Extrusion-based printing frequently requires a hollowing step to remove material from inside of artifacts and subsequently reduce the amount of material, printing time, product weight, energy consumption, and ultimately, the cost. Here, we introduce a novel support-free hollowing method that uses an arrangement of vertically-aligned prolate spheroids. In addition to reducing stress concentration through their inherently smooth boundaries, these spheroids require no additional support structure, when properly designed. Additionally, the resulting spheroidal hollows facilitate the circular printing motion of extruders using G2/G3-codes, which provide three critical advantages compared to the currently popular G1-code-based linear motion: shorter printing time, better printing quality, and smaller tool path file. Here, spheroids are arranged by the Voronoi diagram of 3D ellipsoids and the tool path, including circular printing motions, is produced using the Voronoi diagram of circular 2D disks. The proposed algorithms are implemented as the $\mathtt{HollowTron}$ webserver and are freely available from Voronoi Diagram Research Center.

基于挤出的打印通常需要一个中空步骤，以从工件内部除去材料，并随后减少材料的数量，打印时间，产品重量，能耗以及最终的成本。在这里，我们介绍了一种新颖的无支撑空心方法，该方法使用了垂直对齐的扁球体的排列。这些球体除了通过其固有的平滑边界减小应力集中外，在进行适当设计时也不需要其他支撑结构。此外，所得的球形空心有助于使用G2 / G3代码的挤出机进行圆形印刷运动，与当前流行的基于G1代码的线性运动相比，它提供了三个关键优势：印刷时间短，印刷质量更好，工具路径更短文件。这里，球体通过3D椭圆的Voronoi图进行排列，而刀具路径（包括圆形打印运动）是使用圆形2D圆盘的Voronoi图生成的。所提出的算法实现为$\mathtt{空心龙}$ Web服务器，可从Voronoi Diagram Research Center免费获得。