Approximating Minimum-Weight Triangulations in Three Dimensions

Let S be a set of noncrossing triangular obstacles in R sup 3 with convex hull H. A triangulation T of H is compatible with S if every triangle of S is the union of a subset of the faces of T. The weight of T is the sum of the areas of the triangles of T. We give a polynomial-time algorithm that computes a triangulation compatible with S whose weight is at most a constant times the weight of any compatible triangulation.