Simplifying and Deforming Through Hierarchies of Simplicial Grids

University of Illinois at Urbana-Champaign, 1996 - 176 Seiten
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Abstract: "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. 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."

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