A unified, integral construction for coordinates over closed curves |
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Authors: | S Schaefer T Ju J Warren |
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Affiliation: | aTexas A&M University, Department of Computer Science, 3112 Texas A&M University, College Station, TX, USA |
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Abstract: | We propose a simple generalization of Shephard's interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A third instance of this family yields a previously unknown generalization of discrete harmonic coordinates to smooth curves. For closed, piecewise linear curves, we prove that our interpolant reproduces a general family of barycentric coordinates considered by Floater, Hormann and Kós that includes Wachspress coordinates, mean value coordinates and discrete harmonic coordinates. |
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Keywords: | Barycentric coordinates Shepard's interpolant Boundary value |
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