2D and 3D Perspective Transformation

The most important and additionally intuitive assumptions and properties of 2D and 3D perspective transformations (not projections) are derived in this article. The transformations are considered as central perspective transformations which map the rays starting in the eye-point into parallel rays all perpendicular to the invariant hyperplane. It will be shown that one, two and three point perspective transformations possess the same principle behaviour and could be converted into each other with the help of rotations. The artificial distinction between one, two and three point perspective ttansformations arises because of the different number of zero positions in the related homogeneous transformation matrix and because mostly objects consisting of line parallel to the axes are examined.