Under consideration is the problem of reconstruction of a surface of revolution from the boundary curves of its projection. Two approaches to this problem are suggested. The first approach reduces the problem to a system of functional-differential equations. We describe in detail how to obtain this system. The second approach bases on geometrical considerations and uses a piecewiseconic approximation of the desired surface. The second method rests on the auxiliary statement on the 3D reconstruction of a straight circular cone. We give a formula for calculating the base radius of the cone. In the general case, the surface of revolution is approximated by the surface of rotation of some polygonal curve.

中文翻译：

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从投影到旋转曲面的3D重建算法

正在考虑从其投影的边界曲线重建旋转表面的问题。建议了两种解决此问题的方法。第一种方法将问题简化为泛函微分方程组。我们将详细描述如何获得此系统。第二种方法基于几何考虑，并使用所需表面的分段圆锥近似。第二种方法基于关于直圆锥的3D重建的辅助说明。我们给出一个计算圆锥底半径的公式。在一般情况下，旋转表面近似于某些多边形曲线的旋转表面。