Publication Date


Advisor(s) - Committee Chair

Dr. Uta Ziegler (Director), Dr. Claus Ernst, Dr. Rong Yang

Degree Program

Department of Computer Science

Degree Type

Master of Science


Algorithms to generate walks (chains of unit-length, freely-jointed segments) and polygons (closed walks) in spherical confinements have been developed in the last few years. These algorithms generate polygons inside spherical confinement based on their mathematically derived probability distributions. The generated polygons do not occupy any volume { although that would be useful for some applications. This thesis investigates how to generate walks and polygons which occupy some volume in spherical confinement. More specifically, in this thesis, existing methods described in the literature have been studied and implemented to generate walks and polygons in confinement. Additionally, these methods were adapted to design, develop, and implement an algorithm which generates walks and polygons in confinement with thick segments, that is, segments which occupy volume. Data is collected by generating walks and polygons of different lengths with and without thickness inside the spherical confinements of various radii to compare walks and polygons with thickness with those generated without thickness. The analysis of the collected data shows that a. the newly developed algorithm indeed generates polygons which are thicker than those generated with the volumeless algorithm; and b. the newly developed algorithm generates polygons which are different from the polygons generated by the volumeless algorithm. The analysis also includes an assessment of the computational cost of generating thick polygons.


Computer Sciences | Physics