cgal/Partition_2/include/CGAL/Vertex_visibility_graph_2.C

720 lines
26 KiB
C

// Copyright (c) 2000 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// 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.
//
// $Source$
// $Revision$ $Date$
// $Name$
//
// Author(s) : Susan Hert <hert@mpi-sb.mpg.de>
namespace CGAL {
/*
// ??? need to finish this ???
template <class Traits>
template <class ForwardIterator>
bool
Vertex_visibility_graph_2<Traits>::is_valid(ForwardIterator first,
ForwardIterator beyond)
{
std::vector<Point_2> vertices(first, beyond);
bool edge_there[vertices.size()];
// for each edge in the graph determine if it is either an edge of the
// polygon or, if not, if it intersects the polygon in the interior of the
// edge.
for (iterator e_it = edges.begin(); e_it != edges.end(); e_it++)
{
Segment_2 s = construct_segment_2((*e_it).first, (*e_it).second);
if (is_an_edge(*e_it))
edge_there[edge_num] = true;
else if (do_intersect_in_interior(s, first, beyond))
return false;
}
// check if all the edges of the polygon are present
//
// ??? how do you check if there are missing edges ???
}
*/
// want to determine, for each vertex p of the polygon, the line segment
// immediately below it. For vertical edges, the segment below is not the
// one that begins at the other endpoint of the edge.
template <class Traits>
void
Vertex_visibility_graph_2<Traits>::initialize_vertex_map(
const Polygon& polygon, Vertex_map& vertex_map)
{
typedef typename Vertex_map::value_type Map_pair;
// Create an event list that is a list of circulators for the polygon
Iterator_list<Polygon_const_iterator>
iterator_list(polygon.begin(), polygon.end());
// Sort the event list (iterators to points) from left to right
// (using less_xy)
#ifdef CGAL_CFG_RWSTD_NO_MEMBER_TEMPLATES
iterator_list.sort(&Self::compare);
#else
iterator_list.sort(Indirect_less_xy_2<Traits>());
#endif
// Create an ordered list of edge endpoints (iterators), initially empty
typedef std::set< Point_pair, Segment_less_yx_2 > Ordered_edge_set;
typedef typename Ordered_edge_set::iterator Ordered_edge_set_iterator;
Ordered_edge_set ordered_edges;
Ordered_edge_set_iterator edge_it;
Vertex_map_iterator vm_it;
Vertex_map_iterator vis_it;
Polygon_const_iterator event_it;
Polygon_const_iterator next_endpt;
Polygon_const_iterator prev_endpt;
// initialize the map by associating iterators and points and indicating
// that no points can see anything.
for (Polygon_const_iterator it = polygon.begin();it != polygon.end();it++)
{
vertex_map.insert(Map_pair(*it, Iterator_pair(it, polygon.end())));
}
// now go through the events in sorted order.
while (!iterator_list.empty())
{
event_it = iterator_list.front();
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "event = " << *event_it << std::endl;
#endif
next_endpt = event_it; next_endpt++;
if (next_endpt == polygon.end()) next_endpt = polygon.begin();
iterator_list.pop_front();
// the first edge that is not less than (below) this edge, so ...
edge_it = ordered_edges.lower_bound(Point_pair(*event_it,*next_endpt));
// ...if there is no edge below this one then nothing is visible,
// otherwise....
if (edge_it != ordered_edges.begin())
{
edge_it--; // ...the first visible edge is the previous edge
// find the event point in the vertex map
vm_it = vertex_map.find(*event_it);
// Find the entry for the edge's first endpoint in the vertex map.
vis_it = vertex_map.find((*edge_it).first);
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "the potential visibility point is " << (*vis_it).first
<< endl;
#endif
// an edge that ends at this event point cannot be below this
// endpoint
if (!is_next_to(polygon, (*vis_it).second.first, event_it))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "the edge beginning at " << *(*vis_it).second.first
<< " is visible" << endl;
#endif
// set the visibility iterator for this point to the iterator
// corresponding to the edge endpoint that is to the left of
// the vertical line
if (less_xy_2((*vis_it).first, (*vm_it).first))
{
Polygon_const_iterator next_vtx = (*vis_it).second.first;
next_vtx++;
if (next_vtx == polygon.end()) next_vtx = polygon.begin();
(*vm_it).second.second = next_vtx;
}
else
(*vm_it).second.second = (*vis_it).second.first;
}
// skip over the edge that ends at this event point. If there
// is another edge above this event's edge then it is visible.
// since it can't also end at the event point.
else if (edge_it != ordered_edges.begin() &&
--edge_it != ordered_edges.begin())
{
vis_it = vertex_map.find((*edge_it).first);
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "the edge beginning at " << *(*vis_it).second.first
<< " is visible" << endl;
#endif
// set the visibility iterator for this point to the iterator
// corresponding to the edge endpoint that is to the left of
// the vertical line
if (less_xy_2((*vis_it).first, (*vm_it).first))
{
Polygon_const_iterator next_vtx = (*vis_it).second.first;
next_vtx++;
if (next_vtx == polygon.end()) next_vtx = polygon.begin();
(*vm_it).second.second = next_vtx;
}
else
(*vm_it).second.second = (*vis_it).second.first;
}
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
else
std::cout << "nothing is visible " << endl;
#endif
}
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
else
cout << "nothing is visible " << endl;
#endif
prev_endpt = event_it;
if (prev_endpt == polygon.begin())
prev_endpt = polygon.end();
prev_endpt--;
// if the other endpoint of the next edge is to the right of the
// sweep line, then insert this edge
if (less_xy_2(*event_it, *next_endpt))
{
ordered_edges.insert(Point_pair(*event_it,*next_endpt));
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "inserting edge from "
<< *event_it << " to " << *next_endpt << endl;
#endif
}
else // other endpoint not to the right, so erase it
{
ordered_edges.erase(Point_pair(*event_it,*next_endpt));
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "erasing edge from "
<< *event_it << " to " << *next_endpt << endl;
#endif
}
// if the other endpoint of the previous edge is to the right of the
// sweep line, insert it
if (less_xy_2(*event_it, *prev_endpt))
{
ordered_edges.insert(Point_pair(*prev_endpt,*event_it));
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "inserting edge from "
<< *prev_endpt << " to " << *event_it << endl;
#endif
}
else // other endpoint is not to the right, so erase it
{
ordered_edges.erase(Point_pair(*prev_endpt,*event_it));
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "erasing edge from "
<< *prev_endpt << " to " << *event_it << endl;
#endif
}
}
}
// determines if one makes a left turn going from p to q to q's parent.
// if q's parent is p_infinity, then a left turn is made when p's x value
// is less than q's x value or the x values are the same and p's y value is
// less than q's.
// if p, q, and q's parent are collinear, then one makes a "left turn"
// if q is between p and q's parent (since this means that p can't see
// q's parent and thus should not become a child of that node)
template <class Traits>
bool
Vertex_visibility_graph_2<Traits>::left_turn_to_parent(
Tree_iterator p,
Tree_iterator q,
Tree& tree)
{
if (tree.parent_is_p_infinity(q))
{
return (less_xy_2(*p, *q));
}
else if (orientation_2(*p, *q, *(*q).parent()) == COLLINEAR &&
(collinear_ordered_2(*p, *q, *(*q).parent()) ||
collinear_ordered_2(*p, *q, *(*q).parent())))
{
return true;
}
else
{
return left_turn_2(*p, *q, *(*q).parent());
}
}
// returns true if the diagonal from p to q cuts the interior angle at p
template <class Traits>
bool
Vertex_visibility_graph_2<Traits>::diagonal_in_interior(
const Polygon& polygon,
Polygon_const_iterator p,
Polygon_const_iterator q)
{
Turn_reverser<Point_2, Left_turn_2> right_turn(left_turn_2);
Polygon_const_iterator before_p;
if (p == polygon.begin())
before_p = polygon.end();
else
before_p = p;
before_p--;
Polygon_const_iterator after_p = p; after_p++;
if (after_p == polygon.end()) after_p = polygon.begin();
if (right_turn(*before_p, *p, *after_p))
{
if (right_turn(*before_p, *p, *q) && right_turn(*q, *p, *after_p))
return false;
}
else // left turn or straight at vertex
{
/*
// p should not be able to see q through its own edge
if (are_strictly_ordered_along_line(*p, *after_p, *q))
return false;
*/
if (right_turn(*before_p, *p, *q) || right_turn(*q, *p, *after_p))
return false;
}
return true;
}
// returns true if the looker can see the point_to_see
template <class Traits>
bool Vertex_visibility_graph_2<Traits>::point_is_visible(
const Polygon& polygon,
Polygon_const_iterator point_to_see,
Vertex_map_iterator looker)
{
// Collect pointers to the current visibility segments for the looker
// (the current visibility point and the two vertices flanking this vertex)
Polygon_const_iterator vis_endpt = (*looker).second.second;
Polygon_const_iterator next_vis_endpt = vis_endpt; next_vis_endpt++;
if (next_vis_endpt == polygon.end()) next_vis_endpt = polygon.begin();
Polygon_const_iterator prev_vis_endpt;
if (vis_endpt == polygon.begin())
prev_vis_endpt = polygon.end();
else
prev_vis_endpt = vis_endpt;
prev_vis_endpt--;
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker is " << (*looker).first << " point to see is "
<< *point_to_see;
cout << " visibility points are prev: " << *prev_vis_endpt
<< " vis: " << *vis_endpt << " next: " << *next_vis_endpt << endl;
#endif
// if the point to see is the current visibility point or if the looker
// and the point to see flank the old visibility point, they are visible
// to each other since it is known at this point that the edge from
// the looker to the point to see goes through the interior of the polygon
if ((*looker).second.second == point_to_see)
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "looker sees point" << std::endl;
#endif
return true;
}
else if (((*looker).second.first == prev_vis_endpt &&
point_to_see == next_vis_endpt) ||
((*looker).second.first == next_vis_endpt &&
point_to_see == prev_vis_endpt))
{
if (orientation_2(*prev_vis_endpt, *vis_endpt, *next_vis_endpt) ==
COLLINEAR &&
(collinear_ordered_2((*looker).first, *vis_endpt, *point_to_see) ||
collinear_ordered_2(*point_to_see, *vis_endpt, (*looker).first)))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker does NOT see point" << endl;
#endif
return false;
}
else
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker sees point" << endl;
#endif
return true;
}
}
else if ((*looker).second.first == prev_vis_endpt ||
point_to_see == prev_vis_endpt)
// point to see or looker is not adjacent to old visibility, so check
// intersection with next visibility segment
{
if (orientation_2(*vis_endpt, *next_vis_endpt, (*looker).first) !=
orientation_2(*vis_endpt, *next_vis_endpt, *point_to_see) &&
orientation_2((*looker).first, *point_to_see, *vis_endpt) !=
orientation_2((*looker).first, *point_to_see, *next_vis_endpt))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker does NOT see point" << endl;
#endif
return false;
}
else
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker sees point" << endl;
#endif
return true;
}
}
else if ((*looker).second.first == next_vis_endpt ||
point_to_see == next_vis_endpt)
// point to see or looker is not adjacent to old visibility, so check
// intersection with previous visibility segment
{
if (orientation_2(*vis_endpt, *prev_vis_endpt, (*looker).first) !=
orientation_2(*vis_endpt, *prev_vis_endpt, *point_to_see) &&
orientation_2((*looker).first, *point_to_see, *vis_endpt) !=
orientation_2((*looker).first, *point_to_see, *prev_vis_endpt))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker does NOT see point" << endl;
#endif
return false;
}
else
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker sees point" << endl;
#endif
return true;
}
}
else
// neither is adjacent to the old visibility point so check intersection
// with both visibility segments
{
if (orientation_2(*vis_endpt, *next_vis_endpt, (*looker).first) !=
orientation_2(*vis_endpt, *next_vis_endpt, *point_to_see) &&
orientation_2((*looker).first, *point_to_see, *vis_endpt) !=
orientation_2((*looker).first, *point_to_see, *next_vis_endpt))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker does NOT see point" << endl;
#endif
return false;
}
else if (orientation_2(*vis_endpt, *prev_vis_endpt, (*looker).first) !=
orientation_2(*vis_endpt, *prev_vis_endpt, *point_to_see) &&
orientation_2((*looker).first, *point_to_see, *vis_endpt) !=
orientation_2((*looker).first, *point_to_see, *prev_vis_endpt))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker does NOT see point" << endl;
#endif
return false;
}
else // no intersection
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "looker sees point" << endl;
#endif
return true;
}
}
}
template <class Traits>
void Vertex_visibility_graph_2<Traits>::update_visibility(
Vertex_map_iterator p_it,
Vertex_map_iterator q_it,
const Polygon& polygon,
int are_adjacent)
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "updating visibility: " << std::endl;
#endif
Polygon_const_iterator prev_q;
Polygon_const_iterator turn_q;
if ((*q_it).second.first == polygon.begin())
prev_q = polygon.end();
else
prev_q = (*q_it).second.first;
prev_q--;
// determine if the vertex before or after q is the one that will
// be encountered next when moving in the direction from p to q.
if (prev_q == (*p_it).second.first)
{
turn_q = (*q_it).second.first;
turn_q++;
if (turn_q == polygon.end()) turn_q = polygon.begin();
}
else
turn_q = prev_q;
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "prev_q = " << *prev_q << " turn_q = " << *turn_q
<< std::endl;
#endif
if (are_adjacent)
{
if (orientation_2((*p_it).first, (*q_it).first, *turn_q) == RIGHT_TURN)
{
(*p_it).second.second = (*q_it).second.second; // p sees what q sees
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "adjacent with right turn; p now sees what q sees"
<< std::endl;
#endif
}
else // turn left or go straight
{
(*p_it).second.second = (*q_it).second.first; // p sees q
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "adjacent and NOT right turn; p now sees q "
<< std::endl;
#endif
}
}
// if not adjacent, the edge was an interior one and so the "next" vertex
// (the turn vertex) has to be the one that follows q.
//
// if Segment(q) == vis(p), i.e., p already sees q's segment
else if ((*q_it).second.first == (*p_it).second.second ||
prev_q == (*p_it).second.second)
{
turn_q = (*q_it).second.first; turn_q++;
if (turn_q == polygon.end()) turn_q = polygon.begin();
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "prev_q = " << *prev_q << " turn_q = " << *turn_q
<< std::endl;
#endif
// q sees nothing or there is not a right turn to the point after q
if ((*q_it).second.second == polygon.end() ||
orientation_2((*p_it).first, (*q_it).first, *turn_q) != RIGHT_TURN)
{
(*p_it).second.second = (*q_it).second.first; // p sees q
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p sees q's segment, q sees nothing and not right to "
<< " next point; p sees q " << std::endl;
#endif
}
else
{
(*p_it).second.second = (*q_it).second.second; // p sees what q sees
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p sees q's segment, q sees something;"
<< " p sees what q sees" << std::endl;
#endif
}
}
// Before(p,q,vis(p)) == true if q lies nearer to p than segment vis(p)
// NOTE: it is known that p is always looking to the right.
else if ((*p_it).second.second != polygon.end()) // if p sees something
{
Polygon_const_iterator next_v_p = (*p_it).second.second; next_v_p++;
if (next_v_p == polygon.end()) next_v_p = polygon.begin();
// don't need to do this for the previous visibility point since
// if it were closer to p than q when looking from p to q, q would
// not be visible.
Segment_2 next_seg = construct_segment_2(*(*p_it).second.second,
*next_v_p);
Ray_2 ray = construct_ray_2((*p_it).first, (*q_it).first);
Segment_2 i_seg;
Point_2 i_point;
Object_2 next_result = intersect_2(next_seg, ray);
if (assign_2(i_point, next_result))
{
if (collinear_ordered_2((*p_it).first, (*q_it).first, i_point))
{
(*p_it).second.second = (*q_it).second.first;
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p sees something in direction of q, but q is closer;"
<< " p sees q" << std::endl;
#endif
}
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
else
{
std::cout << "p sees something in direction of q that's closer "
<< "than q; p doesn't see q" << std::endl;
}
#endif
}
else if (assign_2(i_seg, next_result))
{
if (collinear_ordered_2((*p_it).first,(*q_it).first,i_seg.source()) &&
collinear_ordered_2((*p_it).first,(*q_it).first,i_seg.target()))
{
(*p_it).second.second = (*q_it).second.first;
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p sees something in direction of q, but q is closer;"
<< " p sees q" << std::endl;
#endif
}
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
else
{
std::cout << "p sees something in direction of q that's closer "
<< " than q; p doesn't see q" << std::endl;
}
#endif
}
else
{
(*p_it).second.second = (*q_it).second.first;
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p doesn't see something in direction of q; p sees q"
<< std::endl;
#endif
}
}
else // p sees what q sees
{
(*p_it).second.second = (*q_it).second.first;
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p sees nothing; p sees what q sees" << std::endl;
#endif
}
}
template <class Traits>
void Vertex_visibility_graph_2<Traits>::update_collinear_visibility(
Vertex_map_iterator p_it,
Vertex_map_iterator q_it,
const Polygon& polygon)
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "updating collinear visibility" << std::endl;
#endif
Polygon_const_iterator prev_q;
if ((*q_it).second.first == polygon.begin())
prev_q = polygon.end();
else
prev_q = (*q_it).second.first;
prev_q--;
Polygon_const_iterator next_q = (*q_it).second.first;
next_q++;
if (next_q == polygon.end()) next_q = polygon.begin();
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "q's neighbors are: prev " << *prev_q
<< " q " << (*q_it).first
<< " next " << *next_q << std::endl;
#endif
// if the point before q is above the line containing p and q, make
// this p's visibility point
if (left_turn_2((*p_it).first, (*q_it).first, *prev_q))
{
if (point_is_visible(polygon, prev_q, p_it))
(*p_it).second.second = prev_q;
}
// check the same thing for the point after q and, if it is still visible
// (even after possibly updating the visibility in the above if) the
// update again.
if (left_turn_2((*p_it).first, (*q_it).first, *next_q))
{
if (point_is_visible(polygon, next_q, p_it))
(*p_it).second.second = next_q;
}
}
// The segment between points p and q is a potential visibility edge
// This function determines if the edge should be added or not (based
// on p's current visibility point) and updates p's visibility point
// where appropriate
template <class Traits>
void Vertex_visibility_graph_2<Traits>::handle(Tree_iterator p,
Tree_iterator q,
const Polygon& polygon,
Vertex_map& vertex_map)
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "Handling edge from " << (*p).x() << " " << (*p).y()
<< " to " << (*q).x() << " " << (*q).y() << std::endl;
#endif
Vertex_map_iterator p_it = vertex_map.find(*p);
Vertex_map_iterator q_it = vertex_map.find(*q);
CGAL_assertion (p_it != vertex_map.end());
CGAL_assertion (q_it != vertex_map.end());
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p currently sees : ";
if ((*p_it).second.second != polygon.end())
std::cout << *((*p_it).second.second) << endl;
else
std::cout << " NADA" << endl;
#endif
// if p and q are adjacent
if (are_adjacent(polygon, (*p_it).second.first, (*q_it).second.first))
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "are adjacent" << endl;
#endif
insert_edge(Point_pair(*p,*q));
update_visibility(p_it, q_it, polygon, 1);
}
else
{
bool interior_at_p = diagonal_in_interior(polygon, (*p_it).second.first,
(*q_it).second.first);
bool interior_at_q = diagonal_in_interior(polygon, (*q_it).second.first,
(*p_it).second.first);
// line of site is through the interior of the polygon
if (interior_at_p && interior_at_q)
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "both interior" << endl;
#endif
// if p sees something and q is visible only through collinear
// points then update p's visibility if one of the points adjacent
// to q is above the line unless p's current visibility point
// obscures the view.
if ((*p_it).second.second != polygon.end() &&
are_strictly_ordered_along_line_2((*p_it).first,
*(*p_it).second.second,
(*q_it).first))
{
update_collinear_visibility(p_it, q_it, polygon);
}
// p current sees nothing or q is visible to p
else if ((*p_it).second.second == polygon.end() ||
point_is_visible(polygon, (*q_it).second.first, p_it))
{
insert_edge(Point_pair(*p,*q));
update_visibility(p_it, q_it, polygon, 0);
}
}
else if (!interior_at_p && !interior_at_q) // both points exterior
{
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
cout << "both exterior" << endl;
#endif
// p currently sees nothing or q is visible to p
if ((*p_it).second.second == polygon.end() ||
point_is_visible(polygon, (*q_it).second.first, p_it))
{
(*p_it).second.second = (*q_it).second.first;
}
}
}
#ifdef CGAL_VISIBILITY_GRAPH_DEBUG
std::cout << "p now sees : ";
if ((*p_it).second.second != polygon.end())
std::cout << *((*p_it).second.second) << endl;
else
std::cout << " NADA" << endl;
#endif
}
}