Publication Date

2019

Document Type

Dissertation/Thesis

First Advisor

Wang, Ziteng

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Industrial and Systems Engineering

Abstract

The past two decades have seen the development of L1 splines for interpolation and approximation of geometric data. L1 splines have been shown to preserve shapes better than the conventional L2 splines, especially for data with abrupt changes in the magnitude of spacing. Efficient computation plays an important role in the practical application of L1 splines. This thesis creates new computational methods for constructing bicubic L1 interpolating splines and bicubic L1 spline fits. The bicubic splines in this study are piecewise bicubic polynomials defined on a rectangular grid generated by the tensor product of nodes. We developed a hybrid computational method for bicubic L1 interpolating splines that calculates the first-order partial derivatives at the nodes by the univariate 5-point window algorithm and computes the cross partial derivatives by solving an optimization problem. For bicubic L1 splines fits, the existing gradient search method is made significantly more efficient by utilizing the local relation between data points and spline nodes. Further, domain decomposition method is used for computation on larger grids.

Extent

53 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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