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W2198337273 abstract "We tackle in this thesis the problem of computing the topology of plane algebraic curves. We present an algorithm that avoids special treatment of degenerate cases, based on algebraic tools such as Grobner bases and rational univariate representations. We implemented this algorithm and showed its performance by comparing to similar existing programs. We also present an output-sensitive complexity analysis of this algorithm. We then discuss the tools that are necessary for the implementation of non-linear geometric algorithms in CGAL, the reference library in the computational geometry community. We present an univariate algebraic kernel for CGAL, a set of functions aimed to handle curved objects defined by univariate polynomials. We validated our approach by comparing it to other similar implementations." @default.
W2198337273 created "2016-06-24" @default.
W2198337273 creator A5066130387 @default.
W2198337273 date "2010-12-03" @default.
W2198337273 modified "2023-09-23" @default.
W2198337273 title "Non-linear computational geometry for planar algebraic curves" @default.
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