Univel-based computational geometric modeling using high-dimensional material types with application to Monte Carlo nuclear particle transport

Computer graphics and geometric modeling often use unstructured surface meshes to define objects. This can result in complex, time-expensive calculations to simulate surface interactions when simulating physical processes or rendering images. This thesis describes a computational geometric model based on discrete uniform- volume elements (univels), and applies this approach to well-known problem: using the Monte Carlo method to simulate the transport physics of neutral particles (neu- trons and photons) through complex geometric models.;The most consequential product of this work is Juniper, a comprehensive trans- port modeling software system useful for both practical applications and experimental research in particle transport.;Using a structured Cartesian grid of univels has several promising advantages: tracking particles through a univel grid is known to be much faster than alternative geometries. And univel-based particle tracking is particularly insensitive to the com- plexity of the geometric model. To use these advantages Juniper must rasterize the input model into univels.;Antialiasing is a well-known technique in computer graphics to reduce the visual impact of discretization artifacts. In existing graphics applications this is almost entirely done with three-dimensional color vectors. Juniper is designed to explore antialiasing the geometry univelization, while developing novel ways to cope with high-dimensionality material vectors.;Antialiasing creates blended vectors near high-frequency information areas of the rasterization grid. When the grid is an image the vectors are on a three-dimensional color space and can often be stored and interpreted directly. But for particle transport the univel values are high-dimensionality material vectors. An exact representation of their blended forms yields impractically large model sizes. Instead, these vectors can be quantized to a manageable set of prototype vectors, reducing the univel grid to a table of indices. The quantized material vectors retain the computational advan- tages of univelized particle transport while potentially improving the fidelity of the transport results.;Exploring this problem has provided new insights into digitization of high- dimensional values, effects of univel size on transport result accuracy, and the an- tialiasing of high-dimensional vector spaces. A new library of carefully defined high- precision cargo object models in a universal format (XML) is another result.