Composite subdivision surfaces

This paper presents a new unified framework for subdivisions based on a splitting operator, the so-called composite subdivision. The composite subdivision scheme generalizes 4-direction box spline surfaces for processing irregular quadrilateral meshes and is realized through various atomic operators. Several well-known subdivisions based on splitting operator and based on 1-4 splitting operator for quadrilateral meshes are properly included in the newly proposed unified scheme. Typical examples include the midedge and 4-8 subdivisions based on the splitting operator that are now special cases of the unified scheme as the simplest dual and primal subdivisions, respectively. Variants of Catmull–Clark and Doo–Sabin subdivisions based on the 1-4 splitting operator also fall in the proposed unified framework. Furthermore, unified subdivisions as extension of tensor-product B-spline surfaces also become a subset of the proposed unified subdivision scheme. In addition, Kobbelt interpolatory subdivision can also be included into the unified framework using VV-type (vertex to vertex type) averaging operators.