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- W4300551073 abstract "Given a real valued function f(X,Y), a box region B_0 in R^2 and a positive epsilon, we want to compute an epsilon-isotopic polygonal approximation to the restriction of the curve S=f^{-1}(0)={p in R^2: f(p)=0} to B_0. We focus on subdivision algorithms because of their adaptive complexity and ease of implementation. Plantinga and Vegter gave a numerical subdivision algorithm that is exact when the curve S is bounded and non-singular. They used a computational model that relied only on function evaluation and interval arithmetic. We generalize their algorithm to any bounded (but possibly non-simply connected) region that does not contain singularities of S. With this generalization as a subroutine, we provide a method to detect isolated algebraic singularities and their branching degree. This appears to be the first complete purely numerical method to compute isotopic approximations of algebraic curves with isolated singularities." @default.
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- W4300551073 date "2011-02-26" @default.
- W4300551073 modified "2023-09-30" @default.
- W4300551073 title "Complete Subdivision Algorithms, II: Isotopic Meshing of Singular Algebraic Curves" @default.
- W4300551073 doi "https://doi.org/10.48550/arxiv.1102.5463" @default.
- W4300551073 hasPublicationYear "2011" @default.
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