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|Title:||Degeneracy control in geometric programs|
|Doctoral Committee Chair(s):||Edelsbrunner, Herbert|
|Department / Program:||Computer Science|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
|Rights Information:||Copyright 1990 Rosenberger, Harald|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9026308|