Earth’s Cities on a Sphere: Random Points and Nearest-Point Vectors

This example visualizes how points sampled on (or inside) a 3D sphere relate to a set of “city” points by repeatedly finding the closest city for each sampled location and representing the result geometrically. It demonstrates spherical/solid geometry using a globe-like sphere, spatial point coordinates, and the nearest-point concept (shortest distance via closest point). It also incorporates list/sequence handling by building a generated set of random (or discrete) points and then using indexing to identify which city is nearest. Construction focuses on: Sphere to create the spherical Earth model; PointIn to place points in the spherical region; Sequence to generate and iterate through the sampled point set; ClosestPoint to compute the nearest city point; and IndexOf to retrieve the index of that city from the stored list, enabling consistent labeling/highlighting and vector-based visualization. Suitable for secondary school to early university courses in solid geometry, coordinate geometry, and probability & statistics using random experiments, as well as for STEM visualization projects.