Degree Elevation and Reduction of Periodic Surfaces

Recently we developed a periodic surface model to assist the construction of nano structures parametrically for computer-aided nano-design. In this paper, we study the properties of periodic surfaces for degree elevation and reduction. Degree elevation approaches are developed to incrementally increase shape complexities, including native, variational, and boundary constrained elevations. A generic degree reduction operation is defined for surface approximation based on an algebraic distance. The goal is to enhance the flexibility of the periodic surface model and allow for multi-resolution representation.