Transfinite mean value interpolation over polygons
Numerical Analysis
2019-06-21 v1 Numerical Analysis
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.
Cite
@article{arxiv.1906.08358,
title = {Transfinite mean value interpolation over polygons},
author = {Michael S. Floater and Francesco Patrizi},
journal= {arXiv preprint arXiv:1906.08358},
year = {2019}
}