Transfinite mean value interpolation

doi:10.1016/j.cagd.2007.12.003

Computer Aided Geometric Design

Volume 26, Issue 1, January 2009, Pages 117-134

https://doi.org/10.1016/j.cagd.2007.12.003 Get rights and content

Abstract

Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee interpolation when f is continuous. Then, by deriving the normal derivative of the interpolant and of a mean value weight function, we construct a transfinite Hermite interpolant and discuss various applications.

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Transfinite mean value interpolation

Abstract

A transformation for extracting new descriptors of shape

Mean value coordinates

Comp. Aided Geom. Design

Barycentric rational interpolation with no poles and high rates of approximation

Numer. Math.

Mean value coordinates in 3D

Comp. Aided Geom. Design

A general construction of barycentric coordinates over convex polygons

Adv. Comp. Math.

Pseudo-harmonic interpolation on convex domains

SIAM J. Numer. Anal.

Finite Element Methods with B-Splines

Weighted extended B-spline approximation of Dirichlet problems

SIAM J. Numer. Anal.

Mean value coordinates for arbitrary planar polygons

ACM Trans. Graph.

A general geometric construction of coordinates in a convex simplicial polytope

Comp. Aided Geom. Design