# Visulization of Positive Data Using Modified Quadratic Shepard Method: An Optimum Solution.

Mustafa , Ghulam (2008) Visulization of Positive Data Using Modified Quadratic Shepard Method: An Optimum Solution. PhD thesis, University of Engineering & Technology, Lahore.

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## 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.

Item Type: Thesis (PhD) Visualization, Positive, Data, Modified, Quadratic, Shepard, MQS, Method, Optimum, Solution, business, community Physical Sciences (f) 4033 Mr. Javed Memon 26 Jul 2010 10:18 18 Jul 2011 15:10

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