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cgal/Visibility_2/include/CGAL/Simple_polygon_visibility_2.h

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// Copyright (c) 2013 Technical University Braunschweig (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$`
// $Id$
//
//
// Author(s): Francisc Bungiu <fbungiu@gmail.com>
// Michael Hemmer <michael.hemmer@cgal.org>
// Ning Xu <longyin0904@gmail.com>
#ifndef CGAL_SIMPLE_POLYGON_VISIBILITY_2_H
#define CGAL_SIMPLE_POLYGON_VISIBILITY_2_H
#include <CGAL/Arrangement_2.h>
#include <CGAL/tags.h>
#include <CGAL/enum.h>
#include <CGAL/Visibility_2/visibility_utils.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <stack>
#include <map>
namespace CGAL {
template<class Arrangement_2_, class RegularizationCategory = CGAL::Tag_true>
class Simple_polygon_visibility_2 {
public:
// Currently only consider with same type for both
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 Geometry_traits_2::Kernel K;
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 Arrangement_2::Halfedge_around_vertex_const_circulator
Halfedge_around_vertex_const_circulator;
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_false Supports_general_polygon_category;
typedef CGAL::Tag_true Supports_simple_polygon_category;
Simple_polygon_visibility_2() : p_arr(NULL), geom_traits(NULL) {}
/*! Constructor given an arrangement and the Regularization tag. */
Simple_polygon_visibility_2(const Arrangement_2& arr):
p_arr(&arr) {
geom_traits = p_arr->geometry_traits();
query_pt_is_vertex = false;
query_pt_is_on_halfedge = false;
}
const std::string name(){return std::string("S_visibility_2");}
/*! Method to check if the visibility object is attached or not to
an arrangement*/
bool is_attached() const {
return (p_arr != NULL);
}
/*! Attaches the visibility object to the 'arr' arrangement */
void attach(const Arrangement_2& arr) {
if(p_arr != &arr){
detach();
p_arr = &arr;
geom_traits = p_arr->geometry_traits();
}
}
/*! Detaches the visibility object from the arrangement it is
attached to*/
void detach() {
p_arr = NULL;
geom_traits = NULL;
vertices.clear();
query_pt_is_vertex = false;
query_pt_is_on_halfedge = false;
p_cdt.reset();
}
/*! Getter method for the input arrangement*/
const Arrangement_2& arrangement_2() const {
return *p_arr;
}
/*! Computes the visibility object from the query point 'q' in the face
'face' and constructs the output in 'out_arr'*/
template <typename VARR>
typename VARR::Face_handle
compute_visibility(const Point_2& q, Face_const_handle face,
VARR& out_arr) const {
CGAL_precondition_msg(p_arr->number_of_faces() == 2,
"Only simple polygons are supported.");
out_arr.clear();
query_pt_is_vertex = false;
query_pt_is_on_halfedge = false;
// Now retrieve the circulator to first visible vertex from triangulation
Ccb_halfedge_const_circulator circ = find_visible_start(face, q);
Ccb_halfedge_const_circulator curr = circ;
Halfedge_const_handle he;
do {
he = curr;
vertices.push_back(he->source()->point());
} while(++curr != circ);
vertices.push_back(vertices[0]);
visibility_region_impl(q);
return output(q, out_arr);
}
/*! Computes the visibility region of the query point 'q' located on the
halfedge 'he' and constructs the output in 'out_arr'*/
template <typename VARR>
typename VARR::Face_handle
compute_visibility(
const Point_2& q,
const Halfedge_const_handle he,
VARR& out_arr ) const
{
CGAL_precondition_msg(p_arr->number_of_faces() == 2,
"Only simple polygons are supported.");
out_arr.clear();
query_pt_is_vertex = false;
query_pt_is_on_halfedge = false;
bool query_on_target = false;
if (q != he->source()->point()) {
if (q != he->target()->point()) {
vertices.push_back(he->target()->point());
query_pt_is_on_halfedge = true;
}
else {
query_pt_is_vertex = true;
query_on_target = true;
}
} else {
vertices.push_back( he->target()->point() );
query_pt_is_vertex = true;
}
Ccb_halfedge_const_circulator circ = he;
circ++;
Ccb_halfedge_const_circulator curr = circ;
do {
Halfedge_const_handle he_handle = curr;
Point_2 curr_vertex = he_handle->target()->point();
vertices.push_back(curr_vertex);
} while (++curr != circ);
if ( query_on_target ) {
vertices.push_back( vertices[0] );
}
visibility_region_impl(q);
return output(q, out_arr);
// std::vector<Point_2> points;
// if (!s.empty()) {
// Point_2 prev_pt = s.top();
// if (prev_pt != q) {
// points.push_back(prev_pt);
// }
// else if (query_pt_is_vertex) {
// points.push_back(prev_pt);
// }
// if (!s.empty()) {
// s.pop();
// }
// while(!s.empty()) {
// Point_2 curr_pt = s.top();
// if (curr_pt != q) {
// points.push_back(curr_pt);
// }
// else if (query_pt_is_vertex) {
// points.push_back(curr_pt);
// }
// s.pop();
// }
// }
}
private:
typedef CGAL::Triangulation_vertex_base_2<K> Vb;
typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb,Fb> TDS;
typedef CGAL::No_intersection_tag Itag;
typedef CGAL::Constrained_triangulation_2<K, TDS, Itag> CDT;
private:
const Arrangement_2 *p_arr;
const Geometry_traits_2 *geom_traits;
/*! Boost pointer to the constrained Delaunay triangulation object*/
mutable boost::shared_ptr<CDT> p_cdt;
/*! Mapping of the vertices of the input to the corresponding circulator
needed for finding the first visible vertex in case of face queries*/
mutable std::map<Point_2, Ccb_halfedge_const_circulator> point_itr_map;
/*! Stack of visibile points; manipulated when going through the sequence
of input vertices; contains the vertices of the visibility region after
the run of the algorithm*/
mutable std::stack<Point_2> s;
/*! Sequence of input vertices*/
mutable std::vector<Point_2> vertices;
/*! State of visibility region algorithm*/
mutable enum {LEFT, RIGHT, SCANA, SCANB, SCANC, SCAND, FINISH} upcase;
mutable bool query_pt_is_vertex;
mutable bool query_pt_is_on_halfedge;
/*! Regularize output if flag is set to true*/
template <typename VARR>
void conditional_regularize(VARR& out_arr, CGAL::Tag_true) const {
regularize_output(out_arr);
}
/*! No need to regularize output if flag is set to false*/
template <typename VARR>
void conditional_regularize(VARR& out_arr, CGAL::Tag_false) const {
//do nothing
}
/*! Regularizes the output - removes edges that have the same face on both
sides */
template <typename VARR>
void regularize_output(VARR& out_arr) const {
typename VARR::Edge_iterator e_itr;
for (e_itr = out_arr.edges_begin() ;
e_itr != out_arr.edges_end() ; e_itr++) {
typename VARR::Halfedge_handle he = e_itr;
typename VARR::Halfedge_handle he_twin = he->twin();
if (he->face() == he_twin->face()) {
out_arr.remove_edge(he);
}
}
}
/*! Initialized the constrained Delaunay triangulation using the edges of
the outer boundary of 'face' */
void init_cdt(const Face_const_handle &face) const {
point_itr_map.clear();
std::vector<std::pair<Point_2,Point_2> > constraints;
Ccb_halfedge_const_circulator circ = face->outer_ccb();
Ccb_halfedge_const_circulator curr = circ;
do {
Point_2 source = curr->source()->point();
Point_2 target = curr->target()->point();
point_itr_map.insert(std::make_pair(source, curr));
constraints.push_back(std::make_pair(source, target));
} while(++curr != circ);
p_cdt = boost::shared_ptr<CDT>(new CDT(constraints.begin(),
constraints.end()));
}
template <typename VARR>
typename VARR::Face_handle
output(const Point_2& q, VARR& out_arr) const {
std::vector<Point_2> points;
while (!s.empty()) {
points.push_back(s.top());
s.pop();
}
// std::reverse(points.begin(), points.end());
CGAL::Visibility_2::report_while_handling_needles
<Simple_polygon_visibility_2>(geom_traits,
q,
points,
out_arr);
CGAL_postcondition(out_arr.number_of_isolated_vertices() == 0);
CGAL_postcondition(s.empty());
conditional_regularize(out_arr, Regularization_category());
vertices.clear();
if (out_arr.faces_begin()->is_unbounded()) {
return ++out_arr.faces_begin();
}
else {
return out_arr.faces_begin();
}
}
/*! Finds a visible vertex from the query point 'q' in 'face'
to start the algorithm from*/
Ccb_halfedge_const_circulator find_visible_start(Face_const_handle face,
const Point_2 &q) const {
init_cdt(face);
typename CDT::Face_handle fh = p_cdt->locate(q);
Point_2 start_point = fh->vertex(0)->point();
// Now retrieve the circulator to first visible vertex from triangulation
Ccb_halfedge_const_circulator circ = point_itr_map[start_point];
Halfedge_const_handle he_curr = circ;
Halfedge_around_vertex_const_circulator incident_circ =
he_curr->source()->incident_halfedges();
Halfedge_around_vertex_const_circulator incident_curr = incident_circ;
do {
Ccb_halfedge_const_circulator curr_inc = incident_curr;
Halfedge_const_handle he_curr_inc = curr_inc;
if (he_curr_inc->face() == face) {
Ccb_halfedge_const_circulator incident_next = incident_curr;
incident_next++;
Halfedge_const_handle he_next_inc = incident_next;
if (CGAL::Visibility_2::orientation_2(geom_traits,
he_curr_inc->source()->point(),
he_curr_inc->target()->point(),
q) == CGAL::LEFT_TURN
|| CGAL::Visibility_2::orientation_2(geom_traits,
he_next_inc->source()->point(),
he_next_inc->target()->point(),
q) == CGAL::LEFT_TURN)
{
return incident_next;
}
}
} while (++incident_curr != incident_circ);
}
/*! Main method of the algorithm - initializes the stack and variables
and calles the corresponding methods acc. to the algorithm's state;
'q' - query point;
'i' - current vertex' index
'w' - endpoint of ray shot from query point */
void visibility_region_impl(const Point_2& q) const {
int i = 0;
Point_2 w;
CGAL::Orientation orient = CGAL::Visibility_2::orientation_2(geom_traits,
q,
vertices[0],
vertices[1]);
if ( orient != CGAL::RIGHT_TURN ) {
upcase = LEFT;
i = 1;
w = vertices[1];
s.push(vertices[0]);
s.push(vertices[1]);
}
else {
upcase = SCANA;
i = 1;
w = vertices[1];
s.push(vertices[0]);
}
Ray_2 ray_origin( q, vertices[0] );
do {
switch(upcase) {
case LEFT:
left(i, w, q);
break;
case RIGHT:
right(i, w, q);
break;
case SCANA:
scana(i, w, q);
break;
case SCANB:
scanb(i, w, q);
break;
case SCANC:
scanc(i, w, q);
break;
case SCAND:
scand(i, w, q);
break;
}
if ( upcase == LEFT ) {
Point_2 s_t = s.top();
s.pop();
if ( ( CGAL::Visibility_2::orientation_2 <Geometry_traits_2>
( geom_traits, q, vertices[0], s.top() ) == CGAL::RIGHT_TURN ) &&
( CGAL::Visibility_2::orientation_2 <Geometry_traits_2>
( geom_traits, q, vertices[0],s_t ) == CGAL::LEFT_TURN ) ) {
Segment_2 seg( s.top(), s_t );
if (Visibility_2::do_intersect_2(geom_traits, seg, ray_origin ) )
{
Object_2 result = Visibility_2::intersect_2(geom_traits,
seg, ray_origin);
const Point_2 * ipoint = CGAL::object_cast<Point_2>(&result);
assert( ipoint != NULL );
s_t = *ipoint;
upcase = SCANB;
}
}
s.push( s_t );
}
} while(upcase != FINISH);
}
/*! Method that handles the left turns in the vertex algorithm */
void left(int& i, Point_2& w, const Point_2& query_pt) const {
if (i >= vertices.size() - 1) {
upcase = FINISH;
}
else {
Point_2 s_t = s.top();
s.pop();
Point_2 s_t_prev = s.top();
s.push( s_t );
CGAL::Orientation orient1 = Visibility_2::orientation_2
( geom_traits,
query_pt,
vertices[i],
vertices[i+1] );
if ( orient1 != CGAL::RIGHT_TURN ) {
// Case L2
upcase = LEFT;
s.push( vertices[i+1] );
w = vertices[i+1];
i++;
} else {
CGAL::Orientation orient2 = Visibility_2::orientation_2
( geom_traits,
s_t_prev,
vertices[i],
vertices[i+1] );
if ( orient2 == CGAL::RIGHT_TURN ) {
// Case L3
upcase = SCANA;
w = vertices[i+1];
i++;
} else {
// Case L4
upcase = RIGHT;
w = vertices[i];
i++;
}
}
}
}
/*! Scans the stack such that all vertices that were pushed before to the
stack and are now not visible anymore. */
void right(int& i, Point_2& w, const Point_2& query_pt) const {
Point_2 s_j;
Point_2 s_j_prev;
Point_2 u;
int mode = 0;
CGAL::Orientation orient1, orient2;
s_j_prev = s.top();
orient2 = CGAL::Visibility_2::orientation_2 <Geometry_traits_2>
( geom_traits, query_pt, s_j_prev, vertices[i] );
while ( s.size() > 1 ) {
s_j = s_j_prev;
orient1 = orient2;
s.pop();
s_j_prev = s.top();
orient2 = CGAL::Visibility_2::orientation_2 <Geometry_traits_2>
( geom_traits, query_pt, s_j_prev, vertices[i] );
if ( orient1 != CGAL::LEFT_TURN && orient2 != CGAL::RIGHT_TURN ) {
mode = 1;
break;
}
Segment_2 seg2( vertices[i-1], vertices[i] );
Segment_2 seg( s_j_prev, s_j );
if ( vertices[i-1] != s_j &&
Visibility_2::do_intersect_2(geom_traits, seg, seg2) )
{
Object_2 result = Visibility_2::intersect_2(geom_traits, seg, seg2);
const Point_2 * ipoint = CGAL::object_cast<Point_2>(&result);
assert( ipoint != NULL );
u = *ipoint;
mode = 2;
break;
}
}
assert( mode != 0 );
if ( mode == 1 ) {
orient1 = CGAL::Visibility_2::orientation_2 <Geometry_traits_2>
( geom_traits, query_pt, vertices[i], vertices[i+1] );
orient2 = CGAL::Visibility_2::orientation_2 <Geometry_traits_2>
( geom_traits, vertices[i-1], vertices[i], vertices[i+1] );
if ( orient1 == CGAL::RIGHT_TURN ) {
// Case R1
// Since the next action is RIGHT, we do not compute the intersection
// of (s_j,s_j_prev) and the ray (query_pt, vertices[i]),
// thus, (s_j,s_j_prev) is not shortcutted, but it is harmless
upcase = RIGHT;
s.push( s_j );
w = vertices[i];
i++;
} else if ( orient2 == CGAL::RIGHT_TURN ) {
// Case R2
Ray_2 ray( query_pt, vertices[i] );
Segment_2 seg( s_j_prev, s_j );
Object_2 result = CGAL::Visibility_2::intersect_2
<Geometry_traits_2, Segment_2, Ray_2>
( geom_traits, seg, ray );
const Point_2 * ipoint = CGAL::object_cast<Point_2>(&result);
assert( ipoint != NULL );
u = *ipoint;
if ( s.top() != u ) {
s.push( u );
}
upcase = LEFT;
s.push( vertices[i] );
s.push( vertices[i+1] );
w = vertices[i+1];
i++;
} else {
// Case R3
Ray_2 ray( query_pt, vertices[i] );
Segment_2 seg( s_j_prev, s_j );
Object_2 result = CGAL::Visibility_2::intersect_2
<Geometry_traits_2, Segment_2, Ray_2>
( geom_traits, seg, ray );
const Point_2 * ipoint = CGAL::object_cast<Point_2>(&result);
assert( ipoint != NULL );
u = *ipoint;
if ( s.top() != u ) {
s.push( u );
}
upcase = SCANC;
w = vertices[i];
i++;
}
} else if ( mode == 2 ) {
// Case R4
upcase = SCAND;
w = u;
}
}
/*! Scans the vertices starting from index 'i' for the first visible vertex
out of the back hidden window */
void scana(int& i, Point_2& w, const Point_2& query_pt) const {
// Scan v_i, v_i+1, ..., v_n for the first edge to intersect (z, s_t)
Point_2 u;
int k = scan_edges( i, query_pt, s.top(), u, true );
CGAL::Orientation orient1 = CGAL::Visibility_2::orientation_2
<Geometry_traits_2>
( geom_traits,
query_pt,
vertices[k],
vertices[k+1] );
if ( orient1 == CGAL::RIGHT_TURN ) {
bool fwd = CGAL::Visibility_2::collinear_are_ordered_along_line_2
<Geometry_traits_2>
( geom_traits, query_pt, s.top(), u );
if ( !fwd ) {
// Case A1
upcase = RIGHT;
i = k+1;
w = u;
} else {
// Case A2
upcase = SCAND;
i = k+1;
w = u;
}
} else {
// Case A3
upcase = LEFT;
i = k+1;
s.push( u );
if ( u != vertices[k+1] ) {
s.push( vertices[k+1] );
}
w = vertices[k+1];
}
}
/*! Find the first edge interecting the segment (v_0, s_t) */
void scanb(int& i, Point_2& w, const Point_2& query_pt) const {
if ( i == vertices.size() - 1 ) {
upcase = FINISH;
return;
}
Point_2 u;
int k = scan_edges( i, s.top(), vertices[0], u, false );
if ( (k+1 == vertices.size()-1) && (vertices[0] == u) ) {
// Case B1
upcase = FINISH;
s.push( vertices[0] );
} else {
// Case B2
upcase = RIGHT;
i = k+1;
w = u;
}
}
/*! Finds the exit from a general front hidden window by finding the first
vertex to the right of the ray defined by the query_point and w*/
void scanc(int& i, Point_2& w, const Point_2& query_pt) const {
Point_2 u;
int k = scan_edges( i, s.top(), w, u, false );
upcase = RIGHT;
i = k+1;
w = u;
}
/*! find the first edge intersecting the given window (s_t, w) */
void scand(int& i, Point_2& w, const Point_2& query_pt) const {
Point_2 u;
int k = scan_edges( i, s.top(), w, u, false );
upcase = LEFT;
i = k+1;
s.push( u );
if ( u != vertices[k+1] ) {
s.push( vertices[k+1] );
}
w = vertices[k+1];
}
/*! Scan edges v_i,v_{i+1},...,v_n, until find an edge intersecting given ray
or given segment. is_ray = true -> ray, false -> segment.
The intersection point is returned by u */
int scan_edges( int i,
const Point_2& ray_begin,
const Point_2& ray_end,
Point_2& u,
bool is_ray ) const
{
CGAL::Orientation old_orient = CGAL::RIGHT_TURN;
Ray_2 ray( ray_begin, ray_end );
Segment_2 s2( ray_begin, ray_end );
int k;
Object_2 result;
for ( k = i; k+1 < vertices.size(); k++ ) {
CGAL::Orientation curr_orient = CGAL::Visibility_2::orientation_2
( geom_traits,
ray_begin,
ray_end,
vertices[k+1] );
if ( curr_orient != old_orient ) {
// Orientation switch, an intersection may occur
Segment_2 seg( vertices[k], vertices[k+1] );
if ( is_ray ) {
if (CGAL::Visibility_2::do_intersect_2(geom_traits, seg, ray) )
{
result = CGAL::Visibility_2::intersect_2( geom_traits, seg, ray );
break;
}
} else {
if (Visibility_2::do_intersect_2(geom_traits, seg, s2) )
{
result = Visibility_2::intersect_2( geom_traits, seg, s2 );
break;
}
}
}
old_orient = curr_orient;
}
assert( k+1<vertices.size() );
const Point_2 * ipoint = CGAL::object_cast<Point_2>( &result );
if ( ipoint ) {
u = *ipoint;
} else {
u = vertices[k+1];
}
return k;
}
};
} // namespace CGAL
#endif
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