Computational Methods and Function Theory 10 (2010), No. 1, 167--188
Copyright Heldermann Verlag 2010
Yaron Lipman
ylipman@math.princeton.edu , Princeton University, Princeton, NJ 08544, U.S.A.
David Levin
levin@tau.ac.il , Tel-Aviv University, Tel Aviv 69978, Israel.
Green coordinates define a special representation of a point inside a closed polygon in terms of its vertices and the normals to its edges (faces). This representation has been found to be very useful for object manipulation in computer graphics. The mapping defined by Green coordinates is shown to be analytic. It has a closed form formula in 2D and 3D, and it can be extended analytically through a face of the polygon. In 2D the mapping is proved to be conformal.
Keywords: Conformal mapping, Green identities, barycentric coordinates, analytic continuation, quasiconformal mapping.
MSC 2000: 30C30, 65E05.
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