Homogeneous Coordinates

Also found in: Wikipedia.

homogeneous coordinates

[‚hä·mə′jē·nē·əs kō′ȯrd·ən·əts]
To a point in the plane with cartesian coordinates (x,y) there corresponds the homogeneous coordinates (x1, x2, x3), where x1/ x3= x, x2/ x3= y; any polynomial equation in cartesian coordinates becomes homogeneous if a change into these coordinates is made.

Homogeneous Coordinates


of a point, line, and so on, coordinates that have the property that the object determined by them does not change when all coordinates are multiplied by a nonzero number. For example, the homogeneous coordinates of a point M in the plane are three numbers X, Y, and Z, related by the equation X:Y:Z = x:y:1, where x and y are its Cartesian coordinates. The introduction of homogeneous coordinates makes it possible to extend the class of points of the Euclidean plane by the addition of points whose third homogeneous coordinate is zero (ideal points, or points at infinity). This is important in projective geometry.

References in periodicals archive ?
Indeed, the homogeneous coordinates of the point T in the W-frame can be written as a function of [beta]:
r] - homogeneous coordinates of a point expressed in the C-frame
homogeneous coordinates of the wheel center expressed in the C-frame
where d and o are the homogeneous coordinates of the distorted and original input images.
where p represents the homogeneous coordinates of the prewarped image, and s represents the homogeneous coordinates of the scaled original input image.
Points in homogeneous coordinates can be written as [x'.
It is a nice illustration of a utilization of matrices in geometry, application of homogeneous coordinates, homogeneous transformation matrices and matrix algebra (Many similar exercises can be found in [Cox, 1998], [Craig, 1986], [Tsai, 1999]).
T] are the homogeneous coordinates of point m and M , and P is a 3 x 4 is camera projection matrix.

Full browser ?