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/* This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
* See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
* Author(s): Siargey Kachanovich
*
* Copyright (C) 2019 Inria
*
* Modification(s):
* - YYYY/MM Author: Description of the modification
*/
#ifndef MANIFOLD_TRACING_H_
#define MANIFOLD_TRACING_H_
#include <gudhi/IO/output_debug_traces_to_html.h> // for DEBUG_TRACES
#include <gudhi/Coxeter_triangulation/Query_result.h>
#include <boost/functional/hash.hpp>
#include <Eigen/Dense>
#include <queue>
#include <unordered_map>
namespace Gudhi {
namespace coxeter_triangulation {
/**
* \ingroup coxeter_triangulation
*/
/** \class Manifold_tracing
* \brief A class that assembles methods for manifold tracing algorithm.
*
* \tparam Triangulation_ The type of the ambient triangulation.
* Needs to be a model of the concept TriangulationForManifoldTracing.
*/
template <class Triangulation_>
class Manifold_tracing {
public:
using Simplex_handle = typename Triangulation_::Simplex_handle;
struct Simplex_hash {
typedef Simplex_handle argument_type;
typedef std::size_t result_type;
result_type operator()(const argument_type& s) const noexcept {
return boost::hash<typename Simplex_handle::Vertex>()(s.vertex());
}
};
public:
/** \brief Type of the output simplex map with keys of type Triangulation_::Simplex_handle
* and values of type Eigen::VectorXd.
* This type should be used for the output in the method manifold_tracing_algorithm.
*/
typedef std::unordered_map<Simplex_handle, Eigen::VectorXd, Simplex_hash> Out_simplex_map;
/**
* \brief Computes the set of k-simplices that intersect
* a boundaryless implicit manifold given by an intersection oracle, where k
* is the codimension of the manifold.
* The computation is based on the seed propagation --- it starts at the
* given seed points and then propagates along the manifold.
*
* \tparam Point_range Range of points of type Eigen::VectorXd.
* \tparam Intersection_oracle Intersection oracle that represents the manifold.
* Needs to be a model of the concept IntersectionOracle.
*
* \param[in] seed_points The range of points on the manifold from which
* the computation begins.
* \param[in] triangulation The ambient triangulation.
* \param[in] oracle The intersection oracle for the manifold.
* The ambient dimension needs to match the dimension of the
* triangulation.
* \param[out] out_simplex_map The output map, where the keys are k-simplices in
* the input triangulation that intersect the input manifold and the mapped values
* are the intersection points.
*/
template <class Point_range, class Intersection_oracle>
void manifold_tracing_algorithm(const Point_range& seed_points, const Triangulation_& triangulation,
const Intersection_oracle& oracle, Out_simplex_map& out_simplex_map) {
std::size_t cod_d = oracle.cod_d();
std::queue<Simplex_handle> queue;
for (const auto& p : seed_points) {
Simplex_handle full_simplex = triangulation.locate_point(p);
for (Simplex_handle face : full_simplex.face_range(cod_d)) {
Query_result<Simplex_handle> qr = oracle.intersects(face, triangulation);
if (qr.success && out_simplex_map.emplace(face, qr.intersection).second) {
#ifdef DEBUG_TRACES
mt_seed_inserted_list.push_back(MT_inserted_info(qr, face, false));
#endif
queue.emplace(face);
break;
}
}
}
while (!queue.empty()) {
Simplex_handle s = queue.front();
queue.pop();
for (auto cof : s.coface_range(cod_d + 1)) {
for (auto face : cof.face_range(cod_d)) {
Query_result<Simplex_handle> qr = oracle.intersects(face, triangulation);
if (qr.success && out_simplex_map.emplace(face, qr.intersection).second) queue.emplace(face);
}
}
}
}
/**
* \brief Computes the set of k-simplices that intersect
* the dimensional manifold given by an intersection oracle, where k
* is the codimension of the manifold.
* The computation is based on the seed propagation --- it starts at the
* given seed points and then propagates along the manifold.
*
* \tparam Point_range Range of points of type Eigen::VectorXd.
* \tparam Intersection_oracle Intersection oracle that represents the manifold.
* Needs to be a model of the concept IntersectionOracle.
*
* \param[in] seed_points The range of points on the manifold from which
* the computation begins.
* \param[in] triangulation The ambient triangulation.
* \param[in] oracle The intersection oracle for the manifold.
* The ambient dimension needs to match the dimension of the
* triangulation.
* \param[out] interior_simplex_map The output map, where the keys are k-simplices in
* the input triangulation that intersect the relative interior of the input manifold
* and the mapped values are the intersection points.
* \param[out] boundary_simplex_map The output map, where the keys are k-simplices in
* the input triangulation that intersect the boundary of the input manifold
* and the mapped values are the intersection points.
*/
template <class Point_range, class Intersection_oracle>
void manifold_tracing_algorithm(const Point_range& seed_points, const Triangulation_& triangulation,
const Intersection_oracle& oracle, Out_simplex_map& interior_simplex_map,
Out_simplex_map& boundary_simplex_map) {
std::size_t cod_d = oracle.cod_d();
std::queue<Simplex_handle> queue;
for (const auto& p : seed_points) {
Simplex_handle full_simplex = triangulation.locate_point(p);
for (Simplex_handle face : full_simplex.face_range(cod_d)) {
auto qr = oracle.intersects(face, triangulation);
#ifdef DEBUG_TRACES
mt_seed_inserted_list.push_back(MT_inserted_info(qr, face, false));
#endif
if (qr.success) {
if (oracle.lies_in_domain(qr.intersection, triangulation)) {
if (interior_simplex_map.emplace(face, qr.intersection).second) queue.emplace(face);
} else {
for (Simplex_handle cof : face.coface_range(cod_d + 1)) {
auto qrb = oracle.intersects_boundary(cof, triangulation);
#ifdef DEBUG_TRACES
mt_seed_inserted_list.push_back(MT_inserted_info(qrb, cof, true));
#endif
if (qrb.success) boundary_simplex_map.emplace(cof, qrb.intersection);
}
}
// break;
}
}
}
while (!queue.empty()) {
Simplex_handle s = queue.front();
queue.pop();
for (auto cof : s.coface_range(cod_d + 1)) {
for (auto face : cof.face_range(cod_d)) {
auto qr = oracle.intersects(face, triangulation);
#ifdef DEBUG_TRACES
mt_inserted_list.push_back(MT_inserted_info(qr, face, false));
#endif
if (qr.success) {
if (oracle.lies_in_domain(qr.intersection, triangulation)) {
if (interior_simplex_map.emplace(face, qr.intersection).second) queue.emplace(face);
} else {
auto qrb = oracle.intersects_boundary(cof, triangulation);
#ifdef DEBUG_TRACES
mt_inserted_list.push_back(MT_inserted_info(qrb, cof, true));
#endif
if (qrb.success) boundary_simplex_map.emplace(cof, qrb.intersection);
}
}
}
}
}
}
/** \brief Empty constructor */
Manifold_tracing() {}
};
/**
* \brief Static method for Manifold_tracing<Triangulation_>::manifold_tracing_algorithm
* that computes the set of k-simplices that intersect
* a boundaryless implicit manifold given by an intersection oracle, where k
* is the codimension of the manifold.
* The computation is based on the seed propagation --- it starts at the
* given seed points and then propagates along the manifold.
*
* \tparam Point_range Range of points of type Eigen::VectorXd.
* \tparam Triangulation_ The type of the ambient triangulation.
* Needs to be a model of the concept TriangulationForManifoldTracing.
* \tparam Intersection_oracle Intersection oracle that represents the manifold.
* Needs to be a model of the concept IntersectionOracle.
* \tparam Out_simplex_map Needs to be Manifold_tracing<Triangulation_>::Out_simplex_map.
*
* \param[in] seed_points The range of points on the manifold from which
* the computation begins.
* \param[in] triangulation The ambient triangulation.
* \param[in] oracle The intersection oracle for the manifold.
* The ambient dimension needs to match the dimension of the
* triangulation.
* \param[out] out_simplex_map The output map, where the keys are k-simplices in
* the input triangulation that intersect the input manifold and the mapped values
* are the intersection points.
*
* \ingroup coxeter_triangulation
*/
template <class Point_range, class Triangulation, class Intersection_oracle, class Out_simplex_map>
void manifold_tracing_algorithm(const Point_range& seed_points, const Triangulation& triangulation,
const Intersection_oracle& oracle, Out_simplex_map& out_simplex_map) {
Manifold_tracing<Triangulation> mt;
mt.manifold_tracing_algorithm(seed_points, triangulation, oracle, out_simplex_map);
}
/**
* \brief Static method for Manifold_tracing<Triangulation_>::manifold_tracing_algorithm
* the dimensional manifold given by an intersection oracle, where k
* is the codimension of the manifold.
* The computation is based on the seed propagation --- it starts at the
* given seed points and then propagates along the manifold.
*
* \tparam Point_range Range of points of type Eigen::VectorXd.
* \tparam Triangulation_ The type of the ambient triangulation.
* Needs to be a model of the concept TriangulationForManifoldTracing.
* \tparam Intersection_oracle Intersection oracle that represents the manifold.
* Needs to be a model of the concept IntersectionOracle.
* \tparam Out_simplex_map Needs to be Manifold_tracing<Triangulation_>::Out_simplex_map.
*
* \param[in] seed_points The range of points on the manifold from which
* the computation begins.
* \param[in] triangulation The ambient triangulation.
* \param[in] oracle The intersection oracle for the manifold.
* The ambient dimension needs to match the dimension of the
* triangulation.
* \param[out] interior_simplex_map The output map, where the keys are k-simplices in
* the input triangulation that intersect the relative interior of the input manifold
* and the mapped values are the intersection points.
* \param[out] boundary_simplex_map The output map, where the keys are k-simplices in
* the input triangulation that intersect the boundary of the input manifold
* and the mapped values are the intersection points.
*
* \ingroup coxeter_triangulation
*/
template <class Point_range, class Triangulation, class Intersection_oracle, class Out_simplex_map>
void manifold_tracing_algorithm(const Point_range& seed_points, const Triangulation& triangulation,
const Intersection_oracle& oracle, Out_simplex_map& interior_simplex_map,
Out_simplex_map& boundary_simplex_map) {
Manifold_tracing<Triangulation> mt;
mt.manifold_tracing_algorithm(seed_points, triangulation, oracle, interior_simplex_map, boundary_simplex_map);
}
} // namespace coxeter_triangulation
} // namespace Gudhi
#endif
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