A Dirichlet domain is an array of points with a single source point located in a region. This region is defined such that every point within that region is closest to the source point of that territory than to any other source point. The collection of these regions will tessellate the plane forming Dirichlet tessellations. These tessellations have many applications in a multitude of dierent fields, making them very useful. We can recognize a given tessellation as Dirichlet by investigating the boundary lines, examining the sources within each region in relation to other sources and in several other ways. These ideas form the basic theorems and lemmas that allow us to determine if a tessellation is Dirichlet. This work will explore those theorems and lemmas as well as the definition of Dirichlet tessellation. Then we will examine an algorithm that will allow us to compute a Dirichlet tessellation using nearest neighbor techniques from computer science.
Newsome, Nakesha, "Dirichlet Tessellations" (2016). Senior Independent Study Theses. Paper 7379.
Bachelor of Arts
Senior Independent Study Thesis
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