Sphere to Square Grid Mapping

This example demonstrates a parametric transformation that maps points on a sphere onto a square grid, illustrating a geometric conversion from spherical to planar coordinates. The core mathematical concepts involve spherical parametric equations, piecewise functions, exponential functions, and combinatorial grid partitioning. The construction uses GeoGebra commands such as Sequence to generate point arrays, Sphere to create the sphere, and Intersect to compute intersection curves, with objects like Bulb, GridSize, R, Screen, and parameters a, l1-l4 controlling the mapping and grid density. Suitable for high school and above, this visualization helps explore coordinate transformations and is useful for math education or introductory computer graphics. By adjusting sliders, users can observe how spherical points are rearranged onto a square lattice, deepening understanding of mapping between different coordinate systems.