Ternary butterfly subdivision

Abstract

This paper presents an interpolating ternary butterfly subdivision scheme for triangular meshes based on a 1-9 splitting operator. The regular rules are derived from a C^2 interpolating subdivision curve, and the irregular rules are established through the Fourier analysis of the regular case. By analyzing the eigenstructures and characteristic maps, we show that the subdivision surfaces generated by this scheme is C^1 continuous up to valence 100. In addition, the curvature of regular region is bounded. Finally we demonstrate the visual quality of our subdivision scheme with several examples.