Abstract μ-Bases are new representations for rational curves and surfaces which serve as a
bridge between their parametric forms and implicit forms. Geometrically, μ-bases are …

Tessellations are an important tool to model the microstructure of cellular and polycrystalline
materials. Classical tessellation models include the Voronoi diagram and the Laguerre …

This paper presents a new algorithm for implicitizing tensor product surfaces of bi-degree
(m, n) with no base points, assuming that there are no moving planes of bi-degree (m− 1, n …

It was proven by Cox, Goldman and Zhang that a tensor product rational surface without
base points can be implicitized by moving quadrics whenever the rational surface doesn't …

We investigate conditions under which the resultant of a μ-basis for a rational tensor product
surface is the implicit equation of the surface without any extraneous factors. In this case, we …

We provide explicit representations of three moving planes that form a μ-basis for a standard
Dupin cyclide. We also show how to compute μ-bases for Dupin cyclides in general position …

Parametric tessellation models are often used to approximate complex grain morphologies
of polycrystalline microstructures. A big advantage of such models is the substantial …

A Steiner surface is a quadratically parameterizable surface without base points. To make
Steiner surfaces more applicable in Computer Aided Geometric Design and Geometric …

We find a μ-basis for a rational ruled surface, starting from its implicit representation. A
parametrization for this ruled surface is then deduced form this μ-basis. This parametrization …

Implicitizing rational surfaces is a fundamental computational task in Algorithmic Algebraic
Geometry. Although the resultant of a μ-basis for a rational surface is guaranteed to contain …