Bijective Mappings with Generalized Barycentric Coordinates: A Counterexample
نویسنده
چکیده
Many recent works attempt to generalize barycentric coordinates to arbitrary polygons. I construct a counterexample proving that no such generalization will produce purely bijective mappings in the plane provided the coordinates meet the Lagrange, reproduction, and partition of unity properties. The proof concerns generalized barycentric coordinates in a square, but trivially generalizes to arbitrary polygons with degree greater than three.
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عنوان ژورنال:
- J. Graphics Tools
دوره 17 شماره
صفحات -
تاریخ انتشار 2013