Aaron Hall PhD Comprehensive Exam presentation
- Wednesday, November 18, 2015 from 10:00am to 11:00am
- Barnard Hall, Computer Science Conference Room - view map
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 (neutrons and photons) through complex geometric models.
Typically these transport calculations take place on unstructured surface meshes. Using instead a structured Cartesian grid of univels has several promising advantages. Calculating particle-surface intersections is computationally expensive and occupies a large fraction of the time for nonunivel particle transport programs. In contrast tracking particles through a univel grid is known to be much faster. Secondly, univel-based particle tracking is highly insensitive to the complexity of the geometric model, unlike surface-based models.
Univel-based particle transport was originally developed for application to models generated from medical scan data, which are inherently structured grids. But by applying common rasterization techniques to other forms of geometric models they can be converted to a univel grid. Rasterizing an existing model presents a tradeoff: the univel grid must be fine enough to accurately support the particle transport physics, while keeping the grid small enough for the sake of the calculations’ efficiency. What’s more, discretization of continuous functions raises the problem of aliasing: model features with sizes similar to the univel grid’s spacing will be significantly distorted or even disappear altogether when rasterized. Antialiasing is a well-known technique in computer graphics to reduce the visual impact of discretization artifacts. However, in existing graphics applications this is almost entirely done with low-dimensionality color vectors. Juniper is designed to explore using similar methods to antialias the geometry univelization, while developing novel ways to cope with higher-dimensionality material vectors.
If a raster grid is thought of as a Cartesian grid of vectors, antialiasing creates “blended” vectors near high-frequency information areas of the 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 would yield impractically large model sizes and would be incompatible with some of the transport calculations. Instead, these vectors can be quantized to a manageable set of prototype vectors, reducing the univel grid to a table of indices reminiscent of the palletized color schemes used in some image file formats. The quantized material vectors retain the computational advantages of univelized particle transport while potentially improving the fidelity of the transport results.
There are multiple dimensions of tradeoffs inherent in this process: rasterizing a geometric model takes time and the resulting univel grid has a larger storage requirement, but the transport calculations are faster. Antialiased rasterization, especially including quantization, is even slower but the resulting grid can be shown in various instances to have better fidelity to the original model and introduce fewer artifacts into the transport results. Domain-specific similarity measures can improve this fidelity beyond naïve quantization. The more complex the underlying geometry being modeled, the more significant these effects can be. Exploring this problem has provided new insights into digitization of high-dimensional values, effects of univel size on transport result accuracy, and the antialiasing of high-dimensional vector spaces. A new library of carefully defined high-precision cargo object models in a universal format (XML) is another result. Likely the most consequential product of this work is Juniper—a comprehensive transport modeling software system combining aspects of computer science, physics, and mathematics useful for both practical applications and experimental research in particle transport.