Algebraic conditions for classifying the positional relationships between two conics and their applications

Authors:
Yang Liu;Fa-Lai Chen
Affiliations:
Department of Computer Science, The University of Hong Kong, Hong Kong Special Administrative Region, P.R. China;Department of Mathematics, University of Science and Technology of China, Hefei 230026, P.R. China
Venue:
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Year:
2004

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Abstract

In many fields of computer science such as computer animation, computer graphics, computer aided geometric design and robotics, it is a common problem to detect the positional relationships of several entities. Based on generalized characteristic polynomials and projective transformations, algebraic conditions are derived for detecting the various positional relationships between two planar conics, namely, outer separation, exterior contact, intersection, interior contact and inclusion. Then the results are applied to detecting the positional relationships between a cylinder (or a cone) and a quadric. The criteria is very effective and easier to use than other known methods.