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This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space curves, our method finds the involutions in all cases, and all the rotation symmetries in the particular case of… (More)

Given a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide effective methods for solving these questions without any… (More)

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is… (More)

We provide an algorithm to check whether two rational space curves are related by a <i>similarity</i>, i.e., whether they are equal up to position, orientation and scale. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra setting. Helical curves, where curvature and… (More)

A novel and deterministic algorithm is presented to detect whether two given planar rational curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities , and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is… (More)

- Juan G. Alcázar, Carlos Hermoso, Georg Muntingh
- ACCA
- 2015

We present a novel, deterministic, and efficient method to detect whether a given rational space curve C is symmetric. The method combines two ideas. On one hand in a similar way to [1], [2], if C is symmetric then the symmetry provides a second parametrization of the curve; furthermore, whenever the first parametrization is proper, i.e. injective except… (More)