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dc.contributor.authorLuk, Curtis
dc.date.accessioned2008-05-16 18:43:12 (GMT)
dc.date.available2008-05-16 18:43:12 (GMT)
dc.description.abstractThis 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.publisherUniversity of Waterlooen
dc.titleTessellating Algebraic Curves and Surfaces Using A-Patchesen
dc.typeMaster Thesisen
dc.subject.programComputer Scienceen
uws-etd.degree.departmentSchool of Computer Scienceen
uws-etd.degreeMaster of Mathematicsen

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