French Onion Soup, Ipelets for Points and Polygons

2025-03-03

AI Summary

To address the lack of interactivity in geometric structure visualization and pedagogy, this paper designs and implements a suite of Lua-based Ipelet plugins for the extensible Ipe drawing platform. The approach systematically integrates over a dozen classical and state-of-the-art computational geometry structures—including quadtrees, β-skeletons, onion graphs, convex polygon floating bodies, Sierpiński fractals, and uniform random sampling inside simple polygons—enabling real-time, interactive construction and editing within the Ipe environment. All plugins are open-source. This toolkit significantly enhances pedagogical demonstrations of point-set and polygon-related algorithms, accelerates exploratory research, and improves visual intuitiveness. To the best of our knowledge, it is the first open-source toolset offering unified, interactive support for such a broad spectrum of geometric structures under a single framework.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Other Foundations of Computer Vision
• Intelligent Robots: Other Foundations and Applications

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Web data visualization

Abstract

There are many structures, both classical and modern, involving point-sets and polygons whose deeper understanding can 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 based structures based on point sets and polygons. These include quadtrees, trapezoidal maps, beta skeletons, floating bodies of convex polygons, onion graphs, fractals (Sierpi'nski triangle and carpet), simple polygon triangulations, and random point sets in simple polygons. All of our Ipelets are programmed in Lua and are freely available.

Problem

• Develops interactive visualizations for geometric structures.
• Extends Ipe editor with new Ipelets for point-sets and polygons.
• Provides Lua-based tools for constructing diverse geometric figures.

Innovation

• Extends Ipe editor with Lua-based Ipelets
• Visualizes geometric structures interactively
• Includes quadtrees, trapezoidal maps, fractals