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 Title: Numerical variational methods in differential geometry and applications to computer graphics Author(s): Keum, Byoung Joon Doctoral Committee Chair(s): Francis, George K. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: In Chapter 1, we define discrete objects like $\delta$-tangents, $\delta$-normals and $\delta$-curvatures which are analogues of smooth objects in differential geometry. These are incorporated into numerical methods for computer simulation of geometric objects. Some methods to generate geodesic curves on surfaces are discussed.In Chapter 2, we develop several methods to generate approximate models of minimal surfaces, using the tools developed in Chapter 1. Models generated using average methods show quick convergence but some deviations from the actual solution. Normal variation methods require heavier computations, but show less deviation from the actual solution.In Chapter 3, Rubel's Quasi-solution methods are discussed and as applications, methods are developed to find out explicit solutions of partial differential equations defining minimal surfaces and surfaces with restrictions on the man curvature.In Chapter 4, Transversal Scalar Curvature is defined and some relations between scalar curvatures in tangential, transversal and ambient spaces are discussed.The listing of a computer program which demonstrates the methods of Chapter 2 is include in the Appendix. Issue Date: 1989 Type: Text Language: English URI: http://hdl.handle.net/2142/22264 Rights Information: Copyright 1989 Keum, Byoung Joon Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9010915 OCLC Identifier: (UMI)AAI9010915
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