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// Copyright (c) 2002-2004 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Intersections_2/include/CGAL/Intersections_2/Iso_rectangle_2_Triangle_2.h $
// $Id: include/CGAL/Intersections_2/Iso_rectangle_2_Triangle_2.h 08b27d3db14 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Radu Ursu
#ifndef CGAL_INTERSECTIONS_2_ISO_RECTANGLE_2_TRIANGLE_2_H
#define CGAL_INTERSECTIONS_2_ISO_RECTANGLE_2_TRIANGLE_2_H
#include <CGAL/Triangle_2.h>
#include <CGAL/Iso_rectangle_2.h>
#include <CGAL/Intersections_2/Segment_2_Segment_2.h>
#include <CGAL/Intersection_traits_2.h>
#include <CGAL/Intersections_2/Iso_rectangle_2_Segment_2.h>
#include <vector>
#include <list>
namespace CGAL{
namespace Intersections {
namespace internal {
template <class K>
typename Intersection_traits<K, typename K::Triangle_2, typename K::Iso_rectangle_2>::result_type
intersection(const typename K::Triangle_2 &t, const typename K::Iso_rectangle_2 &r, const K& kk)
{
typedef typename K::FT FT;
typedef typename K::Segment_2 Segment;
typedef typename K::Triangle_2 Triangle;
typedef typename K::Point_2 Point;
FT xr1, yr1, xr2, yr2;
bool position[3][4] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}};
bool is_inside[3] = {false, false, false}; //true when a vertex is inside rectangle
xr1 = r.xmin(); xr2 = r.xmax();
yr1 = r.ymax(); yr2 = r.ymin();
Point upper_left, lower_right;
Point p[3]; //the vertices of triangle
upper_left = Point(xr1, yr1); //upper left
lower_right = Point(xr2, yr2); //lower right
p[0] = t.vertex(0);
p[1] = t.vertex(1);
p[2] = t.vertex(2);
//check the points of the triangle
for(int i=0; i<3; i++){
if(!(compare_x(p[i], upper_left) == SMALLER))
if(!(compare_x(p[i], lower_right) == LARGER))
if(!(compare_y(p[i], upper_left) == LARGER))
if(!(compare_y(p[i], lower_right) == SMALLER))
is_inside[i] = true; //the point is inside
else
position[i][2] = true; //South
else
position[i][0] = true; //North
else
{
position[i][3] = true; //East
if(compare_y(p[i], upper_left) == LARGER)
position[i][0] = true; //North
else if(compare_y(p[i], lower_right) == SMALLER)
position[i][2] = true; //South
}
else
{
position[i][1] = true; //West
if(compare_y(p[i], upper_left) == LARGER)
position[i][0] = true; //North
else if(compare_y(p[i], lower_right) == SMALLER)
position[i][2] = true; //South
}
}
//test if the triangle is completely to the left, right, below or above the rectangle
bool intersection = true; //true if it could be a intersection with the rectangle
for(int j=0; j<4; j++)
if(position[0][j] && position[1][j] && position[2][j] ){
intersection = false;
break;
}
if(intersection){
Segment s[4]; //the segments that identify the N, W, S, E
bool outside = false;
bool status_in_list[3] = {false, false, false}; //true if the triangle's points are in the result vector
std::list<int> last_intersected;
int last_intersected_segment = 5; //could be 0=N, 1=W, 2=S, 3=E
last_intersected.push_back(5);
int status_intersected[4] = {0, 0, 0, 0}; //the number of intersections for each segment
std::vector<Point> result; //the vector containing the result vertices
int next; //the index of the next vertex
s[0] = Segment(Point(xr2, yr1), Point(xr1, yr1)); //N
s[1] = Segment(Point(xr1, yr1), Point(xr1, yr2)); //W
s[2] = Segment(Point(xr1, yr2), Point(xr2, yr2)); //S
s[3] = Segment(Point(xr2, yr2), Point(xr2, yr1)); //E
//assign to p[i] the vertices of the triangle in ccw order
if(t.orientation() == CGAL::CLOCKWISE)
{
p[0] = t.vertex(2);
p[2] = t.vertex(0);
is_inside[0] = is_inside[2] ^ is_inside[0];
is_inside[2] = is_inside[2] ^ is_inside[0];
is_inside[0] = is_inside[0] ^ is_inside[2];
for(int i=0; i<4; i++){
position[0][i] = position[2][i] ^ position[0][i];
position[2][i] = position[2][i] ^ position[0][i];
position[0][i] = position[0][i] ^ position[2][i];
}
}
for(int index=0; index<3; index++) //for each vertex
{
next=(index+1)%3;
if(is_inside[index]){ // true if first is inside
if(!status_in_list[index]){ //if is not yet in the list
result.push_back(p[index]);
status_in_list[index] = true;
}
if(is_inside[next]){ //true if second is inside
//add the points in the vector
if(!status_in_list[next]){ // if is not yet in the list
result.push_back(p[next]);
status_in_list[next] = true;
}
} else { //I'm going out, the second is outside
for(int j=0; j<4; j++) // for all directions
if(position[next][j]) // if it's a second point direction
{
//test for intersection
typename Intersection_traits<K, Segment, Segment>::result_type
v = internal::intersection(Segment(p[index], p[next]), s[j], kk);
if(v) {
if(const Point *p_obj = intersect_get<Point>(v))
{
//intersection found
outside = true;
result.push_back(*p_obj); //add the intersection point
if(last_intersected.back()!=j)
last_intersected.push_back(j);
status_intersected[j]++;
}
}
}
}
} else { //the first point is outside
for(int j=0; j<4; j++) // for all directions
if(position[index][j]) //watch only the first point directions
{
//test for intersection
typename Intersection_traits<K, Segment, Segment>::result_type
v = internal::intersection(Segment(p[index], p[next]), s[j], kk);
if(v) {
if(const Point *p_obj = intersect_get<Point>(v))
{
//intersection found
outside = false;
last_intersected_segment = last_intersected.back();
if(last_intersected_segment != 5 && last_intersected_segment != j && status_intersected[j] == 0){
//add the target of each rectangle segment in the list
if(last_intersected_segment < j)
while(last_intersected_segment < j){
result.push_back(s[last_intersected_segment].target());
last_intersected_segment++;
}
else{
while(last_intersected_segment < 4){
result.push_back(s[last_intersected_segment].target());
last_intersected_segment++;
}
last_intersected_segment = 0;
while(last_intersected_segment < j){
result.push_back(s[last_intersected_segment].target());
last_intersected_segment++;
}
}
}
result.push_back(*p_obj); //add the intersection point in the list
if(last_intersected.back()!=j)
last_intersected.push_back(j);
status_intersected[j]++;
if(!is_inside[next]){ //if the second point is not inside search a second intersection point
for(j=0; j<4; j++) // for all directions
if(position[next][j])
{
//test for intersection
typename Intersection_traits<K, Segment, Segment>
::result_type
v = internal::intersection(Segment(p[index], p[next]), s[j], kk);
if(v) {
if(const Point *p_obj = intersect_get<Point>(v))
//found the second intersection
{
outside = true;
result.push_back(*p_obj);
if(last_intersected.back()!=j)
last_intersected.push_back(j);
status_intersected[j]++;
}
}
}
}//end if the second point is not inside
}
} // end v
}
}//end else (the first point is outside)
}//endfor
if(outside){
std::list<int>::const_iterator it = last_intersected.begin();
while(*it == 5)
it++;
last_intersected_segment = *it;
int j = last_intersected.back();
if(last_intersected_segment != 5 && last_intersected_segment != j){
//add the target of each rectangle segment in the list
if(last_intersected_segment > j)
while(last_intersected_segment > j){
result.push_back(s[j].target());
j++;
}
else{
while(j<4){
result.push_back(s[j].target());
j++;
}
j = 0;
while(j<last_intersected_segment){
result.push_back(s[j].target());
j++;
}
}
}
}//end if(outside)
//test if were not intersections
//between the triangle and the rectangle
if(status_intersected[0] == 0 && status_intersected[1] == 0 &&
status_intersected[2] == 0 && status_intersected[3] == 0)
{
//should test if the rectangle is inside the triangle
if(t.bounded_side(upper_left) == CGAL::ON_BOUNDED_SIDE){
for(int k=0; k<4; k++)
result.push_back(s[k].source());
}
}
//remove duplicated consecutive points
typename std::vector<Point>::iterator last = std::unique(result.begin(),result.end());
result.erase(last,result.end());
while(result.size() > 1 && result.back() == result.front())
result.pop_back();
switch(result.size()){
case 0:
return intersection_return<typename K::Intersect_2, Triangle, typename K::Iso_rectangle_2>();
case 1:
return intersection_return<typename K::Intersect_2, Triangle, typename K::Iso_rectangle_2>(result[0]);
case 2:
return intersection_return<typename K::Intersect_2, Triangle, typename K::Iso_rectangle_2>(Segment(result[0], result[1]));
case 3:
return intersection_return<typename K::Intersect_2, Triangle, typename K::Iso_rectangle_2>(Triangle(result[0], result[1], result[2]));
default:
return intersection_return<typename K::Intersect_2, Triangle, typename K::Iso_rectangle_2>(result);
}
}//end if(intersection)
return intersection_return<typename K::Intersect_2, Triangle, typename K::Iso_rectangle_2>();
}//end intersection
template <class K>
typename Intersection_traits<K, typename K::Triangle_2, typename K::Iso_rectangle_2>::result_type
inline intersection(const typename K::Iso_rectangle_2 &r, const typename K::Triangle_2 &t, const K& k)
{
return intersection(t,r,k);
}
template <class K>
typename K::Boolean
do_intersect(const typename K::Triangle_2& tr,
const typename K::Iso_rectangle_2& ir,
const K& k)
{
//1) check if at least one vertex of tr is not outside ir
//2) if not, check if at least on vertex of tr is not outside tr
typename K::Has_on_unbounded_side_2 unbounded_side=k.has_on_unbounded_side_2_object();
typename K::Construct_vertex_2 vertex=k.construct_vertex_2_object();
for (int i=0;i<3;++i)
if ( !unbounded_side( ir,vertex(tr,i) ) ) return true;
for (int i=0;i<4;++i)
if ( !unbounded_side( tr,vertex(ir,i) ) ) return true;
typename K::Construct_segment_2 segment=k.construct_segment_2_object();
for (int i=0;i<3;++i)
if ( do_intersect(
segment(vertex(tr,i),vertex(tr,(i+1)%3)),
ir, k) ) return true;
return false;
}
template <class K>
inline
typename K::Boolean
do_intersect(const typename K::Iso_rectangle_2& ir,
const typename K::Triangle_2& tr,
const K& k)
{
return do_intersect(tr, ir, k);
}
} // namespace internal
} // namespace Intersections
CGAL_INTERSECTION_FUNCTION(Triangle_2, Iso_rectangle_2, 2)
CGAL_DO_INTERSECT_FUNCTION(Triangle_2, Iso_rectangle_2, 2)
} // namespace CGAL
#endif // CGAL_INTERSECTIONS_2_ISO_RECTANGLE_2_TRIANGLE_2_H
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