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TitleCertified rational parametric approximation of real algebraic space curves with local generic position method
Author(s) Jin-San Cheng, Kai Jin, Daniel Lazard
TypeArticle in Journal
AbstractAbstract In this paper, an algorithm is given for determining the topology of an algebraic space curve and to compute a certified G 1 rational parametric approximation of the algebraic space curve. The algorithm works by extending to dimension one the local generic position method for solving zero-dimensional polynomial equation systems. Here, certified means that the approximation curve and the original curve have the same topology and their Hausdorff distance is smaller than a given precision. The main advantage of the algorithm, inherited from the local generic position method, is that the topology computation and approximation for a space curve are directly reduced to the same tasks for two plane curves. In particular, an error bound of the approximation space curve is deduced explicitly from the error bounds of the approximation plane curves. The complexity of the algorithm is also analyzed. Its effectivity is shown on some non-trivial examples.
KeywordsReal algebraic space curve, Topology, Complexity, Rational approximation parameterization, Local generic position
URL http://www.sciencedirect.com/science/article/pii/S0747717113000953
JournalJournal of Symbolic Computation
Pages18 - 40
Translation No
Refereed No