Algebraic curves and surfaces are an old topic of geometric and algebraic investigation.
They have found applications for instance in ancient and modern architectural designs, in …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

Some Algorithmic Problems in Polytope Theory Page 1 Some Algorithmic Problems in
Polytope Theory Volker Kaibel* and Marc E. Pfetsch Technische Universitiit Berlin, Institut fur …

A rational parametrization of an algebraic curve (resp. surface) establishes a rational
correspondence of this curve (resp. surface) with the affine or projective line (resp. affine or …

A rational parametrization of an algebraic curve establishes a rational correspondence of
this curve with the affine or projective line. This correspondence is a birational equivalence if …

We present a new method for implicitization of parametric curves, surfaces and
hypersurfaces usingessen tially numerical linear algebra. The method is applicable for …

CAGD draws from several branches of mathematics and computer science, such as
approximation theory, differential geometry, and numerical analysis. This chapter reviews …

Given an algebraic plane curve C defined by a rational parametrization P (t), we present
formulae for the computation of the degree of C, and the multiplicity of a point. Using the …

In this paper, we present a new algorithm for computing the implicit equation of a rational
surface V from a rational parametrization P (t¯). The algorithm is valid independent of the …

In this paper we characterize the properness of rational parametrizations of hypersurfaces
by means of the existence of intersection points of some additional algebraic hypersurfaces …