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Projective geometry is the study of geometric properties which are invariant under projective transformations.
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: