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oai:www.ideals.illinois.edu:2142/81755 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Edgar A. Ramos Sadri, Bardia 2015-09-25T20:20:18Z 2015-09-25T20:20:18Z 10000-01-01 2006 2006 Specifically, we present an algorithm for homeomorphic reconstruction of surfaces in 3D. This algorithm generalizes to higher dimensions with a slight change in the type of the provided topological guarantee. We also present an algorithm for medial axis approximation that computes a piece-wise linear core for the given sample. This core is guaranteed to be homotopy equivalent to the medial axis of the shape enclosed by the original surface. We then show that the core can be enhanced by any geometric medial axis approximation scheme without compromising the topological equivalence of the output and the medial axis being approximated. Finally, we present an analysis of Herbert Edelsbrunner's well-known WRAP reconstruction algorithm and show that under relative epsilon-sampling in 3D, the output of WRAP is homotopy equivalent to the original shape. Made available in DSpace on 2015-09-25T20:20:18Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3250318.pdf: 5956490 bytes, checksum: 392fac46a6cd3561f4beaca1730c5e70 (MD5) Previous issue date: 2006 Embargo set by: Seth Robbins for item 83036 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 186 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. http://hdl.handle.net/2142/81755 (MiAaPQ)AAI3250318 eng Computer Science Surface and Medial Axis Topology Through Distance Flows Induced by Discrete Samples text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.