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https://hdl.handle.net/2142/22735
Description
Title
Degeneracy control in geometric programs
Author(s)
Rosenberger, Harald
Issue Date
1990
Doctoral Committee Chair(s)
Edelsbrunner, Herbert
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
Degenerate geometric data (e.g., three points on a line, four points on a circle) is known to create all sorts of special cases, some easy and some complicated, that have to be considered in implementations of geometric algorithms. Traditionally, the designers of algorithms coped with these difficulties by assuming special cases away, and left it to the unfortunate implementer to deal with data that would not satisfy the assumption.
This thesis discusses several issues related to the phenomenon of degeneracy itself, and a symbolic perturbation scheme that allows programs to work on degenerate data as if it were nondegenerate. The topics covered are the likelihood of a special case, the computational overhead induced by the symbolic perturbation scheme and ways to reduce it, examples of applications, extensions and modifications of the scheme.
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