Coordinate Systems

Most spatial quantities are represented quantitatively by specifying the quantity relative to a coordinate system. The usual coordinate systems in use are:

Two dimensional (2D)

- usually representing positions in a plane, such as an image plane, or describing flat objects. The letters I&J or X&Y are often used to denote the directions in these 2D spaces. More exotic planar spaces might be a locally flat patch on a curved surface (often using U&V), the parameterization of a curved surface (also using U&V), or the surface orientation (using P&Q).

Three dimensional (3D)

- usually representing the positions of points in our normal 3D world (letters X,Y&Z). Other commonly encountered 3D spaces are: a sequence of images over time (I,J&T), the surface defined by the intensity of light in an image (X,Y & I), or the surface defined by the distance of the scene to a sensor (X,Y & Z).

Four dimensional (4D)

- these spaces usually derive from looking at a 3D world over time (X,Y,Z&T).

The coordinate systems are specified using as many axes as there are dimensions. The axes are usually perpendicular, and there is a ``coordinate system origin'' where all the axes intersect and which has the value (0,0) or (0,0,0), etc, depending on the dimensionality of the space.