Modeling closed surfaces: a comparison of existing methods

Abstract As C 1 overall continuity is not possible in closed surfaces, modeling schemes are closely related to geometric continuity. Algorithms that generate surfaces from a set of polyhedron vertices include recursive subdivision methods, piecewise algebraic interpolation, discrete interpolation or transfinite interpolation of a closed mesh of curves. On the other hand, boolean operations between simple surfaces lead to trimmed surfaces. Volumes can also be modeled by approximate models based on the subdivision of the space. The present paper includes a comparative study of some of these algorithms discussing shape control and fairness of the final surface, geometric continuity, space complexity of the model and their performance in basic solid interrogations.