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https://hdl.handle.net/2142/19896
Description
Title
Visualization and modeling with shape
Author(s)
Moran, Patrick Joseph
Issue Date
1996
Doctoral Committee Chair(s)
Edelsbrunner, Herbert
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
We present scientific visualization techniques where our goal is to strike a better balance between the qualitative information provided by images and the quantitative measures often sought by scientists. Our particular emphasis is on defining, manipulating, and measuring shape. We begin by presenting two novel applications based on alpha shapes for 2-dimensional finite point sets. In the first application we analyze the results from Path Integral Monte Carlo simulations of particles at extremely low temperatures. In our second new application, we investigate the use of a concept closely related to alpha shapes, the area of a union of disks, as a technique for estimating the fractal dimension of a point set.
"We turn next to a more general, flexible system for modeling and visualizing shape which we call the shape calculator. As with alpha shapes, we start with a finite point set S, and we construct the Delaunay triangulation, ${\cal D}(S).$ The triangulation decomposes the space into simplicial ""building blocks"": triangles, edges and vertices in our 2-dimensional implementation. Unlike alpha shapes, we can choose arbitrary subsets of the simplices in ${\cal D}$ to represent shapes. The interface of the calculator consists of a graphical display and an interpreted language supporting the interactive specification and manipulation of shapes. The language contains features inspired by computer aided geometric design as well as by algebraic topology. The language also includes support for programming constructs, such as user function definition. We present numerous examples illustrating the flexibility and potential of our system."
Following our shape calculator exposition, we consider the case where the original data are in the form of a gray-scale image rather than a finite point set. We present a technique for defining a point set S based on the image, allowing us ultimately to represent and manipulate image shapes from within the calculator. We conclude with some thoughts on how our techniques, which we have implemented for data in 2-dimensional space, would generalize to three dimensions.
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