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Positive GordonWixom coordinates (2011)
| Venue: | Computer Aided Design |
| Citations: | 3 - 0 self |
BibTeX
@ARTICLE{Manson11positivegordonwixom,
author = {Josiah Manson and Kuiyu Li and Scott Schaefer},
title = {Positive GordonWixom coordinates},
journal = {Computer Aided Design},
year = {2011},
pages = {1426}
}
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Abstract
We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in 2D. Our method extends weighted Gordon-Wixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boundary curve to define a weight function that is positive and smooth. We derive closed-form expressions for arbitrary polygons in 2D and compare the basis functions of our coordinates with several other types of barycentric coordinates. Key words: barycentric coordinates, transfinite, interpolant 1.
Keyphrases
positive gordonwixom coordinate barycentric coordinate weight function transfinite barycentric coordinate weighted gordon-wixom interpolation derive closed-form expression key word several type arbitrary polygon line tangent non-convex shape boundary curve smooth boundary basis function new construction
