Algebro-geometric analysis of bisectors of two algebraic plane curves

Curves in Cages: An Algebro-Geometric Zoo

This paper is concerned with families of plane algebraic curves that contain a given and quite special set of points X . We focus on the case in which the set X is formed by transversally intersecting pairs of lines selected from two given finite families. The union of all lines from both families is called a cage (this notion of cage will be made more precise later), and the intersection X con...

Robust Approximation of Offsets and Bisectors of Plane Curves

Most methods for computing offsets and bisectors of parametric curves are based on a local formulation of the distance to a curve. As a consequence, the computed objects may contain spurious parts and components, and have to be trimmed. We approach these problems as global optimization problems, and solve them using interval arithmetic, thus generating robust approximations that need not be tri...

Analysis of Real Algebraic Plane Curves

This work describes a new method to compute geometric properties of a real algebraic plane curve of arbitrary degree. These properties contain the topology of the curve as well as the location of singular points and vertical asymptotes. The algorithm is based on the Bitstream Descartes method (Eigenwillig et al.: “A Descartes Algorithm for Polynomials with Bit-Stream Coefficients”, LNCS 3718), ...

Topology of Plane Algebraic Curves

Plane Algebraic Curves

We go over some of the basics of plane algebraic curves, which are planar curves described as the set of solutions of a polynomial in two variables. We study many basic notions, such as projective space, parametrization, and the intersection of two curves. We end with the group law on the cubic and search for torsion points.