Local Control of Bias and Tension in Beta-splines

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Local Control of Bias and Tension in Beta-splines

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ACM Transactions on Graphics (TOG) archive
Volume 2 , Issue 2 (April 1983) table of contents

Pages: 109 - 134

Year of Publication: 1983

ISSN:0730-0301

Authors

Brian A. Barsky	Berkeley Computer Graphics Laboratory, Computer Science Division, University of Calif., Berkeley, CA
John C. Beatty	Computer Graphics Laboratory, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 8, Downloads (12 Months): 35, Citation Count: 17

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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	Brian Andrew Barsky, The beta-spline: a local representation based on shape parameters and fundamental geometric measures, 1981
	2	BARSKY, B.A. Exponential and polynomial methods for applying tension to an interpolating spline curve. Computer Vision Graphic Image Processing 1983, to appear.
	3	Brian A. Barsky, A Study of the Parametric Uniform B-spline Curve and Surface, University of California at Berkeley, Berkeley, CA, 1983
	4	BARSKY, B.A. The Beta-spline: A curve and surface representation for computer graphics and computer aided geometric design. To be published.
	5	BARSKY, B.A. Algorithms for the evaluation and perturbation of Beta-splines. To be published.
	6	BARSKY, B.A., BARTELS, R.H., AND BEATTY, J.C. An introduction to the use of splines in computer graphics. CS-83-9, Dept. of Computer Science, Univ. of Waterloo, Waterloo, Ontario, Canada, 1983.
	7	Brian A. Barsky, Varying the Betas in Beta-splines, University of California at Berkeley, Berkeley, CA, 1982
	8	B~.ZIER, P.E. Emploi des Machines ~ Commande Num~rique. Masson et Cie., Paris, 1970. English ed., Numerical Control--Mathematics and Applications, A. R. Forrest and A. F. Pankhurst, Trans., Wiley, New York, 1972.
	9	BI~.ZIER, P.E. Essai de ddfinition num~rique des courbes et des surfaces exp~rimentales. Ph.D. dissertation, Univ. Pierre et Marie Curie, Paris, Feb. 1977.
	10	BOGEN, R., GOLDEN, J., GZNESERETH, M., AND DOOHOVSKOY, A. MACSYMA Reference Manual, version 9, Massacliussetts Institute of Technology, Cambridge, Mass., 1977.
	11	V~. BooR, C. A Practical Guide to Splines, vol. 27, Applied Mathematical Sciences. Springer- Verlag, New York, 1978.
	12	A. K. Cline, Scalar- and planar-valued curve fitting using splines under tension, Communications of the ACM, v.17 n.4, p.218-220, April 1974 [doi>10.1145/360924.360971]
	13	CooNs, S.A. Surfaces for computer-aided design. Design Div., Mechanical Engineering Dept., Massachusetts Institute of Technology, Cambridge, Mass., 1964.
	14	S. A. Coons, SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS, Massachusetts Institute of Technology, Cambridge, MA, 1967
	15	FATEMAN, R.J. Addendum to the MACSYMA Reference Manual for the VAX. Univ. of Calif., Berkeley, Calif., 1982.
	16	I. D. Faux , M. J. Pratt, Computational Geometry for Design and Manufacture, Halsted Press, New York, NY, 1979
	17	GORDON, W.J., AND RIESENFELD, R.F. B-spline curves and surfaces. In Computer Aided Geometric Design, R. E. Barnhill and R. F. Riesenfeld, Eds. Academic Press, New York, 1974, pp. 95-126.
	18	Jeffrey Michael Lane, Shape operators for computer-aided geometric design., 1977
	19	NIELSON, G.M. Some piecewise polynomial alternatives to splines under tension. In Computer Aided Geometric Design, R. E. Barnhill and R. F. Riesenfeld, Eds. Academic Press, New York, 1974, pp. 209-235.
	20	NIELSON, G.M. Computation of Nu-splines. Dept. of Mathematics, Arizona State Univ., Tempe, Ariz., June 1974.
	21	PILCHER, D.T. Smooth approximation of parametric curves and surfaces. Ph.D. dissertation, Univ. of Utah, Salt Lake City, Utah, Aug. 1973.
	22	Richard Franklin Riesenfeld, Applications of b-spline approximation to geometric problems of computer-aided design., 1973
	23	SCHWEIKERT, D.G. An interpolation curve using a spline in tension. J. Math. Phys. 45 (1966), 312-317.

CITED BY 17

	Barry Joe, Multiple-knot and rational cubic beta-splines, ACM Transactions on Graphics (TOG), v.8 n.2, p.100-120, April 1989
	Thomas A. Foley, Interpolation with interval and point tension controls using cubic weighted v-splines, ACM Transactions on Mathematical Software (TOMS), v.13 n.1, p.68-96, March 1987
	Thomas A. Foley, Weighted bicubic spline interpolation to rapidly varying data, ACM Transactions on Graphics (TOG), v.6 n.1, p.1-18, Jan. 1987
	Hans-Peter Seidel, Polar forms for geometrically continuous spline curves of arbitrary degree, ACM Transactions on Graphics (TOG), v.12 n.1, p.1-34, Jan. 1993
	Francis J M Schmitt , Brian A. Barsky , Wen-hui Du, An adaptive subdivision method for surface-fitting from sampled data, ACM SIGGRAPH Computer Graphics, v.20 n.4, p.179-188, Aug. 1986
	Barry Joe, Discrete Beta-splines, ACM SIGGRAPH Computer Graphics, v.21 n.4, p.137-144, July 1987
	Jules Bloomenthal, Modeling the mighty maple, ACM SIGGRAPH Computer Graphics, v.19 n.3, p.305-311, Jul. 1985
	Dieter Lasser, Two remarks on Tau-splines, ACM Transactions on Graphics (TOG), v.9 n.2, p.198-211, April 1990
	Tony D. DeRose , Brian A. Barsky, Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines, ACM Transactions on Graphics (TOG), v.7 n.1, p.1-41, Jan. 1988
	Peter Comninos, Cubic polynomial curves and surfaces, Handbook of computer animation, Springer-Verlag, London, 2003
	Brian A. Barsky , Tony D. DeRose, Parametric Curves, Part Two, IEEE Computer Graphics and Applications, v.10 n.1, p.60-68, January 1990
	A. Iglesias, Computer graphics for water modeling and rendering: a survey, Future Generation Computer Systems, v.20 n.8, p.1355-1374, November 2004
	Xuli Han, C² quadratic trigonometric polynomial curves with local bias, Journal of Computational and Applied Mathematics, v.180 n.1, p.161-172, 1 August 2005
	Xuli Han, Quadratic trigonometric polynomial curves concerning local control, Applied Numerical Mathematics, v.56 n.1, p.105-115, January 2006
	Xuli Han, Piecewise quartic polynomial curves with a local shape parameter, Journal of Computational and Applied Mathematics, v.195 n.1, p.34-45, 15 October 2006
	A. Masood , M. Sarfraz, Technical Section: An efficient technique for capturing 2D objects, Computers and Graphics, v.32 n.1, p.93-104, February, 2008
	Imre Juhász , Miklós Hoffmann, On the quartic curve of Han, Journal of Computational and Applied Mathematics, v.223 n.1, p.124-132, January, 2009