Methods for computing barycentric coordinates generalized to irregular n-gons and applications of the same
US7061483B2 · kind B2 · utility
Assignee
Inventors
Key dates
| Filing date | Feb 7, 2002 |
| Grant date | Jun 13, 2006 |
| Priority date | — |
| Expiry date | Dec 15, 2022 |
Classification
- Technology area (CPC G)Physics
- CPC primaryG06T17/20
- WIPO fieldComputer technology
- WIPO sectorElectrical engineering
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 δj and γj. Similarly, a method is provided for deriving weights wij for expressing a vertex qi in 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 δj and 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 wij in 3D space (in contrast to parameter space) for each of the vertices in the mesh representation. For a vertex i, iε[1 . . . n], the weights wij allow 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.
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