arXiv subjects

Eriola Hoxhaj

Publications and source records attributed to Eriola Hoxhaj.

3 recordsLinked to original sources

arXiv2024

Classification of Dupin Cyclidic Cubes by Their Singularities

Triple orthogonal coordinate systems having coordinate lines as circles or straight lines are considered. Technically, they are represented by trilinear rational quaternionic maps and are called Dupin cyclidic cubes, naturally generalizing the bilinear rational quaternionic parametrizations of principal patches of Dupin cyclides. Dupin cyclidic cubes and their singularities are studied and classified up to Möbius equivalency in Euclidean space.

math.AG↗

arXiv2023

How to Reconstruct a Planar Map From its Branching Curve

We present an algorithm for constructing a map $\mathbb{P}^2\to\mathbb{P}^2$ with a given branching curve. The stepping stone is the ramification curve, which is obtained as the linear normalization of the branching curve.

math.AG↗

arXiv2023

Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture

The task of recognizing an algebraic surface from a single apparent contour can be reduced to the recovering of a homogeneous equation in four variables from its discriminant. In this paper, we use the fact that Darboux cyclides have a singularity along the absolute conic in order to recognize them up to Euclidean similarity transformations.

math.AG↗