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Summary of Plane Projective Transformations

Geometric properties invariant to commonly occurring plane transformations. Transformations lower in the table inherit the invariants of those above, but the converse is not true. The matrix is an invertible matrix, is a 2D rotation matrix, and a 2D translation. The distortion column shows typical effects of the transformations on a square. Transformations higher in the table can produce all the actions of the ones below. These range from Euclidean, where only translations and rotations occur, to projective where the square can be transformed to any arbitrary quadrilateral (provided no three points are collinear).

Bob Fisher
Wed Apr 16 00:58:54 BST 1997