A polygonal approach for interpolating meshes of curves by subdivision surfaces

Given a polyhedral network P/sub 0/ defining a subdivision surface S and an arbitrary mesh of tagged control polygons (cp/sub i/)/sub 1⩽i⩽n/ on P/sub 0/, this paper describes an approach to force the limit surface S to interpolate the B-spline curves of (cp/sub i/). For each control polygon cp/sub i/, we construct a polygonal complex whose mid-polygon is cp/sub i/ or its first subdivided one. A polygonal complex is a sequence of panels such that every two adjacent panels share exactly one edge and the mid-points of these edges make the mid-polygon of the complex. Since the complexes themselves are embodied in the original polyhedron or its first subdivided the limit surface will interpolate the limit curves of these complexes.