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Conditions for avoiding loss of geometric continuity on spline curves. (English) Zbl 0646.41009
Summary: This paper gives a sufficient condition on the control polygon to avoid loss of geometric continuity on a spline curve of any order whose Bézier polygon can be gained by successively ‘cutting corners’ form its control polygon.

MSC:
41A15 Spline approximation
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[1] Barsky, B., The β-spline: a local representation based on shape parameters and fundamental geometric measures, Diss. univ. of Utah, (1981)
[2] Bézier, P., Numerical control, mathematics and applications, (1972), Wiley New York · Zbl 0251.93002
[3] Boehm, W., Cubic B-spline curves and surfaces in CAGD, Computing, 19, 29-34, (1977)
[4] Boehm, W.; Farin, G.; Kahhmann, J., A survey of curve and surface methods in CAGD, Computer aided geometric design, 1, 1-60, (1984) · Zbl 0604.65005
[5] Boehm, W., Curvature continuous curves and surfaces, Cad, 18, 105-106, (1986)
[6] de Boor, C., A practical guide to splines, (1978), Springer Berlin · Zbl 0406.41003
[7] Cohen, E.; Lyche, T.; Riesenfeld, R.F., Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics, Computer graphics and image processing, 14, 87-111, (1980)
[8] Farin, G.E., Visually C2 cubic splines, Cad, 14, 137-139, (1982)
[9] Forrest, A.R., Interactive interpolation and approximation by Bézier polynomials, Computing J., 15, 71-79, (1972) · Zbl 0243.68015
[10] Goodman, T.N.T., Properties of β-splines, J. approx. theory, 44, 132-153, (1985) · Zbl 0569.41010
[11] Goodman, T.N.T.; Micchelli, C.A., Corner cutting algorithms for the Bézier representation of free form curves, () · Zbl 0652.41003
[12] Goodman, T.N.T.; Unsworth, K., Manipulating shape and producing geometric continuity in β-spline surfaces, IEEE computer graphics appl., 6, 50-56, (1986)
[13] Gordon, W.J.; Riesenfeld, R.F., B-spline curves and surfaces, ()
[14] Sablonnière, P., Spline and Bézier polygons associated with a polynomial spline curve, Cad, 10, 257-261, (1978)
[15] Wang, C.Y., Shape classification of the parametric cubic curve and parametric B-spline cubic curve, Cad, 13, 199-206, (1981)
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