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[Camille Wormser <>]

If I remove CGAL::refine_Delaunay_mesh_2(cdt, Criteria(0.125, 0.5))
function call from the code, the code compiles successfully. Does
refine_Delaunay_mesh_2() support
Triangulation_euclidean_traits_xy_3.h?

Hi, 

Refining the mesh means inserting the circumcenters of some facets. However, in the case of a terrain, the choice of a z-coordinate for the circumcenter is not clear. For this reason, refinement is not supported. 

See the documentation:

http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/Mesh_2_ref/Function_refine_Delaunay_mesh_2.html

The geometric traits class of the constrained Delaunay triangulation must be a model of DelaunayMeshTraits_2.

http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/Mesh_2_ref/Concept_DelaunayMeshTraits_2.html

The concept DelaunayMeshTraits_2 refines the concept ConformingDelaunayTriangulationTraits_2. It provides a construction objectConstruct_circumcenter_2.

http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/Triangulation_2_ref/Class_Triangulation_euclidean_traits_xy_3.html

The class is a model of the concept DelaunayTriangulationTraits_2 except that it does not provide the type and constructors required to build the dual Voronoi diagram.

If you still want to do that, you will have to provide a custom Construct_circumcenter_2 in a traits class derived from Triangulation_euclidean_traits_xy_3. 

-- 

Camille