√2 subdivision for quadrilateral meshes

This paper presents a root2subdivision scheme for quadrilateral meshes that can be regarded as an extension of a 4-8 subdivision with new subdivision rules and improved capability and performance. The proposed scheme adopts a so-called root2split operator to refine a control mesh such that the face number of the refined mesh generally equals the edge number and is thus about twice the face number of the coarse mesh. Smooth rules are designed in reference to the 4-8 subdivision, while a new set of weights is developed to balance the flatness of surfaces at vertices of different valences. Compared to the 4-8 subdivision, the presented scheme can be naturally generalized for arbitrary control nets and is more efficient in both space and computing time management. Analysis shows that limit surfaces produced by the scheme are C-4 continuous for regular control meshes and G(1) continuous at extraordinary vertices.