Symmetry Detection of Rational Space Curves from their Curvature and Torsion

TL;DR

This paper introduces a new, efficient deterministic method for detecting symmetry in rational space curves using curvature and torsion, outperforming previous approaches in speed and simplicity.

Contribution

The paper proposes a novel method leveraging differential invariants for symmetry detection in rational space curves, with improved efficiency and generality over prior techniques.

Findings

Method is significantly faster than previous approaches.

Algorithm is simpler and more general.

Implementation in Sage demonstrates practical efficiency.

Abstract

We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar problem. To support this claim, we present an analysis of the arithmetic complexity of the algorithm and timings from an implementation in Sage.