http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
environment for the visualization of D-dimensional polytopes and algorithms
xii, 107 leaves : illustrations ; 28 cm.
Many open problems and recent algorithms in computational geometry involve hyperplanes, polytopes, and point sets in arbitrary dimensions. Although general E[] computational geometry problems have many applications in computer science, engineering, and mathematics, the confusing nature of the higher dimensions deters many computer scientists from studying these problems. Computer visualizations of formal and mathematical domains are increasingly being used as knowledge enhancement tools. Although a few techniques have been developed to render 4D objects, no models have been proposed for interactive visualization of dimensional objects or algorithms. This thesis presents a model for an E[] visualization tool that allows users to interact extensively with polytopes in E[] and the algorithms that operate on them. The model design incorporates techniques from the recent research area of algorithm animation and techniques generalized from 4D visualization. The model is composed of two main elements: a user interface and a programming interface. A variety of primitive geometric operations allow a user or a programmer to create and manipulate polytopes of any dimension. The programming interface can be used to produce clients: interactive and animated implementations of computational geometry algorithms. A projection of an object in E[] onto a 2D computer monitor necessarily loses depth information along (d-2) axes. Many depth cues, including cross sections, haloing, perspective, and animation, are used to introduce an illusion of depth to the projected images. A new algorithm that produces cross sections of concave polytopes provides the most powerful depth cue for the model. To demonstrate and study the feasibility of the model, a prototype has been developed. The Dimensional Witness (DimWit) was implemented for the Silicon Graphics family of workstations as a library of object-oriented procedures. Experience with several example clients indicates that the prototype contributes to a user's comprehension of the higher dimensions. The use and study of DimWit should determine the utility of the model for teaching and research in computational geometry.