A New {the square rooe of}2-Subdivision Scheme for Arbitrary Surface Design

摘要

Subdivision is a powerful approach for constructing 3D objects in arbitrary shape. With the initial triangular or quadrilateral mesh, subdivision schemes can be employed to adjust coordinates of the initial vertices, generate new vertices, replace original mesh with refined mesh, and thus make the surface of the 3D object much smoother. In this paper, we present a new and efficient {the square rooe of}2 - subdivision approximation scheme, named as "Diamond" scheme. In order to make it work on arbitrary shapes, we also develop an algorithm to process any extraordinary vertices that the initial shapes may have. The "Diamond" scheme is C{sup}2 -continuity, and can be applied to smooth any arbitrary shapes constructed in quadrilateral meshes.