The problem of building 3D models of various types of topological surfaces aimed at their visualization is considered. Up-to-date 3D graphics language (Open GL, VRML, Java3D, etc.) allow users to represent any spatial surface as a polygon mesh approximating the surface. A general approach to generating the mesh is described, where coordinate values of the polygon vertices are calculated with a regular algorithm. Most topological surfaces have peculiar points where a special algorithm has to be applied. The following problems are discussed in the paper: what types of the peculiar points exist; how many of them are on surfaces of various type; how to reduce their number and how to change the regular algorithm in their neighborhood. The paper is illustrated with screen images of typical models such as sphere, torus, hyperboloids, Klein's bottle, etc.
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