Generalization of distance to higher dimensional objects

TL;DR

This paper extends the concept of distance measurement from points to one-dimensional objects, incorporating constraints like curvature and non-crossing, with analytical, numerical results, and applications to biopolymers.

Contribution

It introduces a generalized distance framework for one-dimensional objects considering curvature and non-crossing constraints, with analytical and numerical insights and biopolymer applications.

Findings

Analytical solutions for specific examples

Numerical results demonstrating the framework

Applications to biopolymer modeling

Abstract

The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central to the notion of distance. Analytical and numerical results are given for some specific examples, and applications to biopolymers are discussed.