On the numerical condition of algebraic curves and surfaces 1. Implicit equations
Computer Aided Geometric Design
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Univariate polynomials: nearly optimal algorithms for factorization and rootfinding
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
A formula for separating small roots of a polynomial
ACM SIGSAM Bulletin
Normal parameterizations of algebraic plane curves
Journal of Symbolic Computation
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Parametrization of approximate algebraic curves by lines
Theoretical Computer Science - Algebraic and numerical algorithm
Degree formulae for offset curves
Journal of Pure And Applied Algebra
Distance bounds of ε-points on hypersurfaces
Theoretical Computer Science
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
Rational Algebraic Curves: A Computer Algebra Approach
Rational Algebraic Curves: A Computer Algebra Approach
Parametrization of approximate algebraic surfaces by lines
Computer Aided Geometric Design
On the performance of the approximate parametrization algorithm for curves
Information Processing Letters
A regularization method for computing approximate invariants of plane curves singularities
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Journal of Computational and Applied Mathematics
Implicitization of curves and (hyper)surfaces using predicted support
Theoretical Computer Science
A regularization approach for estimating the type of a plane curve singularity
Theoretical Computer Science
Journal of Symbolic Computation
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance @e0 and an @e-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of @e-rationality, and we provide an algorithm to parametrize approximately affine @e-rational plane curves by means of linear systems of (d-2)-degree curves. The algorithm outputs a rational parametrization of a rational curve C@? of degree d which has the same points at infinity as C. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that C@? and C are close in practice.