This is also the homogeneous representation of the 3D point which has coordinates (0,0,0), that is, the "camera center" (aka the entrance pupil; the position of the pinhole of a pinhole camera) is at O. This means that the camera center (and only this point) cannot be mapped to a point in the image plane by the camera (or equivalently, it maps to all points on the image as every ray on the image goes through this point). For any other 3D point with , the result is well-defined and has the form . This corresponds to a point at infinity in the projective image plane (even though, if the image plane is taken to be a Euclidean plane, no corresponding intersection point exists). Normalized camera matrix and normalized image coordinates The camera matrix derived above can be simplified even further if we assume that f = 1: where here denotes a identity matrix. Note that matrix here is divided into a concatenation of a matrix and a 3-dimensional vector. The camera matrix is sometimes referred to as a canonical form. So far all points in the 3D world have been represented in a camera centered coordinate system, that is, a coordinate system which has its origin at the camera center (the location of the pinhole of a pinhole camera). In practice however, the 3D points may be represented in terms of coordinates relative to an arbitrary coordinate system (X1', X2', X3'). Assuming that the camera coordinate axes (X1, X2, X3) and the axes (X1', X2', X3') are of Euclidean type (orthogonal and isotropic), there is a unique Euclidean 3D transformation (rotation and translation) between the two coordinate systems. In other words, the camera is not necessarily at the origin looking along the z axis. The two operations of rotation and translation of 3D coordinates can be represented as the two matrices and where is a rotation matrix and is a 3-dimensional translation vector. When the first matrix is multiplied onto the homogeneous representation of a 3D point, the result is the homogeneous representation of the rotated point, and the second matrix performs instead a translation. Performing the two operations in sequence, i.e. first the rotation and then the translation (with translation vector given in the already rotated coordinate system), gives a combined rotation and translation matrix Assuming that and are precisely the rotation and translations which relate the two