Numerically stable implicitization of cubic curves

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Numerically stable implicitization of cubic curves

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ACM Transactions on Graphics (TOG) archive
Volume 10 , Issue 3 (July 1991) table of contents

Pages: 255 - 296

Year of Publication: 1991

ISSN:0730-0301

Author

John D. Hobby

AT&T Bell Labs., Murray Hill, NJ

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 27, 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	CH^R, B. W., GEDDES, K. O., GONNET, G. H., MONAGAN, M. B., AND WATT, S.M. MAPLE Reference Manual. WATCOM, Waterloo, Ontario, 1988.
	2	R. T. Farouki , V. T. Rajan, On the numerical condition of polynomials in Berstein form, Computer Aided Geometric Design, v.4 n.3, p.191-216, Nov., 1987 [doi>10.1016/0167-8396(87)90012-4]
	3	GOLUB, G. H., AND VAN LOAN, C. F. Matrix Computations. Johns Hopkins University Press, Baltimore, MD, 1983.
	4	John D. Hobby, Rasterization of nonparametric curves, ACM Transactions on Graphics (TOG), v.9 n.3, p.262-277, July 1990 [doi>10.1145/78964.78966]
	5	Richard R. Patterson, Projective transformations of the parameter of a Bernstein-Bézier curve, ACM Transactions on Graphics (TOG), v.4 n.4, p.276-290, Oct. 1985 [doi>10.1145/6116.6119]
	6	S~-DERSERO, T.W. Implicit and parametric curves and surfaces for computer aided geometric design. Ph.D. thesis, Dept. of Mechanical Engineering, Purdue Univ., 1983.
	7	SEDERBERG, T.W. Planar piecewise algebraic curves. Comput. Aided Geom. Des. I (1984), 241-255.
	8	SEVEaSERO, T. W., AND A~VESSON, D.C. Implicit representation of parametric curves and surfaces. Cornput. Vision Graph. and Image Process. 28, 1 (1984), 72-84.
	9	SEDERBERG, T. W., ANDERSON, D. C., AND GOLDMAN, R.N. Implicitization, inversion, and intersection of planar rational cubic curves. Comput. Vision Graph. and Image Process. 31, 1 (July 1985), 89-102.
	10	Thomas W. Sederberg , Ronald N. Goldman, Algebraic geometry for computer-aided geometric design, IEEE Computer Graphics and Applications, v.6 n.6, p.52-59, June 1986 [doi>10.1109/MCG.1986.276742]
	11	R. N. Goldman , T. W. Sederberg, Analytic approach to intersection of all piecewise parametric rational cubic curves, Computer-Aided Design, v.19 n.6, p.282-292, July/Aug. 1987 [doi>10.1016/0010-4485(87)90281-8]
	12	Thomas W Sederberg , Scott R Parry, Comparison of three curve intersection algorithms, Computer-Aided Design, v.18 n.1, p.58-64, Jan/Feb. 1986 [doi>10.1016/S0010-4485(86)80013-6]
	13	SEattLe., J. G., ANo RoTH, L. Algebraic Geometry. Oxford, 1949.

CITED BY 4

	Dinesh Manocha , James Demmel, Algorithms for intersecting parametric and algebraic curves I: simple intersections, ACM Transactions on Graphics (TOG), v.13 n.1, p.73-100, Jan. 1994
	Jean Gallier, A simple method for drawing a rational curve as two Bézier segments, ACM Transactions on Graphics (TOG), v.18 n.4, p.316-328, Oct. 1999
	John D. Hobby, Rasterization of nonparametric curves, ACM Transactions on Graphics (TOG), v.9 n.3, p.262-277, July 1990
	Hulya Yalcin , Mustafa Unel , William Wolovich, Implicitization of Parametric Curves by Matrix Annihilation, International Journal of Computer Vision, v.54 n.1-3, p.105-115, August-September 2003