dc.contributor.author | Ingram, Christopher | en |
dc.date.accessioned | 2006-08-22 14:23:37 (GMT) | |
dc.date.available | 2006-08-22 14:23:37 (GMT) | |
dc.date.issued | 2003 | en |
dc.date.submitted | 2003 | en |
dc.identifier.uri | http://hdl.handle.net/10012/1039 | |
dc.description.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 <i>C</i>0 continuity between adjacent patches. | en |
dc.format | application/pdf | en |
dc.format.extent | 1297902 bytes | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.rights | Copyright: 2003,
Ingram, Christopher. All rights reserved. | en |
dc.subject | Computer Science | en |
dc.subject | geometric design | en |
dc.subject | b-spline | en |
dc.subject | triangular surfaces | en |
dc.title | A Geometric B-Spline Over the Triangular Domain | en |
dc.type | Master Thesis | en |
dc.pending | false | en |
uws-etd.degree.department | School of Computer Science | en |
uws-etd.degree | Master of Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |