Methods for computing barycentric coordinates generalized to...

Details Methods for computing barycentric coordinates generalized to... Methods for computing barycentric coordinates generalized to...

2006-06-13

2006-06-13

Nguyen, Phu K. (Department: 2673)

Computer graphics processing and selective visual display system

Computer graphics processing

Three-dimension

C345S427000

Reexamination Certificate

active

07061483

ABSTRACT:
A method for deriving barycentric coordinates for a point p within an n-sided polygon is provided wherein, for a particular coordinate wj, corresponding to the vertex qj, the method embodies a formula which depends only on the edge pqj, and the two adjacent angles δjand γj. Similarly, a method is provided for deriving weights wijfor expressing a vertex qiin a mesh representation of an object surface in terms of its one-ring neighbors qj, ∀jεN(i). For a particular vertex qj, and neighbor vertex qj, this method embodies a formula which depends only on the edge qiqj, and the two adjacent angles δjand γj. A method of parameterizing a mesh representation of an object surface using the latter formula is also provided. This method begins with the step of computing the weights wijin3D space (in contrast to parameter space) for each of the vertices in the mesh representation. For a vertex i, iε[1. . . n], the weights wijallow the vertex i to be expressed in terms of its one-ring neighbors jεN(i). The method then proceeds to parameterizing the mesh representation responsive to the weights wij.

REFERENCES:
Desbrun et al. , Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow, Siggraph 1999, pp. 317-324.
Eck et al., Multiresolution Analysis of Arbitrary Meshes, ACM 1995, pp. 173-182.
Mark Meyer, Haeyoung Lee, Alan Barr, Mathieu Desbrun, Caltech—USC,Generalizing Barycentric Coordinates to Irregular N-gonsNov. 2002, Journal Graphics Tool v. 7, Ab. 1.
Mark Meyer, Haeyoung Lee, Alan Barr, Mathieu Desbrun, Caltech—USC,Intrinsic Parameterization of Surface MeshesSep. 2002, EURO graphics 02, conference 2002.

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