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| Volume 2, Number 2, May 2006, pp. 289-317 | ||||||||
| Wei Zhang, Yong Wang, Shu-Cherng Fang and John E. Laver | ||||||||
| Key words: | ||||||||
| bivariate cubic L1 spline, geometric programming, rHCT element, triangulated irregular networks | ||||||||
| Mathematices Subject Classification: 65D07, 65D05, 65K05, 90C30 | ||||||||
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| Abstract: | |||
| Bivariate cubic L1 interpolating splines, which have previously been implemented with Sibson elements on rectangular grids, are implemented with reduced Hsieh-Clough-Tocher (rHCT) elements on triangulated irregular networks (TINs). The calculation of coefficients of a bivariate cubic L1 spline, which minimizes the L1 norm of its second derivatives, turns out to be a nonsmooth convex programming problem. In a generalized geometric programming framework, the dual problem has a linear objective function and convex cubic constraints. The coefficients of an L1 spline can be obtained by solving the dual problem and then converting to a primal solution using a linear programming transformation. Our preliminary computational results show that cubic L1 splines on TINs are flexible and capable of providing interpolation with excellent shape preservation. | |||
| Cubic L1 splines on triangulated irregular networks | ||
| Special Issue of ICOTA6 | ||