A priori Computation of a mesh size for Adaptive Loop Subdivision

Subdivision schemes provide efficient algorithms both for the design and processing of arbitrary control meshes. Theoretically, these techniques are often considered as an elegant algorithmic way to approximate a desired surface from a given surface. In practice, controlling the accuracy of control meshes with regard to the limit surface remains difficult. In this paper, from a bound of the distance between a subdivision surface and its control polyhedron, we a priori compute the subdivision depth according to a given accuracy. From this result, we can exactly predict the number of faces of the control polyhedron for a given accuracy during full subdivision. As full subdivision generates too many faces, we focus in this paper on adaptive subdivision. We work with the adaptive scheme which generates the fewest number of faces and explain how to predict a bound of the number of faces of the subdivided mesh because it is not possible to a priori give the final number of faces during adaptive subdivision.