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

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 Ks that includes Wachspress coordinates, mean value coordinates and discrete harmonic coordinates. 2007 Elsevier B.V. All rights reserved.

authors

• Schaefer, Scott

published proceedings

• COMPUTER AIDED GEOMETRIC DESIGN

author list (cited authors)

• Schaefer, S., Ju, T., & Warren, J.

citation count

• 25

complete list of authors

• Schaefer, S||Ju, T||Warren, J

publication date

• November 2007

publisher

• Elsevier  Publisher

published in

• Computer Aided Geometric Design  Journal

keywords

• Barycentric Coordinates
• Boundary Value
• Shepard's Interpolant

Digital Object Identifier (DOI)

• 10.1016/j.cagd.2006.06.005

start page

• 481

end page

• 493

volume

• 24

issue

• 8-9

URL

• http://dx.doi.org/10.1016/j.cagd.2006.06.005