Structured matrices in the application of bivariate interpolation to curve implicitization |
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Authors: | Ana Marco,José -Javier Martí nez |
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Affiliation: | Departamento de Matemáticas, Universidad de Alcalá, Campus Universitario, 28871-Alcalá de Henares, Madrid, Spain |
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Abstract: | A non-standard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered, and their respective computational complexities are analyzed. Although the techniques employed are usually associated to numerical analysis, in this case all the computations are carried out using exact rational arithmetic. The power of the Kronecker product of matrices in this application is stressed. |
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Keywords: | Interpolation Vandermonde matrix Kronecker product Computer aided geometric design Resultant |
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