Tessellating Algebraic Curves and Surfaces Using A-Patches
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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.
Cite this work
Curtis Luk (2008). Tessellating Algebraic Curves and Surfaces Using A-Patches. UWSpace. http://hdl.handle.net/10012/3693