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

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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.

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Author information

Correspondence to Yang Liu.

Additional information

Supported by the Outstanding Youth Grant of the National Natural Science Foundation of China (Grant No.60225002), the TRAPOYT and the Doctoral Program of MOE of China (Grant No.20010358003).

Yang Liu is a Ph.D. candidate in the Computer Science Department at the University of Hong Kong. He received his B.S. (2000) and M.S. (2003) degrees in mathematics from the University of Science and Technology of China. His research interests include computer-aided design, computer graphics and computational algebraic geometry.

Fa-Lai Chen is currently a professor in the Department of Mathematics at the University of Science and Technology of China. He received his B.S., M.S. and Ph.D. degrees in mathematics in 1997. 1989 and 1994 respectively, all from the University of Science and Technology of China. His research interests include computer aided geometric design and computer graphics.

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Liu, Y., Chen, F. Algebraic conditions for classifying the positional relationships between two conics and their applications. J. Comput. Sci. & Technol. 19, 665–673 (2004). https://doi.org/10.1007/BF02945593

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  • collision detection
  • projective transformation
  • generalized characteristic polynomial
  • positional relationship