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Novel method for exactly evaluating the energy of Catmull-Clark subdivision surfaces. (English) Zbl 1093.65012

Summary: A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh [cf. E. Catmull and J. Clark, Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design 10, No. 6, 350–355 (1978)]. A closed form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.

MSC:

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