In the attached paper, we construct new generalized coordinates for arbitrary polytopes in d-dimensions (polygons and polyhedra in 2- and 3-dimensions, respectively) using the principle of maximum entropy. The paper is to appear in Computer Graphics Forum and will be presented at the SGP'08 Conference in Denmark.
To construct barycentric coordinates on arbitrary polygons (convex and nonconvex), we maximize the Shannon-Jaynes entropy functional subject to the linear precision conditions; the non-negative prior functions used in the S-J entropy functional possess the Kronecker-delta property at boundary nodes and only d of them are non-zero in the interior of any boundary edge. This enables the construction of strictly non-negative linearly precise maximum entropy coordinates (MEC) on arbitrary polygons, and this approach extends to higher-dimensional polytopes. Comparisons and contrasts of MEC with existing barycentric coordinates are made, and their performance assessed for computer graphics applications such as image warping and mesh deformation.
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| mec-sgp2008.pdf | 3.25 MB |