Abstract In this paper, a novel anisotropic Voronoi algorithm is presented, along with its implementation and two application cases. In contrast to standard Voronoi tessellations, the proposed algorithm takes into account preferred growth directions, aspect ratios and areas of individual grains. Therefore, an elliptical growth field, which is defined on a per grain basis, is adopted which specifies the time a single grain seed point needs to grow to a specific point in the domain of interest. Grains can be extracted in a grain-conforming or non-grain-conforming manner. The latter case is applicable to simulations in which a predetermined mesh is used, e.g. voxel-mesh based simulations. The extraction can then be done in a straightforward manner. For the former case, a more elaborate extraction algorithm is presented. Finally, the characteristics of the resulting microstructural geometries of two application cases (wire + arc additively manufactured and cast metal microstructure) are studied. A pronounced correspondence with the experimental grain morphology is obtained. This algorithm is highly versatile for generating polycrystalline (metal) microstructures, especially since it closely mimics the underlying solidification process. However, it is more generally applicable to generate an anisotropic tessellation with spatially varying preferential growth directions.

中文翻译：

---

用于生成具有优选生长方向的多晶微结构的各向异性 Voronoi 算法

摘要 本文提出了一种新的各向异性 Voronoi 算法，及其实现和两个应用案例。与标准的 Voronoi 镶嵌相比，所提出的算法考虑了单个晶粒的首选生长方向、纵横比和面积。因此，采用以每粒为基础定义的椭圆生长场，它指定单个粒种子点需要生长到感兴趣域中的特定点所需的时间。谷物可以以符合谷物或不符合谷物的方式提取。后一种情况适用于使用预定网格的模拟，例如基于体素网格的模拟。然后可以以直接的方式进行提取。对于前一种情况，提出了更精细的提取算法。最后，研究了两种应用情况（线材+电弧增材制造和铸造金属微观结构）的所得微观结构几何形状的特征。获得了与实验晶粒形态的明显对应。该算法非常适用于生成多晶（金属）微观结构，特别是因为它密切模拟了潜在的凝固过程。然而，更普遍地适用于生成具有空间变化的优先生长方向的各向异性镶嵌。该算法非常适用于生成多晶（金属）微观结构，特别是因为它密切模拟了潜在的凝固过程。然而，更普遍地适用于生成具有空间变化的优先生长方向的各向异性镶嵌。该算法非常适用于生成多晶（金属）微观结构，特别是因为它密切模拟了潜在的凝固过程。然而，更普遍地适用于生成具有空间变化的优先生长方向的各向异性镶嵌。