Degree Elevation and Reduction of Periodic Surfaces

Abstract

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.

Metamorphosis of Periodic Surface Models

“…The PS model allows for parametric construction from atomic scale to meso scale. Reconstruction of loci surfaces from crystals [ 3 ], surface degree operations to support fine-grained modeling [4,5], and feature-based approach for crystal construction [6,7] were also studied. In this paper, we propose a surface morphing or metamorphosis approach for PS models.…”

Computing Minkowski Sum of Periodic Surface Models

“…The surface model allows for parametric construction from atomic scale to meso scale. Reconstruction of loci surfaces from crystals [3] and complexity control [4] were also studied. In this paper, we study the Minkowski sum of PS models.…”