Abstract
The bisectors are geometric constructions with different applications in tool path generation, motion planning, NC-milling, etc. We present a new approach to determine an algebraic representation (parameterization or implicit equation) of the bisector surface of two given low degree parametric surfaces. The method uses the so-called generalized Cramer rules, and suitable elimination steps. The new introduced approach allows to easily obtain parameterizations of the plane-quadric, plane-torus, circular cylinder-quadric, circular cylinder-torus, cylinder–cylinder, cylinder-cone and cone–cone bisectors, which are rational in most cases. In the remaining cases the parametrization involves one square root, which is well suited for a good approximation of the bisector.
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Acknowledgments
The authors are partially supported by the Spanish “Ministerio de Economia y Competitividad” and by the European Regional Development Fund (ERDF), under the Project MTM2011-25816-C02-02, and by the SAGA network.
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Adamou, I., Fioravanti, M., Gonzalez-Vega, L. (2014). Parametrization of the Bisector of Two Low Degree Surfaces. In: De Amicis, R., Conti, G. (eds) Future Vision and Trends on Shapes, Geometry and Algebra. Springer Proceedings in Mathematics & Statistics, vol 84. Springer, London. https://doi.org/10.1007/978-1-4471-6461-6_5
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DOI: https://doi.org/10.1007/978-1-4471-6461-6_5
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