From 1c622e0ba50c5903f053609670be5dc8bcd9d6ac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mael=20Rouxel-Labb=C3=A9?=
 <mael.rouxel.labbe@geometryfactory.com>
Date: Thu, 12 Mar 2020 13:11:32 +0100
Subject: [PATCH] Base CDT2's edge sets on geometry to ensure determinism

When using face addresses, we do get the same combinatorics and
geometry in the result, but it is possible to create
different TDS' from one run to another, with a given face
not having the same order of points in memory.
---
 .../Constrained_Delaunay_triangulation_2.h    | 53 ++++++++++++++++---
 .../CGAL/Constrained_triangulation_2.h        | 19 -------
 2 files changed, 46 insertions(+), 26 deletions(-)

diff --git a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
index dd6f110c879..4847cc9fb78 100644
--- a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
@@ -54,10 +54,46 @@ struct Get_iterator_value_type<T,true>{
 } } //namespace CGAL::internal
 #endif //CGAL_TRIANGULATION_2_DONT_INSERT_RANGE_OF_POINTS_WITH_INFO
 
-
-
 namespace CGAL {
+namespace internal {
 
+// Compare geometry to ensure deterministic flips
+template <class Tr>
+class Cdt_2_less_edge
+  : public CGAL::cpp98::binary_function<typename Tr::Edge, typename Tr::Edge, bool>
+{
+  const Tr* tr_ptr;
+
+  typedef typename Tr::Point  Point;
+  typedef typename Tr::Edge   Edge;
+
+public:
+  Cdt_2_less_edge(const Tr* tr_ptr) : tr_ptr(tr_ptr) { }
+
+  // just a manual lexicographical_compare
+  bool operator() (const Edge& e1, const Edge& e2) const
+  {
+    const Point& e1p1 = tr_ptr->point(e1.first, Tr::ccw(e1.second));
+    const Point& e2p1 = tr_ptr->point(e2.first, Tr::ccw(e2.second));
+
+    CGAL::Comparison_result res1 = tr_ptr->compare_xy(e1p1, e2p1);
+    if(res1 == CGAL::SMALLER)
+      return true;
+    if(res1 == CGAL::LARGER)
+      return false;
+
+    const Point& e1p2 = tr_ptr->point(e1.first, Tr::cw(e1.second));
+    const Point& e2p2 = tr_ptr->point(e2.first, Tr::cw(e2.second));
+
+    CGAL::Comparison_result res2 = tr_ptr->compare_xy(e1p2, e2p2);
+    if(res2 == CGAL::SMALLER)
+      return true;
+
+    return false;
+  }
+};
+
+} // namespace internal
 
 template <class Gt,
           class Tds_ = Default ,
@@ -83,13 +119,14 @@ public:
   typedef typename Ctr::Face_circulator       Face_circulator;
   typedef typename Ctr::size_type             size_type;
   typedef typename Ctr::Locate_type           Locate_type;
- 
+
   typedef typename Ctr::List_edges List_edges;  
   typedef typename Ctr::List_faces List_faces;
   typedef typename Ctr::List_vertices  List_vertices;
   typedef typename Ctr::List_constraints List_constraints;
-  typedef typename Ctr::Less_edge less_edge;
-  typedef typename Ctr::Edge_set Edge_set;
+
+  typedef internal::Cdt_2_less_edge<CDt> Less_edge;
+  typedef std::set<Edge, Less_edge> Edge_set;
 
   //Tag to distinguish Delaunay from regular triangulations
   typedef Tag_false Weighted_tag;
@@ -538,8 +575,10 @@ public:
   int i, ii, indf, indn;
   Face_handle ni, f,ff;
   Edge ei,eni; 
-  typename Ctr::Edge_set edge_set;
-  typename Ctr::Less_edge less_edge;
+
+  Less_edge less_edge(this);
+  Edge_set edge_set(less_edge);
+
   Edge e[4];
   typename List_edges::iterator itedge=edges.begin();
 
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index a453d120cd1..d8a7d762f9b 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -165,10 +165,6 @@ public:
   // Tag to distinguish periodic triangulations from others
   typedef Tag_false                          Periodic_tag;
 
-  class Less_edge;
-  typedef std::set<Edge,Less_edge> Edge_set;
-
-
   Constrained_triangulation_2(const Gt& gt = Gt()) : Triangulation(gt) { }
 
   Constrained_triangulation_2(std::list<Constraint>& lc, const Gt& gt=Gt())
@@ -411,21 +407,6 @@ insert_constraint(Vertex_handle  vaa, Vertex_handle vbb, OutputIterator out)
   // template<class OutputItEdges>
   // OutputItEdges incident_constraints(Vertex_handle v, 
   //                                     OutputItEdges out) const;
-  
-
-  class Less_edge 
-    :  public CGAL::cpp98::binary_function<Edge, Edge, bool>
-  {
-  public:
-    Less_edge() {}
-    bool operator() (const Edge& e1, const Edge& e2) const
-      {
-	int ind1=e1.second, ind2=e2.second;
- 	return( (&(*e1.first) < &(*e2.first))
- 		|| ( (&(*e1.first) == &(*e2.first)) && (ind1 < ind2)));
-      } 
-  };
-
 
   void file_output(std::ostream& os) const;