A system of coordinates used in projective geometry. 1. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts; projective transformations are easily represented by a matrix. 2. Coordinates of points, including points at infinity, can be represented using finite coordinates. 3. Modern graphics APIs and graphics cards take advantage of homogeneous coordinate systems by using vector processors with 4-element registers (X, Y, Z, W).