Classification of the relative positions between a small ellipsoid and an elliptic paraboloid
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Classification of the relative positions between a small ellipsoid and an elliptic paraboloidAuthor(s)
Date
2019-06Citation
Brozos-Vázquez, M., Pereira-Sáez, M. J., Souto-Salorio, M. J., & Tarrío-Tobar, A. D. (2019). Classification of the relative positions between a small ellipsoid and an elliptic paraboloid. Computer Aided Geometric Design, 72, 34–48. doi:10.1016/j.cagd.2019.05.002
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https://doi.org/10.1016/j.cagd.2019.05.002
Abstract
[Abstract]: We classify all the relative positions between an ellipsoid and an elliptic paraboloid when the ellipsoid is small in comparison with the paraboloid (small meaning that the two surfaces cannot be tangent at two points simultaneously when one is moved with respect to the other). This provides an easy way to detect contact between the two surfaces by a direct analysis of the coefficients of a fourth degree polynomial.
Keywords
Quadric
Elliptic paraboloid
Ellipsoid
Relative position
Contact detection
Characteristic polynomial
Elliptic paraboloid
Ellipsoid
Relative position
Contact detection
Characteristic polynomial
Description
©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. This version of the article Brozos-Vázquez, M., Pereira-Sáez, M. J., Souto-Salorio, M. J., & Tarrío-Tobar, A. D. (2019). “Classification of the relative positions between a small ellipsoid and an elliptic paraboloid” has been accepted for publication in Computer Aided Geometric Design, 72, 34–48. The Version of Record is available online at https://doi.org/10.1016/j.cagd.2019.05.002.
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
ISSN
0167-8396