Metric spaces defined within convex polygons, such as the Thompson, Funk, reverse Funk, and Hilbert metrics, are subjects of recent exploration and study in computational geometry. This paper contributes an educational piece of software for understanding these unique geometries while also providing a tool to support their research. We provide dynamic software for manipulating the Funk, reverse Funk, and Thompson balls in convex polygonal domains. Additionally, we provide a visualization program for traversing the Hilbert polygonal geometry.

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.

The use of semi-autonomous Unmanned Aerial Vehicles (UAV) to support emergency response scenarios, such as fire surveillance and search and rescue, offers the potential for huge societal benefits. However, designing an effective solution in this complex domain represents a "wicked design" problem, requiring a careful balance between trade-offs associated with drone autonomy versus human control, mission functionality versus safety, and the diverse needs of different stakeholders. This paper focuses on designing for situational awareness (SA) using a scenario-driven, participatory design process. We developed SA cards describing six common design-problems, known as SA demons, and three new demons of importance to our domain. We then used these SA cards to equip domain experts with SA knowledge so that they could more fully engage in the design process. We designed a potentially reusable solution for achieving SA in multi-stakeholder, multi-UAV, emergency response applications.