as a left-handed system of axes): This representation corresponds to rotating by three Euler angles (more properly, Tait–Bryan angles), using the xyz convention, which can be interpreted either as "rotate about the extrinsic axes (axes of the scene) in the order z, y, x (reading right-to-left)" or "rotate about the intrinsic axes (axes of the camera) in the order x, y, z (reading left-to-right)". Note that if the camera is not rotated (), then the matrices drop out (as identities), and this reduces to simply a shift: Alternatively, without using matrices (let us replace with and so on, and abbreviate to and to ): This transformed point can then be projected onto the 2D plane using the formula (here, x/y is used as the projection plane; literature also may use x/z): Or, in matrix form using homogeneous coordinates, the system in conjunction with an argument using similar triangles, leads to division by the homogeneous coordinate, giving The distance of the viewer from the display surface, , directly relates to the field of view, where is the viewed angle. (Note: This assumes that you map the points (-1,-1) and (1,1) to the corners of your viewing surface) The above equations can also be rewritten as: In which is the display size, is the recording surface size (CCD or Photographic film), is the distance from the recording surface to the entrance pupil (camera center), and is the distance, from the 3D point being projected, to the entrance pupil. Subsequent clipping and scaling operations may be necessary to map the 2D plane onto any particular display media. Weak perspective projection A "weak" perspective projection uses the same principles of an orthographic projection, but requires the scaling factor to be specified, thus ensuring that closer objects appear bigger in the projection, and vice versa. It can be seen as a hybrid between an orthographic and a perspective projection, and described either as a perspective projection with individual point depths replaced by an average constant depth , or simply as an orthographic projection plus a scaling. The weak-perspective model thus approximates perspective projection while using a simpler model, similar to the pure (unscaled) orthographic perspective. It is a reasonable approximation when the depth of the object along the line of sight is small compared to the distance from the camera, and the field of view is small. With these conditions, it can be assumed that