The generalised balanced power diagram (GBPD) is regarded in the literature as a suitable geometric model for describing polycrystalline microstructures with curved grain boundaries. This article compiles properties of GBPDs with regard to affine transformations and flat sections. Furthermore, it extends an algorithm known for power diagrams for generating digital images, which is more efficient than the usual brute force approach, on GBPDs.

翻译：广义平衡幂图（GBPD）在文献中被视为描述具有弯曲晶界的多晶微观结构的合适几何模型。本文整理了GBPD在仿射变换和平坦截面方面的性质。此外，本文将一种已知用于幂图生成数字图像的算法推广至GBPD，该算法比通常的暴力方法更为高效。