Degree Operations on Periodic Surfaces

In previous work, a periodic surface model for computer-aided nano-design (CAND) was developed. This implicit surface model can construct Euclidean and hyperbolic nano geometries parametrically and represent morphologies of particle aggregates and polymers. In this paper, we study the characteristics of degree elevation and reduction based on a generalized periodic surface model. Methods of degree elevation and reduction operations are developed in order to support multi-resolution representation and model exchange.