Journal of Computer Science and Technology

, Volume 19, Issue 5, pp 665–673 | Cite as

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

  • Yang LiuEmail author
  • Fa-Lai Chen


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.


collision detection projective transformation generalized characteristic polynomial positional relationship 


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Copyright information

© Science Press, Beijing China and Allerton Press Inc., Beijing China and Allerton Press Inc. 2004

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of Hong KongHong Kong Special Administrative Region, P.R. China
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefeiP.R. China

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