On good triangulations in three dimensions

Abstract

Triangulation of a point set or a polyhedron is an important problem with applicationsfor finite element simulations in CAD/CAM. Though a number of algorithms exist fortriangulating a point set or a polyhedron in two and three dimensions [6, 1, 10, 12], fewof them address the problem of guaranteeing the shape of the triangular elements, theygenerate. To reduce ill-conditioningas well as discretization error, finite element methodsrequire triangular meshes of bounded aspect ratio [2, 11]. By aspect ratio of triangles ortetrahedra, one may consider the ratio of the radii of the circumscribing circle to that ofinscribing circle (spheres in case oftetrahedra).