Download or read book A Journey to Low Spherical Discrepancy written by Kejia Wang and published by . This book was released on 2016 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrepancy is a measurement of how uniform a point distribution is. The lower the discrepancy, the more uniform the distribution is. In the d-dimensional unit cube the notion of low discrepancy is well studied, and low discrepancy sequences are well understood. In recent years, this field has been enriched with sophisticated sequence construction techniques using arithmetic curves over finite fields, known as the Niederreiter-Xing method. However, the spherical discrepancy on the 2-dimensional unit sphere remains largely unexplored. In fact, the definition of low spherical discrepancy is not even officially established. Most "well-spaced" spherical sequences found in literature are obtained by lifting well-spaced sequences form the unit square to the sphere via certain maps (for example, the Lambert Transformation). In this thesis, we will investigate direct sequence construction algorithms on the sphere and the related spherical cap discrepancy. The point distribution is done by a greedy algorithm and triangulating the unit sphere. Counting the number of points inside an arbitrary spherical cap remains the challenge.