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Numerical Algorithms
Published in: Numerical Algorithms 3/2020

02-12-2019 | Original Paper

Transfinite mean value interpolation over polygons

Authors: Michael S. Floater, Francesco Patrizi

Published in: Numerical Algorithms | Issue 3/2020

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Abstract

Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method generalizes to transfinite interpolation, i.e., to any continuous data on the boundary but a mathematical proof that interpolation always holds has so far been missing. The purpose of this note is to complete this gap in the theory.
previous article A note on generalized averaged Gaussian formulas for a class of weight functions
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Literature
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Floater, M.S., Hormann, K., Kós, G.: A general construction of barycentric coordinates over convex polygons. Adv. Comput. Math. 24, 311–331 (2006)CrossRef
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Hormann, K., Floater, M.S.: Mean value coordinates for arbitrary planar polygons. ACM Trans. Graph. 25, 1424–1441 (2006)CrossRef
7.
Ju, T., Schaefer, S., Warren, J.: Mean value coordinates for closed triangular meshes. ACM Trans. Graph. 24, 561–566 (2005)CrossRef
Metadata
Title
Transfinite mean value interpolation over polygons
Authors
Michael S. Floater
Francesco Patrizi
Publication date
02-12-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00849-w

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