Homogeneous coordinates

Homogeneous coordinates are a mathematical system used in computer graphics and geometry to represent points in space more flexibly. Instead of using just (x, y, z) for a point, they add an extra coordinate (w), so a point becomes (x, y, z, w). This allows for easier calculations of transformations like translation, rotation, and scaling using matrix operations. When w equals 1, the coordinates represent a regular point; changing w allows these transformations to be combined efficiently. Homogeneous coordinates unify different types of transformations into a single framework, simplifying complex geometric computations.