From 9ede1f3ee7967652296787ee46fbc507eaf61d90 Mon Sep 17 00:00:00 2001
From: Maxime Gimeno <maxime.gimeno@gmail.com>
Date: Thu, 3 Oct 2019 10:48:52 +0200
Subject: [PATCH] Specialize the cw test to be more robust if the kernel is not
 exact

---
 .../Triangle_2_Triangle_2_intersection_impl.h | 50 +++++++++++++------
 .../Intersections_2/test_intersections_2.cpp  |  6 ++-
 2 files changed, 39 insertions(+), 17 deletions(-)

diff --git a/Intersections_2/include/CGAL/Intersections_2/internal/Triangle_2_Triangle_2_intersection_impl.h b/Intersections_2/include/CGAL/Intersections_2/internal/Triangle_2_Triangle_2_intersection_impl.h
index 1cf2b107762..7d6b32f3239 100644
--- a/Intersections_2/include/CGAL/Intersections_2/internal/Triangle_2_Triangle_2_intersection_impl.h
+++ b/Intersections_2/include/CGAL/Intersections_2/internal/Triangle_2_Triangle_2_intersection_impl.h
@@ -30,6 +30,7 @@
 
 #include <CGAL/Intersections_2/Line_2_Line_2.h>
 #include <CGAL/Intersection_traits_2.h>
+#include <CGAL/Algebraic_structure_traits.h>
 
 namespace CGAL {
   
@@ -281,13 +282,6 @@ Triangle_2_Triangle_2_pair<K>::vertex(int n) const
     return cur->point;
 }
 
-//algorithm taken from here : https://stackoverflow.com/questions/1165647/how-to-determine-if-a-list-of-polygon-points-are-in-clockwise-order
-template <typename K, typename ArrayOfPoints>
-bool is_cw(const ArrayOfPoints& ps)
-{
-  return !CGAL::left_turn(ps[0], ps[1], ps[2]);
-}
-
 template <class K>
 typename K::Triangle_2
 Triangle_2_Triangle_2_pair<K>::intersection_triangle() const
@@ -296,16 +290,18 @@ Triangle_2_Triangle_2_pair<K>::intersection_triangle() const
   if (!_known)
     intersection_type();
   CGAL_kernel_assertion(_result == TRIANGLE);
-  std::array<typename K::Point_2, 3> res;
-  res[0]=_pointlist.first->point;
-  res[1]=_pointlist.first->next->point;
-  res[2]=_pointlist.first->next->next->point;
-  if(!is_cw<K>(res))
+  if(CGAL::left_turn(_pointlist.first->point,
+                     _pointlist.first->next->point,
+                     _pointlist.first->next->next->point))
   {
-    return Triangle_2(res[0], res[1], res[2]);
+    return Triangle_2(_pointlist.first->point,
+                      _pointlist.first->next->point,
+                      _pointlist.first->next->next->point);
   }
   else {
-    return Triangle_2(res[0], res[2], res[1]);
+    return Triangle_2(_pointlist.first->point,
+                      _pointlist.first->next->next->point,
+                      _pointlist.first->next->point);
   }
 }
 
@@ -332,6 +328,30 @@ Triangle_2_Triangle_2_pair<K>::intersection_point() const
 }
 
 
+//algorithm taken from here : https://stackoverflow.com/questions/1165647/how-to-determine-if-a-list-of-polygon-points-are-in-clockwise-order
+template <typename K, typename ArrayOfPoints, typename Exact>
+struct Is_cw{
+bool operator()(const ArrayOfPoints& ps)
+{
+  typename K::FT res(0);
+   std::size_t length = ps.size();
+   for(std::size_t i = 0; i<length; ++i)
+   {
+     res += (ps[(i+1)%length].x() - ps[i].x())*(ps[(i+1)%length].y()+ps[i].y());
+   }
+   return res > 0;
+}
+};
+
+template <typename K, typename ArrayOfPoints>
+struct Is_cw<K, ArrayOfPoints,Tag_true>{
+bool operator()(const ArrayOfPoints& ps)
+{
+  return !CGAL::left_turn(ps[0], ps[1], ps[2]);
+}
+};
+
+
 
 template <class K>
 typename CGAL::Intersection_traits
@@ -358,7 +378,7 @@ intersection(const typename K::Triangle_2 &tr1,
         for (int i =0; i < ispair.vertex_count(); i++) {
             points[i] = ispair.vertex(i);
         }
-        if(is_cw<K>(points))
+        if(Is_cw<K, Container, typename Algebraic_structure_traits<typename K::FT>::Is_exact>()(points))
         {
           std::size_t length = points.size();
 
diff --git a/Intersections_2/test/Intersections_2/test_intersections_2.cpp b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
index aced87d8315..bc1ea6bd322 100644
--- a/Intersections_2/test/Intersections_2/test_intersections_2.cpp
+++ b/Intersections_2/test/Intersections_2/test_intersections_2.cpp
@@ -98,7 +98,8 @@ struct Test
   {
     if (p.size() != q.size())
       return false;
-    if (CGAL::Intersections::internal::is_cw<K>(p))
+    if (CGAL::Intersections::internal::Is_cw<K, Pol,
+        typename CGAL::Algebraic_structure_traits<typename K::FT>::Is_exact>()(p))
       return false;
     for(typename Pol::const_iterator itp = p.begin(), itq = q.begin(); itp != p.end(); ++itp, ++itq)
       if (!approx_equal(*itp, *itq))
@@ -111,7 +112,8 @@ struct Test
   {
     std::vector<P> vec(3);
     for(int i=0; i<3; ++i){vec[i]=p[i];}
-    if (CGAL::Intersections::internal::is_cw<K>(vec))
+    if (CGAL::Intersections::internal::Is_cw<K, std::vector<P>,
+        typename CGAL::Algebraic_structure_traits<typename K::FT>::Is_exact>(vec))
       return false;
     return p == q;
   }