Lau, K. H. Conditions for avoiding loss of geometric continuity on spline curves. (English) Zbl 0646.41009 Comput. Aided Geom. Des. 5, No. 3, 209-214 (1988). 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. Cited in 2 Documents MSC: 41A15 Spline approximation Keywords:Bézier polygon; cutting corners; control polygon PDF BibTeX XML Cite \textit{K. H. Lau}, Comput. Aided Geom. Des. 5, No. 3, 209--214 (1988; Zbl 0646.41009) Full Text: DOI OpenURL References: [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.