!
*
* @tparam TriangleMesh1 a model of the concept `FaceListGraph`
* @tparam TriangleMesh2 a model of the concept `FaceListGraph`
*
* @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
*
* @param tm1 a triangle mesh
* @param tm2 another triangle mesh
*
* @param error_bound a maximum bound by which the Hausdorff distance estimate is
* allowed to deviate from the actual Hausdorff distance.
*
* @param np1 an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
* @param np2 an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{vertex_point_map}
* \cgalParamDescription{a property map associating points to the vertices of `tmX`}
* \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<TriangleMeshX>::%vertex_descriptor`
* as key type and `%Point_3` as value type}
* \cgalParamDefault{`boost::get(CGAL::vertex_point, tmX)`}
* \cgalParamExtra{If this parameter is omitted, an internal property map for `CGAL::vertex_point_t`
* must be available in `TriangleMeshX`.}
* \cgalParamNEnd
* \cgalParamNBegin{match_faces}
* \cgalParamDescription{a boolean tag that turns on the preprocessing step that filters out all faces
* which belong to both meshes and hence do not contribute to the final distance}
* \cgalParamType{Boolean}
* \cgalParamDefault{true}
* \cgalParamExtra{Both `np1` and `np2` must have this tag set to `true` in order to activate this preprocessing.}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* @pre `tm1` and `tm2` are non-empty triangle meshes.
*
* @return the one-sided Hausdorff distance
*/
template <class Concurrency_tag,
class TriangleMesh1,
class TriangleMesh2,
class NamedParameters1 = parameters::Default_named_parameters,
class NamedParameters2 = parameters::Default_named_parameters>
double bounded_error_Hausdorff_distance(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const double error_bound = 0.0001,
const NamedParameters1& np1 = parameters::default_values(),
const NamedParameters2& np2 = parameters::default_values())
{
using Traits = typename GetGeomTraits<TriangleMesh1, NamedParameters1>::type;
using FT = typename Traits::FT;
using parameters::choose_parameter;
using parameters::get_parameter;
CGAL_precondition(!is_empty(tm1) && is_triangle_mesh(tm1));
CGAL_precondition(!is_empty(tm2) && is_triangle_mesh(tm2));
const auto vpm1 = choose_parameter(get_parameter(np1, internal_np::vertex_point),
get_const_property_map(vertex_point, tm1));
const auto vpm2 = choose_parameter(get_parameter(np2, internal_np::vertex_point),
get_const_property_map(vertex_point, tm2));
const bool match_faces1 = choose_parameter(get_parameter(np1, internal_np::match_faces), true);
const bool match_faces2 = choose_parameter(get_parameter(np2, internal_np::match_faces), true);
const bool match_faces = match_faces1 && match_faces2;
auto out = choose_parameter(get_parameter(np1, internal_np::output_iterator),
CGAL::Emptyset_iterator());
CGAL_precondition(error_bound >= 0.);
const FT sq_hdist = internal::bounded_error_squared_one_sided_Hausdorff_distance_impl<Concurrency_tag, Traits>(
tm1, tm2, error_bound, FT(-1) /*distance threshold*/, match_faces, vpm1, vpm2, np1, np2, out);
return to_double(approximate_sqrt(sq_hdist));
}
/**
* \ingroup PMP_distance_grp
*
* returns the the symmetric Hausdorff distance, that is
* the maximum of `bounded_error_Hausdorff_distance(tm1, tm2, error_bound, np1, np2)`
* and `bounded_error_Hausdorff_distance(tm2, tm1, error_bound, np2, np1)`.
*
* This function optimizes all internal calls to shared data structures in order to
* speed up the computation.
*
* See the function `CGAL::Polygon_mesh_processing::bounded_error_Hausdorff_distance()`
* for a complete description of the parameters and requirements.
*/
template <class Concurrency_tag,
class TriangleMesh1,
class TriangleMesh2,
class NamedParameters1 = parameters::Default_named_parameters,
class NamedParameters2 = parameters::Default_named_parameters>
double bounded_error_symmetric_Hausdorff_distance(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const double error_bound,
const NamedParameters1& np1 = parameters::default_values(),
const NamedParameters2& np2 = parameters::default_values())
{
using Traits = typename GetGeomTraits<TriangleMesh1, NamedParameters1>::type;
using FT = typename Traits::FT;
using parameters::choose_parameter;
using parameters::get_parameter;
CGAL_precondition(!is_empty(tm1) && is_triangle_mesh(tm1));
CGAL_precondition(!is_empty(tm2) && is_triangle_mesh(tm2));
const auto vpm1 = choose_parameter(get_parameter(np1, internal_np::vertex_point),
get_const_property_map(vertex_point, tm1));
const auto vpm2 = choose_parameter(get_parameter(np2, internal_np::vertex_point),
get_const_property_map(vertex_point, tm2));
const bool match_faces1 = choose_parameter(get_parameter(np1, internal_np::match_faces), true);
const bool match_faces2 = choose_parameter(get_parameter(np2, internal_np::match_faces), true);
const bool match_faces = match_faces1 && match_faces2;
// TODO: should we return a union of these realizing triangles?
auto out1 = choose_parameter(get_parameter(np1, internal_np::output_iterator),
CGAL::Emptyset_iterator());
auto out2 = choose_parameter(get_parameter(np2, internal_np::output_iterator),
CGAL::Emptyset_iterator());
CGAL_precondition(error_bound >= 0.);
const FT sq_hdist = internal::bounded_error_squared_symmetric_Hausdorff_distance_impl<Concurrency_tag, Traits>(
tm1, tm2, error_bound, FT(-1) /*distance_threshold*/, match_faces, vpm1, vpm2, np1, np2, out1, out2);
return to_double(approximate_sqrt(sq_hdist));
}
/**
* \ingroup PMP_distance_grp
*
* \brief returns `true` if the Hausdorff distance between two meshes is larger than
* the user-defined max distance, otherwise it returns `false`.
*
* The distance used to compute the proximity of the meshes is the bounded-error Hausdorff distance.
* Instead of computing the full distance and checking it against the user-provided
* value, this function returns early if certain criteria show that the meshes
* do not satisfy the provided `distance_bound`.
*
* See the function `CGAL::Polygon_mesh_processing::bounded_error_Hausdorff_distance()`
* for a complete description of the parameters and requirements. The following extra named parameter
* is available for `np1`:
*
* \cgalNamedParamsBegin
* \cgalParamNBegin{use_one_sided_hausdorff}
* \cgalParamDescription{a boolean tag indicating if the one-sided Hausdorff distance should be used.}
* \cgalParamType{Boolean}
* \cgalParamDefault{`true`}
* \cgalParamExtra{If this tag is set to `false`, the symmetric Hausdorff distance is used.}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*/
template< class Concurrency_tag,
class TriangleMesh1,
class TriangleMesh2,
class NamedParameters1 = parameters::Default_named_parameters,
class NamedParameters2 = parameters::Default_named_parameters>
bool is_Hausdorff_distance_larger(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const double distance_bound,
const double error_bound,
const NamedParameters1& np1 = parameters::default_values(),
const NamedParameters2& np2 = parameters::default_values())
{
using Traits = typename GetGeomTraits<TriangleMesh1, NamedParameters1>::type;
using FT = typename Traits::FT;
using parameters::choose_parameter;
using parameters::get_parameter;
CGAL_precondition(!is_empty(tm1) && is_triangle_mesh(tm1));
CGAL_precondition(!is_empty(tm2) && is_triangle_mesh(tm2));
if(distance_bound <= 0.)
return true;
const auto vpm1 = choose_parameter(get_parameter(np1, internal_np::vertex_point),
get_const_property_map(vertex_point, tm1));
const auto vpm2 = choose_parameter(get_parameter(np2, internal_np::vertex_point),
get_const_property_map(vertex_point, tm2));
const bool match_faces1 = choose_parameter(get_parameter(np1, internal_np::match_faces), true);
const bool match_faces2 = choose_parameter(get_parameter(np2, internal_np::match_faces), true);
const bool match_faces = match_faces1 && match_faces2;
const bool use_one_sided = choose_parameter(get_parameter(np1, internal_np::use_one_sided_hausdorff), true);
CGAL_precondition(error_bound >= 0.);
CGAL_precondition(distance_bound > 0.);
const FT sq_distance_bound = square(FT(distance_bound));
auto stub = CGAL::Emptyset_iterator();
FT sq_hdist = FT(-1);
if(use_one_sided)
{
sq_hdist = internal::bounded_error_squared_one_sided_Hausdorff_distance_impl<Concurrency_tag, Traits>(
tm1, tm2, error_bound, sq_distance_bound, match_faces, vpm1, vpm2, np1, np2, stub);
}
else
{
sq_hdist = internal::bounded_error_squared_symmetric_Hausdorff_distance_impl<Concurrency_tag, Traits>(
tm1, tm2, error_bound, sq_distance_bound, match_faces, vpm1, vpm2, np1, np2, stub, stub);
}
#ifdef CGAL_HAUSDORFF_DEBUG
std::cout.precision(17);
std::cout << "- fin distance: " << approximate_sqrt(sq_hdist) << std::endl;
std::cout << "- max distance: " << distance_bound << std::endl;
#endif
return (sq_hdist > sq_distance_bound);
}
// Implementation of the naive Bounded Error Hausdorff distance.
template <class Concurrency_tag,
class TriangleMesh1,
class TriangleMesh2,
class NamedParameters1 = parameters::Default_named_parameters,
class NamedParameters2 = parameters::Default_named_parameters>
double bounded_error_Hausdorff_distance_naive(const TriangleMesh1& tm1,
const TriangleMesh2& tm2,
const double error_bound,
const NamedParameters1& np1 = parameters::default_values(),
const NamedParameters2& np2 = parameters::default_values())
{
using Traits = typename GetGeomTraits<TriangleMesh1, NamedParameters1>::type;
using FT = typename Traits::FT;
using parameters::choose_parameter;
using parameters::get_parameter;
CGAL_precondition(!is_empty(tm1) && is_triangle_mesh(tm1));
CGAL_precondition(!is_empty(tm2) && is_triangle_mesh(tm2));
const auto vpm1 = choose_parameter(get_parameter(np1, internal_np::vertex_point),
get_const_property_map(vertex_point, tm1));
const auto vpm2 = choose_parameter(get_parameter(np2, internal_np::vertex_point),
get_const_property_map(vertex_point, tm2));
CGAL_precondition(error_bound >= 0.);
const FT sq_hdist = internal::bounded_error_squared_Hausdorff_distance_naive_impl<Concurrency_tag, Traits>(
tm1, tm2, error_bound, vpm1, vpm2);
return to_double(approximate_sqrt(sq_hdist));
}
} // namespace Polygon_mesh_processing
} // namespace CGAL
#endif //CGAL_POLYGON_MESH_PROCESSING_DISTANCE_H
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