{"title":"Monotone Rational Trigonometric Interpolation","authors":"Uzma Bashir, Jamaludin Md. Ali","volume":86,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":295,"pagesEnd":298,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9997419","abstract":"

This study is concerned with the visualization of monotone data using a piecewise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and othertwo are leftfree. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves.<\/p>\r\n","references":" M. Grave, Y. L. Lous and W. T. Hewittm, Visualization in Scienti\ufb01c\r\nComputing, Springer-Verlag, Vol. 199, 1994.\r\n M. Z. Hussain and M. Hussain, Visualization of data preserving\r\nmonotonicity, Applied Mathematics and Computation, 2007, pp.\r\n1353\u20131364.\r\n M. Z. Hussain and M. Sarfraz, Monotone piecewise rational cubic\r\ninterpolation, International Journal of Computer Mathematics, Vol. 86,\r\n2009, pp. 423\u2013430.\r\n X. Han, Quadratic trigonometric polynomial curves with a shape\r\nparameter, Computer Aided Geometric Design, vol. 19, 2002, pp.\r\n503\u2013512.\r\n X. Han, Cubic trigonometric polynomial curves with a shape parameter,\r\nComputer Aided Geometric Design, vol. 21, 2004, pp. 535\u2013548.\r\n X. Wu, X. Han and S. Luo, Quadratic trigonometric spline curves\r\nwith multiple shape parameters, 10th IEEE International Conference on\r\nComputer-Aided Design and Computer Graphics, 2007 , pp. 413\u2013416.\r\n N. Choubey and A. Ojha, Trigonometric splines with variable shape\r\nparameter, Journal of Mathematics, vol. 38, 2008. pp. 91-105.\r\n M. Sarfraz, S. Butt and M. Z. Hussain, Visualization of shaped data\r\nby a rational cubic spline interpolation, Computers & Graphics, Vol. 25,\r\n2001, pp. 833\u2013845.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 86, 2014"}