RIA: Data Reduction and New Visualization Techniques for Three-Dimensional Data Sets

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This research is concerned with data reduction and general visualization techniques for scalar-valued 3D data sets. Many practical applications deal with 3D data sets where points in space, with associated function values, are given. Such data sets occur in medicine (tomography), geosciences and physical sciences (temperature, pressure, radiation), and several other sciences and disciplines of engineering measurements or mathematical simulations. Generally, such data sets are huge, aggravating the tasks of data storage, interactive data manipulation, and real-time data visualization. Discrete scalar-valued data sets can be reduced by considering derivative information at the given data points. Curvature information of graphs of functions locally approximating the data can be used to define a measure of the significance of single data points can be weighted and removed iteratively form the 3D point set. The proposed methods for 3D points, and 3D retriangulation strategies. The result of reduction algorithm is a data set consisting of scattered 3D points and an associated triangulation (tetrahedra). Common visualization techniques require structured data sets, points typically being organized in a rectilinear ("cuberille") grid. This research will introduce visualization methodologies allowing discretized scalar fields, with arbitrarily located data points, to be rendered.