Interpolating arbitrary networks of curves by catmull-clark subdivision surfaces

Abstract

This paper pursues an approach for the construction of smooth surfaces for geometric modeling and computer graphics (often referred to as lofting) that starts from a network of polygons representing a set of intersecting curves. The contribution of this paper is in (1) a new method for transforming the initial set of polygons to an equivalent set of polygonal complexes and (2) a new skinning algorithm that adds more vertices and edges thus completing the formation of the control polyhedron. When subdivided, this polyhedron converges on a smooth surface interpolating the initial set of input curves. The resulting surface is C2, except at points where the initial curves meet, where it is at least C1. The approach is modular, easy to understand and implement.