Abstract
What does a query ellipse do (outside, intersects or tangent) with respect to the Apollonius circle of the three black ellipses?
- J. Canny. The Complexity of Robot Motion Planning. ACM -- MIT Press Doctoral Dissertation Award Series. MIT Press, Cambridge, MA, 1987. Google ScholarDigital Library
- I. Z. Emiris and G. M. Tzoumas. Algebraic study of the Apollonius circle of three ellipses. In Proc. European Workshop Computat. Geometry, pages 147--150, Eindhoven, Holland, March 2005.Google Scholar
- I. Hanniel, R. Muthuganapathy, G. Elber, and M.-S. Kim. Precise voronoi cell extraction of free-form rational planar closed curves. In Proc. 2005 ACM Symp. Solid and phys. modeling, pages 51--59, Cambridge, Massachusetts, 2005. Google ScholarDigital Library
Index Terms
- Apollonius circle conflict
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