A smooth curve interpolation scheme for positive, monotonic and convex data is described. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant have been constrained to preserve the shape of the data. The rational spline scheme has a unique representation. In addition to preserving the shape of positive, monotonic and convex data sets, it also possesses extra features to modify the shape of the design curve when desired. The degree of smoothness attained is C1.
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References
McAllister, D.F., and Roulier, J.A. (1981), An algorithm for computing a shape-preserving osculatory quadratic spline, ACM Trans Math Software 7, 331-347.
Passow, E., and Roulier, J.A. (1977), Monotone and convex spline interpolation. SIAM J Num Anal 14, 904-909.
Fritsch, F.N., and Carlson, R.E. (1980), Monotone piecewise cubic interpolation, SIAM J Num Anal 17, 238-246.
Gregory, J.A. (1986), Shape-preserving spline interpolation, Comput Aided Design, 18(1),53-57.
Fritsch, F.N., and Butland, J. (1984), A method for constructing local monotone piece- wise cubic interpolants, SIAM J Sci Stat Comput 5, 303-304.
Schumaker, L.L. (1983), On shape-preserving quadratic spline interpolation, SIAM J Num Anal 20, 854-864.
Brodlie, K.W., and Butt, S. (1991), Preserving convexity using piecewise cubic inter- polation, Comput Graphics, 15, 15-23.
Butt, S., and Brodlie, K.W. (1993), Preserving positivity using piecewise cubic inter- polation, Comput Graphics, 17(1), 55-64.
Sarfraz, M. (1992), Convexity-preserving piecewise rational interpolation for planar curves, Bull Korean Math Soc 29(2), 193-200.
Sarfraz, M. (1997), Preserving monotone shape of the data using piecewise rational cubic functions, Comput Graphics, 21(1), 5-14.
Brodlie, K.W. (1985), Methods for drawing curves. In: Fundamenal Algorithm for Computer Graphics, ed. R.A. Earnshaw, Springer-Verlag, Berlin, pp. 303-323.
DeVore, A., and Yan, Z. (1986), Error analysis for piecewise quadratic curve-fitting algorithms, Comp Aided Geom Design 3, 205-215.
Greiner, K. (1991), A survey on univariate data interpolation and approximation by splines of given shape, Math Comp Mod 15, 97-106.
Constantini, P. (1997), Boundary-valued shape preserving interpolating splines, ACM Trans Math Software, 23(2), 229-251.
Lahtinen, A. (1996), Monotone interpolation with application to estimation of taper curves, Ann Numer Math 3, 151-161.
Sarfraz, M. (1992), Interpolatory rational cubic spline with biased, point and interval tension, Comput Graphics 16(4), 427-430.
Moreton H.P., and Sequin, C.H. (1995), Minimum variation curves and surfaces for computer-aided geometric design, Designing Fair Curves and Surfaces, Nick Sapidis ed., Proc. of SIAM’94 Conference, pp. 123-159.
Sarfraz, M., Butt, S., and Hussain, M.Z. (2001), Visualization of shaped data by a rational cubic spline interpolation, Int J Comput Graphics, Elsevier Science, 25(5), 833-845.
Sarfraz, M. (2000), A rational cubic spline for the visualization of monotonic data, Comput Graphics, 24(4), 509-516.
Sarfraz, M., and Hussain, M.Z. (2006), Data visualization using rational spline inter-polation, Int Computational Appl Math, Elsevier Science, 189(1-2), 513-525.
Sarfraz, M., Hussain, M.Z., and Chaudhry, F.S. (2005), Shape-preserving cubic spline for data visualization, Int J Comput Graphics CAD/CAM, International Scientific, 1(6), 185-194.
Sarfraz, M. (2002), Visualization of positive and convex data by a rational cubic spline, Int J Infor Sci, Elsevier Science,146(1-4), 239-254.
Sarfraz, M. (2002), Modelling for the visualization of monotone data, Int J Modelling Simulation, ACTA Press, 22(3), 176-185.
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(2008). Visualization of Shaped Data by a Rational Cubic Spline. In: Interactive Curve Modeling. Springer, London. https://doi.org/10.1007/978-1-84628-871-5_7
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