12 citations · 27 across the 5 of their papers we have counts for
5 papers
Formula for Dupin Cyclidic Cube and Miquel Point
Jean Michel Menjanahary, Rimvydas Krasauskas
Dupin cyclides are surfaces conformally equivalent to a torus, a circular cone, or a cylinder. Their patches admit rational bilinear quaternionic Bézier parametrizations and are us…
Classification of Dupin Cyclidic Cubes by Their Singularities
Jean Michel Menjanahary, Eriola Hoxhaj, Rimvydas Krasauskas
Triple orthogonal coordinate systems having coordinate lines as circles or straight lines are considered. Technically, they are represented by trilinear rational quaternionic maps…
Surfaces containing two circles through each point
Mikhail Skopenkov, Rimvydas Krasauskas
We find all analytic surfaces in space such that through each point of the surface one can draw two transversal circular arcs fully contained in the surface. The pro…
Surfaces containing two circles through each point and Pythagorean 6-tuples
M. Skopenkov, R. Krasauskas
We study analytic surfaces in 3-dimensional Euclidean space containing two circular arcs through each point. The problem of finding such surfaces traces back to the works of Darbou…
Universal Rational Parametrizations and Toric Varieties
David Cox, Rimvydas Krasauskas, Mircea Mustata
This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first…