This section gives a classical description of projective transformations of the projective line, plane, and 3-space.

Aprojective transformation is a transformation used in projective geometry: it is the composition of a pair ofperspective projections. It describes what happens to the perceived positions of observed objects when the point of view of the observer changes. Projective transformations do not preserve sizes or angles but do preserveincidence andcross-ratio: two properties which are important in projective geometry. A projective transformation can also be called aprojectivity. Projectivities form a group.^[1]

As important special cases, a projective transformation can be in the (real) one-dimensionalprojective lineRP¹, the two-dimensionalprojective planeRP², and the three-dimensional projective 3-spaceRP³; see:

• /Transformations of the projective line
• /Transformations of the projective plane
• /Transformations of projective 3-space

1. ↑Richard Hartley and Andrew Zisserman (2003).Multiple View Geometry in computer vision. Cambridge University Press.ISBN 0-521-54051-8.

• Introduction to Projective Transformations by J. C. Alvarez Paiva

• Book:Projective Geometry