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Type of Document Thesis Author Womeldorff, Geoffrey URN etd-06282008-165305 Title Spherical Centroidal Voronoi Tessellations: Point Generation and Density Functions via Images Degree Master of Science Department Scientific Computing, Department of Advisory Committee
Advisor Name Title Janet Peterson Committee Co-Chair Max Gunzburger Committee Co-Chair Gordon Erlebacher Committee Member Keywords
- Cvt Scvt Centroidal Voronoi Tessellations Sphere D
Date of Defense 2008-06-14 Availability unrestricted Abstract This thesis presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT). First, we discuss the theory of CVTs in general, and speci cally on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following this, we examine and introduce di erent schemes for creating their input values, known as generators, and compare the e ects of these di erent initial points with respect to their ability to converge and the amount of work required to meet a given tolerance goal. In addition, we describe a method for density functions via images so that we can shape generator density in an intuitive manner and then implement this method with examples to demonstrate it's efficacy.Files
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