Symmetry Detection of Rational Space Curves from their Curvature and Torsion

Juan Gerardo Alcázar; Carlos Hermoso; Georg Muntingh

doi:10.1016/j.cagd.2015.01.003

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arXiv · 1406.1451

Symmetry Detection of Rational Space Curves from their Curvature and Torsion

Juan Gerardo Alcázar·Carlos Hermoso·Georg Muntingh

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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.

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Juan Gerardo Alcázar, Carlos Hermoso, Georg Muntingh. 2014-06-05. Symmetry Detection of Rational Space Curves from their Curvature and Torsion. https://doi.org/10.1016/j.cagd.2015.01.003

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