DocumentCode :
467795
Title :
An Explicit Criterion for the Positional Relationship of an Ellipse and a Parabola
Author :
Chen, Min ; Hou, Xiao-rong ; Qiu, Xu-hao
Author_Institution :
Ningbo Univ., Ningbo
Volume :
3
fYear :
2007
fDate :
19-22 Aug. 2007
Firstpage :
1774
Lastpage :
1778
Abstract :
Detecting the positional relationship between two planar conics is a common problem in fields of computer animation, computer graphics, machine vision, robotics, virtual reality and CAD/CAM. Based on the generalized characteristic polynomial and the affine invariants of two conics, explicit conditions are derived for classifying the various positional relationships of an ellipse and a parabola by considering all the cases: separation, exterior tangency, intersection, interior tangency and inclusion. The explicit conditions can be expressed in terms of the coefficients of the quadratic forms representing the ellipse and the parabola.
Keywords :
CAD/CAM; computational geometry; computer animation; polynomials; robot vision; virtual reality; CAD/CAM; computer animation; computer graphics; ellipse; inclusion; intersection; machine vision; parabola; planar conics; polynomial; robotics; tangency; virtual reality; Animation; CADCAM; Computer aided manufacturing; Computer graphics; Cybernetics; Machine learning; Machine vision; Polynomials; Robot vision systems; Virtual reality; Affine invariant; Collision detection; Ellipse; Generalized characteristic polynomial; Parabola;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Machine Learning and Cybernetics, 2007 International Conference on
Conference_Location :
Hong Kong
Print_ISBN :
978-1-4244-0973-0
Electronic_ISBN :
978-1-4244-0973-0
Type :
conf
DOI :
10.1109/ICMLC.2007.4370435
Filename :
4370435
Link To Document :
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