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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|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|
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