Topological classification of non-degenerate intersections of two ring tori

Authors:
Xiaohong Jia;Changhe Tu;Wenping Wang
Affiliations:
KLMM, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China and The University of Hong Kong, China;Shandong University, China;The University of Hong Kong, China
Venue:
Computer Aided Geometric Design
Year:
2013

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Abstract

We study the topological classification of all non-degenerate intersection curves of two arbitrary ring tori. Firstly, all topologically different types of such curves are enumerated. Secondly, an algebraic method is presented for determining the topological type of the non-degenerate intersection curve of two given ring tori. The method works by analyzing the real roots of two univariate quartic polynomials constructed from the two tori.