Tessellating Algebraic Curves and Surfaces Using A-Patches
dc.contributor.author | Luk, Curtis | |
dc.date.accessioned | 2008-05-16 18:43:12 (GMT) | |
dc.date.available | 2008-05-16 18:43:12 (GMT) | |
dc.date.issued | 2008-05-16T18:43:12Z | |
dc.date.submitted | 2008 | |
dc.identifier.uri | http://hdl.handle.net/10012/3693 | |
dc.description.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. | en |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | Spline | en |
dc.subject | Surface | en |
dc.subject | A-Patch | en |
dc.title | Tessellating Algebraic Curves and Surfaces Using A-Patches | en |
dc.type | Master Thesis | en |
dc.pending | false | en |
dc.subject.program | Computer Science | 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 |