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Geometric Modeling and Algebraic Geometry
In this paper, we describe a subdivision method for handling algebraic implicit curves in 2d and 3d. We use the representation of polynomials in the Bernstein basis associated with a given box, to check if the topology of the curve is determined inside this box, from its points on the border of the box. Subdivision solvers are used for computing these points on the faces of the box, and segments joining these points are deduced to get a graph isotopic to the curve. Using envelop of polynomials,doi:10.1007/978-3-540-72185-7_11 fatcat:wf3goegqajgefcwjroi6xwtd7y