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.
Some files may require a special program or browser plug-in. More Information
|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|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
supplemental files is subject to the ProQuest Terms and Conditions of use.