Derived and implemented a compact representation for objects defined by Boolean operations of implicit surfaces. This representation provides a reduced memory footprint and supports algorithms for rapidly evaluating the point inside/outside predicates.Applied advanced techniques from computational topology and numeric computational geometry to create a topologically consistent algorithm that ensures robust particle tracking in physical simulations without the need for exact arithmetic. The improved tracking algorithm was applied to a Monte Carlo radiation transport simulation and resulted in shorter simulation times with fewer lost particles, even for extremely complex model geometries.Designed and implemented algorithms for computing and modifying geometric properties (such as bounding boxes, volume, etc.) for constructive solid geometry (CSG) representations used for solving the transport equation.

Developed and implemented practical and exact geometric algorithms that are robust to numerical inaccuracies by treating precision as a limited resource. Some applications include physical simulation, constructive solid geometry (CSG), image processing, post office queries, k-nearest neighbor queries for crystallographic symmetry groups, surface simplification of irregular terrain data and data structures for streaming input. Member of the Computational Geometry Group.

Topics included: programming, data analysis and visualization, and algorithm design and implementation using MATLAB. Designed: Syllabus, Lectures, Assignments and Exams. Instructor rating 5/5, Course rating 4.5/5.