A unified, integral construction for coordinates over closed curves Academic Article uri icon


  • 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. © 2007 Elsevier B.V. All rights reserved.

author list (cited authors)

  • Schaefer, S., Ju, T., & Warren, J.

citation count

  • 22

publication date

  • November 2007