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A unified approach to subdivision algorithms near extraordinary vertices. (English) Zbl 0872.65007
Summary: We present a unified approach to subdivision algorithms for meshes with arbitrary topology which admits a rigorous analysis of the generated surface and give a sufficient condition for the regularity of the surface, i.e. for the existence of a regular smooth parametrization near the extraordinary point. The criterion is easily applicable to all known algorithms such as those of Doo-Sabin and Catmull-Clark, but will also be useful to construct new algorithms like interpolatory subdivision schemes.

65D17Computer aided design (modeling of curves and surfaces)
68U07Computer aided design
Full Text: DOI
[1] Ball, A. A.; Storry, D. J. T.: A matrix approach to the analysis of recursively generated B-spline surfaces. Computer-aided design 18, 437-442 (1986)
[2] Ball, A. A.; Storry, D. J. T.: Conditions for tangent plane continuity over recursively generated B-spline surfaces. ACM trans. Graph. 7, No. 2, 83-102 (1988) · Zbl 0663.65012
[3] Catmull, E.; Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-aided design 10, 350-355 (1978)
[4] Doo, D.; Sabin, M. A.: Behaviour of recursive division surfaces near extraordinary points. Computer-aided design 10, 356-360 (1978)
[5] Loop, Ch.T.: Smooth subdivision for surfaces based on triangles. Master thesis (1987)
[6] Nasri, A. H.: Polyhedral subdivision methods for free-form surfaces. ACM trans. Graph. 6, No. 1, 29-73 (1987) · Zbl 0637.65144
[7] Reif, U.: Neue aspekte in der theorie der freiformflächen beliebiger topologie. Thesis (1993)
[8] Halstead, M.; Kass, M.; Derose, T. D.: Efficient, fair interpolation using catmull-Clark surfaces. Siggraph ’93, 35-44 (1993)