3 citations · 5 across the 5 of their papers we have counts for
11 papers
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
We fully characterize the mappings that send every Pythagorean-hodograph (PH) curve to a PH curve. We prove that in any dimension, such mappings are precisely the conformal fun…
Minimal Surfaces via Complex Quaternions
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
Minimal surfaces play a fundamental role in differential geometry, with applications spanning physics, material science, and geometric design. In this paper, we explore a novel qua…
Symmetries of discrete curves and point clouds via trigonometric interpolation
Michal Bizzarri, Miroslav Lávička, Jan Vršek
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices…
Reconstruction of rational ruled surfaces from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We de…
Reconstruction of surfaces with ordinary singularities from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette…
Computing projective equivalences of special algebraic varieties
Michal Bizzarri, Miroslav Lávička, Jan Vršek
This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with…
Symmetries and similarities of planar algebraic curves using harmonic polynomials
Juan Gerardo Alcázar, Miroslav Lávička, Jan Vršek
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit plan…
Contour curves and isophotes on rational ruled surfaces
Jan Vršek
The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of sur…
Hermite interpolation by piecewise polynomial surfaces with polynomial area element
Michal Bizzarri, Miroslav Lávička, Zbyňek Šír +1
This paper is devoted to the construction of polynomial 2-surfaces which possess a polynomial area element. In particular we study these surfaces in the Euclidean space $\mathbb R^…
Smooth surface interpolation using patches with rational offsets
Miroslav Lávička, Zbyněk Šír, Jan Vršek
We present a new method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. We give some arguments why a…
Recognizing implicitly given rational canal surfaces
Jan Vršek, Miroslav Lávička
It is still a challenging task of today to recognize the type of a given algebraic surface which is described only by its implicit representation. In~this paper we will investigate…