凸多边形几何的 Ipelets
Ipelets for the Convex Polygonal Geometry
AI总结：
本提交介绍了一组新的 Ipelets，用于在 Ipe 编辑器中构造凸多边形几何对象，如 Macbeath 区域、度量球、极体、最小包围球及最小生成树，并提供多边形运算工具，全部用 Lua 实现且免费可用。
摘要：
有许多经典和现代的结构涉及凸多边形几何，通过交互式可视化可以促进对其更深入的理解。由 Otfried Cheong 开发的 Ipe 可扩展绘图编辑器是一种广泛使用的生成几何图形的软件系统。其特性之一是通过称为 Ipelets 的程序扩展其功能。在本媒体提交中，我们展示了一系列新的 Ipelets，它们基于多边形几何构造各种几何对象。这些包括 Macbeath 区域、向前和反向 Funk 距离中的度量球、Hilbert 度量中的度量球、极体、点集的最小包围球，以及 Funk 和 Hilbert 度量中的最小生成树。我们还包含了许多凸多边形上的实用工具，包括并集、交集、差集和 Minkowski 和（先前作为 CGAL Ipelet 实现）。我们所有的 Ipelets 均使用 Lua 编程，并且可免费获取。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
