Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/30478
Title: | Torus and quadrics intersection using GeoGebra |
Author: | Breda, Ana Maria Reis D'Azevedo Trocado, Alexandre Emanuel Batista da Silva Santos, José Manuel dos Santos dos |
Keywords: | GeoGebra Toric sections Quadrics Intersection curves |
Issue Date: | 2021 |
Publisher: | Springer |
Abstract: | This paper presents the implementation in GeoGebra of algorithms for computing the intersection curve of a quadric surface with a torus surface. We present three approaches to get and visualise the intersection curve in GeoGebra. One of the approaches makes use of the geometric capabilities of GeoGebra. The second described approach makes use of CAS to obtain a parametrization and the corresponding visualisation of the intersection curve. Finally, the third one is based on computing the projection of the intersection curve, determining its singularities and structure, and its lifting to the 3D embedding space. The research carried out reveals some of the difficulties arising from the implementation in GeoGebra of a geometric algorithm based on the algebraic equations characterising the objects in consideration. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/30478 |
DOI: | 10.1007/978-3-030-63403-2_43 |
ISBN: | 978-3-030-63402-5 |
Appears in Collections: | CIDMA - Capítulo de livro AGG - Capítulo de livro |
Files in This Item:
File | Description | Size | Format | |
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Torus and Quadrics Intersection Using GeoGebra.pdf | 1.47 MB | Adobe PDF |
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