Date Approved

12-12-2024

Graduate Degree Type

Project

Degree Name

Applied Computer Science (M.S.)

Degree Program

School of Computing and Information Systems

First Advisor

Christian Trefftz

Academic Year

2024/2025

Abstract

This project delves into computational geometry, a crucial area of computer science, by

implementing algorithms to solve geometric problems using Python libraries like Shapely, SciPy,

and Triangle. It begins with foundational tasks such as creating geometric objects (points, lines,

polygons) and performing operations like calculating distances, intersections, and unions. These

basics lay the groundwork for tackling more advanced applications.

Key implementations include the Convex Hull, which computes the smallest convex

polygon enclosing a set of points, aiding in applications like collision detection and GIS. The

project also explores Voronoi Diagrams, which partition a plane into regions based on proximity,

and their extension into 3D for enhanced versatility.

Using Delaunay Triangulation, the dual of Voronoi diagrams, the project generates

efficient triangular networks critical for terrain modeling and finite element analysis. The Triangle

library is utilized to produce high-quality meshes for computational simulations.

By leveraging the advanced functionalities of SciPy, including linear algebra and Fourier

transforms, the project demonstrates practical applications in robotics, GIS, and scientific

simulations. This work highlights the importance of computational geometry in solving real-world

problems and its impact on fields like engineering, technology, and data analysis.

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