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Update CGAL to 5.1
2020-10-13 12:44:25 +00:00
// Copyright (c) 2017-2018 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Surface_mesh_approximation/include/CGAL/Variational_shape_approximation.h $
// $Id: Variational_shape_approximation.h 038869c 2020-05-12T15:12:21+02:00 Mael Rouxel-Labbé
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Pierre Alliez and Lingjie Zhu
#ifndef CGAL_VARIATIONAL_SHAPE_APPROXIMATION_H
#define CGAL_VARIATIONAL_SHAPE_APPROXIMATION_H
#include <CGAL/license/Surface_mesh_approximation.h>
#include <CGAL/boost/graph/helpers.h>
#include <CGAL/Kernel/global_functions.h>
#include <CGAL/squared_distance_3.h>
#include <CGAL/linear_least_squares_fitting_3.h>
#include <CGAL/array.h>
#include <CGAL/Surface_mesh_approximation/L21_metric_plane_proxy.h>
#include <CGAL/Default.h>
#include <CGAL/tags.h>
#include <CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <boost/graph/subgraph.hpp>
#include <boost/optional.hpp>
#include <CGAL/boost/graph/Named_function_parameters.h>
#include <CGAL/boost/graph/named_params_helper.h>
#include <vector>
#include <stack>
#include <queue>
#include <iterator>
#include <cmath>
#include <cstdlib>
#ifdef CGAL_LINKED_WITH_TBB
#include <tbb/parallel_for.h>
#include <tbb/blocked_range.h>
#endif // CGAL_LINKED_WITH_TBB
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
#include <iostream>
#endif
#define CGAL_VSA_INVALID_TAG (std::numeric_limits<std::size_t>::max)()
namespace CGAL {
namespace Surface_mesh_approximation {
/// \ingroup PkgTSMARef
/// @brief Seeding method enumeration for Variational Shape Approximation algorithm.
enum Seeding_method {
/// Random seeding
RANDOM,
/// Incremental seeding
INCREMENTAL,
/// Hierarchical seeding
HIERARCHICAL
};
} // namespace Surface_mesh_approximation
/// \ingroup PkgTSMARef
/// @brief Main class for Variational Shape Approximation algorithm.
/// It is based on \cgalCite{cgal:cad-vsa-04}. For simple use cases, the function `CGAL::Surface_mesh_approximation::approximate_mesh()` might be sufficient.
/// @tparam TriangleMesh a model of `FaceListGraph`
/// @tparam VertexPointMap a `ReadablePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor` as key and `GeomTraits::Point_3` as value type
/// @tparam ErrorMetricProxy a model of `ErrorMetricProxy`
/// @tparam GeomTraits a model of Kernel
/// @tparam Concurrency_tag concurrency tag.
template <typename TriangleMesh,
typename VertexPointMap,
typename ErrorMetricProxy = CGAL::Default,
typename GeomTraits = CGAL::Default,
typename Concurrency_tag = CGAL::Sequential_tag>
class Variational_shape_approximation {
// public typedefs
public:
/// \name Types
/// @{
#ifndef DOXYGEN_RUNNING
// GeomTraits type
typedef typename CGAL::Default::Get<
GeomTraits,
typename Kernel_traits<
typename boost::property_traits<VertexPointMap>::value_type
>::Kernel >::type Geom_traits;
#else
/// Geometric traits type
typedef GeomTraits Geom_traits;
#endif
// ErrorMetricProxy type
#ifndef DOXYGEN_RUNNING
typedef typename CGAL::Default::Get<ErrorMetricProxy,
Surface_mesh_approximation::L21_metric_plane_proxy<TriangleMesh, VertexPointMap, Geom_traits> >::type Error_metric;
#else
/// Error metric for proxy fitting type
typedef ErrorMetricProxy Error_metric;
#endif
/// Proxy type
typedef typename Error_metric::Proxy Proxy;
/// Indexed triangle type
typedef std::array<std::size_t, 3> Indexed_triangle;
/// @}
// private typedefs and data member
private:
// Geom_traits typedefs
typedef typename Geom_traits::FT FT;
typedef typename Geom_traits::Point_3 Point_3;
typedef typename Geom_traits::Vector_3 Vector_3;
typedef typename Geom_traits::Plane_3 Plane_3;
typedef typename Geom_traits::Construct_vector_3 Construct_vector_3;
typedef typename Geom_traits::Construct_point_3 Construct_point_3;
typedef typename Geom_traits::Construct_scaled_vector_3 Construct_scaled_vector_3;
typedef typename Geom_traits::Construct_sum_of_vectors_3 Construct_sum_of_vectors_3;
typedef typename Geom_traits::Construct_translated_point_3 Construct_translated_point_3;
typedef typename Geom_traits::Construct_cross_product_vector_3 Construct_cross_product_vector_3;
typedef typename Geom_traits::Collinear_3 Collinear_3;
// graph_traits typedefs
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;
// internal typedefs
typedef CGAL::dynamic_vertex_property_t<std::size_t> Vertex_anchor_tag;
typedef typename boost::property_map<TriangleMesh, Vertex_anchor_tag>::type Vertex_anchor_map;
typedef CGAL::dynamic_face_property_t<std::size_t> Face_proxy_tag;
typedef typename boost::property_map<TriangleMesh, Face_proxy_tag>::type Face_proxy_map;
typedef std::vector<halfedge_descriptor> Boundary_chord;
typedef typename Boundary_chord::iterator Boundary_chord_iterator;
/// \cond SKIP_IN_MANUAL
public:
// The proxy wrapper for approximation.
struct Proxy_wrapper {
Proxy_wrapper(const Proxy &p, const std::size_t &i, const face_descriptor s, const FT &e)
: px(p), idx(i), seed(s), err(e) {}
Proxy px; // parameterized proxy
std::size_t idx; // proxy index, maintained to be the same as its position in proxies vector
face_descriptor seed; // proxy seed
FT err; // proxy fitting error
};
/// \endcond
private:
// The proxy fitting plane for meshing.
struct Proxy_plane {
Proxy_plane(const Plane_3 &p, const Vector_3 &n, const FT &a)
: plane(p), normal(n), area(a) {}
Plane_3 plane;
Vector_3 normal;
FT area;
};
// The face candidate to be queued.
struct Face_to_integrate {
Face_to_integrate(const face_descriptor f_, const std::size_t &px_, const FT &err_)
: f(f_), px(px_), err(err_) {}
bool operator<(const Face_to_integrate &rhs) const {
return err > rhs.err;
}
face_descriptor f; // face
std::size_t px; // proxy index
FT err; // fitting error
};
// Proxy error with its index.
struct Proxy_error {
Proxy_error(const std::size_t &px_, const FT &err_)
: px(px_), err(err_) {}
// in ascending order
bool operator<(const Proxy_error &rhs) const {
return err < rhs.err;
}
std::size_t px;
FT err;
};
// The anchor attached to a vertex.
struct Anchor {
Anchor(const vertex_descriptor vtx_, const Point_3 pos_)
: vtx(vtx_), pos(pos_) {}
vertex_descriptor vtx; // The associated vertex.
Point_3 pos; // The position of the anchor.
};
// The boundary cycle of a region.
// One region may have multiple boundary cycles.
struct Boundary_cycle {
Boundary_cycle(const halfedge_descriptor h)
: he_head(h), num_anchors(0) {}
halfedge_descriptor he_head; // Heading halfedge of the boundary cycle.
std::size_t num_anchors; // Number of anchors on the boundary cycle.
};
// member variables
// The triangle mesh.
const TriangleMesh *m_ptm;
// The exact number of faces
const std::size_t m_nb_of_faces;
// The mesh vertex point map.
VertexPointMap m_vpoint_map;
// The approximation object.
const Error_metric *m_metric;
Construct_vector_3 vector_functor;
Construct_scaled_vector_3 scale_functor;
Construct_sum_of_vectors_3 sum_functor;
Construct_translated_point_3 translate_point_functor;
Construct_cross_product_vector_3 cross_product_functor;
Collinear_3 collinear_functor;
// Proxies.
std::vector<Proxy_wrapper> m_proxies;
// Proxy planes
std::vector<Proxy_plane> m_px_planes;
// All anchors.
std::vector<Anchor> m_anchors;
// All boundary cycles.
std::vector<Boundary_cycle> m_bcycles;
// The indexed triangle approximation.
std::vector<Indexed_triangle> m_tris;
// meshing parameters
FT m_average_edge_length;
// The face proxy index map.
Face_proxy_map m_fproxy_map;
// The attached anchor index of a vertex.
Vertex_anchor_map m_vanchor_map;
//member functions
public:
/// \name Construction
/// @{
/*!
* @brief initializes internal data for the approximation.
* @param tm `CGAL TriangleMesh` on which approximation operates
* @param vpoint_map vertex point map of the mesh
* @param error_metric an `ErrorMetricProxy` object
*/
Variational_shape_approximation(const TriangleMesh &tm,
const VertexPointMap &vpoint_map,
const Error_metric &error_metric) :
m_ptm(&tm),
m_nb_of_faces(std::distance(faces(tm).first, faces(tm).second)),
m_vpoint_map(vpoint_map),
m_metric(&error_metric),
m_average_edge_length(0.0),
m_fproxy_map( get(Face_proxy_tag(), *(const_cast<TriangleMesh *>(m_ptm))) ),
m_vanchor_map( get( Vertex_anchor_tag(), *(const_cast<TriangleMesh *>(m_ptm))) )
{
Geom_traits traits;
vector_functor = traits.construct_vector_3_object();
scale_functor = traits.construct_scaled_vector_3_object();
sum_functor = traits.construct_sum_of_vectors_3_object();
translate_point_functor = traits.construct_translated_point_3_object();
cross_product_functor = traits.construct_cross_product_vector_3_object();
collinear_functor = traits.collinear_3_object();
}
/// @}
/// \name Approximation
/// @{
/*!
* @brief initializes the seeds with both maximum number of proxies and minimum error drop stop criteria.
* The first criterion met stops the seeding.
* Parameters out of range are ignored.
* @tparam NamedParameters a sequence of \ref bgl_namedparameters
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
* @return number of proxies initialized
* \cgalNamedParamsBegin{Seeding Named Parameters}
* \cgalParamNBegin{seeding_method}
* \cgalParamDescription{the selection of seeding method}
* \cgalParamType{`CGAL::Surface_mesh_approximation::Seeding_method`}
* \cgalParamDefault{`CGAL::Surface_mesh_approximation::HIERARCHICAL`}
* \cgalParamNEnd
*
* \cgalParamNBegin{max_number_of_proxies}
* \cgalParamDescription{the maximum number of proxies used to approximate the input mesh}
* \cgalParamType{`std::size_t`}
* \cgalParamDefault{`num_faces(tm) / 3`, used when `min_error_drop` is also not provided}
* \cgalParamNEnd
*
* \cgalParamNBegin{min_error_drop}
* \cgalParamDescription{the minimum error drop of the approximation, expressed as
* the ratio between two iterations of proxy addition}
* \cgalParamType{`geom_traits::FT`}
* \cgalParamDefault{`0.1`, used when `max_number_of_proxies` is also not provided}
* \cgalParamNEnd
*
* \cgalParamNBegin{number_of_relaxations}
* \cgalParamDescription{the number of relaxation iterations interleaved within seeding}
* \cgalParamType{`std::size_t`}
* \cgalParamDefault{`5`}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*/
template <typename NamedParameters>
std::size_t initialize_seeds(const NamedParameters &np) {
using parameters::get_parameter;
using parameters::choose_parameter;
const Surface_mesh_approximation::Seeding_method method = choose_parameter(
get_parameter(np, internal_np::seeding_method), Surface_mesh_approximation::HIERARCHICAL);
std::size_t max_nb_proxies = choose_parameter(
get_parameter(np, internal_np::max_number_of_proxies), 0);
FT min_error_drop = choose_parameter(
get_parameter(np, internal_np::min_error_drop), FT(0.0));
const std::size_t nb_relaxations = choose_parameter(
get_parameter(np, internal_np::number_of_relaxations), 5);
// adjust parameters
if (max_nb_proxies < (m_nb_of_faces / 3) && max_nb_proxies > 0) {
if(!(min_error_drop < FT(1.0)) || !(min_error_drop > FT(0.0)))
min_error_drop = FT(-1.0);
}
else {
max_nb_proxies = m_nb_of_faces / 3;
if (!(min_error_drop < FT(1.0)) || !(min_error_drop > FT(0.0)))
min_error_drop = FT(0.1);
}
// initialize proxies and the proxy map to prepare for insertion
bootstrap_from_connected_components();
if (max_nb_proxies <= m_proxies.size())
return m_proxies.size();
switch (method) {
case Surface_mesh_approximation::RANDOM:
return init_random(max_nb_proxies, min_error_drop, nb_relaxations);
case Surface_mesh_approximation::INCREMENTAL:
return init_incremental(max_nb_proxies, min_error_drop, nb_relaxations);
case Surface_mesh_approximation::HIERARCHICAL:
return init_hierarchical(max_nb_proxies, min_error_drop, nb_relaxations);
default:
return 0;
}
}
/*!
* @brief runs the partitioning and fitting processes on the whole surface.
* @param nb_iterations number of iterations.
* @return total fitting error
*/
FT run(std::size_t nb_iterations = 1) {
for (std::size_t i = 0; i < nb_iterations; ++i) {
// tag the whole surface
for(face_descriptor f : faces(*m_ptm))
put(m_fproxy_map, f, CGAL_VSA_INVALID_TAG);
partition(m_proxies.begin(), m_proxies.end());
fit(m_proxies.begin(), m_proxies.end(), Concurrency_tag());
}
return compute_total_error();
}
/*!
* @brief calls `run` while error decrease is greater than `cvg_threshold`.
* @param cvg_threshold the percentage of error change between two successive runs,
* should be in range `(0, 1)`.
* @param max_iterations maximum number of iterations allowed
* @param avg_interval size of error average interval to have smoother convergence curve,
* if 0 is assigned, 1 is used instead.
* @return `true` if converged before hitting the maximum iterations.
*/
bool run_to_convergence(const FT cvg_threshold,
const std::size_t max_iterations = 100,
std::size_t avg_interval = 3) {
if (avg_interval == 0)
avg_interval = 1;
FT drop_pct(0.0);
FT pre_err = compute_total_error();
for (std::size_t itr_count = 0; itr_count < max_iterations; itr_count += avg_interval) {
if (pre_err == FT(0.0))
return true;
FT avg_err(0.0);
for (std::size_t i = 0; i < avg_interval; ++i)
avg_err += run();
avg_err /= static_cast<FT>(avg_interval);
drop_pct = (pre_err - avg_err) / pre_err;
// the error may fluctuate
if (drop_pct < FT(0.0))
drop_pct = -drop_pct;
if (drop_pct < cvg_threshold)
return true;
pre_err = avg_err;
}
return false;
}
/*!
* @brief computes fitting error of current partition to the proxies.
* @return total fitting error
*/
FT compute_total_error() {
FT sum_error(0.0);
for(const Proxy_wrapper& pxw : m_proxies)
sum_error += pxw.err;
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
static std::size_t count = 0;
std::cerr << '#' << count++ << ": " << sum_error << std::endl;
#endif
return sum_error;
}
/*!
* @brief adds proxies to the worst regions one by one.
* The re-fitting is performed after each proxy is inserted.
* @param nb_proxies number of proxies to be added
* @param nb_iterations number of re-fitting iterations
* @return number of proxies added
*/
std::size_t add_to_furthest_proxies(const std::size_t nb_proxies,
const std::size_t nb_iterations = 5) {
std::size_t num_added = 0;
while (num_added < nb_proxies) {
if (!add_to_furthest_proxy())
break;
++num_added;
run(nb_iterations);
}
return num_added;
}
/*!
* @brief adds proxies by diffusing fitting error into current partition.
* Each partition is added with the number of proxies in proportion to its fitting error.
* @param nb_proxies number of proxies to be added
* @return number of proxies successfully added
*/
std::size_t add_proxies_error_diffusion(const std::size_t nb_proxies) {
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#px " << m_proxies.size() << std::endl;
#endif
const double sum_error = CGAL::to_double(compute_total_error());
const double avg_error = sum_error / static_cast<double>(nb_proxies);
// number of proxies to be added to each region
std::vector<std::size_t> num_to_add(m_proxies.size(), 0);
if (avg_error <= 0.0) {
// rare case on extremely regular geometry like a cube
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "zero error, diffuse w.r.t. number of faces" << std::endl;
#endif
const double avg_face =
static_cast<double>(m_nb_of_faces) / static_cast<double>(nb_proxies);
std::vector<double> px_size(m_proxies.size(), 0.0);
for(face_descriptor f : faces(*m_ptm))
px_size[get(m_fproxy_map, f)] += 1.0;
double residual = 0.0;
for (std::size_t i = 0; i < m_proxies.size(); ++i) {
const double to_add = (residual + px_size[i]) / avg_face;
const double to_add_round_up = std::floor(to_add + 0.5);
residual = (to_add - to_add_round_up) * avg_face;
num_to_add[i] = static_cast<std::size_t>(to_add_round_up);
}
}
else {
std::vector<Proxy_error> px_error;
for (std::size_t i = 0; i < m_proxies.size(); ++i)
px_error.push_back(Proxy_error(i, m_proxies[i].err));
// sort partition by error
std::sort(px_error.begin(), px_error.end());
// residual from previous proxy in range (-0.5, 0.5] * avg_error
double residual = 0.0;
for (std::size_t i = 0; i < m_proxies.size(); ++i) {
// add error residual from previous proxy
// to_add maybe negative but greater than -0.5
const double to_add = (residual + CGAL::to_double(px_error[i].err)) / avg_error;
const double to_add_round_up = std::floor(to_add + 0.5);
residual = (to_add - to_add_round_up) * avg_error;
num_to_add[px_error[i].px] = static_cast<std::size_t>(to_add_round_up);
}
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
for (std::size_t i = 0; i < px_error.size(); ++i)
std::cerr << "#px " << px_error[i].px
<< ", #error " << px_error[i].err
<< ", #num_to_add " << num_to_add[px_error[i].px] << std::endl;
#endif
}
std::size_t num_added = 0;
for(face_descriptor f : faces(*m_ptm)) {
const std::size_t px_id = get(m_fproxy_map, f);
if (m_proxies[px_id].seed == f)
continue;
if (num_to_add[px_id] > 0) {
add_one_proxy_at(f);
--num_to_add[px_id];
++num_added;
}
}
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#requested/added "
<< nb_proxies << '/' << num_added << std::endl;
#endif
return num_added;
}
/// @}
/// \name Refinement Operations
/// @{
/*!
* @brief teleports the local minimum to the worst region by combining the merging and adding processes.
* The re-fitting is performed after each teleportation.
* Here if we specify more than one proxy this means we teleport in a naive iterative fashion.
* @param nb_proxies number of proxies requested to teleport.
* @param nb_iterations number of re-fitting iterations.
* @param no_threshold_test if `true`, no check on the approximation error before merging a pair of proxies is done. In other words, `find_best_merge(!no_threshold_test)` is called.
* @return number of proxies teleported.
*/
std::size_t teleport_proxies(const std::size_t nb_proxies,
const std::size_t nb_iterations = 5,
const bool no_threshold_test = false) {
std::size_t num_teleported = 0;
while (num_teleported < nb_proxies) {
// find worst proxy
std::size_t px_worst = 0;
FT max_error = m_proxies.front().err;
for (std::size_t i = 0; i < m_proxies.size(); ++i) {
if (max_error < m_proxies[i].err) {
max_error = m_proxies[i].err;
px_worst = i;
}
}
bool found = false;
face_descriptor tele_to;
for(face_descriptor f : faces(*m_ptm)) {
if (get(m_fproxy_map, f) == px_worst && f != m_proxies[px_worst].seed) {
// teleport to anywhere but the seed
tele_to = f;
found = true;
break;
}
}
if (!found)
return num_teleported;
// find the best merge pair
boost::optional< std::pair<std::size_t, std::size_t> > best_proxies =
find_best_merge(!no_threshold_test);
if (best_proxies==boost::none)
return num_teleported;
if (px_worst == best_proxies->first || px_worst == best_proxies->second)
return num_teleported;
// teleport to a face of the worst region
// update merged proxies
std::list<face_descriptor> merged_patch;
for(face_descriptor f : faces(*m_ptm)) {
std::size_t px_idx = get(m_fproxy_map, f);
if (px_idx == best_proxies->first || px_idx == best_proxies->second) {
put(m_fproxy_map, f, best_proxies->first);
merged_patch.push_back(f);
}
}
m_proxies[best_proxies->first] = fit_proxy_from_patch(merged_patch, best_proxies->first);
// replace the merged proxy position to the newly teleported proxy
m_proxies[best_proxies->second] = fit_proxy_from_face(tele_to, best_proxies->second);
num_teleported++;
// coarse re-fitting
run(nb_iterations);
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "teleported" << std::endl;
#endif
}
return num_teleported;
}
/*!
* @brief merges two specified adjacent regions.
* The overall re-fitting is not performed and the proxy index map is maintained.
* @pre two proxies must be adjacent, and 0 <= px0 < px1 < proxies.size()
* @param px0 the kept proxy index
* @param px1 the merged and erased proxy index,
* proxies with greater indeies are decreased by 1 to fill the gap
* @return change of error
*/
FT merge(const std::size_t px0, const std::size_t px1) {
// ensure px0 < px1
if (px0 >= px1 || px1 >= m_proxies.size())
return FT(0.0);
const FT pre_err = m_proxies[px0].err + m_proxies[px1].err;
// merge px1 to px0
std::list<face_descriptor> merged_patch;
for(face_descriptor f : faces(*m_ptm)) {
std::size_t px_idx = get(m_fproxy_map, f);
if (px_idx == px1 || px_idx == px0) {
put(m_fproxy_map, f, px0);
merged_patch.push_back(f);
}
}
m_proxies[px0] = fit_proxy_from_patch(merged_patch, px0);
// erase px1 and maintain proxy index
m_proxies.erase(m_proxies.begin() + px1);
for (std::size_t i = 0; i < m_proxies.size(); ++i)
m_proxies[i].idx = i;
// keep face proxy map valid
for(face_descriptor f : faces(*m_ptm)) {
if (get(m_fproxy_map, f) > px1)
put(m_fproxy_map, f, get(m_fproxy_map, f) - 1);
}
return m_proxies[px0].err - pre_err;
}
/*!
* @brief simulates merging and local re-fitting of all pairs of adjacent proxies
* and finds the best pair to merge.
* @note The <b>best</b> is defined as the minimum merged sum error
* <b>change</b> (increase or decrease) among all pairs.
* @param use_threshold_test if `true` and a best pair of proxies is found,
* it is returned only if the error change after the merge is lower than the half of the maximum proxy error.
* @return if the best merge pair is found the optional returned contains the proxy indices, and is empty otherwise.
*/
boost::optional< std::pair<std::size_t, std::size_t> >
find_best_merge(const bool use_threshold_test) {
typedef std::pair<std::size_t, std::size_t> Proxy_pair;
typedef std::set<Proxy_pair> Pair_set;
std::size_t px0 = 0, px1 = 0;
std::vector<std::list<face_descriptor> > px_faces(m_proxies.size());
for(face_descriptor f : faces(*m_ptm))
px_faces[get(m_fproxy_map, f)].push_back(f);
// find best merge
Pair_set merged_set;
FT min_error_change = FT(0.0);
bool first_merge = true;
for(edge_descriptor e : edges(*m_ptm)) {
if (CGAL::is_border(e, *m_ptm))
continue;
std::size_t pxi = get(m_fproxy_map, face(halfedge(e, *m_ptm), *m_ptm));
std::size_t pxj = get(m_fproxy_map, face(opposite(halfedge(e, *m_ptm), *m_ptm), *m_ptm));
if (pxi == pxj)
continue;
if (pxi > pxj)
std::swap(pxi, pxj);
if (merged_set.find(Proxy_pair(pxi, pxj)) != merged_set.end())
continue;
merged_set.insert(Proxy_pair(pxi, pxj));
// simulated merge
std::list<face_descriptor> merged_patch(px_faces[pxi]);
for(face_descriptor f : px_faces[pxj])
merged_patch.push_back(f);
const Proxy_wrapper pxw_tmp = fit_proxy_from_patch(merged_patch, CGAL_VSA_INVALID_TAG);
const FT error_change = pxw_tmp.err - (m_proxies[pxi].err + m_proxies[pxj].err);
if (first_merge || error_change < min_error_change) {
first_merge = false;
min_error_change = error_change;
px0 = pxi;
px1 = pxj;
}
}
if (merged_set.empty())
return boost::none;
// test if merge worth it
if (use_threshold_test) {
FT max_error = m_proxies.front().err;
for (std::size_t i = 0; i < m_proxies.size(); ++i) {
if (max_error < m_proxies[i].err)
max_error = m_proxies[i].err;
}
if (min_error_change > max_error / FT(2.0))
return boost::none;
}
return std::make_pair(px0, px1);
}
/*!
* @brief splits within a specified proxy area via N-section (by default bisection),
* other regions are not affected.
* @param px_idx proxy index.
* @param n number of split sections.
* @param nb_relaxations number of relaxations within the proxy area <em>px_idx</em> after the split
* @return `true` if split succeeds, and `false` otherwise.
*/
bool split(const std::size_t px_idx,
const std::size_t n = 2,
const std::size_t nb_relaxations = 10) {
if (px_idx >= m_proxies.size())
return false;
// collect confined proxy area
std::list<face_descriptor> confined_area;
for(face_descriptor f : faces(*m_ptm))
if (get(m_fproxy_map, f) == px_idx)
confined_area.push_back(f);
// not enough faces to split
if (n > confined_area.size())
return false;
// a copy of confined proxies
std::vector<Proxy_wrapper> confined_proxies;
confined_proxies.push_back(m_proxies[px_idx]);
// select seed faces in the confined area
std::size_t count = 1;
for(face_descriptor f : confined_area) {
if (count >= n)
break;
if (f != m_proxies[px_idx].seed) {
add_one_proxy_at(f);
++count;
// copy
confined_proxies.push_back(m_proxies.back());
}
}
// relaxation on confined area and proxies
for (std::size_t i = 0; i < nb_relaxations; ++i) {
for(face_descriptor f : confined_area)
put(m_fproxy_map, f, CGAL_VSA_INVALID_TAG);
partition(confined_proxies.begin(), confined_proxies.end());
fit(confined_proxies.begin(), confined_proxies.end(), Concurrency_tag());
}
// copy back
for(const Proxy_wrapper& pxw : confined_proxies)
m_proxies[pxw.idx] = pxw;
return true;
}
/// @}
/// \name Meshing
/// @{
/*!
* @brief extracts the output mesh in the form of an indexed triangle set.
* @tparam NamedParameters a sequence of \ref bgl_namedparameters
*
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
* @return `true` if the extracted surface mesh is manifold, and `false` otherwise.
*
* \cgalNamedParamsBegin{Meshing Named Parameters}
* \cgalParamNBegin{subdivision_ratio}
* \cgalParamDescription{the chord subdivision ratio threshold to the chord length or average edge length}
* \cgalParamType{`geom_traits::FT`}
* \cgalParamDefault{`5.0`}
* \cgalParamNEnd
*
* \cgalParamNBegin{relative_to_chord}
* \cgalParamDescription{If `true`, the `subdivision_ratio` is the ratio of the furthest vertex distance
* to the chord length, otherwise is the average edge length}
* \cgalParamType{`Boolean`}
* \cgalParamDefault{`false`}
* \cgalParamNEnd
*
* \cgalParamNBegin{with_dihedral_angle}
* \cgalParamDescription{If `true`, the `subdivision_ratio` is weighted by dihedral angle}
* \cgalParamType{`Boolean`}
* \cgalParamDefault{`false`}
* \cgalParamNEnd
*
* \cgalParamNBegin{optimize_anchor_location}
* \cgalParamDescription{If `true`, optimize the anchor locations}
* \cgalParamType{`Boolean`}
* \cgalParamDefault{`true`}
* \cgalParamNEnd
*
* \cgalParamNBegin{pca_plane}
* \cgalParamDescription{If `true`, use PCA plane fitting, otherwise use the default area averaged plane parameters}
* \cgalParamType{`Boolean`}
* \cgalParamDefault{`false`}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*/
template <typename NamedParameters>
bool extract_mesh(const NamedParameters &np) {
using parameters::get_parameter;
using parameters::choose_parameter;
const FT subdivision_ratio = choose_parameter(get_parameter(np, internal_np::subdivision_ratio), FT(5.0));
const bool relative_to_chord = choose_parameter(get_parameter(np, internal_np::relative_to_chord), false);
const bool with_dihedral_angle = choose_parameter(get_parameter(np, internal_np::with_dihedral_angle), false);
const bool optimize_anchor_location = choose_parameter(get_parameter(np, internal_np::optimize_anchor_location), true);
const bool pca_plane = choose_parameter(get_parameter(np, internal_np::pca_plane), false);
// compute averaged edge length, used in chord subdivision
m_average_edge_length = compute_averaged_edge_length(*m_ptm, m_vpoint_map);
// initialize all vertex anchor status
for(vertex_descriptor v : vertices(*m_ptm))
put(m_vanchor_map, v, CGAL_VSA_INVALID_TAG);
m_anchors.clear();
m_bcycles.clear();
m_tris.clear();
m_px_planes.clear();
// compute proxy planes, used for subdivision and anchor location
compute_proxy_planes(pca_plane);
// generate anchors
find_anchors();
find_edges(subdivision_ratio, relative_to_chord, with_dihedral_angle);
add_anchors();
// discrete constrained Delaunay triangulation
pseudo_cdt();
if (optimize_anchor_location)
this->optimize_anchor_location();
// check manifold-oriented
return Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh(m_tris);
}
/// @}
/// \name Output
/// @{
/*!
* @brief outputs approximation results.
* @tparam NamedParameters a sequence of \ref bgl_namedparameters
* @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
* \cgalNamedParamsBegin{Output Named Parameters}
* \cgalParamNBegin{face_proxy_map}
* \cgalParamDescription{a property map to output the proxy index of each face of the input polygon mesh}
* \cgalParamType{a model of `WritablePropertyMap` with `boost::graph_traits<TriangleMesh>::%face_descriptor`
* as key and `std::size_t` as value type}
* \cgalParamDefault{no output operation is performed}
* \cgalParamExtra{A proxy is a set of connected faces which are placed under the same proxy patch (see \cgalFigureRef{iterations})}
* \cgalParamExtra{The proxy-ids are contiguous in range `[0, number_of_proxies - 1]`}
* \cgalParamNEnd
*
* \cgalParamNBegin{proxies}
* \cgalParamDescription{an `OutputIterator` to put proxies in}
* \cgalParamType{a class model of `OutputIterator` with
* `CGAL::Surface_mesh_approximation::L21_metric_vector_proxy_no_area_weighting::Proxy` value type}
* \cgalParamDefault{no output operation is performed}
* \cgalParamNEnd
*
* \cgalParamNBegin{anchors}
* \cgalParamDescription{an `OutputIterator` to put anchor points in}
* \cgalParamType{a class model of `OutputIterator` with `geom_traits::%Point_3` value type}
* \cgalParamDefault{no output operation is performed}
* \cgalParamNEnd
*
* \cgalParamNBegin{triangles}
* \cgalParamDescription{an `OutputIterator` to put indexed triangles in}
* \cgalParamType{a class model of `OutputIterator` with `std::array<std::size_t, 3>` value type}
* \cgalParamDefault{no output operation is performed}
* \cgalParamNEnd
* \cgalNamedParamsEnd
*/
template <typename NamedParameters>
void output(const NamedParameters &np) const {
using parameters::get_parameter;
using parameters::choose_parameter;
// get proxy map
proxy_map( get_parameter(np, internal_np::face_proxy_map) );
// get proxies
proxies( get_parameter(np, internal_np::proxies) );
// get anchor points
anchor_points( get_parameter(np, internal_np::anchors) );
// get indexed triangles
indexed_triangles( get_parameter(np, internal_np::triangles) );
}
/*!
* @brief returns the number of proxies.
*/
std::size_t number_of_proxies() const { return m_proxies.size(); }
/// @cond CGAL_DOCUMENT_INTERNAL
/*!
* @brief gets the face-proxy index map.
* @tparam FaceProxyMap `WritablePropertyMap` with
* `boost::graph_traits<TriangleMesh>::%face_descriptor` as key and `std::size_t` as value type
* @param[out] face_proxy_map face proxy index map
*/
template <typename FaceProxyMap>
void proxy_map(FaceProxyMap face_proxy_map) const {
for(face_descriptor f : faces(*m_ptm))
put(face_proxy_map, f, get(m_fproxy_map, f));
}
/*!
* @brief dummy function for named parameters.
*/
void proxy_map(internal_np::Param_not_found) const {}
/*!
* @brief gets the face region of the specified proxy.
* @tparam OutputIterator output iterator with `boost::graph_traits<TriangleMesh>::%face_descriptor` as value type
* @param px_idx proxy index
* @param out output iterator
*/
template <typename OutputIterator>
void proxy_region(const std::size_t px_idx, OutputIterator out) const {
if (px_idx >= m_proxies.size())
return;
for(face_descriptor f : faces(*m_ptm))
if (get(m_fproxy_map, f) == px_idx)
*out++ = f;
}
/*!
* @brief gets the proxies.
* @tparam OutputIterator output iterator with Proxy as value type
* @param out output iterator
*/
template <typename OutputIterator>
void proxies(OutputIterator out) const {
for(const Proxy_wrapper& pxw : m_proxies)
*out++ = pxw.px;
}
/*!
* @brief dummy function for named parameters.
*/
void proxies(internal_np::Param_not_found) const {}
/*!
* @brief gets the wrapped proxies.
* @tparam OutputIterator output iterator with Proxy_wrapper as value type
* @param out output iterator
*/
template <typename OutputIterator>
void wrapped_proxies(OutputIterator out) const {
for(const Proxy_wrapper& pxw : m_proxies)
*out++ = pxw;
}
/*!
* @brief gets the anchor points, which have the area-averaged position of the projected anchor vertex points on the incident proxies.
* @tparam OutputIterator output iterator with Point_3 as value type
* @param out output iterator
*/
template <typename OutputIterator>
void anchor_points(OutputIterator out) const {
for(const Anchor& a : m_anchors)
*out++ = a.pos;
}
/*!
* @brief dummy function for named parameters.
*/
void anchor_points(internal_np::Param_not_found) const {}
/*!
* @brief gets the anchor vertices.
* @tparam OutputIterator output iterator with vertex_descriptor as value type
* @param out output iterator
*/
template <typename OutputIterator>
void anchor_vertices(OutputIterator out) const {
for(const Anchor& a : m_anchors)
*out++ = a.vtx;
}
/*!
* @brief gets the indexed triangles, with
* one triplet of integers per triangles, which refers to the anchor point indices.
* @tparam OutputIterator output iterator with Indexed_triangle as value type
* @param out output iterator
*/
template <typename OutputIterator>
void indexed_triangles(OutputIterator out) const {
for(const Indexed_triangle& t : m_tris)
*out++ = t;
}
/*!
* @brief dummy function for named parameters.
*/
void indexed_triangles(internal_np::Param_not_found) const {}
/*!
* @brief gets the indexed boundary polygon approximation.
* @tparam OutputIterator output iterator with std::vector<std::size_t> as value type
* @param out output iterator
*/
template <typename OutputIterator>
void indexed_boundary_polygons(OutputIterator out) const {
for(const Boundary_cycle& bcycle : m_bcycles) {
std::vector<std::size_t> plg;
halfedge_descriptor he = bcycle.he_head;
do {
Boundary_chord chord;
walk_to_next_anchor(he, chord);
plg.push_back(get(m_vanchor_map, target(he, *m_ptm)));
} while (he != bcycle.he_head);
*out++ = plg;
}
}
/// @endcond
/// @}
// private member functions
private:
/*!
* @brief randomly initializes proxies
* with both maximum number of proxies and minimum error drop stop criteria,
* where the first criterion met stops the seeding.
* @note To ensure the randomness, call `std::srand()` beforehand.
* @param max_nb_proxies maximum number of proxies, should be in range `(nb_connected_components, nb_faces / 3)`
* @param min_error_drop minimum error drop, should be in range `(0.0, 1.0)`,
* negative value is ignored
* @param nb_relaxations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_random(const std::size_t max_nb_proxies,
const FT min_error_drop,
const std::size_t nb_relaxations) {
if (!(min_error_drop > FT(0.0))) {
// pick from current non seed faces randomly
std::vector<face_descriptor> picked_seeds;
if (random_pick_non_seed_faces(max_nb_proxies - m_proxies.size(), picked_seeds)) {
for(face_descriptor f : picked_seeds)
add_one_proxy_at(f);
run(nb_relaxations);
}
return m_proxies.size();
}
const FT initial_err = compute_total_error();
FT error_drop = min_error_drop * FT(2.0);
while (m_proxies.size() < max_nb_proxies && error_drop > min_error_drop) {
// try to double current number of proxies each time
const std::size_t nb_px = m_proxies.size();
const std::size_t nb_to_add =
(nb_px * 2 > max_nb_proxies) ? max_nb_proxies - nb_px : nb_px;
// pick from current non seed faces randomly
std::vector<face_descriptor> picked_seeds;
if (!random_pick_non_seed_faces(nb_to_add, picked_seeds))
return m_proxies.size();
for(face_descriptor f : picked_seeds)
add_one_proxy_at(f);
const FT err = run(nb_relaxations);
error_drop = err / initial_err;
}
return m_proxies.size();
}
/*!
* @brief incrementally initializes proxies
* with both maximum number of proxies and minimum error drop stop criteria,
* The first criterion met stops the seeding.
* @param max_nb_proxies maximum number of proxies, should be in range `(nb_connected_components, nb_faces / 3)`
* @param min_error_drop minimum error drop, should be in range `(0.0, 1.0)`,
* negative value is ignored
* @param nb_relaxations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_incremental(const std::size_t max_nb_proxies,
const FT min_error_drop,
const std::size_t nb_relaxations) {
if (!(min_error_drop > FT(0.0))) {
if (m_proxies.size() < max_nb_proxies)
add_to_furthest_proxies(max_nb_proxies - m_proxies.size(), nb_relaxations);
return m_proxies.size();
}
const FT initial_err = compute_total_error();
FT error_drop = min_error_drop * FT(2.0);
while (m_proxies.size() < max_nb_proxies && error_drop > min_error_drop) {
add_to_furthest_proxy();
const FT err = run(nb_relaxations);
error_drop = err / initial_err;
}
return m_proxies.size();
}
/*!
* @brief hierarchically initializes proxies
* with both maximum number of proxies and minimum error drop stop criteria,
* where the first criterion met stops the seeding.
* @param max_nb_proxies maximum number of proxies, should be in range `(nb_connected_components, nb_faces / 3)`
* @param min_error_drop minimum error drop, should be in range `(0.0, 1.0)`,
* negative value is ignored
* @param nb_relaxations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_hierarchical(const std::size_t max_nb_proxies,
const FT min_error_drop,
const std::size_t nb_relaxations) {
const FT initial_err = compute_total_error();
FT error_drop = !(min_error_drop > FT(0.0)) ? FT(1.0) : min_error_drop * FT(2.0);
while (m_proxies.size() < max_nb_proxies && error_drop > min_error_drop) {
// try to double current number of proxies each time
std::size_t target_px = m_proxies.size();
if (target_px * 2 > max_nb_proxies)
target_px = max_nb_proxies;
else
target_px *= 2;
add_proxies_error_diffusion(target_px - m_proxies.size());
const FT err = run(nb_relaxations);
error_drop = err / initial_err;
}
return m_proxies.size();
}
/*!
* @brief partitions the area tagged with CGAL_VSA_INVALID_TAG with proxies, global face proxy map is updated.
* Propagates the proxy seed faces and floods the tagged area to minimize the fitting error.
* @tparam ProxyWrapperIterator forward iterator with Proxy_wrapper as value type
* @param beg iterator point to the first element
* @param end iterator point to the one past the last element
*/
template<typename ProxyWrapperIterator>
void partition(const ProxyWrapperIterator beg, const ProxyWrapperIterator end) {
std::priority_queue<Face_to_integrate> face_pqueue;
for (ProxyWrapperIterator pxw_itr = beg; pxw_itr != end; ++pxw_itr) {
face_descriptor f = pxw_itr->seed;
put(m_fproxy_map, f, pxw_itr->idx);
for(face_descriptor fadj : faces_around_face(halfedge(f, *m_ptm), *m_ptm)) {
if (fadj != boost::graph_traits<TriangleMesh>::null_face()
&& get(m_fproxy_map, fadj) == CGAL_VSA_INVALID_TAG) {
face_pqueue.push(Face_to_integrate(
fadj, pxw_itr->idx, m_metric->compute_error(fadj, *m_ptm, pxw_itr->px)));
}
}
}
while (!face_pqueue.empty()) {
const Face_to_integrate c = face_pqueue.top();
face_pqueue.pop();
if (get(m_fproxy_map, c.f) == CGAL_VSA_INVALID_TAG) {
put(m_fproxy_map, c.f, c.px);
for(face_descriptor fadj : faces_around_face(halfedge(c.f, *m_ptm), *m_ptm)) {
if (fadj != boost::graph_traits<TriangleMesh>::null_face()
&& get(m_fproxy_map, fadj) == CGAL_VSA_INVALID_TAG) {
face_pqueue.push(Face_to_integrate(
fadj, c.px, m_metric->compute_error(fadj, *m_ptm, m_proxies[c.px].px)));
}
}
}
}
}
/*!
* @brief refits and updates input range of proxies, sequential.
* @tparam ProxyWrapperIterator forward iterator with Proxy_wrapper as value type
* @param beg iterator point to the first element
* @param end iterator point to the one past the last element
* @param t concurrency tag
*/
template<typename ProxyWrapperIterator>
void fit(const ProxyWrapperIterator beg, const ProxyWrapperIterator end, const CGAL::Sequential_tag &) {
std::vector<std::list<face_descriptor> > px_faces(m_proxies.size());
for(face_descriptor f : faces(*m_ptm))
px_faces[get(m_fproxy_map, f)].push_back(f);
// update proxy parameters and seed
for (ProxyWrapperIterator pxw_itr = beg; pxw_itr != end; ++pxw_itr) {
const std::size_t px_idx = pxw_itr->idx;
*pxw_itr = fit_proxy_from_patch(px_faces[px_idx], px_idx);
}
}
#ifdef CGAL_LINKED_WITH_TBB
/*!
* @brief refits and updates input range of proxies, parallel.
* @tparam ProxyWrapperIterator forward iterator with Proxy_wrapper as value type
* @param beg iterator point to the first element
* @param end iterator point to the one past the last element
* @param t concurrency tag
*/
template<typename ProxyWrapperIterator>
void fit(const ProxyWrapperIterator beg, const ProxyWrapperIterator end, const CGAL::Parallel_tag &) {
std::vector<std::list<face_descriptor> > px_faces(m_proxies.size());
for(face_descriptor f : faces(*m_ptm))
px_faces[get(m_fproxy_map, f)].push_back(f);
// update proxy parameters and seed
tbb::parallel_for(tbb::blocked_range<ProxyWrapperIterator>(beg, end),
[&](tbb::blocked_range<ProxyWrapperIterator> &r) {
for (ProxyWrapperIterator pxw_itr = r.begin(); pxw_itr != r.end(); ++pxw_itr) {
const std::size_t px_idx = pxw_itr->idx;
*pxw_itr = fit_proxy_from_patch(px_faces[px_idx], px_idx);
}
});
}
#endif // CGAL_LINKED_WITH_TBB
/*!
* @brief adds a proxy seed at the face with the maximum fitting error.
* @return `true` if add is successfully, and `false` otherwise
*/
bool add_to_furthest_proxy() {
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "add furthest " << m_proxies.size() << std::endl;
#endif
FT max_error = m_proxies.front().err;
std::size_t px_worst = 0;
for (std::size_t i = 0; i < m_proxies.size(); ++i) {
if (max_error < m_proxies[i].err) {
max_error = m_proxies[i].err;
px_worst = i;
}
}
face_descriptor fworst;
bool first = true;
for(face_descriptor f : faces(*m_ptm)) {
std::size_t px_idx = get(m_fproxy_map, f);
if (px_idx != px_worst || f == m_proxies[px_idx].seed)
continue;
FT err = m_metric->compute_error(f, *m_ptm, m_proxies[px_idx].px);
if (first || max_error < err) {
first = false;
max_error = err;
fworst = f;
}
}
if (first)
return false;
add_one_proxy_at(fworst);
return true;
}
/*!
* @brief fits a new (wrapped) proxy from a region patch.
* 1. Compute proxy parameters from a list of faces.
* 2. Find proxy seed face.
* 3. Sum the proxy error.
* @tparam FacePatch container with `face_descriptor` as data type
* @param px_patch proxy patch container
* @param px_idx the assigned proxy index
* @return fitted wrapped proxy
*/
template<typename FacePatch>
Proxy_wrapper fit_proxy_from_patch(const FacePatch &px_patch, const std::size_t px_idx) {
CGAL_assertion(!px_patch.empty());
// use Proxy_fitting functor to fit proxy parameters
const Proxy px = m_metric->fit_proxy(px_patch, *m_ptm);
// find proxy seed and sum error
face_descriptor seed = *px_patch.begin();
FT err_min = m_metric->compute_error(seed, *m_ptm, px);
FT sum_error(0.0);
for(face_descriptor f : px_patch) {
const FT err = m_metric->compute_error(f, *m_ptm, px);
sum_error += err;
if (err < err_min) {
err_min = err;
seed = f;
}
}
return Proxy_wrapper(px, px_idx, seed, sum_error);
}
/*!
* @brief adds a proxy at face f.
* @param f where to the proxy is initialized from
*/
void add_one_proxy_at(const face_descriptor f) {
m_proxies.push_back(fit_proxy_from_face(f, m_proxies.size()));
}
/*!
* @brief fits a new (wrapped) proxy from a face.
* 1. Compute proxy parameters from the face.
* 2. Set seed to this face.
* 3. Update the proxy error.
* 4. Update proxy map.
* @pre current face proxy map is valid
* @param face_descriptor face
* @param px_idx proxy index
* @return fitted wrapped proxy
*/
Proxy_wrapper fit_proxy_from_face(const face_descriptor f, const std::size_t px_idx) {
// fit proxy parameters
std::vector<face_descriptor> fvec(1, f);
const Proxy px = m_metric->fit_proxy(fvec, *m_ptm);
const FT err = m_metric->compute_error(f, *m_ptm, px);
// original proxy map should always be falid
const std::size_t prev_px_idx = get(m_fproxy_map, f);
CGAL_assertion(prev_px_idx != CGAL_VSA_INVALID_TAG);
// update the proxy error and proxy map
m_proxies[prev_px_idx].err -= m_metric->compute_error(f, *m_ptm, m_proxies[prev_px_idx].px);
put(m_fproxy_map, f, px_idx);
return Proxy_wrapper(px, px_idx, f, err);
}
/*!
* @brief picks a number of non-seed faces into an empty vector randomly.
* @param nb_requested requested number of faces
* @param[out] picked_faces shuffled faces vector
* @return `true` if the requested number of faces are selected, and `false` otherwise
*/
bool random_pick_non_seed_faces(const std::size_t nb_requested,
std::vector<face_descriptor> &picked_faces) {
if (nb_requested + m_proxies.size() >= m_nb_of_faces)
return false;
std::set<face_descriptor> seed_faces_set;
for(const Proxy_wrapper& pxw : m_proxies)
seed_faces_set.insert(pxw.seed);
const std::size_t nb_nsf = m_nb_of_faces - m_proxies.size();
std::vector<face_descriptor> non_seed_faces;
non_seed_faces.reserve(nb_nsf);
for(face_descriptor f : faces(*m_ptm)) {
if (seed_faces_set.find(f) != seed_faces_set.end())
continue;
non_seed_faces.push_back(f);
}
// random shuffle first few faces
for (std::size_t i = 0; i < nb_requested; ++i) {
// swap ith element with a random one
std::size_t r = static_cast<std::size_t>(
static_cast<double>(std::rand()) / static_cast<double>(RAND_MAX) *
static_cast<double>(nb_nsf - 1));
std::swap(non_seed_faces[i], non_seed_faces[r]);
}
for (std::size_t i = 0; i < nb_requested; ++i)
picked_faces.push_back(non_seed_faces[i]);
return true;
}
/*!
* @brief initializes proxies from each connected component of the input mesh.
* @note This function clears proxy vector and sets face proxy map to initial state,
* intended only for bootstrapping initialization.
* Coarse approximation iteration is not performed, because it is inaccurate anyway
* and may yield degenerate cases (e.g. a standard cube model).
*/
void bootstrap_from_connected_components() {
// set all faces invalid to mark as unvisited / untagged
for(face_descriptor f : faces(*m_ptm))
put(m_fproxy_map, f, CGAL_VSA_INVALID_TAG);
// prepare for connected components visiting
std::vector<std::list<face_descriptor> > cc_patches;
bool if_all_visited = false;
std::size_t cc_idx = 0;
face_descriptor seed_face = *(faces(*m_ptm).first);
while (!if_all_visited) {
// use current seed face to traverse the conneceted componnets
std::list<face_descriptor> cc_patch;
cc_patch.push_back(seed_face);
std::stack<face_descriptor> fstack;
fstack.push(seed_face);
put(m_fproxy_map, seed_face, cc_idx);
while (!fstack.empty()) {
face_descriptor active_face = fstack.top();
fstack.pop();
for(face_descriptor fadj :
faces_around_face(halfedge(active_face, *m_ptm), *m_ptm)) {
if (fadj != boost::graph_traits<TriangleMesh>::null_face()
&& get(m_fproxy_map, fadj) == CGAL_VSA_INVALID_TAG) {
cc_patch.push_back(fadj);
fstack.push(fadj);
put(m_fproxy_map, fadj, cc_idx);
}
}
}
cc_patches.push_back(cc_patch);
// check if all visited
if_all_visited = true;
for(face_descriptor f : faces(*m_ptm)) {
if (get(m_fproxy_map, f) == CGAL_VSA_INVALID_TAG) {
if_all_visited = false;
++cc_idx;
seed_face = f;
break;
}
}
}
m_proxies.clear();
for(const std::list<face_descriptor>& cc_patch : cc_patches)
m_proxies.push_back(fit_proxy_from_patch(cc_patch, m_proxies.size()));
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#cc " << m_proxies.size() << std::endl;
#endif
}
/*!
* @brief computes proxy planes.
* The proxy may not contain the plane related properties, so we need these internal planes,
* used in the chord subdivision and anchor location.
* @param if_pca_plane set `true` to use the PCA plane fitting
*/
void compute_proxy_planes(const bool if_pca_plane) {
// fit proxy planes, areas, normals
std::vector<std::list<face_descriptor> > px_faces(m_proxies.size());
for(face_descriptor f : faces(*m_ptm))
px_faces[get(m_fproxy_map, f)].push_back(f);
for(const std::list<face_descriptor>& px_patch : px_faces) {
Plane_3 fit_plane = if_pca_plane ?
fit_plane_pca(px_patch.begin(), px_patch.end()) :
fit_plane_area_averaged(px_patch.begin(), px_patch.end());
Vector_3 norm = CGAL::NULL_VECTOR;
FT area(0.0);
for(face_descriptor f : px_patch) {
halfedge_descriptor he = halfedge(f, *m_ptm);
const Point_3 &p0 = m_vpoint_map[source(he, *m_ptm)];
const Point_3 &p1 = m_vpoint_map[target(he, *m_ptm)];
const Point_3 &p2 = m_vpoint_map[target(next(he, *m_ptm), *m_ptm)];
const FT farea = CGAL::approximate_sqrt(CGAL::squared_area(p0, p1, p2));
const Vector_3 fnorm =
collinear_functor(p0, p1, p2) ? CGAL::NULL_VECTOR : CGAL::unit_normal(p0, p1, p2);
norm = sum_functor(norm, scale_functor(fnorm, farea));
area += farea;
}
if (norm.squared_length() > FT(0.0))
norm = scale_functor(norm, FT(1.0) / CGAL::approximate_sqrt(norm.squared_length()));
else
norm = Vector_3(FT(0.0), FT(0.0), FT(1.0));
m_px_planes.push_back(Proxy_plane(fit_plane, norm, area));
}
}
/*!
* @brief finds the anchors.
*/
void find_anchors() {
for(vertex_descriptor vtx : vertices(*m_ptm)) {
std::size_t border_count = 0;
for(halfedge_descriptor h : halfedges_around_target(vtx, *m_ptm)) {
if (CGAL::is_border_edge(h, *m_ptm))
++border_count;
else if (get(m_fproxy_map, face(h, *m_ptm)) != get(m_fproxy_map, face(opposite(h, *m_ptm), *m_ptm)))
++border_count;
}
if (border_count >= 3)
attach_anchor(vtx);
}
}
/*!
* @brief finds and approximates the chord connecting the anchors.
* @param subdivision_ratio boundary chord approximation recursive split creterion
* @param relative_to_chord set `true` if the subdivision_ratio is relative to the chord length (relative sense),
* otherwise it's relative to the average edge length (absolute sense).
* @param with_dihedral_angle if set to `true`, add dihedral angle weight to the distance.
*/
void find_edges(const FT subdivision_ratio,
const bool relative_to_chord,
const bool with_dihedral_angle) {
// collect candidate halfedges in a set
std::set<halfedge_descriptor> he_candidates;
for(halfedge_descriptor h : halfedges(*m_ptm)) {
if (!CGAL::is_border(h, *m_ptm)
&& (CGAL::is_border(opposite(h, *m_ptm), *m_ptm)
|| get(m_fproxy_map, face(h, *m_ptm)) != get(m_fproxy_map, face(opposite(h, *m_ptm), *m_ptm))))
he_candidates.insert(h);
}
// pick up one candidate halfedge each time and traverse the connected boundary cycle
while (!he_candidates.empty()) {
halfedge_descriptor he_start = *he_candidates.begin();
walk_to_first_anchor(he_start);
// no anchor in this connected boundary cycle, make a new anchor
if (!is_anchor_attached(he_start))
attach_anchor(he_start);
// a new connected boundary cycle
m_bcycles.push_back(Boundary_cycle(he_start));
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#bcycle " << m_bcycles.size() << std::endl;
#endif
const halfedge_descriptor he_mark = he_start;
do {
Boundary_chord chord;
walk_to_next_anchor(he_start, chord);
m_bcycles.back().num_anchors += subdivide_chord(chord.begin(), chord.end(),
subdivision_ratio, relative_to_chord, with_dihedral_angle);
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#chord_anchor " << m_bcycles.back().num_anchors << std::endl;
#endif
for(const halfedge_descriptor he : chord)
he_candidates.erase(he);
} while (he_start != he_mark);
}
}
/*!
* @brief adds anchors to the boundary cycles with only 2 anchors.
*/
void add_anchors() {
for(const Boundary_cycle& bcycle : m_bcycles) {
if (bcycle.num_anchors > 2)
continue;
// 2 initial anchors at least
CGAL_assertion(bcycle.num_anchors == 2);
// borders with only 2 initial anchors
Point_3 pt_begin = m_vpoint_map[target(bcycle.he_head, *m_ptm)];
Point_3 pt_end = pt_begin;
halfedge_descriptor he = bcycle.he_head;
Boundary_chord chord;
std::size_t count = 0;
do {
walk_to_next_border_halfedge(he);
if (!is_anchor_attached(he))
chord.push_back(he);
else {
if (count == 0)
pt_end = m_vpoint_map[target(he, *m_ptm)];
++count;
}
} while (he != bcycle.he_head);
// anchor count may be increased to more than 2 afterwards
// due to the new anchors added by the neighboring boundary cycle (< 2 anchors)
if (count > 2) {
const_cast<Boundary_cycle &>(bcycle).num_anchors = count;
continue;
}
CGAL_assertion(!chord.empty());
halfedge_descriptor he_max = *chord.begin();
Vector_3 chord_vec = vector_functor(pt_begin, pt_end);
if (chord_vec.squared_length() > FT(0.0)) {
FT dist_max(0.0);
chord_vec = scale_functor(chord_vec,
FT(1.0) / CGAL::approximate_sqrt(chord_vec.squared_length()));
for(const halfedge_descriptor he : chord) {
Vector_3 vec = vector_functor(pt_begin, m_vpoint_map[target(he, *m_ptm)]);
vec = cross_product_functor(chord_vec, vec);
const FT dist = CGAL::approximate_sqrt(vec.squared_length());
if (dist > dist_max) {
dist_max = dist;
he_max = he;
}
}
}
else {
FT dist_max(0.0);
for(const halfedge_descriptor he : chord) {
const FT dist = CGAL::approximate_sqrt(CGAL::squared_distance(
pt_begin, m_vpoint_map[target(he, *m_ptm)]));
if (dist > dist_max) {
dist_max = dist;
he_max = he;
}
}
}
// add one anchors to this boundary cycle
attach_anchor(he_max);
const_cast<Boundary_cycle &>(bcycle).num_anchors++;
}
}
/*!
* @brief runs the pseudo Constrained Delaunay Triangulation at each proxy region,
* and stores the extracted indexed triangles in @a tris.
* @pre all anchors are found, i.e. all boundary cycles have been visited
* and attached with at least 3 anchors.
*/
void pseudo_cdt() {
// subgraph attached with vertex anchor status and edge weight
typedef boost::property<boost::vertex_index1_t, std::size_t,
boost::property<boost::vertex_index2_t, std::size_t> > VertexProperty;
typedef boost::property<boost::edge_weight_t, FT,
boost::property<boost::edge_index_t, std::size_t> > EdgeProperty;
typedef boost::subgraph<boost::adjacency_list<
boost::listS, boost::vecS,
boost::undirectedS,
VertexProperty, EdgeProperty> > SubGraph;
typedef typename boost::property_map<SubGraph, boost::vertex_index1_t>::type VertexIndex1Map;
typedef typename boost::property_map<SubGraph, boost::vertex_index2_t>::type VertexIndex2Map;
typedef typename boost::property_map<SubGraph, boost::edge_weight_t>::type EdgeWeightMap;
typedef typename SubGraph::vertex_descriptor sg_vertex_descriptor;
typedef std::vector<sg_vertex_descriptor> VertexVector;
typedef boost::unordered_map<vertex_descriptor, sg_vertex_descriptor> VertexMap;
typedef boost::associative_property_map<VertexMap> ToSGVertexMap;
VertexMap vmap;
ToSGVertexMap to_sgv_map(vmap);
// mapping the TriangleMesh mesh into a SubGraph
SubGraph gmain;
VertexIndex1Map global_vanchor_map = get(boost::vertex_index1, gmain);
VertexIndex2Map global_vtag_map = get(boost::vertex_index2, gmain);
EdgeWeightMap global_eweight_map = get(boost::edge_weight, gmain);
for(vertex_descriptor v : vertices(*m_ptm)) {
sg_vertex_descriptor sgv = add_vertex(gmain);
global_vanchor_map[sgv] = get(m_vanchor_map, v);
global_vtag_map[sgv] = get(m_vanchor_map, v);
vmap.insert(std::pair<vertex_descriptor, sg_vertex_descriptor>(v, sgv));
}
for(edge_descriptor e : edges(*m_ptm)) {
const vertex_descriptor vs = source(e, *m_ptm);
const vertex_descriptor vt = target(e, *m_ptm);
const FT len = CGAL::approximate_sqrt(CGAL::squared_distance(
m_vpoint_map[vs], m_vpoint_map[vt]));
add_edge(to_sgv_map[vs], to_sgv_map[vt], len, gmain);
}
std::vector<VertexVector> vertex_patches(m_proxies.size());
for(vertex_descriptor v : vertices(*m_ptm)) {
std::set<std::size_t> px_set;
for(face_descriptor f : faces_around_target(halfedge(v, *m_ptm), *m_ptm)) {
if (f != boost::graph_traits<TriangleMesh>::null_face())
px_set.insert(get(m_fproxy_map, f));
}
for(std::size_t p : px_set)
vertex_patches[p].push_back(to_sgv_map[v]);
}
for(VertexVector& vpatch : vertex_patches) {
// add a super vertex connecting to its boundary anchors in each patch
const sg_vertex_descriptor superv = add_vertex(gmain);
global_vanchor_map[superv] = CGAL_VSA_INVALID_TAG;
global_vtag_map[superv] = CGAL_VSA_INVALID_TAG;
int anchor_count = 0;
for(sg_vertex_descriptor v : vpatch) {
if (is_anchor_attached(v, global_vanchor_map)) {
add_edge(superv, v, FT(0.0), gmain);
anchor_count++;
}
}
CGAL_assertion(anchor_count >=3 || anchor_count == 0);
// ball patch has no boundary or anchor, usually are small floating parts
// push dummy source vertex in the patch
if (anchor_count == 0)
vpatch.push_back(boost::graph_traits<SubGraph>::null_vertex());
else
vpatch.push_back(superv);
}
// multi-source Dijkstra's shortest path algorithm applied to each proxy patch
for(VertexVector& vpatch : vertex_patches) {
// ignore ball patch
if (vpatch.back() == boost::graph_traits<SubGraph>::null_vertex())
continue;
// construct subgraph
SubGraph &glocal = gmain.create_subgraph();
for(sg_vertex_descriptor v : vpatch)
add_vertex(v, glocal);
// most subgraph functions work with local descriptors
VertexIndex1Map local_vanchor_map = get(boost::vertex_index1, glocal);
VertexIndex2Map local_vtag_map = get(boost::vertex_index2, glocal);
EdgeWeightMap local_eweight_map = get(boost::edge_weight, glocal);
const sg_vertex_descriptor source = glocal.global_to_local(vpatch.back());
VertexVector pred(num_vertices(glocal),
boost::graph_traits<SubGraph>::null_vertex());
boost::dijkstra_shortest_paths(glocal, source,
boost::predecessor_map(&pred[0]).weight_map(local_eweight_map));
// backtrack to the anchor and tag each vertex in the local patch graph
for(sg_vertex_descriptor v : make_range(vertices(glocal))) {
// skip the added super source vertex in the patch
if (v == source)
continue;
sg_vertex_descriptor curr = v;
while (!is_anchor_attached(curr, local_vanchor_map))
curr = pred[curr];
local_vtag_map[v] = local_vanchor_map[curr];
}
}
// tag all boundary chords
for(const Boundary_cycle& bcycle : m_bcycles) {
halfedge_descriptor he = bcycle.he_head;
do {
Boundary_chord chord;
walk_to_next_anchor(he, chord);
std::vector<FT> vdist;
vdist.push_back(FT(0.0));
for(halfedge_descriptor h : chord) {
FT elen = global_eweight_map[edge(
to_sgv_map[source(h, *m_ptm)],
to_sgv_map[target(h, *m_ptm)],
gmain).first];
vdist.push_back(vdist.back() + elen);
}
FT half_chord_len = vdist.back() / FT(2.0);
const std::size_t anchorleft = get(m_vanchor_map, source(chord.front(), *m_ptm));
const std::size_t anchorright = get(m_vanchor_map, target(chord.back(), *m_ptm));
typename std::vector<FT>::iterator ditr = vdist.begin() + 1;
for (Boundary_chord_iterator citr = chord.begin(); citr != chord.end() - 1; ++citr, ++ditr) {
if (*ditr < half_chord_len)
global_vtag_map[to_sgv_map[target(*citr, *m_ptm)]] = anchorleft;
else
global_vtag_map[to_sgv_map[target(*citr, *m_ptm)]] = anchorright;
}
} while (he != bcycle.he_head);
}
// collect triangles
for(face_descriptor f : faces(*m_ptm)) {
halfedge_descriptor he = halfedge(f, *m_ptm);
std::size_t i = global_vtag_map[to_sgv_map[source(he, *m_ptm)]];
std::size_t j = global_vtag_map[to_sgv_map[target(he, *m_ptm)]];
std::size_t k = global_vtag_map[to_sgv_map[target(next(he, *m_ptm), *m_ptm)]];
if (i != j && i != k && j != k) {
std::array<std::size_t, 3> t;
t[0] = i;
t[1] = j;
t[2] = k;
m_tris.push_back(t);
}
}
}
/*!
* @brief walks along the region boundary cycle to the first halfedge
* pointing to a vertex associated with an anchor.
* @param[in/out] he_start region boundary halfedge
*/
void walk_to_first_anchor(halfedge_descriptor &he_start) {
const halfedge_descriptor start_mark = he_start;
while (!is_anchor_attached(he_start)) {
// no anchor attached to the halfedge target
walk_to_next_border_halfedge(he_start);
if (he_start == start_mark) // back to where started, a boundary cycle without anchor
return;
}
}
/*!
* @brief walks along the region boundary cycle to the next anchor
* and records the path as a `Boundary_chord`.
* @param[in/out] he_start starting region boundary halfedge
* pointing to a vertex associated with an anchor
* @param[out] chord recorded path chord
*/
void walk_to_next_anchor(halfedge_descriptor &he_start, Boundary_chord &chord) const {
do {
walk_to_next_border_halfedge(he_start);
chord.push_back(he_start);
} while (!is_anchor_attached(he_start));
}
/*!
* @brief walks to the next boundary cycle halfedge.
* @param[in/out] he_start region boundary halfedge
*/
void walk_to_next_border_halfedge(halfedge_descriptor &he_start) const {
const std::size_t px_idx = get(m_fproxy_map, face(he_start, *m_ptm));
for(halfedge_descriptor h : halfedges_around_target(he_start, *m_ptm)) {
if (CGAL::is_border(h, *m_ptm) || get(m_fproxy_map, face(h, *m_ptm)) != px_idx) {
he_start = opposite(h, *m_ptm);
return;
}
}
}
/*!
* @brief subdivides a chord recursively in range `[@a chord_begin, @a chord_end).`
* @param chord_begin begin iterator of the chord
* @param chord_end end iterator of the chord
* @param subdivision_ratio the chord recursive split error threshold
* @param relative_to_chord set `true` if the subdivision_ratio is relative to the the chord length (relative sense),
* otherwise it's relative to the average edge length (absolute sense).
* @param with_dihedral_angle if set to `true` add dihedral angle weight to the distance.
* @return the number of anchors of the chord apart from the first one
*/
std::size_t subdivide_chord(
const Boundary_chord_iterator &chord_begin,
const Boundary_chord_iterator &chord_end,
const FT subdivision_ratio,
const bool relative_to_chord,
const bool with_dihedral_angle) {
const std::size_t chord_size = std::distance(chord_begin, chord_end);
const halfedge_descriptor he_first = *chord_begin;
const halfedge_descriptor he_last = *(chord_end - 1);
const std::size_t anchor_first = get(m_vanchor_map, source(he_first, *m_ptm));
const std::size_t anchor_last = get(m_vanchor_map, target(he_last, *m_ptm));
// do not subdivide trivial non-circular chord
if ((anchor_first != anchor_last) && (chord_size < 4))
return 1;
bool if_subdivide = false;
Boundary_chord_iterator chord_max = chord_begin;
const Point_3 &pt_begin = m_vpoint_map[source(he_first, *m_ptm)];
const Point_3 &pt_end = m_vpoint_map[target(he_last, *m_ptm)];
if (anchor_first == anchor_last) {
// circular chord
CGAL_assertion(chord_size > 2);
FT dist_max(0.0);
for (Boundary_chord_iterator citr = chord_begin; citr != chord_end; ++citr) {
const FT dist = CGAL::approximate_sqrt(CGAL::squared_distance(
pt_begin, m_vpoint_map[target(*citr, *m_ptm)]));
if (dist > dist_max) {
chord_max = citr;
dist_max = dist;
}
}
if_subdivide = true;
}
else {
FT dist_max(0.0);
Vector_3 chord_vec = vector_functor(pt_begin, pt_end);
const FT chord_len = CGAL::approximate_sqrt(chord_vec.squared_length());
bool degenerate_chord = false;
if (chord_len > FT(0.0)) {
chord_vec = scale_functor(chord_vec, FT(1.0) / chord_len);
for (Boundary_chord_iterator citr = chord_begin; citr != chord_end; ++citr) {
Vector_3 vec = vector_functor(pt_begin, m_vpoint_map[target(*citr, *m_ptm)]);
vec = cross_product_functor(chord_vec, vec);
const FT dist = CGAL::approximate_sqrt(vec.squared_length());
if (dist > dist_max) {
chord_max = citr;
dist_max = dist;
}
}
}
else {
degenerate_chord = true;
for (Boundary_chord_iterator citr = chord_begin; citr != chord_end; ++citr) {
const FT dist = CGAL::approximate_sqrt(CGAL::squared_distance(
pt_begin, m_vpoint_map[target(*citr, *m_ptm)]));
if (dist > dist_max) {
chord_max = citr;
dist_max = dist;
}
}
}
FT criterion = dist_max;
if (relative_to_chord && !degenerate_chord)
criterion /= chord_len;
else
criterion /= m_average_edge_length;
if (with_dihedral_angle) {
// suppose the proxy normal angle is acute
std::size_t px_left = get(m_fproxy_map, face(he_first, *m_ptm));
std::size_t px_right = px_left;
if (!CGAL::is_border(opposite(he_first, *m_ptm), *m_ptm))
px_right = get(m_fproxy_map, face(opposite(he_first, *m_ptm), *m_ptm));
FT norm_sin(1.0);
if (!CGAL::is_border(opposite(he_first, *m_ptm), *m_ptm)) {
Vector_3 vec = cross_product_functor(
m_px_planes[px_left].normal, m_px_planes[px_right].normal);
norm_sin = CGAL::approximate_sqrt(vec.squared_length());
}
criterion *= norm_sin;
}
if (criterion > subdivision_ratio)
if_subdivide = true;
}
if (if_subdivide) {
// subdivide at the most remote vertex
attach_anchor(*chord_max);
const std::size_t num_left = subdivide_chord(chord_begin, chord_max + 1,
subdivision_ratio, relative_to_chord, with_dihedral_angle);
const std::size_t num_right = subdivide_chord(chord_max + 1, chord_end,
subdivision_ratio, relative_to_chord, with_dihedral_angle);
return num_left + num_right;
}
return 1;
}
/*!
* @brief tests if the target vertex of a halfedge is attached with an anchor.
* @param he a halfedge descriptor
* @return `true` is attached with an anchor, and `false` otherwise.
*/
bool is_anchor_attached(const halfedge_descriptor he) const {
return is_anchor_attached(target(he, *m_ptm), m_vanchor_map);
}
/*!
* @brief checks if a vertex is attached with an anchor.
* @tparam VertexAnchorIndexMap `ReadablePropertyMap`
* with `boost::graph_traights<TriangleMesh>::vertex_descriptor` as key and `std::size_t` as value type
* @param vtx a vertex descriptor
* @param vanchor_map vertex anchor index map
*/
template<typename VertexAnchorIndexMap>
bool is_anchor_attached(
const typename boost::property_traits<VertexAnchorIndexMap>::key_type vtx,
const VertexAnchorIndexMap &vanchor_map) const {
return get(vanchor_map, vtx) != CGAL_VSA_INVALID_TAG;
}
/*!
* @brief attaches an anchor to the vertex.
* @param vtx vertex
*/
void attach_anchor(const vertex_descriptor vtx) {
put(m_vanchor_map, vtx, m_anchors.size());
// default anchor location is the vertex point
m_anchors.push_back(Anchor(vtx, m_vpoint_map[vtx]));
}
/*!
* @brief attaches an anchor to the target vertex of the halfedge.
* @param he halfedge
*/
void attach_anchor(const halfedge_descriptor he) {
attach_anchor(target(he, *m_ptm));
}
/*!
* @brief optimizes the anchor location by averaging the projection points of
* the anchor vertex to the incident proxy plane.
*/
void optimize_anchor_location() {
for(Anchor& a : m_anchors) {
const vertex_descriptor v = a.vtx;
// incident proxy set
std::set<std::size_t> px_set;
for(halfedge_descriptor h : halfedges_around_target(v, *m_ptm)) {
if (!CGAL::is_border(h, *m_ptm))
px_set.insert(get(m_fproxy_map, face(h, *m_ptm)));
}
// projection
FT sum_area(0.0);
Vector_3 vec = CGAL::NULL_VECTOR;
const Point_3 vtx_pt = m_vpoint_map[v];
for(const std::size_t px_idx : px_set) {
const Vector_3 proj = vector_functor(
CGAL::ORIGIN, m_px_planes[px_idx].plane.projection(vtx_pt));
const FT area = m_px_planes[px_idx].area;
vec = sum_functor(vec, scale_functor(proj, area));
sum_area += area;
}
if (sum_area > FT(0.0))
a.pos = translate_point_functor(
CGAL::ORIGIN,
scale_functor(vec, FT(1.0) / sum_area));
else
a.pos = vtx_pt;
}
}
/*!
* @brief calculates the averaged edge length of a triangle mesh.
* @param tm the input triangle mesh
* @param vpoint_map vertex point map
* @return averaged edge length
*/
FT compute_averaged_edge_length(const TriangleMesh &tm, const VertexPointMap &vpoint_map) const {
// compute average edge length
FT sum(0.0);
for(edge_descriptor e : edges(tm)) {
const vertex_descriptor vs = source(e, tm);
const vertex_descriptor vt = target(e, tm);
sum += CGAL::approximate_sqrt(CGAL::squared_distance(
vpoint_map[vs], vpoint_map[vt]));
}
return sum / num_edges(tm);
}
/*!
* @brief fits an area averaged plane from a range of faces.
* @tparam FaceIterator face_descriptor container iterator
* @param beg container begin
* @param end container end
* @return fitted plane
*/
template <typename FaceIterator>
Plane_3 fit_plane_area_averaged(const FaceIterator &beg, const FaceIterator &end) {
CGAL_assertion(beg != end);
// area average normal and centroid
Vector_3 norm = CGAL::NULL_VECTOR;
Vector_3 cent = CGAL::NULL_VECTOR;
FT sum_area(0.0);
for (FaceIterator fitr = beg; fitr != end; ++fitr) {
const halfedge_descriptor he = halfedge(*fitr, *m_ptm);
const Point_3 &p0 = m_vpoint_map[source(he, *m_ptm)];
const Point_3 &p1 = m_vpoint_map[target(he, *m_ptm)];
const Point_3 &p2 = m_vpoint_map[target(next(he, *m_ptm), *m_ptm)];
Vector_3 vec = vector_functor(CGAL::ORIGIN, CGAL::centroid(p0, p1, p2));
const FT farea = CGAL::approximate_sqrt(CGAL::squared_area(p0, p1, p2));
Vector_3 fnorm =
collinear_functor(p0, p1, p2) ? CGAL::NULL_VECTOR : CGAL::unit_normal(p0, p1, p2);
norm = sum_functor(norm, scale_functor(fnorm, farea));
cent = sum_functor(cent, scale_functor(vec, farea));
sum_area += farea;
}
if (norm.squared_length() > FT(0.0))
norm = scale_functor(norm, FT(1.0) / CGAL::approximate_sqrt(norm.squared_length()));
else
norm = Vector_3(FT(0.0), FT(0.0), FT(1.0));
if (sum_area > FT(0.0))
cent = scale_functor(cent, FT(1.0) / sum_area);
return Plane_3(CGAL::ORIGIN + cent, norm);
}
/*!
* @brief fits a plane from a range of faces with PCA algorithm.
* @tparam FaceIterator face_descriptor container iterator
* @param beg container begin
* @param end container end
* @return fitted plane
*/
template <typename FaceIterator>
Plane_3 fit_plane_pca(const FaceIterator &beg, const FaceIterator &end) {
CGAL_assertion(beg != end);
typedef typename Geom_traits::Triangle_3 Triangle_3;
std::list<Triangle_3> tri_list;
for (FaceIterator fitr = beg; fitr != end; ++fitr) {
halfedge_descriptor he = halfedge(*fitr, *m_ptm);
const Point_3 &p0 = m_vpoint_map[source(he, *m_ptm)];
const Point_3 &p1 = m_vpoint_map[target(he, *m_ptm)];
const Point_3 &p2 = m_vpoint_map[target(next(he, *m_ptm), *m_ptm)];
tri_list.push_back(Triangle_3(p0, p1, p2));
}
// construct and fit proxy plane
Plane_3 fit_plane;
CGAL::linear_least_squares_fitting_3(
tri_list.begin(),
tri_list.end(),
fit_plane,
CGAL::Dimension_tag<2>());
return fit_plane;
}
};
} // end namespace CGAL
#undef CGAL_VSA_INVALID_TAG
#endif // CGAL_VARIATIONAL_SHAPE_APPROXIMATION_H