Comparison of 2D Regular Lattices for the CPWL Approximation of Functions
M. Pourya, M. Nogarotto, M. Unser
Proceedings of the Fifteenth International Workshop on Sampling Theory and Applications (SampTA'25), Vienna, Republic of Austria, July 28-August 1, 2025.
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.
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AUTHOR="Pourya, M. and Nogarotto, M. and Unser, M.",
TITLE="Comparison of {2D} Regular Lattices for the {CPWL} Approximation
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BOOKTITLE="Proceedings of the Fifteenth International Workshop on
Sampling Theory and Applications ({SampTA'25})",
YEAR="2025",
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address="Vienna, Republic of Austria",
month="July 28-August 1,",
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