A unified, integral construction for coordinates over closed curves
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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 Ks that includes Wachspress coordinates, mean value coordinates and discrete harmonic coordinates. 2007 Elsevier B.V. All rights reserved.
Computer Aided Geometric Design
author list (cited authors)
Schaefer, S., Ju, T., & Warren, J.
complete list of authors
Schaefer, S||Ju, T||Warren, J