For a smooth bounded real algebraic surface in ${\mathbb{R}}^n$, a roadmap of it is a one-dimensional semi-algebraic subset of the surface whose intersection with each connected component of the surface is nonempty and semi-algebraically connected. In this paper, we introduce the notion of a numerical roadmap of a surface, which is a set of disjoint polygonal chains such that there is a bijective map between the chains and the connected components of a given roadmap of the surface. Moreover, the chains are ϵ-close to the connected components. We present an algorithm to compute such a numerical roadmap through constructing a topological graph. The topological graph also enables us to compute an approximate graph and a more intrinsic connectivity graph to represent the roadmap and its connectivity property, which is important for applications such as determining if two points on the surface belong to the same connected component and if so, finding a connected path between them.

对于光滑有界实数代数曲面 ${\mathbb{[R}}^{ñ}$，它的路线图是该表面的一维半代数子集，该子集与该表面的每个已连接组件的交集都是非空的并且是半代数的。在本文中，我们介绍了曲面的数字路线图的概念，该路线图是一组不相交的多边形链，因此在链与曲面的给定路线图的连接组件之间存在双射图。而且，链条是ϵ-靠近连接的组件。我们提出一种通过构造拓扑图来计算此类数字路线图的算法。拓扑图还使我们能够计算一个近似图和一个更内在的连通图，以表示路线图及其连通性，这对于诸如确定曲面上的两个点是否属于同一连接的组件等应用非常重要，在它们之间找到一条连接的路径。