System, method, and program product for re-parameterizing...

Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression

Reexamination Certificate

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C345S420000

Reexamination Certificate

active

07369972

ABSTRACT:
A system, method, and program product for re-parameterizing one or more three-dimensional Catmull-Clark models is disclosed. Each of the models has one or more surfaces and one or more extraordinary vertices. One or more adjacent iso-parameter lines of the model have a spacing between them that increases as the iso-parameter lines approach the extraordinary vertex. A re-parameterization process that re-parameterizes the model so that one or more of the extraordinary vertices have adjacent iso-parameter lines with spacing that does not increase as the lines approach the extraordinary vertex.

REFERENCES:
patent: 6108006 (2000-08-01), Hoppe
patent: 6806874 (2004-10-01), Biermann et al.
Henning Biermann, Ioana Martin, Fausto Bernardini, Denis Zorin, “Cut-and-paste editing of multiresolution surfaces” ACM Transactions on Graphics (TOG) Jul. 2002, pp. 312-321.
Jos Stam, Exact Evaluation of Catmull-Clark Subdivision Surfaces At Arbitrary Parameter Values, pp. 1-10, Jul. 19, 1998.
Recursively Generated B-Spline Surfaces On Arbitrary Topological Meshes by: E Catmull and J Clark, pp. 350-355, 1978.
Evaluation of Piecewise Smooth Subdivision Surfaces by Denis Zorin, Daniel Kristjansson, Media Research Lab, New York University, 719 Broadway, 12th Floor, New York, New York 10003, USA, pp. 299-315, 2002.
Implicitization Using Moving Curves and Surfaces, by: Thomas W. Sederberg and Falai Chen, Brigham Young University, pp. 301-311, 1995.
Stationary Subdivision and Multiresolution Surface Representations, by: Denis N. Zorin, pp. 1-302, 1998, (Sep. 23, 1997).

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