Evaluating a distance function

TL;DR

This paper introduces a rapid method for approximating distance functions to surfaces or lines by linking the problem to elliptic equations, improving computational efficiency.

Contribution

It proposes a novel, fast approach to approximate distance functions by connecting the problem to elliptic partial differential equations.

Findings

The method significantly speeds up distance computations.

It establishes a theoretical link between distance functions and elliptic problems.

The approach outperforms traditional approximation techniques.

Abstract

Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approximation of this function, using for example technique originating from the approximation of Hamilton Jacobi problems, or the fast sweeping method. Here we make a link with some elliptic problem and propose a very fast way to approximate the distance function.