From 5bc5ec4f469806b9738da62e30516eb9ecbebf5c Mon Sep 17 00:00:00 2001
From: Laurent Rineau <laurent.rineau@cgal.org>
Date: Mon, 25 Sep 2023 17:58:03 +0200
Subject: [PATCH] fix cheese18 --merge-facets

The explanation of the bug:
`split_graph_into_polylines` can reverse the orientation of a polygon
---
 .../Constrained_Delaunay_triangulation_3.h    |  6 ++---
 .../test/Triangulation_3/cdt_3_from_off.cpp   | 24 +++++++++++++++++--
 2 files changed, 24 insertions(+), 6 deletions(-)

diff --git a/Triangulation_3/include/CGAL/Constrained_Delaunay_triangulation_3.h b/Triangulation_3/include/CGAL/Constrained_Delaunay_triangulation_3.h
index d569f82fd04..13df3eddfb5 100644
--- a/Triangulation_3/include/CGAL/Constrained_Delaunay_triangulation_3.h
+++ b/Triangulation_3/include/CGAL/Constrained_Delaunay_triangulation_3.h
@@ -534,7 +534,7 @@ public:
       const auto vb = *circ;
       const auto c_id = this->constraint_from_extremities(va, vb);
       if(c_id != Constraint_id{}) {
-        const bool constraint_c_id_is_reversed = true;
+        const bool constraint_c_id_is_reversed = va != (*this->constraint_hierarchy.vertices_in_constraint_begin(c_id));
         border.push_back(Face_edge{c_id, constraint_c_id_is_reversed});
         constraint_to_faces.emplace(c_id, polygon_contraint_id);
       } else {
@@ -635,9 +635,7 @@ private:
           const auto v_end = this->constraint_hierarchy.vertices_in_constraint_end(c_id);
           CGAL_assertion(std::distance(v_begin, v_end) >= 2);
           auto va = *v_begin;
-          auto vb_it = v_end;
-          --vb_it;
-          auto vb = *vb_it;
+          auto vb = *std::prev(v_end);
           if(reversed) {
             using std::swap;
             swap(va, vb);
diff --git a/Triangulation_3/test/Triangulation_3/cdt_3_from_off.cpp b/Triangulation_3/test/Triangulation_3/cdt_3_from_off.cpp
index 3e91be160d6..70e8c330212 100644
--- a/Triangulation_3/test/Triangulation_3/cdt_3_from_off.cpp
+++ b/Triangulation_3/test/Triangulation_3/cdt_3_from_off.cpp
@@ -132,7 +132,7 @@ int main(int argc, char* argv[])
     try {
       go(mesh, output_filename);
     } catch(CGAL::Failure_exception& e) {
-      if(e.expression().find(std::string("orientation(p0, p1, p2, p3) == POSITIVE")) != std::string::npos)
+      if(e.expression().find(std::string("handles.back() == va")) != std::string::npos)
       {
         std::cerr << "BAD MESH! " << mesh.number_of_faces() << " faces\n";
         std::ofstream bad("bad.off");
@@ -302,8 +302,28 @@ int go(Mesh mesh, std::string output_filename) {
   CDT_3_try {
     if(merge_facets) {
       for(int i = 0; i < nb_patches; ++i) {
-        const auto& edges = patch_edges[i];
+        auto& edges = patch_edges[i];
         auto polylines = segment_soup_to_polylines(edges);
+        while(true) {
+          const auto non_closed_polylines_begin =
+              std::partition(polylines.begin(), polylines.end(),
+                             [](const auto& polyline) { return polyline.front() == polyline.back(); });
+          if(non_closed_polylines_begin == polylines.end())
+            break;
+          edges.clear();
+          for(auto it = non_closed_polylines_begin; it != polylines.end(); ++it) {
+            auto& polyline = *it;
+            for(auto it = polyline.begin(), end = polyline.end() - 1; it != end; ++it) {
+              edges.emplace_back(*it, *(it + 1));
+            }
+          }
+          polylines.erase(non_closed_polylines_begin, polylines.end());
+          auto other_polylines = segment_soup_to_polylines(edges);
+          polylines.insert(polylines.end(),
+                           std::make_move_iterator(other_polylines.begin()),
+                           std::make_move_iterator(other_polylines.end()));
+        }
+
         std::optional<int> face_index;
         for(auto& polyline: polylines) {
           assert(polyline.front() == polyline.back());