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 <i>C</i>0 continuity between adjacent patches.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OWTU.10012/1039 |
| Date | January 2003 |
| Creators | Ingram, Christopher |
| Publisher | University of Waterloo |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | application/pdf, 1297902 bytes, application/pdf |
| Rights | Copyright: 2003, Ingram, Christopher. All rights reserved. |
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