The article delves into the utilization of Ipelets, specifically in the context of convex polygonal geometries. It highlights the significance of interactive visualizations in comprehending various geometric structures. The Ipe extensible drawing editor, known for generating geometric figures, allows functionality extension through programs called Ipelets. The authors showcase a collection of new Ipelets that construct diverse geometric objects based on polygonal geometries. These include Macbeath regions, metric balls in Funk and Hilbert distances, polar bodies, minimum enclosing ball of a point set, and minimum spanning trees. Additionally, utilities on convex polygons like union, intersection, subtraction, and Minkowski sum are explored. All Ipelets are programmed in Lua and freely accessible.
The content further elaborates on specific geometric structures computed by the Ipelets such as Macbeath regions around points in a convex polygon and Funk/Hilbert balls with their respective metrics. It also discusses the concept of polar bodies and their applications across different fields. Moreover, it introduces Funk and Hilbert minimum spanning trees along with operations like Boolean operations (union, subtraction, intersection), Minkowski sum computation between polygons, and determination of the minimum enclosing ball for a point set.
Furthermore, installation instructions for accessing these Ipelets are provided along with references to related works in computational geometry.
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