Avoid needless orientation checks / distance computations

If we are right of the edge, the distance is minimum over the edge...
...and that's it. Computing the distance to a segment is about
as expensive as the orientation check, so no point pinpointing
to check if the min is at a vertex.

Author: MaelRL

Distance_3/include/CGAL/Distance_3/Point_3_Triangle_3.h

@@ -64,26 +64,38 @@ squared_distance_to_triangle(const typename K::Point_3& pt,
   const Vector_3 oe3 = vector(t0, t2);
   const Vector_3 normal = wcross(e1, oe3, k);
 
-  if(normal != NULL_VECTOR &&
-     on_left_of_triangle_edge(pt, normal, t0, t1, k) &&
-     on_left_of_triangle_edge(pt, normal, t1, t2, k) &&
-     on_left_of_triangle_edge(pt, normal, t2, t0, k))
-  {
-    // the projection of pt is inside the triangle
-    inside = true;
-    return squared_distance_to_plane(normal, vector(t0, pt), k);
-  }
-  else
+  if(normal == NULL_VECTOR)
   {
     // The case normal == NULL_VECTOR covers the case when the triangle
     // is colinear, or even more degenerate. In that case, we can
     // simply take also the distance to the three segments.
+    //
+    // Note that in the degenerate case, at most 2 edges cover the full triangle,
+    // and only two distances could be used, but leaving 3 for the case of
+    // inexact constructions as it might improve the accuracy.
+
     typename K::FT d1 = internal::squared_distance(pt, segment(t2, t0), k);
     typename K::FT d2 = internal::squared_distance(pt, segment(t1, t2), k);
     typename K::FT d3 = internal::squared_distance(pt, segment(t0, t1), k);
 
     return (std::min)( (std::min)(d1, d2), d3);
   }
+
+  const bool b01 = on_left_of_triangle_edge(pt, normal, t0, t1, k);
+  if(!b01)
+    return internal::squared_distance(pt, segment(t0, t1), k);
+
+  const bool b12 = on_left_of_triangle_edge(pt, normal, t1, t2, k);
+  if(!b12)
+    return internal::squared_distance(pt, segment(t1, t2), k);
+
+  const bool b20 = on_left_of_triangle_edge(pt, normal, t2, t0, k);
+  if(!b20)
+    return internal::squared_distance(pt, segment(t2, t0), k);
+
+  // The projection of pt is inside the triangle
+  inside = true;
+  return squared_distance_to_plane(normal, vector(t0, pt), k);
 }
 
 template <class K>