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Composite \(\sqrt{2}\) subdivision surfaces. (English) Zbl 1171.65342
Summary: This paper presents a new unified framework for subdivisions based on a \(\sqrt{2}\) splitting operator, the so-called composite \(\sqrt{2}\) 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 \(\sqrt{2}\) 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 \(\sqrt{2}\) 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.

MSC:
65D17 Computer-aided design (modeling of curves and surfaces)
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