Dissertation/Thesis Abstract

Computational techniques to enable visualizing shapes of objects of extra spatial dimensions
by Black, Don Vaughn, II, Ph.D., University of California, Irvine, 2010, 182; 3412348
Abstract (Summary)

Envisioning extra dimensions beyond the three of common experience is a daunting challenge for three dimensional observers. Intuition relies on experience gained in a three dimensional environment. Gaining experience with virtual four dimensional objects and virtual three manifolds in four-space on a personal computer may provide the basis for an intuitive grasp of four dimensions.

In order to enable such a capability for ourselves, it is first necessary to devise and implement a computationally tractable method to visualize, explore, and manipulate objects of dimension beyond three on the personal computer. A technology is described in this dissertation to convert a representation of higher dimensional models into a format that may be displayed in realtime on graphics cards available on many off-the-shelf personal computers. As a result, an opportunity has been created to experience the shape of four dimensional objects on the desktop computer.

The ultimate goal has been to provide the user a tangible and memorable experience with mathematical models of four dimensional objects such that the user can see the model from any user selected vantage point.

By use of a 4D GUI, an arbitrary convex hull or 3D silhouette of the 4D model can be rotated, panned, scrolled, and zoomed until a suitable dimensionally reduced view or Aspect is obtained. The 4D GUI then allows the user to manipulate a 3-flat hyperplane cutting tool to slice the model at an arbitrary orientation and position to extract or "pluck" an embedded 3D slice or "aspect" from the embedding four-space. This plucked 3D aspect can be viewed from all angles via a conventional 3D viewer using three multiple POV viewports, and optionally exported to a third party CAD viewer for further manipulation.

Plucking and Manipulating the Aspect provides a tangible experience for the end-user in the same manner as any 3D Computer Aided Design viewing and manipulation tool does for the engineer or a 3D video game provides for the nascent student.

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Indexing (document details)
Advisor: Jenks, Stephen
Commitee: Gajski, Daniel, Lang, Tomas
School: University of California, Irvine
Department: Electrical and Computer Engineering - Ph.D.
School Location: United States -- California
Source: DAI-B 71/08, Dissertation Abstracts International
Subjects: Electrical engineering, Theoretical physics, Computer science
Keywords: Computer graphics, Dimensional morphology, Extra dimensions, Relativity, Visualization
Publication Number: 3412348
ISBN: 978-1-124-10415-7
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