arXiv subjects

Hüsnü Anıl Çoban

Publications and source records attributed to Hüsnü Anıl Çoban.

3 recordsLinked to original sources

arXiv2024

Computation of symmetries of rational surfaces

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the algorithm works well for sparse parametrizations (e.g. toric surfaces) and PN surfaces. Additionally, we provide a specific, also symbolic algorithm for computing the symmetries of ruled surfaces; this algorithm works extremely well in practice, since the problem is reduced to that of rational space curves, which can be efficiently solved by using existing methods. The algorithm for ruled surfaces is based on the fact, proven in the paper, that every symmetry of a rational surface must also be a symmetry of its line of striction, which is a rational space curve. The algorithms have been implemented in the computer algebra system Maple, and the implementations have been made public; evidence of their performance is given in the paper.

cs.CG↗

arXiv2024

Detecting affine equivalences between certain types of parametric curves, in any dimension

Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In this paper we generalize previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves of certain types, in any dimension. In more detail, the algorithm is valid for rational curves, and for parametric curves with non-rational but meromorphic components admitting a rational inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and uses bivariate factoring, instead, as a fundamental tool. The algorithm has been implemented in the computer algebra system {\tt Maple}, and can be freely downloaded and used.

math.AG↗

arXiv2022

A new method to detect projective equivalences and symmetries of rational $3D$ curves

We present a new approach using differential invariants to detect projective equivalences and symmetries between two rational parametric $3D$ curves properly parametrized. In order to do this, we introduce two differential invariants that commute with Möbius transformations, which are the transformations in the parameter space associated with the projective equivalences between the curves. The Möbius transformations are found by first computing the gcd of two polynomials built from the differential invariants, and then searching for the Möbius-like factors of this gcd. The projective equivalences themselves are easily computed from the Möbius transformations. In particular, and unlike previous approaches, we avoid solving big polynomial systems. The algorithm has been implemented in Maple, and evidences of its efficiency as well as a comparison with previous approaches are given.

math.AG↗