Combining algebraic rigor with geometric robustness for the detection and calculation of conic sections in the intersection of two natural quadric surfaces

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Combining algebraic rigor with geometric robustness for the detection and calculation of conic sections in the intersection of two natural quadric surfaces

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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: 221 - 231

Year of Publication: 1991

ISBN:0-89791-427-9

Authors

Ronald N. Goldman	Rice University
James R. Miller	University of Kansas

Sponsor

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

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 1, Downloads (12 Months): 13, Citation Count: 7

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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	Dresden, A., Solid Analytic Geometry and Determinants, Wiley, New York, 1930.
	2	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]
	3	Goldman, R. N., Quadrics of Revolution, IEEE Computer Graphics and Applications, Vol. 3, No. 2, March/April 1983, pp. 68-76.
	4	Goldman, R. N. and Miller, J. R., Detecting and Calculating Conic Sections in the Intersection of Two Natural Quadric Surfaces, Part I: Detection, submitted for publication.
	5	Hakala, D. G., Hillyard, R. C., Nourse, B. E., and Malraison, P. J., Natural Quadrics in Mechanical Design, Proceedings Autofact West, Vol. 1, November, 1980.
	6	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]
	7	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]
	8	Miller, J. R. and Goldman, R. N., Detecting and Calculating Conic Sections in the Intersection of Two Natural Quadric Surfaces, Part II: Calculation, submitted for publication.
	9	Miller, J. R. and Goldman, R. N., Using Tangent Balls to Find Plane Sections of Natural Quadric Surfaces, in preparation.
	10	Ocken, S., Schwartz, J. T., and Sharir, M., Precise Implementation of CAD Primitives Using Rational Parameterizations of Standard Surfaces, in Solid Modeling By Computers" From Theory to Applications, M. S. Pickett and J. W. Boyse, editors, Plenum Press, 1984.
	11	M. A. O'Connor, Natural quadrics: projections and intersections, IBM Journal of Research and Development, v.33 n.4, p.417-446, July 1989
	12	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]
	13	Sarraga, R. F., Algebraic Methods for Intersections of Quadric Surfaces in GMSOLID, Computer Vision, Graphics, and Image Processing, Vol. 22, No. 2, May 1983, pp. 222-238.
	14	Joe David Warren, On algebraic surfaces meeting with geometric continuity, Cornell University, Ithaca, NY, 1986
	15	J. Warren, Blending algebraic surfaces, ACM Transactions on Graphics (TOG), v.8 n.4, p.263-278, Oct. 1989 [doi>10.1145/77269.77270]

CITED BY 7

	Zhi-qiang Xu , Xiaoshen Wang , Xiao-diao Chen , Jia-guang Sun, A robust algorithm for finding the real intersections of three quadric surfaces, Computer Aided Geometric Design, v.22 n.6, p.515-530, September 2005
	Laurent Dupont , Daniel Lazard , Sylvain Lazard , Sylvain Petitjean, Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm, Journal of Symbolic Computation, v.43 n.3, p.168-191, March, 2008
	Laurent Dupont , Daniel Lazard , Sylvain Lazard , Sylvain Petitjean, Near-optimal parameterization of the intersection of quadrics, Proceedings of the nineteenth annual symposium on Computational geometry, June 08-10, 2003, San Diego, California, USA
	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
	Wenping Wang , Barry Joe , Ronald Goldman, Computing quadric surface intersections based on an analysis of plane cubic curves, Graphical Models, v.64 n.6, p.335-367, November 2002
	John Keyser , Shankar Krishnan , Dinesh Manocha, Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.42-55, May 14-16, 1997, Atlanta, Georgia, United States
	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