In the Search for Good Neck Cuts

TL;DR

This paper introduces a new formal definition of surface bottlenecks for identifying neck-like features, proposing algorithms inspired by isoperimetric principles that perform well in applications like mesh segmentation and robotics.

Contribution

It provides a novel formalization of surface bottlenecks and develops algorithms based on these concepts for practical surface analysis tasks.

Findings

Algorithms perform well in practice for mesh segmentation.

New formal definition of surface bottlenecks inspired by isoperimetric inequality.

Applications demonstrated in robotics and algorithmic surface processing.

Abstract

We study the problem of finding neck-like features on a surface. Applications for such cuts include robotics, mesh segmentation, and algorithmic applications. We provide a new definition for a surface bottleneck -- informally, it is the shortest cycle relative to the size of the areas it separates. Inspired by the isoperimetric inequality, we formally define such optimal cuts, study their properties, and present several algorithms inspired by these ideas that work surprisingly well in practice. For examples of our algorithms, see https://neckcut.space.