MSc Thesis

March 28, 2021, at 09:40 AMerika

MSc Thesis: Equal Area Spherical Subdivision

Erika Harrison
University of Calgary, 2012


Numerous subdivision techniques currently aim to attain smoothness of shape. Some extend this to achieve interpolating conditions, while others aim to additionally preserve volume. Perimeters, for closed curves, or surface area, for closed surfaces, has had less exploration, yet it is of great importance to geographics and manufacturing industries. Read more... Particularly with technological advances, and the ability for increased computing power to store and represent the vast data of the Earth's surface, a transition from traditional visualization and analysis approaches - such as the equal area projection described by Snyder - would greatly benefit the cartographic community. An improved integration of visualization with data storage will increase the data that can be analyzed at any given time.

This work, after an initial investigation of traditional projections, and how they may be be improved for visualization purposes, explores the merging of traditional subdivision surfaces with equal area representations. Global as well as local preservations are initially explored on a curve, and then extended to surfaces. Given the requirement of the cartographic community, the problem is simplified to curves that converge to circles, and surfaces that converge to spheres. A limited discussion on extending the approaches to arbitrary shapes is also presented.

Of particular interest, a collection of polyhedral subdivision approaches are tested against the presented equal area subdivision. The results illustrate a variety of issues inherent within unaltered traditional subdivision approaches, and preferential subdivisions. Statistical analysis illustrates a technique which minimizes global area error as compared with the original surface area, or a maximal face distortion of 16%. Future explorations include the extension to arbitrary curves and surfaces, as well as an association of the subdivision surface its regional data.


	author = "Erika Harrison",
	title = "Equal Area Spherical Subdivision",
	institution = "University of Calgary",
	year = "2012"

[pdf] [slides]

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