Homogeneous Coordinates
A four-component representation of 3D points that unifies rotation, translation, and perspective projection into single matrix operations.
Instead of (x, y, z), use (x, y, z, w). When w = 1, the point is real; when w ≠ 1, divide all components by w to recover the actual location. This looks artificial, but it is powerful: a single 4×4 matrix can now encode rotation, translation, and perspective all at once. Perspective division — dividing x, y, z by w — is what makes the math work for camera projection. This was the mathematical trick that made 3D graphics tractable on hardware that could only do matrix multiplication fast. Demos exploited it to death.