Isotopic epsilon-meshing of real algebraic space curves

Based on an efficient generic position checking method and on a method to solve bivariate polynomial systems, we give a new algorithm to compute the topology of an algebraic space curve. Compared to the method presented by the authors, in a joint work with Lazard, the new algorithm is efficient because of two reasons. One is the bitsize of the coefficients that may appear in projections is improved. The other is that one projection is enough for most general case in the new algorithm. We also give an e-meshing of the space curve after we obtain its topology. Many nontrivial experiments show the efficiency of the algorithm.