In
mathematics,
homogeneous coordinates or
projective coordinates, introduced by
August Ferdinand Möbius in his 1827 work
Der barycentrische Calcül, are a system of coordinates used in
projective geometry, as
Cartesian coordinates are used in
Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including
computer graphics and 3D
computer vision, where they allow
affine transformations and, in general,
projective transformations to be easily represented by a matrix.