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Data visualization using rational spline interpolation. (English) Zbl 1086.65010
Summary: A smooth curve interpolation scheme for positive, monotonic, and convex data is developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, are constrained to preserve the shape of the data. The rational spline scheme has a unique representation. The degree of smoothness attained is $C^{1}$.

MSC:
65D18Computer graphics, image analysis, and computational geometry
65D07Splines (numerical methods)
65D05Interpolation (numerical methods)
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References:
[1] Brodlie, K. W.: Methods for drawing curves. Fundamental algorithm for computer graphics, 303-323 (1985)
[2] Brodlie, K. W.; Butt, S.: Preserving convexity using piecewise cubic interpolation. Comput. & graphics 15, 15-23 (1991)
[3] Butt, S.; Brodlie, K. W.: Preserving positivity using piecewise cubic interpolation. Comput. & graphics 17, No. 1, 55-64 (1993)
[4] Constantini, P.: Boundary-valued shape preserving interpolating splines. ACM trans. Math. software 23, No. 2, 229-251 (1997) · Zbl 0887.65010
[5] Devore, A.; Yan, Z.: Error analysis for piecewise quadratic curve Fitting algorithms. Comput. aided geom. Design 3, 205-215 (1986) · Zbl 0614.65008
[6] Fritsch, F. N.; Butland, J.: A method for constructing local monotone piecewise cubic interpolants. SIAM J. Sci. statist. Comput. 5, 303-304 (1984) · Zbl 0577.65003
[7] Fritsch, F. N.; Carlson, R. E.: Monotone piecewise cubic interpolation. SIAM J. Numer. anal. 17, 238-246 (1980) · Zbl 0423.65011
[8] Gregory, J. A.: Shape preserving spline interpolation. Comput. aided design 18, No. 1, 53-57 (1986)
[9] Greiner, K.: A survey on univariate data interpolation and approximation by splines of given shape. Math. comput. Modelling 15, 97-l06 (1991) · Zbl 0757.41002
[10] Lahtinen, A.: Monotone interpolation with application to estimation of taper curves. Ann. numer. Math. 3, 151-161 (1996) · Zbl 0854.65008
[11] Mcallister, D. F.; Roulier, J. A.: An algorithm for computing a shape preserving osculatory quadratic spline. ACM trans. Math. software 7, 331-347 (1981) · Zbl 0464.65003
[12] H.P. Moreton, C.H. Sequin, Minimum variation curves and surfaces for computer-aided geometric design, designing fair curves and surfaces, Nick Sapidis (Ed.), Proc. of SIAM’94 Conference, 1995, pp. 123 -- 159.
[13] Passow, E.; Roulier, J. A.: Monotone and convex spline interpolation. SIAM J. Numer. anal. 14, 904-909 (1977) · Zbl 0378.41002
[14] Sarfraz, M.: Convexity preserving piecewise rational interpolation for planar curves. Bull. korean math. Soc. 29, No. 2, 193-200 (1992) · Zbl 0763.65004
[15] Sarfraz, M.: Interpolatory rational cubic spline with biased, point and interval tension. Comput. & graphics 16, No. 4, 427-430 (1992)
[16] Sarfraz, M.: Preserving monotone shape of the data using piecewise rational cubic functions. Comput. & graphics 21, No. 1, 5-14 (1997)
[17] Sarfraz, M.; Butt, S.; Hussain, M. Z.: Visualization of shaped data by a rational cubic spline interpolation. Internat. J. Comput. & graphics 25, No. 5, 833-845 (2001)
[18] Schumaker, L. L.: On shape preserving quadratic spline interpolation. SIAM J. Numer. anal. 20, 854-864 (1983) · Zbl 0521.65009