Dual mesh resampling

Computer graphics processing and selective visual display system – Computer graphics processing – Three-dimension

Reexamination Certificate

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Reexamination Certificate

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06943790

ABSTRACT:
Methods, systems and apparatus which resample a primal mesh signal composed of primal points associated with primal mesh vertices of a primal mesh connectivity of a primal mesh producing a dual mesh signal composed of dual points associated with primal mesh faces of said primal mesh connectivity. The dual points are computed by minimizing a quadratic energy function. The quadratic energy function is composed of a sum of square terms. The invention also constructs a dual mesh from a primal mesh, with the dual mesh signal constructed with the resampling method. It also smoothes a primal mesh signal of a primal mesh. It also constructs a primal-dual mesh from a primal mesh, with the primal-dual mesh connectivity of said primal-dual mesh constructed using a prior art method, and the primal-dual mesh signal constructed by concatenating said primal mesh signal and a dual mesh signal computed with the resampling method.

REFERENCES:
patent: 5506947 (1996-04-01), Taubin
Hoppe et al., Mesh Optimization, 1993, ACM SIGGRAPH, pp. 19-26.
“Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes.” by E Catmull and J Clark,CAD, vol. 10, pp. 350-355, 1978.
“Behavior of Recursive Division Surfaces Near Extraordinary Points”, by D. Doo, and M. Sabin, CAD, vol. 10, pp. 356-360, 1978.
“Course 23: Subdivision for Modeling and Animation,” by D. Zorin and P. Schroder (eds.), Siggraph 2000 Course Notes, Jul. 2000.
“Square Root of 3 Subdivision,” by L. Kobbelt, Siggraph 2000 Conference Proceedings, pp. 103-112, Jul. 2000.
“A Signal Processing Approach to Fair Surface Design.” G. Taubin, Siggraph '95 Conf Proceedings, Aug. 1995, pp. 351-358.
“Dual Mesh Resampling,” by G. Taubin, Pacific Graphics Conference Proceedings, Tokyo, Japan, Oct. 2001.
“Smooth Subdivision Surfaces Based on Triangles,” by C. Loop, Master Thesis, Dept of Mathematics, University of Utah, Aug. “1987”.

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