3D Rotation
The mathematics of transforming 3D coordinates by rotation matrices, a fundamental operation in realtime graphics and the core of spinning cube demos.
To spin a point in 3D space, multiply its coordinates by a rotation matrix. A cube has 8 corners; a complex mesh has thousands. Every frame, every corner gets rotated, often around multiple axes simultaneously. Demo coders obsessed over this operation — assembly hand-tuning to squeeze out every cycle, lookup tables instead of trigonometric functions, and clever bit tricks to avoid expensive operations. The math was linear algebra; the execution was a grinding optimization problem.