Hi Jacek-- I'm surprised the delaunay function works when DelaunayTri won't because the current version of delaunay calls DelaunayTri. On the other hand, delaunayn seems to be independent code.
Also, I'll add another issue to this thread. I noticed this morning that running DelaunayTri repeatedly on the same data produces *different* triangulation matrices. Actually the matrix members are the same, but their order varies from one run to another. That can be a real problem! My code, for example, uses the triangulation as a mesh for solving Laplace's equation, and with a different triangulation matrix, the solution is quite different. I've implemented a sort after calling DelaunayTri, which fixes the problem.
So a kind request to the folks at Mathworks: please fix up DelaunayTri so that identical inputs produce identical output. Thanks guys!