Fix Convex_hull_3 so it becomes minimal.

Convex_hull_3/doc/Convex_hull_3/CGAL/Convex_hull_traits_3.h

@@ -98,6 +98,11 @@ unspecified_type Has_on_positive_side_3;
 
 /*!
 
+*/ 
+unspecified_type Has_on_negative_side_3;
+
+/*!
+
 */ 
 unspecified_type Less_signed_distance_to_plane_3;
 

Convex_hull_3/doc/Convex_hull_3/Concepts/ConvexHullTraits_3.h

@@ -85,6 +85,13 @@ Predicate object type that provides
 */ 
 typedef unspecified_type Has_on_positive_side_3; 
   
+  /*!
+  Predicate object type that provides 
+  `bool operator()(Plane_3 h, Point_3 q)`, which determines if the point 
+  `q` is on the negative side of the halfspace `h`. 
+  */ 
+  typedef unspecified_type Has_on_negative_side_3; 
+
 /*!
 Predicate object type that provides 
 a constructor taking a single `Point_3` object and 

Convex_hull_3/include/CGAL/Convex_hull_traits_3.h

@@ -95,6 +95,23 @@ public:
 
   typedef bool result_type;
 };
+
+template <class K>
+class Point_triple_has_on_negative_side_3 {
+
+public:
+    typedef typename K::Point_3 Point_3;
+    typedef Point_triple<K> Plane_3;
+  bool
+    operator()( const Plane_3& pl, const Point_3& p) const
+    {
+      typename K::Orientation_3 o; 
+      return ( o(pl.p(), pl.q(), pl.r(), p) == CGAL::NEGATIVE);
+    }
+
+  typedef bool result_type;
+};
+
 template <class K, class OldK>
 class Point_triple_construct_orthogonal_vector_3 
 {
@@ -167,6 +184,8 @@ struct GT3_for_CH3 {
 template <class R_, class Has_filtered_predicates_tag /* = Tag_false */>
 struct Convex_hull_traits_base_3 {
   typedef Point_triple_has_on_positive_side_3<R_>     Has_on_positive_side_3;
+  typedef Point_triple_has_on_negative_side_3<R_>     Has_on_negative_side_3;
+  
 
   typedef  Point_triple_less_signed_distance_to_plane_3<R_>
                                                   Less_signed_distance_to_plane_3;
@@ -181,6 +200,13 @@ struct Convex_hull_traits_base_3<R_, Tag_true>{
       Point_triple_converter<R_,typename R_::Approximate_kernel>
   > Has_on_positive_side_3;
   
+  typedef Filtered_predicate<
+      Point_triple_has_on_negative_side_3< typename R_::Exact_kernel_rt >,
+      Point_triple_has_on_negative_side_3< typename R_::Approximate_kernel >,
+      Point_triple_converter<R_,typename R_::Exact_kernel_rt>,
+      Point_triple_converter<R_,typename R_::Approximate_kernel>
+  > Has_on_negative_side_3;
+
   typedef Filtered_predicate<
       Point_triple_less_signed_distance_to_plane_3< typename R_::Exact_kernel_rt >,
       Point_triple_less_signed_distance_to_plane_3< typename R_::Approximate_kernel >,
@@ -230,6 +256,8 @@ class Convex_hull_traits_3 :
 
   typedef typename Convex_hull_traits_base_3<R_, Has_filtered_predicates_tag>
     ::Has_on_positive_side_3 Has_on_positive_side_3;
+  typedef typename Convex_hull_traits_base_3<R_, Has_filtered_predicates_tag>
+    ::Has_on_negative_side_3 Has_on_negative_side_3;
 
   typedef typename Convex_hull_traits_base_3<R_, Has_filtered_predicates_tag>
     ::Less_signed_distance_to_plane_3 Less_signed_distance_to_plane_3;
@@ -290,6 +318,10 @@ class Convex_hull_traits_3 :
   has_on_positive_side_3_object() const
   { return Has_on_positive_side_3(); }
   
+  Has_on_negative_side_3
+  has_on_negative_side_3_object() const
+  { return Has_on_negative_side_3(); }
+
   Oriented_side_3
   oriented_side_3_object() const
   { return Oriented_side_3(); }

Convex_hull_3/include/CGAL/convex_hull_3.h

@@ -358,8 +358,8 @@ find_visible_set(TDS_2& tds,
    typedef typename Traits::Plane_3                   Plane_3;
    typedef typename TDS_2::Face_handle Face_handle;
    typedef typename TDS_2::Vertex_handle Vertex_handle;
-   typename Traits::Has_on_positive_side_3 has_on_positive_side =
+   typename Traits::Has_on_negative_side_3 has_on_negative_side =
-            traits.has_on_positive_side_3_object();
+      traits.has_on_negative_side_3_object();
 
    std::vector<Vertex_handle> vertices;
    vertices.reserve(10);
@@ -387,7 +387,7 @@ find_visible_set(TDS_2& tds,
           f->info() = VISITED;
           Plane_3 plane(f->vertex(0)->point(),f->vertex(1)->point(),f->vertex(2)->point());
           int ind = f->index(*vis_it);
-          if ( has_on_positive_side(plane, point) ){  // is visible
+          if ( !has_on_negative_side(plane, point) ){  // is visible
             visible.push_back(f);
             Vertex_handle vh = f->vertex(ind);
             if(vh->info() == 0){ vertices.push_back(vh); vh->info() = VISITED;}
@@ -717,6 +717,56 @@ ch_quickhull_polyhedron_3(std::list<typename Traits::Point_3>& points,
   
 }
 
+template <class P3_iterator, 
+          class Point_3_list>
+void init_iterators(P3_iterator& minx, 
+                    P3_iterator& maxx, 
+                    P3_iterator& miny,
+                    const P3_iterator& start,
+                    const Point_3_list& points)
+{
+  P3_iterator it = start;
+  for(; it != points.end(); ++it){
+    if(it->x() < minx->x())  minx = it;
+    else if(it->x() ==  minx->x())
+    {
+      if(it->y() < minx->y()) minx = it;
+      else if(it->y() == minx->y())
+      {
+        if(it->z() < minx->z()) minx = it;
+      }
+    }
+  }
+  it = start;
+  for(; it != points.end(); ++it){
+    if(it == minx )
+      continue;
+    if(it->x() > maxx->x()) maxx = it;
+    else if(it->x() == maxx->x())
+    {
+      if(it->y() > maxx->y()) maxx = it;
+      else if(it->y() == maxx->y())
+      {
+        if(it->z() > maxx->z()) maxx = it;
+      }
+    }
+  }
+  it = start;
+  for(; it != points.end(); ++it){
+    if(it == minx || it == maxx)
+      continue;
+    if(it->y() < miny->y()) miny = it;
+    else if(it->y() == miny->y())
+    {
+      if(it->x() > miny->x()) miny = it;
+      else if(it->x() == miny->x())
+      {
+        if(it->z() < miny->z()) miny = it;
+      }
+    }
+  }
+}
+
 } } //namespace internal::Convex_hull_3
 
 
@@ -810,13 +860,7 @@ convex_hull_3(InputIterator first, InputIterator beyond,
   Polyhedron P;
 
   P3_iterator minx, maxx, miny, it;
-  minx = maxx = miny = it = points.begin();
+  internal::Convex_hull_3::init_iterators(minx, maxx, miny, it, points);
-  ++it;
-  for(; it != points.end(); ++it){
-    if(it->x() < minx->x()) minx = it;
-    if(it->x() > maxx->x()) maxx = it;
-    if(it->y() < miny->y()) miny = it;
-  }
   if(! collinear(*minx, *maxx, *miny) ){  
     internal::Convex_hull_3::ch_quickhull_polyhedron_3(points, minx, maxx, miny, P, traits);
   } else {
@@ -893,8 +937,20 @@ void convex_hull_3(InputIterator first, InputIterator beyond,
   
   clear(polyhedron);
   // result will be a polyhedron
-  internal::Convex_hull_3::ch_quickhull_polyhedron_3(points, point1_it, point2_it, point3_it,
+  P3_iterator minx, maxx, miny, it;
-                                                     polyhedron, traits);
+  minx = maxx = miny = it = points.begin();
+  ++it;
+  
+  
+  //take extreme points to begin with.
+  internal::Convex_hull_::init_iterators(minx, maxx, miny, it, points);
+  if(! collinear(*minx, *maxx, *miny) ){
+    internal::Convex_hull_3::ch_quickhull_polyhedron_3(points, minx, maxx, miny,
+                                                       polyhedron, traits);
+  } else {//to do : this case leads to bad init a risk of non minimal convex hull
+    internal::Convex_hull_3::ch_quickhull_polyhedron_3(points, point1_it, point2_it, point3_it,
+                                                       polyhedron, traits);
+  }
 
 }
 

Convex_hull_3/test/Convex_hull_3/convex_hull_traits_3_fp_bug.cpp

@@ -1,10 +1,14 @@
 #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Polyhedron_3.h>
 #include <CGAL/convex_hull_3.h>
+#include <CGAL/Side_of_triangle_mesh.h>
+#include <CGAL/convexity_check_3.h>
 #include <fstream>
 #include <cassert>
 
 typedef CGAL::Epick K;
+typedef CGAL::Epeck EK;
 
 int main()
 {
@@ -18,8 +22,20 @@ int main()
 
   CGAL::Polyhedron_3<K> r;
   CGAL::convex_hull_3(pointset.begin(), pointset.end(), r);
-
   assert(r.size_of_vertices()==82);
   
+  CGAL::Polyhedron_3<EK> s;
+  CGAL::copy_face_graph(r,s);
+  assert(CGAL::is_strongly_convex_3(s));
+
+  CGAL::Cartesian_converter<K, EK> to_EK;
+  CGAL::Side_of_triangle_mesh<CGAL::Polyhedron_3<EK>, EK> sotm(s);
+  
+  
+  BOOST_FOREACH(K::Point_3 p, pointset)
+  {
+    assert(sotm(to_EK(p)) != CGAL::ON_UNBOUNDED_SIDE);
+  }
+
   return 0;
 }