Using multivariate resultants to find the intersection of three quadric surfaces

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Using multivariate resultants to find the intersection of three quadric surfaces

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ACM Transactions on Graphics (TOG) archive
Volume 10 , Issue 4 (October 1991) table of contents

Pages: 378 - 400

Year of Publication: 1991

ISSN:0730-0301

Authors

Eng-Wee Chionh	National Univ. of Singapore, Singapore
Ronald N. Goldman	Rice Univ., Houston, TX
James R. Miller	Univ. of Kansas, Lawrence

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 37, Citation Count: 6

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references cited by index terms review collaborative colleagues

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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	BAJAJ, C., GARRrrY, T., AND WARREN, J. On the applications of multi.equational resultants. Tech. Rep. CSD-TR-826, CAPO Rep. CER-88-39, Computer Science Department, Purdue University, West Lafayette, Ind., Nov. 1988.
	2	John F. Canny, The complexity of robot motion planning, MIT Press, Cambridge, MA, 1988
	3	CHAR, B. W., GEDDES, K. O., GONNET, G. H., AND WATT, S. M. Maple User's Guide. WATCOM Publications Ltd., 1985.
	4	CmoNn, E.W. Base points, resultants, and the implicit representation of rational surfaces Ph.D. dissertation, University of Waterloo, Waterloo, Ont., Canada, 1990.
	5	George E. Collins, The Calculation of Multivariate Polynomial Resultants, Journal of the ACM (JACM), v.18 n.4, p.515-532, Oct. 1971 [doi>10.1145/321662.321666]
	6	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]
	7	GOLDMAN, R.N. Two approaches to a computer model for quadric surfaces. IEEE Comput. Graph. Applications 3, 6 (Sept. 1983), 21-24.
	8	LrvI~, J. Mathematical models for determining the intersections of quadric surfaces. Comput. Graph. Image Process. 11, 1 (Sept. 1979), 73-87.
	9	MACAULAY, F. S. Note on the resultant of a number of polynomials of the same degree. Proc. London Math. Soc. (June 1921), 14-21.
	10	MACAULAY, F. S. On some formula in elimination. Proc. London Math. Soc. (May 1902), 3-27.
	11	MACAULAY, F. S. The Algebraic Theory of Modular Systems. Stechert-Hafner Service Agency, New York, 1964.
	12	James R. Miller, Analysis of Quadric-Surface-Based Solid Models, IEEE Computer Graphics and Applications, v.8 n.1, p.28-42, January 1988 [doi>10.1109/38.488]
	13	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]
	14	MORGAN, A. P., AND SARRAGA, R. F. A Method For Computing Three Surface Intersection Points in GMSOLID. Research Publication GMR-3964, General Motors Research Lab. 1982.
	15	MORRIS, J. L. Computational Methods in Elementary Numerical Analysis. Wiley, New York, 1983.
	16	OCKEN, S., SCHWARTZ, J. T., AND SHARm, 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, Eds., Plenum Press, New York, 1984.
	17	M. A. O'Connor, Natural quadrics: projections and intersections, IBM Journal of Research and Development, v.33 n.4, p.417-446, July 1989
	18	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]
	19	REQUICHA, A. A. G., AND VOELCKER, H.B. Boolean operations in solid modeling: Boundary evaluation and merging algorithms. Proc. 1EEE 73, 1 (Jan. 1985), 30-44.
	20	SALMON, G. Lessons Introductory to the Modern Higher Algebra. G. E. $techert, New York, 924.
	21	SARRAGA, R. F. Algebraic methods for intersections of quadric surfaces in GMSOLID. Comput. Vision, Graph. Image Process. 22, 2 (May 1983), 222-238.
	22	VAN OER WAERDEN, B.L. Modern Algebra, 2nd ed, Frederick Ungar, New York, 1950.

CITED BY 6

	Nicola Geismann , Michael Hemmer , Elmar Schömer, Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!, Proceedings of the seventeenth annual symposium on Computational geometry, p.264-273, June 2001, Medford, Massachusetts, United States
	Elmar Schömer , Joachim Reichel , Thomas Warken, Efficient Collision Detection for Curved Solid Objects, Proceedings of the seventh ACM symposium on Solid modeling and applications, June 17-21, 2002, Saarbrücken, Germany
	Chionh Eng Wee , Ronald N. Goldman, Elimination and Resultants - Part 1: Elimination and Bivariate Resultants, IEEE Computer Graphics and Applications, v.15 n.1, p.69-77, January 1995
	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
	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
	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

INDEX TERMS

Primary Classification:
J. Computer Applications
J.6 COMPUTER-AIDED ENGINEERING
Subjects: Computer-aided design (CAD)

Additional Classification:
I. Computing Methodologies
I.3 COMPUTER GRAPHICS
I.3.5 Computational Geometry and Object Modeling
Subjects: Curve, surface, solid, and object representations; Physically based modeling; Geometric algorithms, languages, and systems

General Terms:
Algorithms, Design, Theory

REVIEW

"Maharaj Mukherjee : Reviewer"

Boundary representation and evaluation is an important problem in geometric modeling. Boolean operations between two solids require partitioning of the faces of one solid with respect to the other as inside, outside, or on. This paper presents more...

Collaborative Colleagues:

Eng-Wee Chionh: colleagues

Ronald N. Goldman: colleagues

James R. Miller: colleagues

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