Interpolatory √2-subdivision surfaces

This paper presents a new interpolatory subdivision for quadrilateral meshes. The proposed scheme employs a √2 split operator to refine a given control mesh such that the face number of the refined mesh is doubled after each refinement. For regular meshes, the smallest mask is chosen to calculate newly inserted vertices and special rules are developed to compute the F-vertices for irregular faces based on the Fourier analysis of block circulant matrices. Numerical analysis manifests that the scheme yields globally C1 continuous limit surfaces. Finally, an extension to arbitrary polygonal meshes is considered.