Oddly Satisfying Voronoi Diagram with Symmetry

This example lets you drag control points to dynamically generate a Voronoi diagram, revealing how the partition boundaries reorganize smoothly as the sites move—often with striking symmetry and “satisfying” geometric structure. The key mathematics includes Voronoi diagrams (distance-dominance regions), the idea that each boundary consists of points equidistant to competing sites, and geometric relationships among polygonal regions under symmetric transformations. Construction-wise, it is built using GeoGebra commands Voronoi to compute the diagram, PointIn to determine region membership/selection, Polygon to form polygonal boundaries, and Mirror to impose or reveal mirrored symmetry. The scene uses multiple site points (e.g., A, B, C, …) and the resulting diagram/graph object (e.g., graph1) to drive the interactive behavior. Suitable for high school through early university, especially for geometry visualization, distance-based regions, and transformation-driven exploration.