On the computability of the Fr\'echet distance of surfaces in the bit-model of real computation

TL;DR

This paper proves that the Fréchet distance between parametrized surfaces in a metric space is computable within the bit-model of real computation, extending previous results to a more general computational framework.

Contribution

It establishes the computability of the Fréchet distance for surfaces in the bit-model, generalizing prior work limited to piecewise-linear surfaces in the real RAM model.

Findings

Fréchet distance of surfaces is computable in the bit-model

Extends previous results from piecewise-linear surfaces

Provides a theoretical foundation for surface similarity measures

Abstract

We show that the Fr\'echet distance of two-dimensional parametrised surfaces in a metric space is computable in the bit-model of real computation. An analogous result in the real RAM model for piecewise-linear surfaces has recently been obtained by Nayyeri and Xu (2016).