We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles, ellipses, crosses, multiply connected domains and even to the cardioid. For many of the cases that we have studied no previous result was available. The fundamental idea in our approach is the introduction of "image" disks, which allows one to work with a fixed container, thus lifting the limitations of the packing algorithms of \cite{Nurmela97,Amore21,Amore23}. We believe that the extension of our algorithm to three (or higher) dimensional containers (not considered here) can be done straightforwardly.

翻译：我们描述了一种算法，能够在二维或更高维度的任意域中实现多个全等圆盘的密集堆积配置。我们将该算法应用于大量二维域，如矩形、椭圆、十字形、多连通域乃至心形域。在我们研究的许多案例中，此前尚无可用结果。该方法的核心思想是引入"镜像"圆盘，从而能够使用固定容器，突破了\cite{Nurmela97,Amore21,Amore23}中堆积算法的限制。我们相信，该算法向三维（或更高维）容器（本文未涉及）的扩展可以直接实现。