We consider the problem of approximating given shapes so that the surface normals are restricted to a prescribed discrete set. Such shape approximations are commonly required in the context of manufacturing shapes. We provide an algorithm that first computes maximal interior polytopes and, then, selects a subset of offsets from the interior polytopes that cover the shape. This provides prescribed Hausdorff error approximations that use only a small number of primitives.

中文翻译：

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PolyCover：具有离散表面方向的近似形状

我们考虑逼近给定形状的问题，以便将表面法线限制在规定的离散集合中。在制造形状的上下文中通常需要这种形状近似。我们提供了一种算法，该算法首先计算最大内部多面体，然后从覆盖形状的内部多面体中选择偏移量的子集。这提供了仅使用少量基元的规定 Hausdorff 误差近似值。