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| Title: | A Geometric B-Spline Over the Triangular Domain |
| Authors: | Ingram, Christopher |
| Keywords: | Computer Science
geometric design
b-spline
triangular surfaces |
| Approved Date: | 2003 |
| Date Submitted: | 2003 |
| Abstract: | For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular.
The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains?
In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing C0 continuity between adjacent patches. |
| Department: | School of Computer Science |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/1039 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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