There are many structures, both classical and modern, involving convex polygonal geometries whose deeper understanding would be facilitated through interactive visualizations. The Ipe extensible drawing editor, developed by Otfried Cheong, is a widely used software system for generating geometric figures. One of its features is the capability to extend its functionality through programs called Ipelets. In this media submission, we showcase a collection of new Ipelets that construct a variety of geometric objects based on polygonal geometries. These include Macbeath regions, metric balls in the forward and reverse Funk distance, metric balls in the Hilbert metric, polar bodies, the minimum enclosing ball of a point set, and minimum spanning trees in both the Funk and Hilbert metrics. We also include a number of utilities on convex polygons, including union, intersection, subtraction, and Minkowski sum (previously implemented as a CGAL Ipelet). All of our Ipelets are programmed in Lua and are freely available.

翻译：在凸多边形几何领域，无论是经典还是现代结构中，许多复杂对象都需要通过交互式可视化来加深理解。由Otfried Cheong开发的可扩展绘图编辑器Ipe是一款广泛用于生成几何图形的软件系统，其特色之一是通过名为Ipelets的程序扩展功能。本次媒体投稿中，我们展示了一系列基于多边形几何构造多种几何对象的新型Ipelets插件，包括Macbeath区域、前向与反向Funk距离度量球、Hilbert度量球、极体、点集的最小包围球，以及Funk与Hilbert度量下的最小生成树。此外，我们还提供了若干凸多边形实用工具，包括并集、交集、差集及闵可夫斯基和（此功能此前已作为CGAL Ipelet实现）。所有Ipelets均使用Lua语言编写，并可免费获取。