Homogenization-based topology optimization has been shown to be effective but does not directly create mechanical structures. Instead, the method gives a multi-scale description of the optimized design, e.g., lamination thicknesses and directions. To obtain a realizable single-scale design, one can perform a subsequent de-homogenization step. This is done by converting the lamination directions to integrable vector fields from which it is possible to compute a parameterization of the domain. Unfortunately, however, singularities often make it impossible to find integrable vector fields that align with lamination directions. We present a short introduction to homogenization-based topology optimization followed by an overview of different types of singularities and how they impinge on the problem. Based on this, we propose a singularity aware de-homogenization pipeline, where we use a method for vector field combing which produces consistent labeling of the lamination directions but also introduces necessary seams in the domain. We demonstrate how methods from computer graphics can subsequently be used to compute the final parameterization from which the mechanical structure can easily be extracted. We demonstrate the method on several test cases.

基于均质化的拓扑优化已被证明是有效的，但不能直接创建机械结构。相反，该方法给出了优化设计的多尺度描述，例如，层压厚度和方向。为了获得可实现的单尺度设计，可以执行后续的去均质化步骤。这是通过将层叠方向转换为可积分矢量场来完成的，可以从中计算出域的参数化。然而，不幸的是，奇异性常常使得不可能找到与层叠方向对齐的可积矢量场。我们简要介绍了基于均质化的拓扑优化，然后概述了不同类型的奇点及其对问题的影响。基于此，我们提出了一种奇异性感知去均质化管道，其中我们使用了一种矢量场梳理方法，该方法不仅可以产生一致的层压方向标记，还可以在域中引入必要的接缝。我们演示了如何将计算机图形学中的方法随后用于计算最终参数化，从而可以轻松地提取机械结构。我们在几个测试案例上演示该方法。