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cgal/Surface_mesh_approximation/include/CGAL/vsa_approximation.h

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#ifndef CGAL_SURFACE_MESH_APPROXIMATION_VSA_APPROXIMATION_H
#define CGAL_SURFACE_MESH_APPROXIMATION_VSA_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/Polyhedron_incremental_builder_3.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/linear_least_squares_fitting_3.h>
#include <CGAL/vsa_metrics.h>
#include <CGAL/Default.h>
#include <boost/unordered_map.hpp>
#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/foreach.hpp>
#include <boost/optional.hpp>
#include <vector>
#include <queue>
#include <iterator>
#include <cmath>
#include <cstdlib>
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
#include <iostream>
#endif
#define CGAL_VSA_INVALID_TAG std::numeric_limits<std::size_t>::max()
namespace CGAL {
namespace VSA {
/*!
* \ingroup PkgTSMA
* @brief Seeding method enumeration for Variational Shape Approximation algorithm.
*/
enum Seeding {
/// Random seeding
Random,
/// Incremental seeding
Incremental,
/// Hierarchical seeding
Hierarchical
};
/*!
* \ingroup PkgTSMA
* @brief Main class for Variational Shape Approximation algorithm.
* @tparam TriangleMesh a CGAL TriangleMesh
* @tparam VertexPointMap vertex point map
* @tparam ErrorMetric error metric type
* @tparam ProxyFitting proxy fitting type
* @tparam GeomTraits geometric traits type
*/
template <typename TriangleMesh,
typename VertexPointMap,
typename ErrorMetric = CGAL::Default,
typename ProxyFitting = CGAL::Default,
typename GeomTraits = CGAL::Default>
class Mesh_approximation {
// public typedefs
public:
// Default typedefs
/// Geometric trait type
typedef typename CGAL::Default::Get<
GeomTraits,
typename Kernel_traits<
typename boost::property_traits<VertexPointMap>::value_type
>::Kernel >::type Geom_traits;
/// ErrorMetric type
typedef typename CGAL::Default::Get<ErrorMetric,
CGAL::VSA::L21_metric<TriangleMesh, VertexPointMap, false, Geom_traits> >::type Error_metric;
/// ProxyFitting type
typedef typename CGAL::Default::Get<ProxyFitting,
CGAL::VSA::L21_proxy_fitting<TriangleMesh, VertexPointMap, Geom_traits> >::type Proxy_fitting;
/// Proxy type
typedef typename Error_metric::Proxy Proxy;
// 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_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::Compute_scalar_product_3 Compute_scalar_product_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 boost::associative_property_map<boost::unordered_map<vertex_descriptor, std::size_t> > Vertex_anchor_map;
typedef std::vector<halfedge_descriptor> Chord_vector;
typedef typename Chord_vector::iterator Chord_vector_iterator;
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
public:
#endif
// The proxy wrapper for approximation.
struct Proxy_wrapper {
Proxy_wrapper(const Proxy &p, const std::size_t &i, const face_descriptor &s)
: px(p), idx(i), seed(s), err(0.0) {}
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
};
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
private:
#endif
// 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 facet candidate to be queued.
struct Facet_to_integrate {
Facet_to_integrate(const face_descriptor &_f, const std::size_t &_px, const FT &_err)
: f(_f), px(_px), err(_err) {}
bool operator<(const Facet_to_integrate &rhs) const {
return err > rhs.err;
}
face_descriptor f; // facet
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 average positioned 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 border cycle of a region.
// One region may have multiple border cycles.
struct Border {
Border(const halfedge_descriptor &h)
: he_head(h), num_anchors(0) {}
halfedge_descriptor he_head; // The heading halfedge of the border cylce.
std::size_t num_anchors; // The number of anchors on the border.
};
// Triangle polyhedron builder.
template <typename HDS>
class Triangle_polyhedron_builder : public CGAL::Modifier_base<HDS> {
const std::vector<Point_3> &vtxs;
const std::vector<std::vector<std::size_t> > &tris;
public:
bool is_manifold;
Triangle_polyhedron_builder(const std::vector<Point_3> &_vtxs,
const std::vector<std::vector<std::size_t> > &_tris)
: vtxs(_vtxs), tris(_tris), is_manifold(true) {}
void operator()(HDS &hds) {
CGAL::Polyhedron_incremental_builder_3<HDS> builder(hds, true);
typedef typename HDS::Vertex Vertex;
typedef typename Vertex::Point Point;
builder.begin_surface(vtxs.size(), tris.size());
BOOST_FOREACH(const Point_3 &v, vtxs)
builder.add_vertex(Point(v));
BOOST_FOREACH(const std::vector<std::size_t> &t, tris) {
std::vector<std::size_t>::const_iterator itr = t.begin();
if (builder.test_facet(itr, itr + 3)) {
builder.begin_facet();
builder.add_vertex_to_facet(*itr);
builder.add_vertex_to_facet(*(itr + 1));
builder.add_vertex_to_facet(*(itr + 2));
builder.end_facet();
}
else
is_manifold = false;
}
builder.end_surface();
}
};
// member variables
// The triangle mesh.
const TriangleMesh *m_pmesh;
// The mesh vertex point map.
VertexPointMap point_pmap;
// The error metric.
const Error_metric *fit_error;
// The proxy fitting functor.
const Proxy_fitting *proxy_fitting;
Construct_vector_3 vector_functor;
Construct_scaled_vector_3 scale_functor;
Construct_sum_of_vectors_3 sum_functor;
Compute_scalar_product_3 scalar_product_functor;
// The facet proxy index map.
boost::unordered_map<face_descriptor, std::size_t> internal_fidx_map;
boost::associative_property_map<boost::unordered_map<face_descriptor, std::size_t> > fproxy_map;
// The attached anchor index of a vertex.
boost::unordered_map<vertex_descriptor, std::size_t> internal_vidx_map;
Vertex_anchor_map vanchor_map;
// Proxies.
std::vector<Proxy_wrapper> proxies;
// Proxy planes
std::vector<Proxy_plane> px_planes;
// All anchors.
std::vector<Anchor> anchors;
// All borders cycles.
std::vector<Border> borders;
// The indexed triangle approximation.
std::vector<std::vector<std::size_t> > tris;
// meshing parameters
FT average_edge_length;
//member functions
public:
/*!
* %Default constructor.
*/
Mesh_approximation() :
m_pmesh(NULL),
fit_error(NULL),
proxy_fitting(NULL),
fproxy_map(internal_fidx_map),
vanchor_map(internal_vidx_map),
average_edge_length(0.0) {
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();
scalar_product_functor = traits.compute_scalar_product_3_object();
}
/*!
* Initialize and prepare for the approximation.
* @param _mesh `CGAL TriangleMesh` on which approximation operates.
* @param _point_pmap vertex point map of the mesh
*/
Mesh_approximation(const TriangleMesh &_mesh,
const VertexPointMap &_point_pmap) :
m_pmesh(&_mesh),
point_pmap(_point_pmap),
fit_error(NULL),
proxy_fitting(NULL),
fproxy_map(internal_fidx_map),
vanchor_map(internal_vidx_map),
average_edge_length(0.0) {
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();
scalar_product_functor = traits.compute_scalar_product_3_object();
}
/*!
* Set the mesh for approximation and rebuild the internal data structure.
* @pre @a _mesh.is_pure_triangle()
* @param _mesh `CGAL TriangleMesh` on which approximation operates.
* @param _point_pmap vertex point map of the mesh
*/
void set_mesh(const TriangleMesh &_mesh, const VertexPointMap &_point_pmap) {
m_pmesh = &_mesh;
point_pmap = _point_pmap;
rebuild();
}
/*!
* Set the error and fitting functor.
* @param _error_metric a `ErrorMetric` functor.
* @param _proxy_fitting a `ProxyFitting` functor.
*/
void set_metric(const Error_metric &_error_metric,
const Proxy_fitting &_proxy_fitting) {
fit_error = &_error_metric;
proxy_fitting = &_proxy_fitting;
}
/*!
* Rebuild the internal data structure.
*/
void rebuild() {
// cleanup
proxies.clear();
px_planes.clear();
anchors.clear();
borders.clear();
tris.clear();
if (!m_pmesh)
return;
// rebuild internal data structure
internal_fidx_map.clear();
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
internal_fidx_map[f] = CGAL_VSA_INVALID_TAG;
internal_vidx_map.clear();
BOOST_FOREACH(vertex_descriptor v, vertices(*m_pmesh))
internal_vidx_map.insert(
std::pair<vertex_descriptor, std::size_t>(v, CGAL_VSA_INVALID_TAG));
// compute average edge length
FT sum(0.0);
BOOST_FOREACH(edge_descriptor e, edges(*m_pmesh)) {
const vertex_descriptor vs = source(e, *m_pmesh);
const vertex_descriptor vt = target(e, *m_pmesh);
sum += FT(std::sqrt(CGAL::to_double(
CGAL::squared_distance(point_pmap[vs], point_pmap[vt]))));
}
average_edge_length = sum / num_edges(*m_pmesh);
}
/*!
* @brief Initialize the seeds with both maximum number of proxies
* and minmum error drop stop criteria.
* The first criterion met stops the seeding.
* Parameters out of range are ignored.
* @param method seeding method
* @param max_nb_proxies maximum target number of proxies,
* should be in range (0, num_faces(_mesh) / 3)
* @param min_error_drop minimum error drop,
* should be in range (0.0, 1.0)
* @param nb_relaxations number of interleaved refitting relaxations
* in incremental and hierarchical seeding
* @return number of proxies initialized
*/
std::size_t seeding(const Seeding method = Hierarchical,
const boost::optional<std::size_t> max_nb_proxies = boost::optional<std::size_t>(),
const boost::optional<FT> min_error_drop = boost::optional<FT>(),
const std::size_t nb_relaxations = 5) {
// maximum number of proxies internally, maybe better choice?
const std::size_t nb_px = num_faces(*m_pmesh) / 3;
if (min_error_drop && *min_error_drop > FT(0.0) && *min_error_drop < FT(1.0)) {
// as long as minimum error is specified and valid
// maximum number of proxies always exist, no matter specified or not or out of range
// there is always a maximum number of proxies explicitly (max_nb_proxies) or implicitly (nb_px)
std::size_t max_nb_px_adjusted = nb_px;
if (max_nb_proxies && *max_nb_proxies < nb_px && *max_nb_proxies > 0)
max_nb_px_adjusted = *max_nb_proxies;
switch (method) {
case Random:
return init_random_error(max_nb_px_adjusted, *min_error_drop, nb_relaxations);
case Incremental:
return init_incremental_error(max_nb_px_adjusted, *min_error_drop, nb_relaxations);
case Hierarchical:
return init_hierarchical_error(max_nb_px_adjusted, *min_error_drop, nb_relaxations);
default:
return 0;
}
}
else if (max_nb_proxies && *max_nb_proxies < nb_px && *max_nb_proxies > 0) {
// no valid min_error_drop provided, only max_nb_proxies
switch (method) {
case Random:
return init_random(*max_nb_proxies, nb_relaxations);
case Incremental:
return init_incremental(*max_nb_proxies, nb_relaxations);
case Hierarchical:
return init_hierarchical(*max_nb_proxies, nb_relaxations);
default:
return 0;
}
}
else {
// both parameters are unspecified or out of range
const FT e(0.1);
switch (method) {
case Random:
return init_random_error(nb_px, e, nb_relaxations);
case Incremental:
return init_incremental_error(nb_px, e, nb_relaxations);
case Hierarchical:
return init_hierarchical_error(nb_px, e, nb_relaxations);
default:
return 0;
}
}
}
/*!
* @brief Run the partitioning and fitting processes on the whole surface.
* @param nb_iterations number of iterations.
*/
void run(std::size_t nb_iterations = 1) {
for (std::size_t i = 0; i < nb_iterations; ++i) {
// tag the whole surface
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
fproxy_map[f] = CGAL_VSA_INVALID_TAG;
partition(proxies.begin(), proxies.end());
fit(proxies.begin(), proxies.end());
}
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
static std::size_t count = 0;
std::cerr << '#' << count++ << ": " << compute_fitting_error() << std::endl;
#endif
}
/*!
* @brief Run the partitioning and fitting process until no significant error change
* @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, false otherwise
*/
bool run_to_converge(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_fitting_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) {
run();
avg_err += compute_fitting_error();
}
avg_err /= static_cast<FT>(avg_interval);
drop_pct = (pre_err - avg_err) / pre_err;
// the error may fluctuates
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_fitting_error() {
BOOST_FOREACH(Proxy_wrapper &pxw, proxies)
pxw.err = FT(0.0);
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
std::size_t pxidx = fproxy_map[f];
proxies[pxidx].err += (*fit_error)(f, proxies[pxidx].px);
}
FT sum_error(0.0);
BOOST_FOREACH(const Proxy_wrapper &pxw, proxies)
sum_error += pxw.err;
return sum_error;
}
/*!
* @brief Add proxies to the worst regions one by one.
* The re-fitting is performed after each proxy is inserted.
* @pre current facet proxy map is valid
* @note after the addition, the facet proxy map remains valid
* @param num_proxies number of proxies to be added
* @param nb_iterations number of re-fitting iterations
* @return number of proxies added
*/
std::size_t add_proxies_furthest(const std::size_t num_proxies,
const std::size_t nb_iterations = 5) {
std::size_t num_added = 0;
for (; num_added < num_proxies; ++num_added) {
if (!add_proxy_furthest())
break;
run(nb_iterations);
}
return num_added;
}
/*!
* @brief Add proxies by diffusing fitting error into current partitions.
* Each partition is added with the number of proxies in proportional to its fitting error.
* @pre current facet proxy map is valid
* @note after the addition, the facet proxy map is invalid
* @param num_proxies number of proxies to be added
* @return number of proxies successfully added
*/
std::size_t add_proxies_error_diffusion(const std::size_t num_proxies) {
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#px " << proxies.size() << std::endl;
#endif
const FT sum_error = compute_fitting_error();
const FT avg_error = sum_error / FT(static_cast<double>(num_proxies));
std::vector<Proxy_error> px_error;
for (std::size_t i = 0; i < proxies.size(); ++i)
px_error.push_back(Proxy_error(i, proxies[i].err));
// sort partition by error
std::sort(px_error.begin(), px_error.end());
// number of proxies to be added to each region
std::vector<std::size_t> num_to_add(proxies.size(), 0);
if (avg_error == FT(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 facets" << std::endl;
#endif
const FT avg_facet = FT(
static_cast<double>(num_faces(*m_pmesh)) / static_cast<double>(num_proxies));
std::vector<FT> px_size(proxies.size(), FT(0.0));
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
px_size[fproxy_map[f]] += FT(1.0);
FT residual(0.0);
for (std::size_t i = 0; i < proxies.size(); ++i) {
FT to_add = (residual + px_size[i]) / avg_facet;
FT floor_to_add = FT(std::floor(CGAL::to_double(to_add)));
FT q_to_add = FT(CGAL::to_double(
((to_add - floor_to_add) > FT(0.5)) ? (floor_to_add + FT(1.0)) : floor_to_add));
residual = (to_add - q_to_add) * avg_facet;
num_to_add[i] = static_cast<std::size_t>(CGAL::to_double(q_to_add));
}
}
else {
// residual from previous proxy in range (-0.5, 0.5] * avg_error
FT residual(0.0);
BOOST_FOREACH(const Proxy_error &pxe, px_error) {
// add error residual from previous proxy
// to_add maybe negative but greater than -0.5
FT to_add = (residual + pxe.err) / avg_error;
// floor_to_add maybe negative but no less than -1
FT floor_to_add = FT(std::floor(CGAL::to_double(to_add)));
FT q_to_add = FT(CGAL::to_double(
((to_add - floor_to_add) > FT(0.5)) ? (floor_to_add + FT(1.0)) : floor_to_add));
residual = (to_add - q_to_add) * avg_error;
num_to_add[pxe.px] = static_cast<std::size_t>(CGAL::to_double(q_to_add));
}
}
#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;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
const std::size_t px_id = fproxy_map[f];
if (proxies[px_id].seed == f)
continue;
if (num_to_add[px_id] > 0) {
proxies.push_back(fit_new_proxy(f, proxies.size()));
--num_to_add[px_id];
++num_added;
}
}
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#requested/added "
<< num_proxies << '/' << num_added << std::endl;
#endif
return num_added;
}
/*!
* @brief Teleport the local minima to the worst region, this combines 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 num_proxies number of proxies request to teleport
* @param num_iterations number of re-fitting iterations
* @param if_test true if do the merge test before the teleportation (attempt to escape from local minima).
* @return number of proxies teleported.
*/
std::size_t teleport_proxies(const std::size_t num_proxies,
const std::size_t num_iterations = 5,
const bool if_test = true) {
std::size_t num_teleported = 0;
while (num_teleported < num_proxies) {
// find worst proxy
compute_fitting_error();
std::size_t px_worst = 0;
FT max_error = proxies.front().err;
for (std::size_t i = 0; i < proxies.size(); ++i) {
if (max_error < proxies[i].err) {
max_error = proxies[i].err;
px_worst = i;
}
}
bool found = false;
face_descriptor tele_to;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
if (fproxy_map[f] == px_worst && f != 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
std::size_t px_enlarged = 0, px_merged = 0;
if (!find_best_merge(px_enlarged, px_merged, if_test))
return num_teleported;
if (px_worst == px_enlarged || px_worst == px_merged)
return num_teleported;
// teleport to a facet of the worst region
// update merged proxies
std::list<face_descriptor> merged_patch;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
std::size_t &px_idx = fproxy_map[f];
if (px_idx == px_enlarged || px_idx == px_merged) {
px_idx = px_enlarged;
merged_patch.push_back(f);
}
}
proxies[px_enlarged] = fit_new_proxy(merged_patch.begin(), merged_patch.end(), px_enlarged);
// replace the merged proxy position to the newly teleported proxy
proxies[px_merged] = fit_new_proxy(tele_to, px_merged);
fproxy_map[tele_to] = px_merged;
num_teleported++;
// coarse re-fitting
run(num_iterations);
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "teleported" << std::endl;
#endif
}
return num_teleported;
}
/*!
* @brief Merge two specified adjacent regions.
* The overall re-fitting is not performed and the proxy map is maintained.
* @pre two proxies must be adjacent, and px0 < px1 < proxies.size()
* @param px0 the enlarged proxy
* @param px1 the merged proxy
* @return change of error
*/
FT merge(const std::size_t px0, const std::size_t px1) {
// ensure px0 < px1
if (px0 >= px1 || px1 >= proxies.size())
return FT(0.0);
// merge px1 to px0
FT err_sum(0.0);
std::list<face_descriptor> merged_patch;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
std::size_t px_idx = fproxy_map[f];
if (px_idx == px1 || px_idx == px0) {
err_sum += (*fit_error)(f, proxies[px_idx].px);
fproxy_map[f] = px0;
merged_patch.push_back(f);
}
}
proxies[px0] = fit_new_proxy(merged_patch.begin(), merged_patch.end(), px0);
// erase px1 and maintain proxy index
proxies.erase(proxies.begin() + px1);
for (std::size_t i = 0; i < proxies.size(); ++i)
proxies[i].idx = i;
// keep facet proxy map valid
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
if (fproxy_map[f] > px1)
--fproxy_map[f];
}
FT err_merged(0.0);
BOOST_FOREACH(face_descriptor f, merged_patch)
err_merged += (*fit_error)(f, proxies[px0].px);
return err_merged - err_sum;
}
/*!
* @brief Simulate merging and local re-fitting of all two adjacent proxies
* and find the best two regions to merge.
* Currently, the 'best' is defined as the minimum merged sum error among all adjacent pairs.
* @param px_enlarged the proxy to be enlarged
* @param px_merged the proxy to be merged
* @param if_test set true to activate the merge test
* @return true if found, false otherwise
*/
bool find_best_merge(std::size_t &px_enlarged, std::size_t &px_merged, const bool if_test) {
typedef typename boost::graph_traits<TriangleMesh>::edge_descriptor edge_descriptor;
typedef std::pair<std::size_t, std::size_t> ProxyPair;
typedef std::set<ProxyPair> MergedPair;
std::vector<std::list<face_descriptor> > px_facets(proxies.size());
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
px_facets[fproxy_map[f]].push_back(f);
// find best merge
MergedPair merged_set;
FT min_merged_error = FT(0.0);
bool first_merge = true;
BOOST_FOREACH(edge_descriptor e, edges(*m_pmesh)) {
if (CGAL::is_border(e, *m_pmesh))
continue;
std::size_t pxi = fproxy_map[face(halfedge(e, *m_pmesh), *m_pmesh)];
std::size_t pxj = fproxy_map[face(opposite(halfedge(e, *m_pmesh), *m_pmesh), *m_pmesh)];
if (pxi == pxj)
continue;
if (pxi > pxj)
std::swap(pxi, pxj);
if (merged_set.find(ProxyPair(pxi, pxj)) != merged_set.end())
continue;
std::list<face_descriptor> merged_patch(px_facets[pxi]);
BOOST_FOREACH(face_descriptor f, px_facets[pxj])
merged_patch.push_back(f);
Proxy_wrapper pxw = fit_new_proxy(merged_patch.begin(), merged_patch.end(), CGAL_VSA_INVALID_TAG);
FT sum_error(0.0);
BOOST_FOREACH(face_descriptor f, merged_patch)
sum_error += (*fit_error)(f, pxw.px);
merged_set.insert(ProxyPair(pxi, pxj));
if (first_merge || sum_error < min_merged_error) {
first_merge = false;
min_merged_error = sum_error;
px_enlarged = pxi;
px_merged = pxj;
}
}
// test if merge worth it
if (if_test) {
compute_fitting_error();
FT max_error = proxies.front().err;
for (std::size_t i = 0; i < proxies.size(); ++i) {
if (max_error < proxies[i].err)
max_error = proxies[i].err;
}
const FT merge_thre = max_error / FT(2.0);
const FT increase = min_merged_error - (proxies[px_enlarged].err + proxies[px_merged].err);
if (increase > merge_thre)
return false;
}
return true;
}
/*!
* @brief Split one proxy area by default bisection, but N-section is also possible.
* @pre valid facet proxy map
* @param px_idx proxy index
* @param n number of split sections
* @param nb_relaxations number of relaxation on the confined proxy area
* @return true if split succeeds, 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 >= proxies.size() || n < 2)
return false;
// collect confined proxy area
std::vector<face_descriptor> confined_area;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
if (fproxy_map[f] == px_idx)
confined_area.push_back(f);
// not enough facets to split
if (n > confined_area.size())
return false;
// a copy of confined proxies
std::vector<Proxy_wrapper> confined_proxies;
confined_proxies.push_back(proxies[px_idx]);
// select seed facets in the confiend area
std::size_t count = 1;
BOOST_FOREACH(face_descriptor f, confined_area) {
if (count >= n)
break;
if (fproxy_map[f] == px_idx && f != proxies[px_idx].seed) {
fproxy_map[f] = proxies.size();
proxies.push_back(fit_new_proxy(f, proxies.size()));
++count;
// copy
confined_proxies.push_back(proxies.back());
}
}
// relaxation on confined area and proxies
for (std::size_t i = 0; i < nb_relaxations; ++i) {
BOOST_FOREACH(face_descriptor f, confined_area)
fproxy_map[f] = CGAL_VSA_INVALID_TAG;
partition(confined_proxies.begin(), confined_proxies.end());
fit(confined_proxies.begin(), confined_proxies.end());
}
// copy back
BOOST_FOREACH(const Proxy_wrapper &pxw, confined_proxies)
proxies[pxw.idx] = pxw;
return true;
}
/*!
* @brief Extract the approximated surface mesh.
* @note If the extracted surface mesh contains non-manifold facets,
* they are not built into the output polyhedron.
* @tparam PolyhedronSurface should be `CGAL::Polyhedron_3`
* @param[out] tm_out output triangle mesh
* @param chord_error boundary approximation recursively split criterion
* @param is_relative_to_chord true if the chord_error is relative to the the chord length (relative sense),
* otherwise it's relative to the average edge length (absolute sense).
* @param with_dihedral_angle true if add dihedral angle weight to the distance, false otherwise
* @param pca_plane true if use PCA plane fitting, otherwise use the default area averaged plane parameters
* @return true if the extracted surface mesh is manifold, false otherwise.
*/
template <typename PolyhedronSurface>
bool extract_mesh(PolyhedronSurface &tm_out,
const FT chord_error = FT(5.0),
const bool is_relative_to_chord = false,
const bool with_dihedral_angle = false,
const bool pca_plane = false) {
// initialize all vertex anchor status
BOOST_FOREACH(vertex_descriptor v, vertices(*m_pmesh))
internal_vidx_map[v] = CGAL_VSA_INVALID_TAG;
anchors.clear();
borders.clear();
tris.clear();
px_planes.clear();
init_proxy_planes(pca_plane);
find_anchors();
find_edges(chord_error, is_relative_to_chord, with_dihedral_angle);
add_anchors();
pseudo_cdt();
return build_polyhedron_surface(tm_out);
}
/*!
* @brief Get the facet-proxy index map.
* @tparam FacetProxyMap `WritablePropertyMap` with
* `boost::graph_traits<TriangleMesh>::%face_descriptor` as key and `std::size_t` as value type
* @param[out] facet_proxy_map facet proxy index map
*/
template <typename FacetProxyMap>
void get_proxy_map(FacetProxyMap &facet_proxy_map) const {
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
facet_proxy_map[f] = fproxy_map[f];
}
/*!
* @brief Get the facet 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_itr output iterator
*/
template <typename OutputIterator>
void get_proxy_region(const std::size_t px_idx, OutputIterator out_itr) const {
if (px_idx >= proxies.size())
return;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
if (fproxy_map[f] == px_idx)
*out_itr++ = f;
}
/*!
* @brief Get the proxies.
* @tparam OutputIterator output iterator with Proxy as value type
* @param out_itr output iterator
*/
template <typename OutputIterator>
void get_proxies(OutputIterator out_itr) const {
BOOST_FOREACH(const Proxy_wrapper &pxw, proxies)
*out_itr++ = pxw.px;
}
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
/*!
* @brief Get the wrapped proxies.
* @tparam OutputIterator output iterator with Proxy_wrapper as value type
* @param out_itr output iterator
*/
template <typename OutputIterator>
void get_wrapped_proxies(OutputIterator out_itr) const {
BOOST_FOREACH(const Proxy_wrapper &pxw, proxies)
*out_itr++ = pxw;
}
#endif
/*!
* @brief Get the proxies size.
* @return number of proxies
*/
std::size_t get_proxies_size() const { return proxies.size(); }
/*!
* @brief Get 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_itr output iterator
*/
template <typename OutputIterator>
void get_anchor_points(OutputIterator out_itr) const {
BOOST_FOREACH(const Anchor &a, anchors)
*out_itr++ = a.pos;
}
/*!
* @brief Get the anchor vertices.
* @tparam OutputIterator output iterator with vertex_descriptor as value type
* @param out_itr output iterator
*/
template <typename OutputIterator>
void get_anchor_vertices(OutputIterator out_itr) const {
BOOST_FOREACH(const Anchor &a, anchors)
*out_itr++ = a.vtx;
}
/*!
* @brief Get the indexed triangles,
* one triplet of integers per triangles, which refers to the anchor point indexes.
* @tparam OutputIterator output iterator with std::vector<size_t> as value type
* @param out_itr output iterator
*/
template <typename OutputIterator>
void get_indexed_triangles(OutputIterator out_itr) const {
BOOST_FOREACH(const std::vector<std::size_t> &t, tris)
*out_itr++ = t;
}
/*!
* @brief Get the indexed boundary polygon approximation.
* @tparam OutputIterator output iterator with std::vector<std::size_t> as value type
*/
template <typename OutputIterator>
void get_indexed_boundary_polygons(OutputIterator out_itr) const {
for (typename std::vector<Border>::const_iterator bitr = borders.begin();
bitr != borders.end(); ++bitr) {
std::vector<std::size_t> bdr;
const halfedge_descriptor he_mark = bitr->he_head;
halfedge_descriptor he = he_mark;
do {
Chord_vector chord;
walk_to_next_anchor(he, chord);
bdr.push_back(vanchor_map[target(he, *m_pmesh)]);
} while (he != he_mark);
*out_itr++ = bdr;
}
}
// private member functions
private:
/*!
* @brief Random initialize proxies to target number of proxies.
* @note To ensure the randomness, call `std::srand()` beforehand.
* @param max_nb_proxies maximum number of proxies,
* should be in range (0, num_faces(*m_pmesh))
* @param num_iterations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_random(const std::size_t max_nb_proxies,
const std::size_t num_iterations) {
// fill a temporary vector of facets
std::vector<face_descriptor> facets;
random_shuffle_facets(facets);
proxies.clear();
// reach to the number of proxies
for (std::size_t i = 0; i < max_nb_proxies; ++i)
proxies.push_back(fit_new_proxy(facets[i], proxies.size()));
run(num_iterations);
return proxies.size();
}
/*!
* @brief Incremental initialize proxies to target number of proxies.
* @param max_nb_proxies maximum number of proxies,
* should be in range (0, num_faces(*m_pmesh))
* @param num_iterations number of re-fitting iterations
* before each incremental proxy insertion
* @return number of proxies initialized
*/
std::size_t init_incremental(const std::size_t max_nb_proxies,
const std::size_t num_iterations) {
// initialize a proxy and the proxy map to prepare for the insertion
bootstrap_from_first_facet();
add_proxies_furthest(max_nb_proxies - 1, num_iterations);
return proxies.size();
}
/*!
* @brief Hierarchical initialize proxies to target number of proxies.
* @param max_nb_proxies maximum number of proxies,
* should be in range (0, num_faces(*m_pmesh))
* @param num_iterations number of re-fitting iterations
* before each hierarchical proxy insertion
* @return number of proxies initialized
*/
std::size_t init_hierarchical(const std::size_t max_nb_proxies,
const std::size_t num_iterations) {
// initialize a proxy and the proxy map to prepare for the insertion
bootstrap_from_first_facet();
while (proxies.size() < max_nb_proxies) {
// try to double current number of proxies each time
std::size_t target_px = proxies.size();
if (target_px * 2 > max_nb_proxies)
target_px = max_nb_proxies;
else
target_px *= 2;
// add proxies by error diffusion
add_proxies_error_diffusion(target_px - proxies.size());
run(num_iterations);
}
return proxies.size();
}
/*!
* @brief Randomly initialize proxies
* with both maximum number of proxies and minimum error drop stop criteria,
* 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 (0, num_faces(_mesh) / 3)
* @param min_error_drop minimum error drop, should be in range (0.0, 1.0)
* @param num_iterations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_random_error(const std::size_t max_nb_proxies,
const FT min_error_drop,
const std::size_t num_iterations) {
// fill a temporary vector of facets
std::vector<face_descriptor> facets;
random_shuffle_facets(facets);
bootstrap_from_first_facet();
const FT initial_err = compute_fitting_error();
FT error_drop = min_error_drop * FT(2.0);
while (proxies.size() < max_nb_proxies && error_drop > min_error_drop) {
// try to double current number of proxies each time
std::size_t target_px = proxies.size();
if (target_px * 2 > max_nb_proxies)
target_px = max_nb_proxies;
else
target_px *= 2;
proxies.clear();
for (std::size_t j = 0; j < target_px; ++j)
proxies.push_back(fit_new_proxy(facets[j], proxies.size()));
run(num_iterations);
const FT err = compute_fitting_error();
error_drop = err / initial_err;
}
return proxies.size();
}
/*!
* @brief Incrementally initialize 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 (0, num_faces(_mesh) / 3)
* @param min_error_drop minimum error drop, should be in range (0.0, 1.0)
* @param num_iterations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_incremental_error(const std::size_t max_nb_proxies,
const FT min_error_drop,
const std::size_t num_iterations) {
// initialize a proxy and the proxy map to prepare for the insertion
bootstrap_from_first_facet();
const FT initial_err = compute_fitting_error();
FT error_drop = min_error_drop * FT(2.0);
while (proxies.size() < max_nb_proxies && error_drop > min_error_drop) {
add_proxy_furthest();
run(num_iterations);
const FT err = compute_fitting_error();
error_drop = err / initial_err;
}
return proxies.size();
}
/*!
* @brief Hierarchically initialize 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 (0, num_faces(_mesh) / 3)
* @param min_error_drop minimum error drop, should be in range (0.0, 1.0)
* @param num_iterations number of re-fitting iterations
* @return number of proxies initialized
*/
std::size_t init_hierarchical_error(const std::size_t max_nb_proxies,
const FT min_error_drop,
const std::size_t num_iterations) {
// initialize a proxy and the proxy map to prepare for the insertion
bootstrap_from_first_facet();
const FT initial_err = compute_fitting_error();
FT error_drop = min_error_drop * FT(2.0);
while (proxies.size() < max_nb_proxies && error_drop > min_error_drop) {
// try to double current number of proxies each time
std::size_t target_px = proxies.size();
if (target_px * 2 > max_nb_proxies)
target_px = max_nb_proxies;
else
target_px *= 2;
add_proxies_error_diffusion(target_px - proxies.size());
run(num_iterations);
const FT err = compute_fitting_error();
error_drop = err / initial_err;
}
return proxies.size();
}
/*!
* @brief Partition the area tagged with CGAL_VSA_INVALID_TAG with proxies, global facet proxy map is updated.
* Propagates the proxy seed facets 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<Facet_to_integrate> facet_pqueue;
for (ProxyWrapperIterator pxw_itr = beg; pxw_itr != end; ++pxw_itr) {
face_descriptor f = pxw_itr->seed;
fproxy_map[f] = pxw_itr->idx;
BOOST_FOREACH(face_descriptor fadj, faces_around_face(halfedge(f, *m_pmesh), *m_pmesh)) {
if (fadj != boost::graph_traits<TriangleMesh>::null_face()
&& fproxy_map[fadj] == CGAL_VSA_INVALID_TAG) {
facet_pqueue.push(Facet_to_integrate(
fadj, pxw_itr->idx, (*fit_error)(fadj, pxw_itr->px)));
}
}
}
while (!facet_pqueue.empty()) {
const Facet_to_integrate c = facet_pqueue.top();
facet_pqueue.pop();
if (fproxy_map[c.f] == CGAL_VSA_INVALID_TAG) {
fproxy_map[c.f] = c.px;
BOOST_FOREACH(face_descriptor fadj, faces_around_face(halfedge(c.f, *m_pmesh), *m_pmesh)) {
if (fadj != boost::graph_traits<TriangleMesh>::null_face()
&& fproxy_map[fadj] == CGAL_VSA_INVALID_TAG) {
facet_pqueue.push(Facet_to_integrate(
fadj, c.px, (*fit_error)(fadj, proxies[c.px].px)));
}
}
}
}
}
/*!
* @brief Refitting and update input range of proxies.
* @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 fit(const ProxyWrapperIterator beg, const ProxyWrapperIterator end) {
std::vector<std::list<face_descriptor> > px_facets(proxies.size());
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
px_facets[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_new_proxy(px_facets[px_idx].begin(), px_facets[px_idx].end(), px_idx);
}
}
/*!
* @brief Add a proxy seed at the facet with the maximum fitting error.
* @pre current facet proxy map is valid, proxy error is computed
* @note No re-fitting is performed. After the operation, the facet proxy map remains valid.
* @return true add successfully, false otherwise
*/
bool add_proxy_furthest() {
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "add furthest " << proxies.size() << std::endl;
#endif
compute_fitting_error();
FT max_error = proxies.front().err;
std::size_t px_worst = 0;
for (std::size_t i = 0; i < proxies.size(); ++i) {
if (max_error < proxies[i].err) {
max_error = proxies[i].err;
px_worst = i;
}
}
face_descriptor fworst;
bool first = true;
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
std::size_t px_idx = fproxy_map[f];
if (px_idx != px_worst || f == proxies[px_idx].seed)
continue;
FT err = (*fit_error)(f, proxies[px_idx].px);
if (first || max_error < err) {
first = false;
max_error = err;
fworst = f;
}
}
if (first)
return false;
fproxy_map[fworst] = proxies.size();
proxies.push_back(fit_new_proxy(fworst, proxies.size()));
return true;
}
/*!
* @brief Fitting a new proxy.
* 1. Fit proxy parameters from a list of facets.
* 2. Set seed.
* @tparam FacetIterator face_descriptor container iterator
* @param beg container begin
* @param end container end
* @param px_idx proxy index
* @return fitted proxy wrapped with internal data
*/
template<typename FacetIterator>
Proxy_wrapper fit_new_proxy(const FacetIterator &beg,
const FacetIterator &end,
const std::size_t &px_idx) {
CGAL_assertion(beg != end);
// use proxy_fitting functor to fit proxy parameters
Proxy px = (*proxy_fitting)(beg, end);
// find proxy seed
face_descriptor seed = *beg;
FT err_min = (*fit_error)(*beg, px);
std::pair<FacetIterator, FacetIterator> facets(beg, end);
BOOST_FOREACH(face_descriptor f, facets) {
FT err = (*fit_error)(f, px);
if (err < err_min) {
err_min = err;
seed = f;
}
}
return Proxy_wrapper(px, px_idx, seed);
}
/*!
* @brief Fitting a new proxy from a single facet.
* 1. Fit proxy parameters from one facet.
* 2. Set seed.
* @param face_descriptor facet
* @param px_idx proxy index
* @return fitted proxy wrapped with internal data
*/
Proxy_wrapper fit_new_proxy(const face_descriptor &f, const std::size_t &px_idx) {
std::vector<face_descriptor> fvec(1, f);
// fit proxy parameters
Proxy px = (*proxy_fitting)(fvec.begin(), fvec.end());
return Proxy_wrapper(px, px_idx, f);
}
/*!
* @brief Random shuffle the surface facets into an empty vector.
* @param[out] facets shuffled facets vector
*/
void random_shuffle_facets(std::vector<face_descriptor> &facets) {
const std::size_t nbf = num_faces(*m_pmesh);
facets.reserve(nbf);
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
facets.push_back(f);
// random shuffle
for (std::size_t i = 0; i < nbf; ++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>(nbf - 1));
face_descriptor tmp = facets[r];
facets[r] = facets[i];
facets[i] = tmp;
}
}
/*!
* @brief Initialize a proxy from the first facet of the surface.
* @note This function clears proxy vector and set facet proxy map to initial state,
* intended only for bootstrapping initialization.
* Coarse approximation iteration is not performed, because it's inaccurate anyway
* and may cause serious degenerate cases(e.g. a standard cube mode).
*/
void bootstrap_from_first_facet() {
proxies.clear();
proxies.push_back(fit_new_proxy(*(faces(*m_pmesh).first), proxies.size()));
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
fproxy_map[f] = 0;
}
/*!
* @brief Initialize proxy planes.
* @param if_pca_plane true to use the PCA plane fitting
*/
void init_proxy_planes(const bool if_pca_plane) {
// fit proxy planes, areas, normals
std::vector<std::list<face_descriptor> > px_facets(proxies.size());
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh))
px_facets[fproxy_map[f]].push_back(f);
BOOST_FOREACH(const std::list<face_descriptor> &px_patch, px_facets) {
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);
BOOST_FOREACH(face_descriptor f, px_patch) {
halfedge_descriptor he = halfedge(f, *m_pmesh);
const Point_3 &p0 = point_pmap[source(he, *m_pmesh)];
const Point_3 &p1 = point_pmap[target(he, *m_pmesh)];
const Point_3 &p2 = point_pmap[target(next(he, *m_pmesh), *m_pmesh)];
const FT farea(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
const Vector_3 fnorm = CGAL::unit_normal(p0, p1, p2);
norm = sum_functor(norm, scale_functor(fnorm, farea));
area += farea;
}
norm = scale_functor(norm, FT(1.0 / std::sqrt(CGAL::to_double(norm.squared_length()))));
px_planes.push_back(Proxy_plane(fit_plane, norm, area));
}
}
/*!
* @brief Finds the anchors.
*/
void find_anchors() {
BOOST_FOREACH(vertex_descriptor vtx, vertices(*m_pmesh)) {
std::size_t border_count = 0;
BOOST_FOREACH(halfedge_descriptor h, halfedges_around_target(vtx, *m_pmesh)) {
if (CGAL::is_border_edge(h, *m_pmesh))
++border_count;
else if (fproxy_map[face(h, *m_pmesh)] != fproxy_map[face(opposite(h, *m_pmesh), *m_pmesh)])
++border_count;
}
if (border_count >= 3)
attach_anchor(vtx);
}
}
/*!
* @brief Finds and approximates the chord connecting the anchors.
* @param chord_error boundary chord approximation recursive split creterion
* @param is_relative_to_chord true if the chord_error is relative to the the chord length (relative sense),
* otherwise it's relative to the average edge length (absolute sense).
* @param with_dihedral_angle true if add dihedral angle weight to the distance, false otherwise
*/
void find_edges(const FT chord_error,
const bool is_relative_to_chord,
const bool with_dihedral_angle) {
// collect candidate halfedges in a set
std::set<halfedge_descriptor> he_candidates;
BOOST_FOREACH(halfedge_descriptor h, halfedges(*m_pmesh)) {
if (!CGAL::is_border(h, *m_pmesh)
&& (CGAL::is_border(opposite(h, *m_pmesh), *m_pmesh)
|| fproxy_map[face(h, *m_pmesh)] != fproxy_map[face(opposite(h, *m_pmesh), *m_pmesh)]))
he_candidates.insert(h);
}
// pick up one candidate halfedge each time and traverse the connected border
while (!he_candidates.empty()) {
halfedge_descriptor he_start = *he_candidates.begin();
walk_to_first_anchor(he_start);
// no anchor in this connected border, make a new anchor
if (!is_anchor_attached(he_start))
attach_anchor(he_start);
// a new connected border
borders.push_back(Border(he_start));
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#border " << borders.size() << std::endl;
#endif
const halfedge_descriptor he_mark = he_start;
do {
Chord_vector chord;
walk_to_next_anchor(he_start, chord);
borders.back().num_anchors += subdivide_chord(chord.begin(), chord.end(),
chord_error, is_relative_to_chord, with_dihedral_angle);
#ifdef CGAL_SURFACE_MESH_APPROXIMATION_DEBUG
std::cerr << "#chord_anchor " << borders.back().num_anchors << std::endl;
#endif
for (Chord_vector_iterator citr = chord.begin(); citr != chord.end(); ++citr)
he_candidates.erase(*citr);
} while (he_start != he_mark);
}
}
/*!
* @brief Adds anchors to the border cycles with only 2 anchors.
*/
void add_anchors() {
typedef typename std::vector<Border>::iterator BorderIterator;
for (BorderIterator bitr = borders.begin(); bitr != borders.end(); ++bitr) {
if (bitr->num_anchors > 2)
continue;
// 2 initial anchors at least
CGAL_assertion(bitr->num_anchors == 2);
// borders with only 2 initial anchors
const halfedge_descriptor he_mark = bitr->he_head;
Point_3 pt_begin = point_pmap[target(he_mark, *m_pmesh)];
Point_3 pt_end = pt_begin;
halfedge_descriptor he = he_mark;
Chord_vector 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 = point_pmap[target(he, *m_pmesh)];
++count;
}
} while (he != he_mark);
// anchor count may be increased to more than 2 afterwards
// due to the new anchors added by the neighboring border (< 2 anchors)
if (count > 2) {
bitr->num_anchors = count;
continue;
}
FT dist_max(0.0);
halfedge_descriptor he_max;
Vector_3 chord_vec = vector_functor(pt_begin, pt_end);
chord_vec = scale_functor(chord_vec,
FT(1.0 / std::sqrt(CGAL::to_double(chord_vec.squared_length()))));
for (Chord_vector_iterator citr = chord.begin(); citr != chord.end(); ++citr) {
Vector_3 vec = vector_functor(pt_begin, point_pmap[target(*citr, *m_pmesh)]);
vec = CGAL::cross_product(chord_vec, vec);
FT dist(std::sqrt(CGAL::to_double(vec.squared_length())));
if (dist > dist_max) {
dist_max = dist;
he_max = *citr;
}
}
attach_anchor(he_max);
// increase border anchors by one
bitr->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);
BOOST_FOREACH(vertex_descriptor v, vertices(*m_pmesh)) {
sg_vertex_descriptor sgv = add_vertex(gmain);
global_vanchor_map[sgv] = vanchor_map[v];
global_vtag_map[sgv] = vanchor_map[v];
vmap.insert(std::pair<vertex_descriptor, sg_vertex_descriptor>(v, sgv));
}
BOOST_FOREACH(edge_descriptor e, edges(*m_pmesh)) {
vertex_descriptor vs = source(e, *m_pmesh);
vertex_descriptor vt = target(e, *m_pmesh);
FT len(std::sqrt(CGAL::to_double(
CGAL::squared_distance(point_pmap[vs], point_pmap[vt]))));
add_edge(to_sgv_map[vs], to_sgv_map[vt], len, gmain);
}
std::vector<VertexVector> vertex_patches(proxies.size());
BOOST_FOREACH(vertex_descriptor v, vertices(*m_pmesh)) {
std::set<std::size_t> px_set;
BOOST_FOREACH(face_descriptor f, faces_around_target(halfedge(v, *m_pmesh), *m_pmesh)) {
if (f != boost::graph_traits<TriangleMesh>::null_face())
px_set.insert(fproxy_map[f]);
}
BOOST_FOREACH(std::size_t p, px_set)
vertex_patches[p].push_back(to_sgv_map[v]);
}
BOOST_FOREACH(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;
BOOST_FOREACH(sg_vertex_descriptor v, vpatch) {
if (is_anchor_attached(v, global_vanchor_map))
add_edge(superv, v, FT(0.0), gmain);
}
vpatch.push_back(superv);
}
// multi-source Dijkstra's shortest path algorithm applied to each proxy patch
BOOST_FOREACH(VertexVector &vpatch, vertex_patches) {
// construct subgraph
SubGraph &glocal = gmain.create_subgraph();
BOOST_FOREACH(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::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
BOOST_FOREACH(sg_vertex_descriptor v, 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 chord
BOOST_FOREACH(const Border &bdr, borders) {
const halfedge_descriptor he_mark = bdr.he_head;
halfedge_descriptor he = he_mark;
do {
Chord_vector chord;
walk_to_next_anchor(he, chord);
std::vector<FT> vdist;
vdist.push_back(FT(0.0));
BOOST_FOREACH(halfedge_descriptor h, chord) {
FT elen = global_eweight_map[edge(
to_sgv_map[source(h, *m_pmesh)],
to_sgv_map[target(h, *m_pmesh)],
gmain).first];
vdist.push_back(vdist.back() + elen);
}
FT half_chord_len = vdist.back() / FT(2.0);
const std::size_t anchorleft = vanchor_map[source(chord.front(), *m_pmesh)];
const std::size_t anchorright = vanchor_map[target(chord.back(), *m_pmesh)];
typename std::vector<FT>::iterator ditr = vdist.begin() + 1;
for (typename Chord_vector::iterator hitr = chord.begin();
hitr != chord.end() - 1; ++hitr, ++ditr) {
if (*ditr < half_chord_len)
global_vtag_map[to_sgv_map[target(*hitr, *m_pmesh)]] = anchorleft;
else
global_vtag_map[to_sgv_map[target(*hitr, *m_pmesh)]] = anchorright;
}
} while (he != he_mark);
}
// collect triangles
BOOST_FOREACH(face_descriptor f, faces(*m_pmesh)) {
halfedge_descriptor he = halfedge(f, *m_pmesh);
std::size_t i = global_vtag_map[to_sgv_map[source(he, *m_pmesh)]];
std::size_t j = global_vtag_map[to_sgv_map[target(he, *m_pmesh)]];
std::size_t k = global_vtag_map[to_sgv_map[target(next(he, *m_pmesh), *m_pmesh)]];
if (i != j && i != k && j != k) {
std::vector<std::size_t> t;
t.push_back(i);
t.push_back(j);
t.push_back(k);
tris.push_back(t);
}
}
}
/*!
* @brief Walks along the region border to the first halfedge pointing to a vertex associated with an anchor.
* @param[in/out] he_start region border 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 circular border
return;
}
}
/*!
* @brief Walks along the region border to the next anchor and records the path as @a chord.
* @param[in/out] he_start starting region border halfedge pointing to a vertex associated with an anchor
* @param[out] chord recorded path chord
*/
void walk_to_next_anchor(halfedge_descriptor &he_start, Chord_vector &chord) const {
do {
walk_to_next_border_halfedge(he_start);
chord.push_back(he_start);
} while (!is_anchor_attached(he_start));
}
/*!
* @brief Walks to next border halfedge.
* @param[in/out] he_start region border halfedge
*/
void walk_to_next_border_halfedge(halfedge_descriptor &he_start) const {
const std::size_t px_idx = fproxy_map[face(he_start, *m_pmesh)];
BOOST_FOREACH(halfedge_descriptor h, halfedges_around_target(he_start, *m_pmesh)) {
if (CGAL::is_border(h, *m_pmesh) || fproxy_map[face(h, *m_pmesh)] != px_idx) {
he_start = opposite(h, *m_pmesh);
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 chord_error the chord recursive split error threshold
* @param is_relative_to_chord true if the chord_error is relative to the the chord length (relative sense),
* otherwise it's relative to the average edge length (absolute sense).
* @param with_dihedral_angle true if add dihedral angle weight to the distance, false otherwise
* @return the number of anchors of the chord apart from the first one
*/
std::size_t subdivide_chord(
const Chord_vector_iterator &chord_begin,
const Chord_vector_iterator &chord_end,
const FT chord_error,
const bool is_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 = vanchor_map[source(he_first, *m_pmesh)];
const std::size_t anchor_last = vanchor_map[target(he_last, *m_pmesh)];
// do not subdivide trivial non-circular chord
if ((anchor_first != anchor_last) && (chord_size < 4))
return 1;
bool if_subdivide = false;
Chord_vector_iterator chord_max;
const Point_3 &pt_begin = point_pmap[source(he_first, *m_pmesh)];
const Point_3 &pt_end = point_pmap[target(he_last, *m_pmesh)];
if (anchor_first == anchor_last) {
// circular chord
CGAL_assertion(chord_size > 2);
FT dist_max(0.0);
for (Chord_vector_iterator citr = chord_begin; citr != chord_end; ++citr) {
FT dist = CGAL::squared_distance(pt_begin, point_pmap[target(*citr, *m_pmesh)]);
dist = FT(std::sqrt(CGAL::to_double(dist)));
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);
FT chord_len(std::sqrt(CGAL::to_double(chord_vec.squared_length())));
chord_vec = scale_functor(chord_vec, FT(1.0) / chord_len);
for (Chord_vector_iterator citr = chord_begin; citr != chord_end; ++citr) {
Vector_3 vec = vector_functor(pt_begin, point_pmap[target(*citr, *m_pmesh)]);
vec = CGAL::cross_product(chord_vec, vec);
FT dist(std::sqrt(CGAL::to_double(vec.squared_length())));
if (dist > dist_max) {
chord_max = citr;
dist_max = dist;
}
}
FT criterion = dist_max;
if (is_relative_to_chord)
criterion /= chord_len;
else
criterion /= average_edge_length;
if (with_dihedral_angle) {
// suppose the proxy normal angle is acute
std::size_t px_left = fproxy_map[face(he_first, *m_pmesh)];
std::size_t px_right = px_left;
if (!CGAL::is_border(opposite(he_first, *m_pmesh), *m_pmesh))
px_right = fproxy_map[face(opposite(he_first, *m_pmesh), *m_pmesh)];
FT norm_sin(1.0);
if (!CGAL::is_border(opposite(he_first, *m_pmesh), *m_pmesh)) {
Vector_3 vec = CGAL::cross_product(
px_planes[px_left].normal, px_planes[px_right].normal);
norm_sin = FT(std::sqrt(CGAL::to_double(scalar_product_functor(vec, vec))));
}
criterion *= norm_sin;
}
if (criterion > chord_error)
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,
chord_error, is_relative_to_chord, with_dihedral_angle);
const std::size_t num_right = subdivide_chord(chord_max + 1, chord_end,
chord_error, is_relative_to_chord, with_dihedral_angle);
return num_left + num_right;
}
return 1;
}
/*!
* @brief Return true if the target vertex of a halfedge is attached with an anchor, and false otherwise.
* @param he halfedge
*/
bool is_anchor_attached(const halfedge_descriptor &he) const {
return is_anchor_attached(target(he, *m_pmesh), vanchor_map);
}
/*!
* @brief Check if a vertex is attached with an anchor.
* @tparam VertexAnchorIndexMap `WritablePropertyMap` with `boost::graph_traights<TriangleMesh>::vertex_descriptor` as key and `std::size_t` as value type
* @param v vertex
* @param vertex_anchor_map vertex anchor index map
*/
template<typename VertexAnchorIndexMap>
bool is_anchor_attached(
const typename boost::property_traits<VertexAnchorIndexMap>::key_type &v,
const VertexAnchorIndexMap &vertex_anchor_map) const {
return vertex_anchor_map[v] != CGAL_VSA_INVALID_TAG;
}
/*!
* @brief Attachs an anchor to the vertex.
* @param vtx vertex
*/
void attach_anchor(const vertex_descriptor &vtx) {
vanchor_map[vtx] = anchors.size();
anchors.push_back(Anchor(vtx, compute_anchor_position(vtx)));
}
/*!
* @brief Attachs an anchor to the target vertex of the halfedge.
* @param he halfedge
*/
void attach_anchor(const halfedge_descriptor &he) {
vertex_descriptor vtx = target(he, *m_pmesh);
attach_anchor(vtx);
}
/*!
* @brief Calculate the anchor positions from a vertex.
* @param v the vertex descriptor
* @return the anchor position
*/
Point_3 compute_anchor_position(const vertex_descriptor &v) {
// construct an anchor from vertex and the incident proxies
std::set<std::size_t> px_set;
BOOST_FOREACH(halfedge_descriptor h, halfedges_around_target(v, *m_pmesh)) {
if (!CGAL::is_border(h, *m_pmesh))
px_set.insert(fproxy_map[face(h, *m_pmesh)]);
}
// construct an anchor from vertex and the incident proxies
FT avgx(0.0), avgy(0.0), avgz(0.0), sum_area(0.0);
const Point_3 vtx_pt = point_pmap[v];
for (std::set<std::size_t>::iterator pxitr = px_set.begin();
pxitr != px_set.end(); ++pxitr) {
std::size_t px_idx = *pxitr;
Point_3 proj = px_planes[px_idx].plane.projection(vtx_pt);
FT area = px_planes[px_idx].area; // TOFIX: use Vector and CGAL::ORIGIN + vector
avgx += proj.x() * area;
avgy += proj.y() * area;
avgz += proj.z() * area;
sum_area += area;
}
return Point_3(avgx / sum_area, avgy / sum_area, avgz / sum_area);
}
/*!
* @brief Use an incremental builder to build and test if the indexed triangle surface is manifold
* @tparam PolyhedronSurface should be `CGAL::Polyhedron_3`
* @param[out] poly input polyhedorn mesh
* @return true if build manifold surface successfully
*/
template <typename PolyhedronSurface>
bool build_polyhedron_surface(PolyhedronSurface &poly) {
std::vector<Point_3> vtx;
BOOST_FOREACH(const Anchor &a, anchors)
vtx.push_back(a.pos);
typedef typename PolyhedronSurface::HalfedgeDS HDS;
Triangle_polyhedron_builder<HDS> tpbuilder(vtx, tris);
poly.delegate(tpbuilder);
return tpbuilder.is_manifold;
}
/*!
* @brief Fit an area averaged plane from a range of facets.
* @tparam FacetIterator face_descriptor container iterator
* @param beg container begin
* @param end container end
* @return fitted plane
*/
template <typename FacetIterator>
Plane_3 fit_plane_area_averaged(const FacetIterator &beg, const FacetIterator &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 (FacetIterator fitr = beg; fitr != end; ++fitr) {
const halfedge_descriptor he = halfedge(*fitr, *m_pmesh);
const Point_3 &p0 = point_pmap[source(he, *m_pmesh)];
const Point_3 &p1 = point_pmap[target(he, *m_pmesh)];
const Point_3 &p2 = point_pmap[target(next(he, *m_pmesh), *m_pmesh)];
Vector_3 vec = vector_functor(CGAL::ORIGIN, CGAL::centroid(p0, p1, p2));
FT farea(std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
Vector_3 fnorm = 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;
}
norm = scale_functor(norm,
FT(1.0 / std::sqrt(CGAL::to_double(norm.squared_length()))));
cent = scale_functor(cent, FT(1.0) / sum_area);
return Plane_3(CGAL::ORIGIN + cent, norm);
}
/*!
* @brief Fit a plane from a range of facets with PCA algorithm.
* @tparam FacetIterator face_descriptor container iterator
* @param beg container begin
* @param end container end
* @return fitted plane
*/
template <typename FacetIterator>
Plane_3 fit_plane_pca(const FacetIterator &beg, const FacetIterator &end) {
CGAL_assertion(beg != end);
typedef typename Geom_traits::Triangle_3 Triangle_3;
std::list<Triangle_3> tri_list;
for (FacetIterator fitr = beg; fitr != end; ++fitr) {
halfedge_descriptor he = halfedge(*fitr, *m_pmesh);
const Point_3 &p0 = point_pmap[source(he, *m_pmesh)];
const Point_3 &p1 = point_pmap[target(he, *m_pmesh)];
const Point_3 &p2 = point_pmap[target(next(he, *m_pmesh), *m_pmesh)];
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 VSA
} // end namespace CGAL
#undef CGAL_VSA_INVALID_TAG
#endif // CGAL_SURFACE_MESH_APPROXIMATION_VSA_APPROXIMATION_H
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