Approximating the Maxmin-angle Covering Triangulation

Given a planar straight line graph we seek a covering triangulation whose minimumangle is as large as possible A covering triangulation is a Steiner triangulation with the following restriction No Steiner vertices may be added on an input edge We give an explicit upper bound on the largest possible minimum angle in any covering triangulation of a given input This upper bound depends only on local ge ometric features of the input We then show that our covering triangulation has minimum angle at least a constant factor times this up per bound This is the rst known algorithm for gener ating a covering triangulation with a provable bound on triangle shape Covering triangula tions can be used to triangulate intersecting re gions independently and so solve several sub problems of mesh generation