Title | ||
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Rational Hausdorff divisors: A new approach to the approximate parametrization of curves. |
Abstract | ||
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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. |
Year | DOI | Venue |
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2014 | 10.1016/j.cam.2013.12.052 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
approximate parametrization problem,hausdorff curve,associated linear system,algebraic plane curve,finite hausdorff distance,rational hausdorff divisor,irreducible real curve,plane curve,linear system,irreducible hausdorff curve,new approach,input curve,hausdorff distance | Hausdorff dimension,Effective dimension,Mathematical optimization,Algebraic number,Urysohn and completely Hausdorff spaces,Mathematical analysis,Hausdorff distance,Plane curve,Hausdorff space,Hausdorff measure,Mathematics | Journal |
Volume | ISSN | Citations |
263 | Journal of Computational and Applied Mathematics 263 (2014)
445-465 | 1 |
PageRank | References | Authors |
0.37 | 31 | 3 |
Name | Order | Citations | PageRank |
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Sonia L. Rueda | 1 | 48 | 6.45 |
Juana Sendra | 2 | 193 | 19.65 |
J. Rafael Sendra | 3 | 621 | 68.33 |