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Edelsbrunner, Herbert Mucke, Ernst Peter 2011-05-07T13:38:33Z 2011-05-07T13:38:33Z 10000-01-01 1994 "Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the ""shape"" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three-dimensional space. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case." Implementations of the algorithms are discussed, with an emphasis on the robust construction of three-dimensional Delaunay triangulations. A general-purpose programming technique, called Simulation of Simplicity, is used to cope with degenerate input data. This method relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than others. Made available in DSpace on 2011-05-07T13:38:33Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9416411.pdf: 4809473 bytes, checksum: 2b85da150e9fd93a64b69dff9316bacc (MD5) Previous issue date: 1994 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:21Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:26:53-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9416411 (UMI)AAI9416411 http://hdl.handle.net/2142/22398 eng Copyright 1994 Mucke, Ernst Peter Computer Science Shapes and implementations in three-dimensional geometry text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.