2026-09-21T06:34:50Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/21633 2023-07-10 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

http://hdl.handle.net/2142/21633 eng Copyright 1996 Waupotitsch, Roman AAI9712479 (UMI)AAI9712479 Edelsbrunner, Herbert Waupotitsch, Roman 2011-05-07T13:14:31Z 2011-05-07T13:14:31Z 10000-01-01 1996 This thesis consists of three parts. In the first part we study the maintenance of a simplicial grid under changing density requirements. The proposed method works in any fixed dimension and generates grids by projecting cross-sections of a monotone simplicial complex that lives in one dimension higher than the grid. The density of the grid is adapted by locally moving the cross-section up or down along the extra dimension. In the method was implemented for grids in two and three dimensions. In the second part we show an application of monotone simplicial complexes to the problem of constructing cartograms. In the third part we describe an algorithm that constructs homeomorphisms with prescribed area distortion. Such homeomorphisms can be used to generate cartograms, which are geographic maps purposely distorted so its area distribution reflects a variable different from area, as for example population density. The algorithm generates the homeomorphism through a sequence of local piecewise linear homeomorphic changes. Sample results are included. Made available in DSpace on 2011-05-07T13:14:31Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712479.pdf: 4042137 bytes, checksum: 25f2231d9c144cdf0623b78b6f83fd6b (MD5) Previous issue date: 1996 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:52:10Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:23:59-05:00 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 9780591199611 Computer Science Simplifying and deforming through hierarchies of simplicial grids text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.