El ~SEVIER Computer Aided Geometric Design 16 (1999) 107-126 COMPUTER AIDED GEOMETRIC DESIGN Directional adaptive surface triangulation Marc Vigo Anglada *, Ntiria Pla Garcia, Pere Brunet Crosa Univ. Politecnica de Catalunva Dept. LiSI, Diagonal 647 Edifici ETSE1B planta 8, 08028 Barcelona, Spain Received June 1997; revised September 1998 Abstract 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. © 1999 Elsevier Science B.V. All rights reserved. Kevwords: Surfaces Directional curvature bounds; Adaptive triangulation; Constrained Delaunay triangulation 1. Introduction Discretization and triangulation of surfaces are common needs in many CAD appli- cations. Surface triangulation is required for instance in finite element methods (FEM), stereolitography (SLA) and surface rendering. Classical problems such as the Delaunay triangulations and the triangulation of polygons have been well studied by computational geometry and they are a good theoretical base for the approximation and discretization of surfaces. Several authors have addressed the problem of triangulating implicit surfaces (see (Allgower and Gnutzmann, 1987; Brown, 1991) among others), but their main drawback is that their results are not directly applicable to the parametric case. * Corresponding author. E-mail: marc@lsi.upc.es. 0167-8396/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: $01 67-8396(98)00040-5