This paper presents a new algorithm for computing the topology of an algebraic space curve. Based on an efficient weak generic position-checking method and a method for solving bivariate polynomial systems, the authors give a first deterministic and efficient algorithm to compute the topology of an algebraic space curve. Compared to extant methods, the new algorithm is efficient for two reasons. The bit size of the coefficients appearing in the sheared polynomials are greatly improved. The other is that one projection is enough for most general cases in the new algorithm. After the topology of an algebraic space curve is given, the authors also provide an isotopic-meshing (approximation) of the space curve. Moreover, an approximation of the algebraic space curve can be generated automatically if the approximations of two projected plane curves are first computed. This is also an advantage of our method. Many non-trivial experiments show the efficiency of the algorithm.

中文翻译：

---

实数代数空间曲线的同位素网格划分

本文提出了一种计算代数空间曲线拓扑的新算法。基于有效的弱泛型位置检查方法和求解双变量多项式系统的方法，作者给出了确定性和有效的算法来计算代数空间曲线的拓扑。与现有方法相比，该新算法有效是有两个原因。剪切多项式中出现的系数的位大小大大提高。另一个是对于新算法中的大多数一般情况，一个投影就足够了。在给出了代数空间曲线的拓扑结构之后，作者还提供了空间曲线的同位素网格（近似）。此外，如果首先计算两条投影平面曲线的近似值，则可以自动生成代数空间曲线的近似值。这也是我们方法的优点。许多非平凡的实验证明了该算法的有效性。