On the planar intersection of natural quadrics

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On the planar intersection of natural quadrics

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ACM Symposium on Solid and Physical Modeling archive
Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications table of contents

Austin, Texas, United States

Pages: 233 - 242

Year of Publication: 1991

ISBN:0-89791-427-9

Authors

Ching-Kuang Shene	Department of Computer Science, The Johns Hopkins University, Baltimore, Maryland
John K. Johnstone	Department of Computer Science, The Johns Hopkins University, Baltimore, Maryland

Sponsor

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 19, Citation Count: 4

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	G. P. Dandelin, M~moire sur quelque~ propri~t4s remarquables de la Focal Parabolique, Nouveauz Mdmoires de l'Acadgmie Royale des Sciences et Belles-lettres de Bruzelles, Vol. 2 (1822), pp. 171- 202.
	2	William H. Drew, A Geometrical Treatise on Conic Sections, fifth edition, Macmillan and Co., 1875.
	3	R. T. Farouki , C. Neff , M. A. O'Conner, Automatic parsing of degenerate quadric-surface intersections, ACM Transactions on Graphics (TOG), v.8 n.3, p.174-203, July 1989 [doi>10.1145/77055.77058]
	4	Ronald N. Goldman and james R. Miller, Detecting and Calculating Conic Sections in the Intersection of Two Natural Quadric Surfaces, Part I: Detection, Draft, October 1990.
	5	Ronald N. Goldman and Joe D. Warren, A Sufficient Condition for the Intersection of Two Quadrics of Revolution to Degenerate into a Pair of Conic Sections, Technical Report, Rice University, December 1990.
	6	D. G. IIakala, R. C. Hillyard, B. E. Nourse and P. J. Malraison, Natural Quadrics in Mechanical Design, Proceedings of A utofact West 1, Anaheim, CA., Nov. 1980, pp. 363-378.
	7	J. Henrici and P. Treutlein, Lehrbuch der Elementar-Geometrie, Vol. i, Teubner, Leipzig, 1897.
	8	D. ttilbert and S. Cohn-Vossen, Geometry and the Imagination, translated by P. Nememyi, Chelsea, New York, 1983.
	9	Joshua Levin, A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces, Communications of the ACM, v.19 n.10, p.555-563, Oct. 1976 [doi>10.1145/360349.360355]
	10	Joshua Zev Levin, Mathematical Models for Determining the Intersections of Quadric Surfaces, Computer Graphics and Image Processing, Vol. 11(1979), pp. 73-87.
	11	Francis S. Macaulay, Geometrical Conics, Cambridge University Press, London, 1895.
	12	James R. Miller, Geometric approaches to nonplanar quadric surface intersection curves, ACM Transactions on Graphics (TOG), v.6 n.4, p.274-307, Oct. 1987 [doi>10.1145/35039.35041]
	13	Pierce Morton, On the Focus of a Conic Section, Transactions of the Cambridge Philosophical Society, Vol. 3 (1827-1830), pp. 185-191.
	14	S. Ocken, Jacob T. SchwartT. and Micha Sharir, Precise implementation of CAD Primitives Using Rational Parameterizations of Standard Surfaces, in Planning, Geometry, and Complezity of Robot Motion, edited by Jacob T. Schwartz, Micha Sharir and John Hopcroft, Ablex Publishing Co., Norwood, New Jersey, 1987, pp. 245-266.
	15	L. Piegl, Geometric method of intersecting natural quadrics represented in trimmed surface form, Computer-Aided Design, v.21 n.4, p.201-212, May 1989 [doi>10.1016/0010-4485(89)90045-6]
	16	M. J. Pratt, Cyclides in computer aided geometric design, Computer Aided Geometric Design, v.7 n.1-4, p.221-242, Jun. 1990 [doi>10.1016/0167-8396(90)90033-N]
	17	Ramon F. Sarraga, Algebraic Methods for Intersections of Quadric Surfaces in GMSOLID, Computer Vision, Graphics, and Image Processing, Vol. 22(1983), pp. 222-238.
	18	Charles Taylor, An Introduction to Ancient and Modern Geometry of Conics, Cambridge University Press, London, 1881.
	19	J. Warren, Blending quadric surfaces with quadric and cubic surfaces, Proceedings of the third annual symposium on Computational geometry, p.341-347, June 08-10, 1987, Waterloo, Ontario, Canada [doi>10.1145/41958.41995]

CITED BY 4

	Ching-Kuang Shene, Planar intersection, common inscribed sphere and Dupin blending cyclides, Proceedings on the second ACM symposium on Solid modeling and applications, p.487-488, May 19-21, 1993, Montreal, Quebec, Canada
	Yang Liu , Fa-Lai Chen, Algebraic conditions for classifying the positional relationships between two conics and their applications, Journal of Computer Science and Technology, v.19 n.5, p.665-673, September 2004
	Ching-Kuang Shene , John K. Johnstone, On the lower degree intersections of two natural quadrics, ACM Transactions on Graphics (TOG), v.13 n.4, p.400-424, Oct. 1994
	Elmar Schömer , Nicola Wolpert, An exact and efficient approach for computing a cell in an arrangement of quadrics, Computational Geometry: Theory and Applications, v.33 n.1-2, p.65-97, January 2006