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Title of Thesis

Visualization of Positive Data Using Modified Quadratic Shepard Method: An Optimum Solution

Author(s)

Ghulam Mustafa

Institute/University/Department Details
Department of Computer Science & Engineering / University of Engineering & Technology, Lahore
Session
2008
Subject
Computer Science
Number of Pages
121
Keywords (Extracted from title, table of contents and abstract of thesis)
Visualization, Positive, Data, Modified, Quadratic, Shepard, MQS, Method, Optimum, Solution, business, community

Abstract
Many methods arc available to construct the models from data sets that arc sampled on scattered grid. For Scattered data, the inverse distance weighted methods are considered better due to their efficiency, extendibility to higher dimensions, global in nature and ease in implementation. Modified Quadratic Shepard (MQS) method, being smooth with C' continuity, is a commonly used method in the field of science and engineering such as geophysics, astronomy and meteorology. The method is available with many libraries and visualization environments such as Numerical Analysis Group (NAG) and FORTRAN and Surfer 8. However, it has problem that being a C' continuous method it interpolates values extending beyond the inherently limits of the data, which is sometimes meaningless for scientific and business community. So it is not suitable for applications where there is some inherent constraint on value of data. Examples of such value constraints arc non negativity, upper and/or lower bounds, and more general constraint defined by a function. Such constraints commonly arise in science and engineering applications. Non-negativity (for simplicity we use the term positivity to mean non- negativity) is a special case of the generalized bounds preserving problem. Positivity of data is commonly encountered in science, engineering and business. The significance of positivity lies in the fact that sometimes it does not make sense to talk of some quantity to be negative. For example the quantities like mass, volume, density, absolute temperate & pressure, radiation dose, number of persons, chemical concentration, hydraulic conductivity and porosity are meaningless when negative.
In this thesis we formulate five methods, based on the MQS method, to preserve the arbitrary lower and upper bounds of data and fulfilling various requirements of Visualizations and other applications such as efficiency, accuracy, continuity, case in implementation, extendibility to higher dimensionality and gradient estimation etc. All these constrained interpolation functions are C continuous. An optimum solution having most of the above given required characteristics for different sizes and dimensionality of data has been identified.

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8,509 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

viii
298 KB
2

1

INTRODUCTION 1
802 KB
3 2 RESEARCH CONTEXT 10
1,986 KB
4 3 CONSTRAINT MODELING USING MQS METHOD 37
2,195 KB
5 4 IMPROVING ACCURACY OF CONSTRAINED MQS METHOD 53
1,142 KB
6 5 EMPIRICAL CONSTRAINED SHEPARD METHOD 72
532 KB
7 6 IMPLEMENTATION, TESTING AND AN OPTIMAL SOLUTION 81
1,262 KB
8 7 CONCLUSIONS AND FUTURE WORK 100
112 KB
9 8 REFERENCES 102
497 KB