Interpolating scattered data points by catmull-clark subdivision surfaces

Abstract

This paper outlines an approach for the interpolation of scattered data points by Catmull-Clark subdivision surfaces. This approach relies in a fundamental way on an algorithm that groups the initial data points into a sequence of control polygons. Each one of these polygons is transformed in such a way that its corresponding limit curve interpolates its original control points. A polygonal complex is then constructed to embody each one of these polygons, which is then transformed to correspond to the original polygon it was embodying. Finally, automatic connection of each complex to its immediate neighbors is established. This process results in a control polyhedron whose limit surface interpolates the initial control points. This process is straightforward and easy to implement. While not utilizing too many auxiliary data points, these additional points can be used to tailor the interpolating surface to suit additional user requirements, without affecting the initial interpolation constraints.