Brian A. Barsky
- 1 BARSKY, B.A. The Beta-spline: A local representation based on shape parameters and fundamental geometric measures. Ph.D. dissertation, Dept. of Computer Science, Univ. of Utah, Salt Lake City, Utah, Dec., 1981. Google Scholar
- 2 BARSKY, B.A. Exponential and polynomial methods for applying tension to an interpolating spline curve. Computer Vision Graphic Image Processing 1983, to appear.Google Scholar
- 3 BARSKY, B.A. A study of the parametric uniform B-spline curve and surface representations. Tech. Rep. CSD 83/118, Computer Science Div., Univ. of Calif., Berkeley, Calif., May 1983. Google Scholar
- 4 BARSKY, B.A. The Beta-spline: A curve and surface representation for computer graphics and computer aided geometric design. To be published.Google Scholar
- 5 BARSKY, B.A. Algorithms for the evaluation and perturbation of Beta-splines. To be published.Google Scholar
- 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.Google Scholar
- 7 BARSKY, B.A., AND BEATT~, J.C. Varying the betas in Beta-splines. CS-82-49, Dept. of Computer Science, Univ. of Waterloo, Waterloo, Ontario, Canada, 1982. Also Tech. Rep. CSD 82/112, Computer Science Division, Univ. of Calif., Berkeley, Calif., Dec. 1982. Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 10 BOGEN, R., GOLDEN, J., GZNESERETH, M., AND DOOHOVSKOY, A. MACSYMA Reference Manual, version 9, Massacliussetts Institute of Technology, Cambridge, Mass., 1977.Google Scholar
- 11 V~. BooR, C. A Practical Guide to Splines, vol. 27, Applied Mathematical Sciences. Springer- Verlag, New York, 1978.Google Scholar
- 12 CLINE, A.K. Scalar- and planar-valued curve fitting using splines under tension. Commun. ACM 17, 4 (Apr. 1974), 218-220. Google Scholar
- 13 CooNs, S.A. Surfaces for computer-aided design. Design Div., Mechanical Engineering Dept., Massachusetts Institute of Technology, Cambridge, Mass., 1964.Google Scholar
- 14 CooNs, S.A. Surfaces for computer-aided design of space forms. MAC-TR-41, Project MAC, Massachusetts Institute of Technology, Cambridge, Mass., June 1967. Google Scholar
- 15 FATEMAN, R.J. Addendum to the MACSYMA Reference Manual for the VAX. Univ. of Calif., Berkeley, Calif., 1982.Google Scholar
- 16 FAUX, I.D., AND PRATT, M.J. Computational Geometry for Design and Manufacture. Wiley, New York, 1979. Google Scholar
- 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.Google Scholar
- 18 LANE, J.M. Shape operators for computer aided geometric design. Ph.D. dissertation, Univ. of Utah, Salt Lake City, Utah, June 1977. Google Scholar
- 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.Google Scholar
- 20 NIELSON, G.M. Computation of Nu-splines. Dept. of Mathematics, Arizona State Univ., Tempe, Ariz., June 1974.Google Scholar
- 21 PILCHER, D.T. Smooth approximation of parametric curves and surfaces. Ph.D. dissertation, Univ. of Utah, Salt Lake City, Utah, Aug. 1973.Google Scholar
- 22 RIESENFELD, R.F. Applications of B-spline approximation to geometric problems of computeraided design. Ph.D. dissertation, Dept. of Systems and Information Science, Syracuse Univ., New York, May 1973. Google Scholar
- 23 SCHWEIKERT, D.G. An interpolation curve using a spline in tension. J. Math. Phys. 45 (1966), 312-317.Google Scholar
Index Terms
- Local Control of Bias and Tension in Beta-splines
Recommendations
Discrete Beta-splines
Goodman (1985) and Joe (1986) have given explicit formulas for (cubic) Beta-splines on uniform knot sequences with varying ß1 and ß2 values at the knots, and nonuniform knot sequences with varying ß2 values at the knots, respectively. ...
Local control of bias and tension in beta-splines
SIGGRAPH '83: Proceedings of the 10th annual conference on Computer graphics and interactive techniquesThe Beta-spline introduced recently by Barsky is a generalization of the uniform cubic B-spline: parametric discontinuities are introduced in such a way as to preserve continuity of the unit tangent and curvature vectors at joints (geometric continuity) ...
Local control of bias and tension in beta-splines
The Beta-spline introduced recently by Barsky is a generalization of the uniform cubic B-spline: parametric discontinuities are introduced in such a way as to preserve continuity of the unit tangent and curvature vectors at joints (geometric continuity) ...
Comments