Voronoi Diagram on a Sphere: Nearest-Neighbor Spherical Partition

This example demonstrates how to construct a Voronoi diagram on a sphere from a set of seed points, partitioning the spherical surface into cells where each point on the sphere belongs to the region of its nearest seed (under spherical distance). The key math ideas include Voronoi (nearest-neighbor) decomposition, distance-based region boundaries on the sphere, and the resulting adjacency structure that forms a spherical analogue of polygonal subdivision. In the GeoGebra setup, the construction leverages the provided workflow “Sequence, Zip” to generate and bundle multiple seeds and their parameters: objects such as N and speed control the number and update behavior, while variables like a, M, Lm, and point coordinates (Px, Py, Pz) together with spherical parameter sets (Ps, Ss) are organized via lists produced by Sequence and zipped into coherent collections. This drives the dynamic computation and visualization of the spherical Voronoi partition. Suitable for secondary school advanced geometry, and for undergraduate geometry/computational geometry explorations and classroom demonstrations.