937 lines
32 KiB
C
937 lines
32 KiB
C
|
// Copyright (c) 2013 Technical University Braunschweig (Germany).
|
||
|
|
// All rights reserved.
|
||
|
|
//
|
||
|
|
// This file is part of CGAL (www.cgal.org).
|
||
|
|
//
|
||
|
|
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Visibility_2/include/CGAL/Rotational_sweep_visibility_2.h $
|
||
|
|
// $Id: Rotational_sweep_visibility_2.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
|
||
|
|
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// Author(s): Kan Huang <huangkandiy@gmail.com>
|
||
|
|
//
|
||
|
|
|
||
|
|
#ifndef CGAL_ROTATIONAL_SWEEP_VISIBILITY_2_H
|
||
|
|
#define CGAL_ROTATIONAL_SWEEP_VISIBILITY_2_H
|
||
|
|
|
||
|
|
#include <CGAL/license/Visibility_2.h>
|
||
|
|
|
||
|
|
|
||
|
|
#include <CGAL/Visibility_2/visibility_utils.h>
|
||
|
|
#include <CGAL/Arrangement_2.h>
|
||
|
|
#include <CGAL/bounding_box.h>
|
||
|
|
#include <CGAL/assertions.h>
|
||
|
|
#include <CGAL/Kernel/global_functions_2.h>
|
||
|
|
#include <boost/unordered_map.hpp>
|
||
|
|
#include <iterator>
|
||
|
|
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
|
||
|
|
template<class Arrangement_2_ , class RegularizationCategory = CGAL::Tag_true >
|
||
|
|
class Rotational_sweep_visibility_2 {
|
||
|
|
public:
|
||
|
|
typedef Arrangement_2_ Arrangement_2;
|
||
|
|
typedef typename Arrangement_2::Traits_2 Traits_2;
|
||
|
|
typedef typename Arrangement_2::Geometry_traits_2 Geometry_traits_2;
|
||
|
|
typedef typename Arrangement_2::Vertex_const_handle Vertex_const_handle;
|
||
|
|
typedef typename Arrangement_2::Vertex_handle Vertex_handle;
|
||
|
|
typedef typename Arrangement_2::Halfedge_const_handle Halfedge_const_handle;
|
||
|
|
typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
|
||
|
|
typedef typename Arrangement_2::
|
||
|
|
Ccb_halfedge_const_circulator Ccb_halfedge_const_circulator;
|
||
|
|
typedef typename Arrangement_2::Face_const_handle Face_const_handle;
|
||
|
|
typedef typename Arrangement_2::Face_handle Face_handle;
|
||
|
|
|
||
|
|
typedef typename Geometry_traits_2::Kernel K;
|
||
|
|
typedef typename Geometry_traits_2::Point_2 Point_2;
|
||
|
|
typedef typename Geometry_traits_2::Ray_2 Ray_2;
|
||
|
|
typedef typename Geometry_traits_2::Segment_2 Segment_2;
|
||
|
|
typedef typename Geometry_traits_2::Line_2 Line_2;
|
||
|
|
typedef typename Geometry_traits_2::Vector_2 Vector_2;
|
||
|
|
typedef typename Geometry_traits_2::Direction_2 Direction_2;
|
||
|
|
typedef typename Geometry_traits_2::FT Number_type;
|
||
|
|
typedef typename Geometry_traits_2::Object_2 Object_2;
|
||
|
|
|
||
|
|
typedef RegularizationCategory Regularization_category;
|
||
|
|
typedef CGAL::Tag_true Supports_general_polygon_category;
|
||
|
|
typedef CGAL::Tag_true Supports_simple_polygon_category;
|
||
|
|
|
||
|
|
private:
|
||
|
|
typedef std::vector<Point_2> Points;
|
||
|
|
typedef Vertex_const_handle VH;
|
||
|
|
typedef std::vector<VH> VHs;
|
||
|
|
typedef Halfedge_const_handle EH;
|
||
|
|
typedef std::vector<EH> EHs;
|
||
|
|
|
||
|
|
class Less_edge: public CGAL::cpp98::binary_function<EH, EH, bool> {
|
||
|
|
const Geometry_traits_2* geom_traits;
|
||
|
|
public:
|
||
|
|
Less_edge() {}
|
||
|
|
Less_edge(const Geometry_traits_2* traits):geom_traits(traits) {}
|
||
|
|
bool operator() (const EH e1, const EH e2) const {
|
||
|
|
if (e1 == e2)
|
||
|
|
return false;
|
||
|
|
else {
|
||
|
|
return &(*e1)<&(*e2);
|
||
|
|
}
|
||
|
|
// if (e1->source() == e2->source())
|
||
|
|
// return Visibility_2::compare_xy_2(geom_traits,
|
||
|
|
// e1->target()->point(), e2->target()->point()) == SMALLER;
|
||
|
|
// else
|
||
|
|
// return Visibility_2::compare_xy_2(geom_traits,
|
||
|
|
// e1->source()->point(), e2->source()->point()) == SMALLER;
|
||
|
|
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
class Less_vertex: public CGAL::cpp98::binary_function<VH, VH, bool> {
|
||
|
|
const Geometry_traits_2* geom_traits;
|
||
|
|
public:
|
||
|
|
Less_vertex() {}
|
||
|
|
Less_vertex(const Geometry_traits_2* traits):geom_traits(traits) {}
|
||
|
|
bool operator() (const VH v1, const VH v2) const {
|
||
|
|
if (v1 == v2)
|
||
|
|
return false;
|
||
|
|
else
|
||
|
|
// I know this is dirty but it speeds up by 25%. Michael
|
||
|
|
return &(*v1)<&(*v2);
|
||
|
|
// return Visibility_2::
|
||
|
|
// compare_xy_2(geom_traits, v1->point(), v2->point()) == SMALLER;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
class Closer_edge: public CGAL::cpp98::binary_function<EH, EH, bool> {
|
||
|
|
const Geometry_traits_2* geom_traits;
|
||
|
|
Point_2 q;
|
||
|
|
public:
|
||
|
|
Closer_edge() {}
|
||
|
|
Closer_edge(const Geometry_traits_2* traits, const Point_2& q) :
|
||
|
|
geom_traits(traits), q(q) {}
|
||
|
|
|
||
|
|
int vtype(const Point_2& c, const Point_2& p) const {
|
||
|
|
switch(Visibility_2::orientation_2(geom_traits, q, c, p)) {
|
||
|
|
case COLLINEAR:
|
||
|
|
if (Visibility_2::less_distance_to_point_2(geom_traits, q, c, p))
|
||
|
|
return 0;
|
||
|
|
else
|
||
|
|
return 3;
|
||
|
|
case RIGHT_TURN:
|
||
|
|
return 1;
|
||
|
|
case LEFT_TURN:
|
||
|
|
return 2;
|
||
|
|
default: CGAL_assume(false);
|
||
|
|
}
|
||
|
|
return -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
bool operator() (const EH& e1, const EH& e2) const {
|
||
|
|
if (e1 == e2)
|
||
|
|
return false;
|
||
|
|
const Point_2& s1=e1->source()->point(),
|
||
|
|
t1=e1->target()->point(),
|
||
|
|
s2=e2->source()->point(),
|
||
|
|
t2=e2->target()->point();
|
||
|
|
if (e1->source() == e2->source()) {
|
||
|
|
|
||
|
|
int vt1 = vtype(s1, t1),
|
||
|
|
vt2 = vtype(s1, t2);
|
||
|
|
if (vt1 != vt2)
|
||
|
|
return vt1 > vt2;
|
||
|
|
else
|
||
|
|
return (Visibility_2::orientation_2(geom_traits, s1, t2, t1)==
|
||
|
|
Visibility_2::orientation_2(geom_traits, s1, t2, q));
|
||
|
|
}
|
||
|
|
|
||
|
|
if (e1->target() == e2->source()) {
|
||
|
|
// const Point_2& p1 = s1,
|
||
|
|
// p2 = t2,
|
||
|
|
// c = s2;
|
||
|
|
int vt1 = vtype(t1, s1),
|
||
|
|
vt2 = vtype(t1, t2);
|
||
|
|
if (vt1 != vt2)
|
||
|
|
return vt1 > vt2;
|
||
|
|
else
|
||
|
|
return (Visibility_2::orientation_2(geom_traits, s2, t2, s1)==
|
||
|
|
Visibility_2::orientation_2(geom_traits, s2, t2, q));
|
||
|
|
}
|
||
|
|
|
||
|
|
if (e1->source() == e2->target()) {
|
||
|
|
// const Point_2& p1 = t1,
|
||
|
|
// p2 = s2,
|
||
|
|
// c = s1;
|
||
|
|
int vt1 = vtype(s1, t1),
|
||
|
|
vt2 = vtype(s1, s2);
|
||
|
|
if (vt1 != vt2)
|
||
|
|
return vt1 > vt2;
|
||
|
|
else return (Visibility_2::orientation_2(geom_traits, s1, s2, t1)==
|
||
|
|
Visibility_2::orientation_2(geom_traits, s1, s2, q));
|
||
|
|
}
|
||
|
|
|
||
|
|
if (e1->target() == e2->target()) {
|
||
|
|
// const Point_2& p1 = s1,
|
||
|
|
// p2 = s2,
|
||
|
|
// c = t1;
|
||
|
|
int vt1 = vtype(t1, s1),
|
||
|
|
vt2 = vtype(t1, s2);
|
||
|
|
if (vt1 != vt2)
|
||
|
|
return vt1 > vt2;
|
||
|
|
else return (Visibility_2::orientation_2(geom_traits, t1, s2, s1)==
|
||
|
|
Visibility_2::orientation_2(geom_traits, t1, s2, q));
|
||
|
|
}
|
||
|
|
|
||
|
|
Orientation e1q = Visibility_2::orientation_2(geom_traits, s1, t1, q);
|
||
|
|
switch (e1q)
|
||
|
|
{
|
||
|
|
case COLLINEAR:
|
||
|
|
if (Visibility_2::collinear(geom_traits, q, s2, t2)) {
|
||
|
|
//q is collinear with e1 and e2.
|
||
|
|
return (Visibility_2::less_distance_to_point_2(geom_traits, q, s1, s2)
|
||
|
|
|| Visibility_2::less_distance_to_point_2(geom_traits, q, t1, t2));
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
//q is collinear with e1 not with e2.
|
||
|
|
if (Visibility_2::collinear(geom_traits, s2, t2, s1))
|
||
|
|
return (Visibility_2::orientation_2(geom_traits, s2, t2, q)
|
||
|
|
== Visibility_2::orientation_2(geom_traits, s2, t2, t1));
|
||
|
|
else
|
||
|
|
return (Visibility_2::orientation_2(geom_traits, s2, t2, q)
|
||
|
|
== Visibility_2::orientation_2(geom_traits, s2, t2, s1));
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
case RIGHT_TURN:
|
||
|
|
switch (Visibility_2::orientation_2(geom_traits, s1, t1, s2)) {
|
||
|
|
case COLLINEAR:
|
||
|
|
return Visibility_2::orientation_2(geom_traits, s1, t1, t2)!=e1q;
|
||
|
|
case RIGHT_TURN:
|
||
|
|
if (Visibility_2::orientation_2(geom_traits, s1, t1, t2) == LEFT_TURN)
|
||
|
|
return Visibility_2::orientation_2(geom_traits, s2, t2, q)
|
||
|
|
== Visibility_2::orientation_2(geom_traits, s2, t2, s1);
|
||
|
|
else
|
||
|
|
return false;
|
||
|
|
case LEFT_TURN:
|
||
|
|
if(Visibility_2::orientation_2(geom_traits, s1, t1, t2) == RIGHT_TURN)
|
||
|
|
return Visibility_2::orientation_2(geom_traits, s2, t2, q)
|
||
|
|
== Visibility_2::orientation_2(geom_traits, s2, t2, s1);
|
||
|
|
else
|
||
|
|
return true;
|
||
|
|
default: CGAL_assume(false);
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
case LEFT_TURN:
|
||
|
|
switch (Visibility_2::orientation_2(geom_traits, s1, t1, s2)) {
|
||
|
|
case COLLINEAR:
|
||
|
|
return Visibility_2::orientation_2(geom_traits, s1, t1, t2)!=e1q;
|
||
|
|
case LEFT_TURN:
|
||
|
|
if(Visibility_2::orientation_2(geom_traits, s1, t1, t2) == RIGHT_TURN)
|
||
|
|
return Visibility_2::orientation_2(geom_traits, s2, t2, q)
|
||
|
|
== Visibility_2::orientation_2(geom_traits, s2, t2, s1);
|
||
|
|
else
|
||
|
|
return false;
|
||
|
|
case RIGHT_TURN:
|
||
|
|
if (Visibility_2::orientation_2(geom_traits, s1, t1, t2) == LEFT_TURN)
|
||
|
|
return Visibility_2::orientation_2(geom_traits, s2, t2, q)
|
||
|
|
== Visibility_2::orientation_2(geom_traits, s2, t2, s1);
|
||
|
|
else
|
||
|
|
return true;
|
||
|
|
default: CGAL_assume(false);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL_assume(false);
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
const Arrangement_2 *p_arr;
|
||
|
|
const Geometry_traits_2 *geom_traits;
|
||
|
|
|
||
|
|
|
||
|
|
mutable Point_2 q; //query point
|
||
|
|
mutable Points polygon; //visibility polygon
|
||
|
|
|
||
|
|
mutable std::map<VH, EHs, Less_vertex> incident_edges;
|
||
|
|
|
||
|
|
mutable std::map<EH, int, Less_edge> edx; //index of active edges in
|
||
|
|
//the heap
|
||
|
|
|
||
|
|
mutable std::set<EH, Closer_edge> active_edges; //a set of edges that
|
||
|
|
//intersect the current
|
||
|
|
//vision ray.
|
||
|
|
|
||
|
|
mutable VHs vs; //angular sorted vertices
|
||
|
|
mutable EHs bad_edges; //edges that pass the query point
|
||
|
|
mutable VH cone_end1; //an end of visibility cone
|
||
|
|
mutable VH cone_end2; //another end of visibility cone
|
||
|
|
|
||
|
|
mutable typename Points::size_type cone_end1_idx;
|
||
|
|
//index of cone_end1->point() in
|
||
|
|
//visibility polygon
|
||
|
|
|
||
|
|
mutable typename Points::size_type cone_end2_idx;
|
||
|
|
//index of cone_end2->point() in
|
||
|
|
//visibility polygon
|
||
|
|
|
||
|
|
mutable bool is_vertex_query;
|
||
|
|
mutable bool is_edge_query;
|
||
|
|
mutable bool is_face_query;
|
||
|
|
mutable bool is_big_cone; //whether the angle of
|
||
|
|
//visibility_cone is greater than pi.
|
||
|
|
|
||
|
|
public:
|
||
|
|
Rotational_sweep_visibility_2(): p_arr(nullptr), geom_traits(nullptr) {}
|
||
|
|
Rotational_sweep_visibility_2(const Arrangement_2& arr): p_arr(&arr) {
|
||
|
|
geom_traits = p_arr->geometry_traits();
|
||
|
|
}
|
||
|
|
|
||
|
|
const std::string name() const { return std::string("R_visibility_2"); }
|
||
|
|
|
||
|
|
template <typename VARR>
|
||
|
|
typename VARR::Face_handle
|
||
|
|
compute_visibility(
|
||
|
|
const Point_2& q, const Halfedge_const_handle e, VARR& arr_out) const
|
||
|
|
{
|
||
|
|
arr_out.clear();
|
||
|
|
bad_edges.clear();
|
||
|
|
this->q = q;
|
||
|
|
|
||
|
|
if (Visibility_2::compare_xy_2(geom_traits, q, e->target()->point())==EQUAL)
|
||
|
|
{
|
||
|
|
is_vertex_query = true;
|
||
|
|
is_edge_query = false;
|
||
|
|
is_face_query = false;
|
||
|
|
cone_end1 = e->source();
|
||
|
|
cone_end2 = e->next()->target();
|
||
|
|
is_big_cone = CGAL::right_turn(cone_end1->point(), q, cone_end2->point());
|
||
|
|
|
||
|
|
typename Arrangement_2::
|
||
|
|
Halfedge_around_vertex_const_circulator first, curr;
|
||
|
|
first = curr = e->target()->incident_halfedges();
|
||
|
|
do {
|
||
|
|
if (curr->face() == e->face())
|
||
|
|
bad_edges.push_back(curr);
|
||
|
|
else if (curr->twin()->face() == e->face())
|
||
|
|
bad_edges.push_back(curr->twin());
|
||
|
|
} while (++curr != first);
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
is_vertex_query = false;
|
||
|
|
is_edge_query = true;
|
||
|
|
is_face_query = false;
|
||
|
|
cone_end1 = e->source();
|
||
|
|
cone_end2 = e->target();
|
||
|
|
bad_edges.push_back(e);
|
||
|
|
is_big_cone = false;
|
||
|
|
}
|
||
|
|
visibility_region_impl(e->face(), q);
|
||
|
|
|
||
|
|
//decide which inside of the visibility butterfly is needed.
|
||
|
|
typename Points::size_type small_idx, big_idx;
|
||
|
|
if ( cone_end1_idx < cone_end2_idx ) {
|
||
|
|
small_idx = cone_end1_idx;
|
||
|
|
big_idx = cone_end2_idx;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
small_idx = cone_end2_idx;
|
||
|
|
big_idx = cone_end1_idx;
|
||
|
|
}
|
||
|
|
typename Points::size_type next_idx = small_idx + 1;
|
||
|
|
bool is_between;
|
||
|
|
//indicate whether the shape between small_idx and big_idx is the visibility
|
||
|
|
//region required.
|
||
|
|
if (CGAL::right_turn(cone_end1->point(), q, cone_end2->point())) {
|
||
|
|
is_between = false;
|
||
|
|
while (next_idx != big_idx) {
|
||
|
|
if (CGAL::left_turn(cone_end1->point(), q, polygon[next_idx]) ||
|
||
|
|
CGAL::left_turn(q, cone_end2->point(), polygon[next_idx]))
|
||
|
|
{
|
||
|
|
is_between = true;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
next_idx++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
is_between = true;
|
||
|
|
while (next_idx != big_idx) {
|
||
|
|
if (CGAL::right_turn(cone_end1->point(), q, polygon[next_idx]) ||
|
||
|
|
CGAL::right_turn(q, cone_end2->point(), polygon[next_idx]))
|
||
|
|
{
|
||
|
|
is_between = false;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
next_idx++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
typename Points::iterator first = polygon.begin();
|
||
|
|
std::advance(first, small_idx);
|
||
|
|
typename Points::iterator last = polygon.begin();
|
||
|
|
std::advance(last, big_idx);
|
||
|
|
|
||
|
|
if (is_between) {
|
||
|
|
Points polygon_out(first, last+1);
|
||
|
|
if (is_vertex_query)
|
||
|
|
polygon_out.push_back(q);
|
||
|
|
Visibility_2::report_while_handling_needles<Rotational_sweep_visibility_2>
|
||
|
|
(geom_traits, q, polygon_out, arr_out);
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
Points polygon_out(polygon.begin(), first+1);
|
||
|
|
if (is_vertex_query) polygon_out.push_back(q);
|
||
|
|
for (typename Points::size_type i = big_idx; i != polygon.size(); i++) {
|
||
|
|
polygon_out.push_back(polygon[i]);
|
||
|
|
}
|
||
|
|
Visibility_2::report_while_handling_needles<Rotational_sweep_visibility_2>
|
||
|
|
(geom_traits, q, polygon_out, arr_out);
|
||
|
|
}
|
||
|
|
|
||
|
|
Visibility_2::conditional_regularize(arr_out, Regularization_category());
|
||
|
|
|
||
|
|
if (arr_out.faces_begin()->is_unbounded())
|
||
|
|
return ++arr_out.faces_begin();
|
||
|
|
else
|
||
|
|
return arr_out.faces_begin();
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename VARR>
|
||
|
|
typename VARR::Face_handle
|
||
|
|
compute_visibility(
|
||
|
|
const Point_2& q, const Face_const_handle f, VARR& arr_out) const
|
||
|
|
{
|
||
|
|
arr_out.clear();
|
||
|
|
this->q = q;
|
||
|
|
is_vertex_query = false;
|
||
|
|
is_edge_query = false;
|
||
|
|
is_face_query = true;
|
||
|
|
|
||
|
|
visibility_region_impl(f, q);
|
||
|
|
|
||
|
|
Visibility_2::report_while_handling_needles<Rotational_sweep_visibility_2>
|
||
|
|
(geom_traits, q, polygon, arr_out);
|
||
|
|
|
||
|
|
Visibility_2::conditional_regularize(arr_out, Regularization_category());
|
||
|
|
|
||
|
|
if (arr_out.faces_begin()->is_unbounded())
|
||
|
|
return ++arr_out.faces_begin();
|
||
|
|
else
|
||
|
|
return arr_out.faces_begin();
|
||
|
|
}
|
||
|
|
|
||
|
|
bool is_attached() const {
|
||
|
|
return (p_arr != nullptr);
|
||
|
|
}
|
||
|
|
|
||
|
|
void attach(const Arrangement_2& arr) {
|
||
|
|
p_arr = &arr;
|
||
|
|
geom_traits = p_arr->geometry_traits();
|
||
|
|
}
|
||
|
|
|
||
|
|
void detach() {
|
||
|
|
p_arr = nullptr;
|
||
|
|
geom_traits = nullptr;
|
||
|
|
}
|
||
|
|
|
||
|
|
const Arrangement_2& arrangement_2() const {
|
||
|
|
return *p_arr;
|
||
|
|
}
|
||
|
|
|
||
|
|
private:
|
||
|
|
//get the neighbor of v along edge e
|
||
|
|
VH get_neighbor(const EH e, const VH v) const {
|
||
|
|
if (e->source() == v)
|
||
|
|
return e->target();
|
||
|
|
else
|
||
|
|
return e->source();
|
||
|
|
}
|
||
|
|
|
||
|
|
//check whether ray(q->dp) intersects segment(p1, p2)
|
||
|
|
bool do_intersect_ray(const Point_2& q,
|
||
|
|
const Point_2& dp,
|
||
|
|
const Point_2& p1,
|
||
|
|
const Point_2& p2) const
|
||
|
|
{
|
||
|
|
return (CGAL::orientation(q, dp, p1) != CGAL::orientation(q, dp, p2) &&
|
||
|
|
CGAL::orientation(q, p1, dp) == CGAL::orientation(q, p1, p2));
|
||
|
|
}
|
||
|
|
|
||
|
|
//arrange vertices that on a same vision ray in a 'funnel' order
|
||
|
|
void funnel(typename VHs::size_type i, typename VHs::size_type j) const {
|
||
|
|
VHs right, left;
|
||
|
|
//whether the edges incident to a vertex block the left side and right side
|
||
|
|
//of current vision ray.
|
||
|
|
bool block_left(false), block_right(false);
|
||
|
|
VH former = vs[i], nb;
|
||
|
|
for (typename VHs::size_type l=i; l<j; l++) {
|
||
|
|
bool left_v(false), right_v(false), has_predecessor(false);
|
||
|
|
EHs& edges = incident_edges[vs[l]];
|
||
|
|
for (typename EHs::size_type k=0; k<edges.size(); k++) {
|
||
|
|
nb = get_neighbor(edges[k], vs[l]);
|
||
|
|
if ( nb == former ) {
|
||
|
|
has_predecessor = true;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
if (CGAL::left_turn(q, vs[l]->point(), nb->point()))
|
||
|
|
left_v = true;
|
||
|
|
else
|
||
|
|
right_v = CGAL::right_turn(q, vs[l]->point(), nb->point());
|
||
|
|
}
|
||
|
|
if (has_predecessor) {
|
||
|
|
//if the current vertex connects to the vertex before by an edge,
|
||
|
|
//the vertex before can help it to block.
|
||
|
|
block_left = block_left || left_v;
|
||
|
|
block_right = block_right || right_v;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
block_left = left_v;
|
||
|
|
block_right = right_v;
|
||
|
|
}
|
||
|
|
if (block_left && block_right) {
|
||
|
|
//when both sides are blocked,
|
||
|
|
//there is no need to change the vertex after.
|
||
|
|
right.push_back(vs[l]);
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
if (block_left)
|
||
|
|
left.push_back(vs[l]);
|
||
|
|
else
|
||
|
|
right.push_back(vs[l]);
|
||
|
|
}
|
||
|
|
former = vs[l];
|
||
|
|
}
|
||
|
|
for (typename VHs::size_type l=0; l!=right.size(); l++)
|
||
|
|
vs[i+l] = right[l];
|
||
|
|
for (typename VHs::size_type l=0; l!=left.size(); l++)
|
||
|
|
vs[i+l+right.size()] = left[left.size()-1-l];
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
void visibility_region_impl(const Face_const_handle f, const Point_2& q) const
|
||
|
|
{
|
||
|
|
vs.clear();
|
||
|
|
polygon.clear();
|
||
|
|
active_edges = std::set<EH, Closer_edge>(Closer_edge(geom_traits, q));
|
||
|
|
incident_edges = std::map<VH, EHs, Less_vertex>(Less_vertex(geom_traits));
|
||
|
|
edx = std::map<EH, int, Less_edge>(Less_edge(geom_traits));
|
||
|
|
|
||
|
|
EHs relevant_edges; //edges that can affect the visibility of query point.
|
||
|
|
Arrangement_2 bbox;
|
||
|
|
if (is_face_query)
|
||
|
|
input_face(f);
|
||
|
|
else
|
||
|
|
input_face(f, relevant_edges, bbox);
|
||
|
|
//the following code is the initiation of vision ray.
|
||
|
|
//the direction of the initial ray is between the direction from q to last
|
||
|
|
//vertex in vs and positive x-axis. By choosing this direction, we make sure
|
||
|
|
//that all plane is swept and there is not needle at the beginning of
|
||
|
|
//sweeping.
|
||
|
|
Vector_2 dir;
|
||
|
|
if (Direction_2(-1, 0) < Direction_2(Vector_2(q, vs.back()->point())))
|
||
|
|
dir = Vector_2(1, 0) + Vector_2(q, vs.back()->point());
|
||
|
|
else
|
||
|
|
dir = Vector_2(0, -1);
|
||
|
|
Point_2 dp = q + dir;
|
||
|
|
|
||
|
|
//initiation of active_edges. for face queries,
|
||
|
|
//all edges on the boundary can affect visibility.
|
||
|
|
//for non-face queries, only relevant_edges has to be considered.
|
||
|
|
if (is_face_query) {
|
||
|
|
Ccb_halfedge_const_circulator curr = f->outer_ccb();
|
||
|
|
Ccb_halfedge_const_circulator circ = curr;
|
||
|
|
do {
|
||
|
|
if (do_intersect_ray(
|
||
|
|
q, dp, curr->target()->point(), curr->source()->point()))
|
||
|
|
active_edges.insert(curr);
|
||
|
|
|
||
|
|
} while (++curr != circ);
|
||
|
|
|
||
|
|
typename Arrangement_2::Hole_const_iterator hi;
|
||
|
|
for (hi = f->holes_begin(); hi != f->holes_end(); ++hi) {
|
||
|
|
Ccb_halfedge_const_circulator curr = circ = *hi;
|
||
|
|
do {
|
||
|
|
if (do_intersect_ray(
|
||
|
|
q, dp, curr->target()->point(), curr->source()->point()))
|
||
|
|
active_edges.insert(curr);
|
||
|
|
} while (++curr != circ);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
for (typename EHs::size_type i=0; i!=relevant_edges.size(); i++)
|
||
|
|
if (do_intersect_ray(q, dp, relevant_edges[i]->source()->point(),
|
||
|
|
relevant_edges[i]->target()->point()))
|
||
|
|
active_edges.insert(relevant_edges[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
//angular sweep begins
|
||
|
|
// std::cout<<active_edges.size()<<std::endl;
|
||
|
|
for (typename VHs::size_type i=0; i!=vs.size(); i++) {
|
||
|
|
VH vh = vs[i];
|
||
|
|
EH closest_e = *active_edges.begin();
|
||
|
|
EHs& edges = incident_edges[vh];
|
||
|
|
EHs insert_ehs, remove_ehs;
|
||
|
|
for (typename EHs::size_type j=0; j!=edges.size(); j++) {
|
||
|
|
EH& e = edges[j];
|
||
|
|
if (active_edges.find(e) == active_edges.end())
|
||
|
|
insert_ehs.push_back(e);
|
||
|
|
else
|
||
|
|
remove_ehs.push_back(e);
|
||
|
|
}
|
||
|
|
typename EHs::size_type insert_cnt = insert_ehs.size();
|
||
|
|
typename EHs::size_type remove_cnt = remove_ehs.size();
|
||
|
|
if (insert_cnt == 1 && remove_cnt == 1) {
|
||
|
|
const EH& ctemp_eh = *active_edges.find(remove_ehs.front());
|
||
|
|
EH& temp_eh = const_cast<EH&>(ctemp_eh);
|
||
|
|
temp_eh = insert_ehs.front();
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
for (typename EHs::size_type j=0; j!=remove_cnt; j++)
|
||
|
|
active_edges.erase(remove_ehs[j]);
|
||
|
|
for (typename EHs::size_type j=0; j!=insert_cnt; j++)
|
||
|
|
active_edges.insert(insert_ehs[j]);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (closest_e != *active_edges.begin()) {
|
||
|
|
//when the closest edge changed
|
||
|
|
if (is_face_query) {
|
||
|
|
if (remove_cnt > 0 && insert_cnt > 0) {
|
||
|
|
//some edges are added and some are deleted,
|
||
|
|
//which means the vertex swept is part of visibility polygon.
|
||
|
|
update_visibility(vh->point());
|
||
|
|
}
|
||
|
|
if (remove_cnt == 0 && insert_cnt > 0) {
|
||
|
|
//only add some edges, means the view ray is blocked by new edges.
|
||
|
|
//therefore first add the intersection of view ray and
|
||
|
|
//former closet edge, then add the vertice swept.
|
||
|
|
update_visibility(ray_seg_intersection(q,
|
||
|
|
vh->point(),
|
||
|
|
closest_e->target()->point(),
|
||
|
|
closest_e->source()->point())
|
||
|
|
);
|
||
|
|
update_visibility(vh->point());
|
||
|
|
}
|
||
|
|
if (remove_cnt > 0 && insert_cnt == 0) {
|
||
|
|
//only delete some edges, means some block is moved and the view ray
|
||
|
|
//can reach the segments after the block.
|
||
|
|
update_visibility(vh->point());
|
||
|
|
update_visibility(
|
||
|
|
ray_seg_intersection(q,
|
||
|
|
vh->point(),
|
||
|
|
(*active_edges.begin())->target()->point(),
|
||
|
|
(*active_edges.begin())->source()->point()
|
||
|
|
)
|
||
|
|
);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
//extra work here for edge/vertex query is the index of cone_end1 and
|
||
|
|
//cone_end2 will be recorded.
|
||
|
|
if (remove_cnt > 0 && insert_cnt > 0) {
|
||
|
|
//some edges are added and some are deleted,
|
||
|
|
//which means the vertice swept is part of visibility polygon.
|
||
|
|
if (update_visibility(vh->point())) {
|
||
|
|
if (vh == cone_end1)
|
||
|
|
cone_end1_idx = polygon.size()-1;
|
||
|
|
else if (vh == cone_end2)
|
||
|
|
cone_end2_idx = polygon.size()-1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (remove_cnt == 0 && insert_cnt > 0) {
|
||
|
|
//only add some edges, means the view ray is blocked by new edges.
|
||
|
|
//therefore first add the intersection of view ray and former closet
|
||
|
|
//edge, then add the vertice swept.
|
||
|
|
update_visibility(ray_seg_intersection(q,
|
||
|
|
vh->point(),
|
||
|
|
closest_e->target()->point(),
|
||
|
|
closest_e->source()->point())
|
||
|
|
);
|
||
|
|
if (update_visibility(vh->point())) {
|
||
|
|
if (vh == cone_end1)
|
||
|
|
cone_end1_idx = polygon.size()-1;
|
||
|
|
else if (vh == cone_end2)
|
||
|
|
cone_end2_idx = polygon.size()-1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (remove_cnt > 0 && insert_cnt == 0) {
|
||
|
|
//only delete some edges, means some block is removed and the vision
|
||
|
|
//ray can reach the segments after the block.
|
||
|
|
if (update_visibility(vh->point())) {
|
||
|
|
if (vh == cone_end1)
|
||
|
|
cone_end1_idx = polygon.size()-1;
|
||
|
|
else if (vh == cone_end2)
|
||
|
|
cone_end2_idx = polygon.size()-1;
|
||
|
|
}
|
||
|
|
update_visibility(
|
||
|
|
ray_seg_intersection(q,
|
||
|
|
vh->point(),
|
||
|
|
(*active_edges.begin())->target()->point(),
|
||
|
|
(*active_edges.begin())->source()->point())
|
||
|
|
);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void print_edge(const EH e) const {
|
||
|
|
std::cout << e->source()->point() <<"->"<< e->target()->point() <<std::endl;
|
||
|
|
}
|
||
|
|
|
||
|
|
//compute the intersection of ray(q->dp) and segment(s, t)
|
||
|
|
//if they are collinear then return the endpoint which is closer to q.
|
||
|
|
|
||
|
|
Point_2 ray_seg_intersection(
|
||
|
|
const Point_2& q, const Point_2& dp, // the ray
|
||
|
|
const Point_2& s, const Point_2& t) // the segment
|
||
|
|
const
|
||
|
|
{
|
||
|
|
if (CGAL::collinear(q, dp, s)) {
|
||
|
|
if (CGAL::collinear(q, dp, t)) {
|
||
|
|
if (CGAL::compare_distance_to_point(q, s, t)==CGAL::SMALLER)
|
||
|
|
return s;
|
||
|
|
else
|
||
|
|
return t;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
return s;
|
||
|
|
}
|
||
|
|
Ray_2 ray(q,dp);
|
||
|
|
Segment_2 seg(s,t);
|
||
|
|
CGAL::Object result = CGAL::intersection(ray, seg);
|
||
|
|
return *(CGAL::object_cast<Point_2>(&result));
|
||
|
|
}
|
||
|
|
|
||
|
|
//check if p has been discovered before, if not update the visibility polygon
|
||
|
|
bool update_visibility(const Point_2& p) const {
|
||
|
|
if (polygon.empty()) {
|
||
|
|
polygon.push_back(p);
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
else if (Visibility_2::compare_xy_2(geom_traits, polygon.back(), p)
|
||
|
|
!= EQUAL)
|
||
|
|
{
|
||
|
|
polygon.push_back(p);
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
//functor to decide which vertex is swept earlier by the rotational sweeping
|
||
|
|
//ray
|
||
|
|
class Is_swept_earlier:public CGAL::cpp98::binary_function<VH, VH, bool> {
|
||
|
|
const Point_2& q;
|
||
|
|
const Geometry_traits_2* geom_traits;
|
||
|
|
public:
|
||
|
|
Is_swept_earlier(const Point_2& q, const Geometry_traits_2* traits) :
|
||
|
|
q(q), geom_traits(traits) {}
|
||
|
|
|
||
|
|
bool operator() (const VH v1, const VH v2) const {
|
||
|
|
const Point_2& p1 = v1->point();
|
||
|
|
const Point_2& p2 = v2->point();
|
||
|
|
int qua1 = quadrant(q, p1);
|
||
|
|
int qua2 = quadrant(q, p2);
|
||
|
|
if (qua1 < qua2)
|
||
|
|
return true;
|
||
|
|
if (qua1 > qua2)
|
||
|
|
return false;
|
||
|
|
if (collinear(q, p1, p2))
|
||
|
|
return (CGAL::compare_distance_to_point(q, p1, p2) == CGAL::SMALLER);
|
||
|
|
else
|
||
|
|
return CGAL::right_turn(p1, q, p2);
|
||
|
|
}
|
||
|
|
|
||
|
|
//return the quadrant of p with respect to o.
|
||
|
|
int quadrant(const Point_2& o, const Point_2& p) const {
|
||
|
|
typename Geometry_traits_2::Compare_x_2 compare_x =
|
||
|
|
geom_traits->compare_x_2_object();
|
||
|
|
|
||
|
|
typename Geometry_traits_2::Compare_y_2 compare_y =
|
||
|
|
geom_traits->compare_y_2_object();
|
||
|
|
|
||
|
|
Comparison_result dx = compare_x(p, o);
|
||
|
|
Comparison_result dy = compare_y(p, o);
|
||
|
|
if (dx==LARGER && dy!=SMALLER)
|
||
|
|
return 1;
|
||
|
|
if (dx!=LARGER && dy==LARGER)
|
||
|
|
return 2;
|
||
|
|
if (dx==SMALLER && dy!=LARGER)
|
||
|
|
return 3;
|
||
|
|
if (dx!=SMALLER && dy==SMALLER)
|
||
|
|
return 4;
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
//when the query point is in face, every edge is good.
|
||
|
|
void input_neighbor_f( const Halfedge_const_handle e) const {
|
||
|
|
VH v = e->target();
|
||
|
|
if (!incident_edges.count(v))
|
||
|
|
vs.push_back(v);
|
||
|
|
incident_edges[v].push_back(e);
|
||
|
|
incident_edges[v].push_back(e->next());
|
||
|
|
}
|
||
|
|
|
||
|
|
//check if p is in the visibility cone
|
||
|
|
bool is_in_cone(const Point_2& p) const{
|
||
|
|
if (is_big_cone)
|
||
|
|
return (!CGAL::right_turn(cone_end1->point(), q, p)) ||
|
||
|
|
(!CGAL::left_turn(cone_end2->point(), q, p));
|
||
|
|
else
|
||
|
|
return (!CGAL::right_turn(cone_end1->point(), q, p)) &&
|
||
|
|
(!CGAL::left_turn(cone_end2->point(), q, p));
|
||
|
|
}
|
||
|
|
|
||
|
|
//for vertex and edge query: the visibility is limited in a cone.
|
||
|
|
void input_edge(const Halfedge_const_handle e,
|
||
|
|
EHs& good_edges) const {
|
||
|
|
for (typename EHs::size_type i = 0; i < bad_edges.size(); i++)
|
||
|
|
if (e == bad_edges[i])
|
||
|
|
return;
|
||
|
|
VH v1 = e->target();
|
||
|
|
VH v2 = e->source();
|
||
|
|
//an edge will affect visibility only if it has an endpoint in the
|
||
|
|
//visibility cone or it crosses the boundary of the cone.
|
||
|
|
if (is_in_cone(v1->point()) || is_in_cone(v2->point()) ||
|
||
|
|
do_intersect_ray(q, cone_end1->point(), v1->point(), v2->point()))
|
||
|
|
{
|
||
|
|
good_edges.push_back(e);
|
||
|
|
if (!incident_edges.count(v1))
|
||
|
|
vs.push_back(v1);
|
||
|
|
incident_edges[v1].push_back(e);
|
||
|
|
if (!incident_edges.count(v2))
|
||
|
|
vs.push_back(v2);
|
||
|
|
incident_edges[v2].push_back(e);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//for face query: traverse the face to get all edges
|
||
|
|
//and sort vertices in counter-clockwise order.
|
||
|
|
void input_face (Face_const_handle fh) const
|
||
|
|
{
|
||
|
|
Ccb_halfedge_const_circulator curr = fh->outer_ccb();
|
||
|
|
Ccb_halfedge_const_circulator circ = curr;
|
||
|
|
do {
|
||
|
|
CGAL_assertion(curr->face() == fh);
|
||
|
|
input_neighbor_f(curr);
|
||
|
|
} while (++curr != circ);
|
||
|
|
|
||
|
|
typename Arrangement_2::Hole_const_iterator hi;
|
||
|
|
for (hi = fh->holes_begin(); hi != fh->holes_end(); ++hi) {
|
||
|
|
Ccb_halfedge_const_circulator curr = *hi, circ = *hi;
|
||
|
|
do {
|
||
|
|
CGAL_assertion(curr->face() == fh);
|
||
|
|
input_neighbor_f(curr);
|
||
|
|
} while (++curr != circ);
|
||
|
|
}
|
||
|
|
|
||
|
|
std::sort(vs.begin(), vs.end(), Is_swept_earlier(q, geom_traits));
|
||
|
|
|
||
|
|
for (typename VHs::size_type i=0; i!=vs.size(); i++) {
|
||
|
|
typename VHs::size_type j = i+1;
|
||
|
|
while (j != vs.size()) {
|
||
|
|
if (!CGAL::collinear(q, vs[i]->point(), vs[j]->point()))
|
||
|
|
break;
|
||
|
|
j++;
|
||
|
|
}
|
||
|
|
if (j-i>1)
|
||
|
|
funnel(i, j);
|
||
|
|
i = j-1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
//for vertex or edge query: traverse the face to get all edges
|
||
|
|
//and sort vertices in counter-clockwise order.
|
||
|
|
void input_face (Face_const_handle fh,
|
||
|
|
EHs& good_edges,
|
||
|
|
Arrangement_2& bbox) const
|
||
|
|
{
|
||
|
|
Ccb_halfedge_const_circulator curr = fh->outer_ccb();
|
||
|
|
Ccb_halfedge_const_circulator circ = curr;
|
||
|
|
do {
|
||
|
|
CGAL_assertion(curr->face() == fh);
|
||
|
|
input_edge(curr, good_edges);
|
||
|
|
} while (++curr != circ);
|
||
|
|
|
||
|
|
typename Arrangement_2::Hole_const_iterator hi;
|
||
|
|
for (hi = fh->holes_begin(); hi != fh->holes_end(); ++hi) {
|
||
|
|
Ccb_halfedge_const_circulator curr = circ = *hi;
|
||
|
|
do {
|
||
|
|
CGAL_assertion(curr->face() == fh);
|
||
|
|
input_edge(curr, good_edges);
|
||
|
|
} while (++curr != circ);
|
||
|
|
}
|
||
|
|
|
||
|
|
//create a box that cover all vertices such that during the sweeping,
|
||
|
|
//the vision ray will always intersect at least an edge.
|
||
|
|
//this box doesn't intersect any relevant_edge.
|
||
|
|
Points points;
|
||
|
|
for (typename VHs::size_type i=0; i<vs.size(); i++) {
|
||
|
|
points.push_back(vs[i]->point());
|
||
|
|
}
|
||
|
|
points.push_back(q);
|
||
|
|
//first get the bounding box of all relevant points.
|
||
|
|
typename Geometry_traits_2::Iso_rectangle_2 bb =
|
||
|
|
bounding_box(points.begin(), points.end());
|
||
|
|
|
||
|
|
Number_type xmin, xmax, ymin, ymax;
|
||
|
|
typename Geometry_traits_2::Compute_x_2 compute_x =
|
||
|
|
geom_traits->compute_x_2_object();
|
||
|
|
|
||
|
|
typename Geometry_traits_2::Compute_y_2 compute_y =
|
||
|
|
geom_traits->compute_y_2_object();
|
||
|
|
|
||
|
|
//make the box a little bigger than bb so that it won't intersect any
|
||
|
|
//relevant_edge.
|
||
|
|
xmin = compute_x((bb.min)())-1;
|
||
|
|
ymin = compute_y((bb.min)())-1;
|
||
|
|
xmax = compute_x((bb.max)())+1;
|
||
|
|
ymax = compute_y((bb.max)())+1;
|
||
|
|
Point_2 box[4] = {Point_2(xmin, ymin), Point_2(xmax, ymin),
|
||
|
|
Point_2(xmax, ymax), Point_2(xmin, ymax)};
|
||
|
|
|
||
|
|
Halfedge_handle e1 = bbox.insert_in_face_interior(Segment_2(box[0], box[1]),
|
||
|
|
bbox.unbounded_face());
|
||
|
|
|
||
|
|
Halfedge_handle e2 = bbox.insert_from_left_vertex(Segment_2(box[1], box[2]),
|
||
|
|
e1->target());
|
||
|
|
|
||
|
|
Halfedge_handle e3 = bbox.insert_from_right_vertex(Segment_2(box[2],box[3]),
|
||
|
|
e2->target());
|
||
|
|
|
||
|
|
bbox.insert_at_vertices(Segment_2(box[0], box[3]),
|
||
|
|
e1->source(), e3->target());
|
||
|
|
|
||
|
|
circ = curr = e1->face()->outer_ccb();
|
||
|
|
do {
|
||
|
|
VH v = curr->target();
|
||
|
|
vs.push_back(v);
|
||
|
|
incident_edges[v].push_back(curr);
|
||
|
|
incident_edges[v].push_back(curr->next());
|
||
|
|
good_edges.push_back(curr);
|
||
|
|
} while(++curr != circ);
|
||
|
|
|
||
|
|
std::sort(vs.begin(), vs.end(), Is_swept_earlier(q, geom_traits));
|
||
|
|
|
||
|
|
for (typename VHs::size_type i=0; i!=vs.size(); i++) {
|
||
|
|
typename VHs::size_type j = i+1;
|
||
|
|
while (j != vs.size()) {
|
||
|
|
if (!CGAL::collinear(q, vs[i]->point(), vs[j]->point()))
|
||
|
|
break;
|
||
|
|
j++;
|
||
|
|
}
|
||
|
|
if (j-i>1)
|
||
|
|
funnel(i, j);
|
||
|
|
i = j-1;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
} // end namespace CGAL
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|