On the topology of real algebraic plane curves
J Cheng, S Lazard, L Peñaranda, M Pouget… - … in Computer Science, 2010 - Springer
We revisit the problem of computing the topology and geometry of a real algebraic plane
curve. The topology is of prime interest but geometric information, such as the position of …
curve. The topology is of prime interest but geometric information, such as the position of …
The Voronoi diagram of three lines
We give a complete description of the Voronoi diagram of three lines in R3. In particular, we
show that the topology of the Voronoi diagram is invariant for three lines in general position …
show that the topology of the Voronoi diagram is invariant for three lines in general position …
An elimination method for solving bivariate polynomial systems: Eliminating the usual drawbacks
We present an exact and complete algorithm to isolate the real solutions of a zero-
dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination …
dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination …
On the complexity of solving a bivariate polynomial system
We study the complexity of computing the real solutions of a bivariate polynomial system
using the recently presented algorithm Bisolve [2]. Bisolve is an elimination method which, in …
using the recently presented algorithm Bisolve [2]. Bisolve is an elimination method which, in …
On the boolean complexity of real root refinement
We assume that a real square-free polynomial A has a degree d, a maximum coefficient
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …
Nearly optimal refinement of real roots of a univariate polynomial
We assume that a real square-free polynomial A has a degree d, a maximum coefficient
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …
bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we …
A worst-case bound for topology computation of algebraic curves
Computing the topology of an algebraic plane curve C means computing a combinatorial
graph that is isotopic to C and thus represents its topology in R2. We prove that, for a …
graph that is isotopic to C and thus represents its topology in R2. We prove that, for a …
Computing the topology of a plane or space hyperelliptic curve
JG Alcázar, J Caravantes, GM Diaz-Toca… - … Aided Geometric Design, 2020 - Elsevier
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The
algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the …
algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the …
[HTML][HTML] A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points
A simple algorithm for computing an approximate parameterization of real space algebraic
curves using their graphs of critical points is designed and studied in this paper. The first …
curves using their graphs of critical points is designed and studied in this paper. The first …
Homeomorphic approximation of the intersection curve of two rational surfaces
We present an approach of computing the intersection curve C of two rational parametric
surface S1 (u, s) and S2 (v, t), one being projectable and hence can easily be implicitized …
surface S1 (u, s) and S2 (v, t), one being projectable and hence can easily be implicitized …