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Issue No.02 - February (1986 vol.6)
pp: 50-56
T.N.T. Goodman , University of Dundee
K. Unsworth , University of Dundee
This article examines some of the desirable features of ?-splines that make them particularly suitable for computer-aided design. First, a theoretical analysis is presented regarding the effects upon the shape of a design curve when the bias and tension parameters are allowed to vary in certain ways. Second, the concept of geometric continuity is discussed, and conditions are derived upon the control vertices to ensure that the design curve has second-order geometric continuity. Illustrations of ,?-spline curves are presented to support the theoretical conclusions.
T.N.T. Goodman, K. Unsworth, "Manipulating Shape and Producing Geometuic Contnuity in ?-Spline Curves", IEEE Computer Graphics and Applications, vol.6, no. 2, pp. 50-56, February 1986, doi:10.1109/MCG.1986.276692
1. B.A.Barsky, "The Beta-spline: A Local Representation Based on Shape Parameters and Fundamental Geometric Measures," Dec. 1981
2. B.A.Barsky, Computer Graphics and Computer Aided Geometric Design Using Beta-splines , Springer-Verlag to appear
3. T.N.T.Goodman, "Properties of ,β-splines," J. Approx. Theory Vol. 44, No. 2, pp. 132-153 June 1985
4. A.D.DeRose, "Geometric Continuity: A Parametrization Independent Measure of Continuity for Computer Aided Geometric Design," 1985
5. M.A.Sabin, "Spline Curves," , British Aircraft Corp. 1969 unpublished
6. J.R.Manning, "Continuity Conditions for Spline Curves," Computer J. Vol. 17, No. 2, pp. 181-186 1974
7. Boor, Applied Mathematical Sciences , Springer-Verlag 1978 Vol. 27,
8. B.A.Barsky and J.C.Beatty, "Varying the Betas in Beta-splines," , Dept. of Computer Science Mar. 1983 University of Waterloo Also available as report TR CSD-82-112 from the Computer Science Division, Electrical Engineering and Computer Sciences Dept., University of California, Berkeley
9. B.A.Barsky and J.C.Beatty, "Local Control of Bias and Tension in Beta-splines," Computer Graphics (Proc. SIGGRAPH 83) July 1983 Vol. 17, No. 3, pp. 193-218
10. R.H.Bartels and J.C.Beatty, "Beta-splines with a Difference," tech , Dept. of Computer Science, University of Waterloo May 1984
11. T.N.T.Goodman and K.Unsworth, in Fundamental Algorithms for Computer Graphics , Springer-Verlag 1985 Vol. 17, pp. 325-357 Also available as Computer Science Report 85/02, Dept. of Mathematical Sciences, University of Dundee, Scotland
12. T.N.T.Goodman and S.L.Lee, "Interpolatory and Variation-Diminishing Properties of Generalized B-splines," Proc. Royal Society Edinburgh (A) 1984 Vol. 96, pp. 249-259
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