Interpolatory ternary subdivision surfaces

This paper proposes an interpolatory ternary subdivision for quadrilateral meshes that produces C2 continuous limit surfaces for regular meshes while achieves G1 continuity with bounded curvature at extraordinary vertices. The subdivision splits each quad into nine by inserting two E-vertices onto each edge and four F-vertices onto each face, and connecting them along vertical and horizontal directions respectively. The regular subdivision masks of the scheme are obtained as tensor products of the masks of the interpolatory ternary subdivision for curves while irregular geometric rules are established based on discrete Fourier transformation. For efficient practical use, an adaptive refinement algorithm is developed based on the decomposition of intermediate meshes into divisible and indivisible subsets for each refinement.