Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6861258 | Journal of Symbolic Computation | 2013 | 23 Pages |
Abstract
In this paper, an algorithm is given for determining the topology of an algebraic space curve and to compute a certified G1 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.
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Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Jin-San Cheng, Kai Jin, Daniel Lazard,