Spherical Centroidal Voronoi Tessellations: Point Generation and Density Functions via Images

• Other Authors: Womeldorff, Geoffrey A. (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Numerical analysis
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-0843

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 specifically 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 different schemes for creating their input values, known as generators, and compare the effects of these different 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. === A Thesis submitted to the School of Computational Science in partial fulfillment of the requirements for the degree of Master of Science. === Degree Awarded: Summer Semester, 2008. === Date of Defense: June 18, 2008. === Cvt Scvt Centroidal Voronoi Tessellations Sphere D === Includes bibliographical references. === Max Gunzburger, Professor Co-Directing Thesis; Janet Peterson, Professor Co-Directing Thesis; Gordon Erlebacher, Committee Member.