Shape-preserving curve interpolation
نویسندگان
چکیده
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. This work is a contribution towards the graphical display of 2D data when they are convex, monotone and positive. A piecewise rational function in a cubic/cubic form is proposed, which, in each interval, involves four free parameters in its construction. These four free parameters have a direct geometric interpretation, making their use straightforward. Illustrations of their effect on the shape of the rational function are given. Two of these free parameters are constrained to preserve the shape of convex, monotone and positive data, while the other two parameters are utilized for the modification of positive, monotone and convex curves to obtain a visually pleasing curve. The problem of shape preservation of data lying above a line is also discussed. The method that is presented applies equally well to data or data with derivatives. The developed scheme is computationally economical and pleasing. The error of rational interpolating function is also derived when the arbitrary function being interpolated is C 3 in an interpolating interval. The order of approximation is O(h 3 i).
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ورودعنوان ژورنال:
- Int. J. Comput. Math.
دوره 89 شماره
صفحات -
تاریخ انتشار 2012