Marc Vigo Anglada

An improved incremental algorithm for constructing restricted Delaunay triangulations

Abstract This work presents an algorithm that given a generalized planar graph obtains its Constrained Delaunay triangulation (CDT). The proposed method, which follows the general approach of de Floriani and Puppo ( Computer Vision, Graphics and Image Processing , 1992, 54 , pp. 290–300, [1]), works incrementally based on two improved procedures. The first improvement gives a procedure that inserts a new point in a CDT; the second one is an algorithm that enforces a new constraining edge in a CDT. In particular, an algorithm that generates the CDT of a given polygon (possibly with holes) is also obtained. These algorithms have been implemented and included in several applications, showing their robustness and efficiency, even when the original graph has many vertices or edges.

Directional adaptive surface triangulation

Several CAD applications require a surface model of the modeled object consisting of a mesh of triangular facets. In this paper, a new algorithm for triangulation of trimmed surfaces is presented. The algorithm generates a triangulation that approximates the initial surface within a predefined tolerance. The approximation is conformal, without cracks in edges: a closed polyhedron is obtained in the case of a closed initial surface. The proposed algorithm improves the algorithm presented in (Brunet and Vigo, 1995) because it is based on more precise bounds which take into account the directional behavior of local surface curvature, and the resulting triangulation has a lower number of triangles.