Comparison of 2D Regular Lattices for the CPWL Approximation of Functions

Published: 25 Mar 2025, Last Modified: 20 May 2025SampTA 2025 PosterEveryoneRevisionsBibTeXCC BY 4.0
Session: General
Keywords: Approximation error bounds, Cartesian grids, continuous and piecewise linear, Fourier-domain analysis, hexagonal grids
Abstract:

We investigate the approximation error of functions with continuous and piecewise-linear (CPWL) representations. We focus on the CPWL search spaces generated by translates of box splines on two-dimensional regular lattices. We compute the approximation error in terms of the stepsize, length ratio, and angle that define the lattice. Our results show that hexagonal lattices are optimal, in the sense that they minimize the asymptotic approximation error.

Submission Number: 16
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