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Zbl 1171.65342
Li, Guiqing; Ma, Weiyin
Composite $\sqrt{2}$ subdivision surfaces.
(English)
[J] Comput. Aided Geom. Des. 24, No. 6, 339-360 (2007). ISSN 0167-8396

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 2000:
*65D17 Computer aided design (modeling of curves and surfaces)

Keywords: composite subdivision surfaces; unified subdivision surfaces; box splines

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