Abstract
The main objective of this work is focused on classifying the families of curves defined by the intersection of an arbitrary ellipsoid with an arbitrary torus, sharing the same center, based on the number of their connected components and on the number of their auto-intersection points. The graphic geometric representation of these curves, in GeoGebra, and the respective algebraic descriptions, supported from a theoretical and computational point of view, were of fundamental importance for the development of this work. In this paper, we describe a procedure and the necessary implementations to achieve the objective outlined.
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Acknowledgements
This research was supported by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020; The Centre for Research and Innovation in Education (inED), through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/05198/2020; and Organization of Ibero-American States for Education, Science and Culture (OEI).
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Breda, A.M.R.D., da Silva Trocado, A.E.B., Santos, J.M.D.S.D. (2023). The Intersection Curve of an Ellipsoid with a Torus Sharing the Same Center. In: Cheng, LY. (eds) ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. ICGG 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-031-13588-0_11
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