3 papers
math.AG2025
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…
math.AG2024
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…
math.AG2003
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…