Details:
Title  Certified rational parametric approximation of real algebraic space curves with local generic position method  Author(s)  JinSan Cheng, Kai Jin, Daniel Lazard  Type  Article in Journal  Abstract  Abstract 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 zerodimensional 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 nontrivial examples.  Keywords  Real algebraic space curve, Topology, Complexity, Rational approximation parameterization, Local generic position  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717113000953 
Language  English  Journal  Journal of Symbolic Computation  Volume  58  Number  0  Pages  18  40  Year  2013  Edition  0  Translation 
No  Refereed 
No 
