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http://hdl.handle.net/10012/3693
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| Title: | Tessellating Algebraic Curves and Surfaces Using A-Patches |
| Authors: | Luk, Curtis |
| Keywords: | Spline
Surface
A-Patch |
| Approved Date: | 16-May-2008 |
| Date Submitted: | 2008 |
| Abstract: | This work approaches the problem of triangulating algebraic curves/surfaces with a subdivision-style algorithm using A-Patches. An implicit algebraic curve is converted from the monomial basis to the bivariate Bernstein-Bezier basis while implicit algebraic surfaces are converted to the trivariate Bernstein basis. The basis is then used to determine the scalar coefficients of the A-patch, which are used to find whether or not the patch contains a separation layer of coefficients. Those that have such a separation have only a single sheet of the surface passing through the domain while one that has all positive or negative coefficients does not contain a zero-set of the surface. Ambiguous cases are resolved by subdividing the structure into a set of smaller patches and repeating the algorithm.
Using A-patches to generate a tessellation of the surface has potential advantages by reducing the amount of subdivision required compared to other subdivision algorithms and guarantees a single-sheeted surface passing through it. This revelation allows the tessellation of surfaces with acute features and perturbed features in greater accuracy. |
| Program: | Computer Science |
| Department: | School of Computer Science |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/3693 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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