Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Parametric generalized offsets to hypersurfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
On the practical solution of genus zero diophantine equations
Journal of Symbolic Computation
Towards factoring bivariate approximate polynomials
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
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Interactive versus Symbolic Approaches to Plane Loci Generation in Dynamic Geometry Environments
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Parametrization of approximate algebraic curves by lines
Theoretical Computer Science - Algebraic and numerical algorithm
Distance bounds of ε-points on hypersurfaces
Theoretical Computer Science
A predictor–corrector-type technique for the approximate parameterization of intersection curves
Applicable Algebra in Engineering, Communication and Computing
An Algebraic Approach to Lens Distortion by Line Rectification
Journal of Mathematical Imaging and Vision
Parametrization of approximate algebraic surfaces by lines
Computer Aided Geometric Design
Approximate parametrization of plane algebraic curves by linear systems of curves
Computer Aided Geometric Design
From an approximate to an exact absolute polynomial factorization
Journal of Symbolic Computation
Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer
The Visual Computer: International Journal of Computer Graphics
Rational general solutions of first order non-autonomous parametrizable ODEs
Journal of Symbolic Computation
Polyline approach for approximating Hausdorff distance between planar free-form curves
Computer-Aided Design
Radical parametrizations of algebraic curves by adjoint curves
Journal of Symbolic Computation
An adapted version of the Bentley-Ottmann algorithm for invariants of plane curves singularities
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Envelope computation in the plane by approximate implicitization
Applicable Algebra in Engineering, Communication and Computing
Approximate GCD of several univariate polynomials with small degree perturbations
Journal of Symbolic Computation
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
First steps towards radical parametrization of algebraic surfaces
Computer Aided Geometric Design
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
Efficient detection of symmetries of polynomially parametrized curves
Journal of Computational and Applied Mathematics
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In this paper, we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are rational and are at finite Hausdorff distance among them. As a consequence, we provide a projective linear subspace where all (irreducible) elements are solutions of the approximate parametrization problem for a given algebraic plane curve. Furthermore, we identify the linear system with a plane curve that is shown to be rational and we develop algorithms to parametrize it analyzing its fields of parametrization. Therefore, we present a generic answer to the approximate parametrization problem. In addition, we introduce the notion of Hausdorff curve, and we prove that every irreducible Hausdorff curve can always be parametrized with a generic rational parametrization having coefficients depending on as many parameters as the degree of the input curve.