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

本研究关注标量值三维数据集的数据约简和通用可视化技术。许多实际应用处理三维数据集，其中空间中的点具有相关的函数值。这样的数据集出现在医学（断层扫描）、地球科学和物理科学（温度、压力、辐射）以及其他一些科学和学科的工程测量或数学模拟中。通常，这样的数据集是巨大的，加重了数据存储、交互式数据操作和实时数据可视化的任务。通过考虑给定数据点上的导数信息，可以简化离散的标量值数据集。局部逼近数据的函数图的曲率信息可以用来定义单个数据点的重要性度量，可以从三维点集中迭代地加权和去除。提出了三维点的定位方法，以及三维再测量策略。约简算法的结果是由分散的三维点和相关的三角形（四面体）组成的数据集。常见的可视化技术需要结构化的数据集，点通常被组织在一个直线（“立方体”）网格中。这项研究将引入可视化方法，允许离散的标量场，任意位置的数据点，呈现。

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.