| The Ontario Research Centre for Computer Algebra
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Abstract In this paper we plan to briefly describe some of the most relevant results in the symbolic manipulation of curves and surfaces and their applications in Computer Aided Geometric Design (CAGD), as well as report on the main research achivements in the frame of the Spanish research project DGES PB98-0713-C02 entitled ``Metodos Algebraico-Geometricos para la manipulacion de curvas y superficies". More precisely, we will focus on the following levels: Algorithms for rational curves and Sufaces; Applications in CAGD; Practical performance of applications in CAGD. We comment the results and basic ideas on the symbolic manipulation of rational curves and surfaces. In this paper we will essentially describe the intuitive ideas underlying the parametrization methods by adjoints of curves as well as how implicitization implicitation techniques can be used to deal with rational curves and surfaces.
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