Date: | January 28th |
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Location: | DC 2314 |
Time: | 1:30 |
Chair: | Andrea Bunt |
Date: | February 4th | February 11th | February 18th | February 25th |
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Location: | DC 1331 1:30 | DC 1331 1:30 | DC 1331 1:30 | DC 1331 1:30 | Chair: | Bill Cowan |
Gabriel Esteves |
Elodie Fourquet |
Richard Fung |
Technical Presentation: | Cam Zwarich |
Andrea Bunt |
Bill Cowan |
Gabriel Esteves |
Stephen Mann |
Title : Tessellating Algebraic Curves and Surfaces Using A-Patches
Abstract: This work approaches the problem of triangulating algebraic curves and surfaces with a subdivision-style algorithm using A-patches. An algebraic curve or surface is converted from the monomial basis to the Bernstein-B\'ezier basis over a simplex. If the coefficients are all positive or all negative, then the curve or surface does not pass through the domain simplex. If the scalar Bernstein coefficients are of mixed sign and have a layer separating the positive from the negative, then the patch is in A-patch format and can be efficiently tessellated. Cases of mixed sign without a separating layer 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 the advantage of reducing the amount of subdivision required. And because of the A-patch properties, we are guaranteed that features within the designated region will not be missed. |
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