Interpolatory Subdivision on Open Quadrilateral Nets with Arbitrary Topology

A simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented which generates C¹ surfaces in the limit. The scheme satisfies important requirements for practical applications in computer graphics and engineering. These requirements include the necessity to generate smooth surfaces with local creases and cusps. The scheme can be applied to open nets in which case it generates boundary curves that allow a C⁰-join of several subdivision patches. Due to the local support of the scheme, adaptive refinement strategies can be applied. We present a simple device to preserve the consistency of such adaptively refined nets.