Since Pierre wanted this feature (providing points without primitive to the KD_tree),

and it does not cost much in terms of implementation, and it is useful for cases like the
Polyhedron, I put it back. 

The code already supports that (as can be seen from the fact that the test suite runs).

Still, I need the Id to have a default constructor. How do you document that?

AABB_tree/doc_tex/AABB_tree_ref/AABB_tree.tex

@@ -145,7 +145,7 @@ closest_point_and_primitive(const Point& query,
 \ccMethod{template <class InputIterator>
 bool accelerate_distance_queries(InputIterator begin,
                                  InputIterator beyond);}
-{ Constructs the internal search KD-tree used to accelerate the distance queries from a specified point set. Iterator \ccc{InputIterator} must have \ccc{Point_and_primitive_id} as value type. Each point from the specified \ccc{Point_and_primitive_id} set must be located on the corresponding input primitive. For a triangle surface mesh this point set can be provided, e.g., as the vertices of the mesh or as the triangle centroids. It is not required to provide one point per primitive, such that, e.g., large input primitive can be sampled with several sample points or, conversely, such that a single point is provided for clusters of small input primitives. Returns \ccc{true}, iff the memory allocation is successful.}
+{ Constructs the internal search KD-tree used to accelerate the distance queries from a specified point set. Iterator \ccc{InputIterator} must have \ccc{Point} or \ccc{Point_and_primitive_id} as value type. Each point from the specified \ccc{Point_and_primitive_id} set must be located on the corresponding input primitive. If the value type of the iterator is \ccc{Point}, in the rare cases where the hint from the KD-tree would be returned by the \ccc{closest_point_and_primitive method}, the default primitive id would be returned as primitive id. For a triangle surface mesh this point set can be provided, e.g., as the vertices of the mesh or as the triangle centroids. It is not required to provide one point per primitive, such that, e.g., large input primitive can be sampled with several sample points or, conversely, such that a single point is provided for clusters of small input primitives. Returns \ccc{true}, iff the memory allocation is successful.}
 \end{ccAdvanced}
 
 \ccSeeAlso