Entropy guided visualization and analysis of multivariate spatio-temporal data generated by physically based simulation

Official URL: http://risc01.sabanciuniv.edu/record=b1534391 (Table of Contents)

Flow fields produced by physically based simulations are subsets of multivariate spatiotemporal data, and have been in interest of many researchers for visualization, since the data complexity makes it difficult to extract representative views for the interpretation of fluid behavior. In this thesis, we utilize Information Theory to find entropy maps for vector flow fields, and use entropy maps to aid visualization and analysis of the flow fields. Our major contribution is to use Principal Component Analyses (PCA) to find a projection that has the maximal directional variation in polar coordinates for each sampling window in order to generate histograms according to the projected 3D vector field, producing results with fewer artifacts than the traditional methods. Entropy guided visualization of different data sets are presented to evaluate proposed method for the generation of entropy maps. High entropy regions and coherent directional components of the flow fields are visible without cluttering to reveal fluid behavior in rendered images. In addition to using data sets those are available for research purposes, we have developed a fluid simulation framework using Smoothed Particle Hydrodynamics (SPH) to produce flow fields. SPH is a widely used method for fluid simulations, and used to generate data sets that are difficult to interpret with direct visualization techniques. A moderate improvement for the performance and stability of SPH implementations is also proposed with the use of fractional derivatives, which are known to be useful for approximating particle behavior immersed in fluids.