Jump to navigation Jump to search
- (geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments.
- An affine transformation does not in general preserve angles between lines or distances between points, but it does preserve ratios of distances between points lying on a straight line.
- 1965, Michael B. P. Slater (translator), P. S. Modenov, A. S. Parkhomenko, Geometric Transformations, Volume 1: Euclidean and Affine Transformations, Academic Press, page 145,
- Just as for plane transformations, we may show that the set of all affine transformations of space form a group.
- Under an affine transformation of space, the image of a line is a line, and the image of a plane is a plane.
- 1982, George E. Martin, Transformation Geometry, Springer, page 169,
- Theorem 15.2 A transformation such that the images of every three collinear points are themselves collinear is an affine transformation.
- Are the affine transformations the same as those transformations for which the images of any three noncollinear points are themselves noncollinear? We shall see the answer is "Yes."
- 2004, Solomon Khmelnik, Computer Arithmetic of Geometrical Figures: Algorithms and Hardware Design, Mathematics in Computer Comp., page 8,
- Most striking and well-known examples of affine transformation applications are computer tomography (see for instance ) and information compression for telecommunication systems (see ).
- This book describes affine transformations (displacements, turns, scaling, shifts) of -dimensional figures, where .
- (geometric transformation that preserves lines and parallelism): affinity
- affine map, affine mapping, affine homomorphism (mappings from one space to a (generally) different one)
geometric transformation that preserves lines and parallelism
- Geometric transformation on Wikipedia.Wikipedia
- Affine geometry on Wikipedia.Wikipedia
- Affine group on Wikipedia.Wikipedia
- Affine space on Wikipedia.Wikipedia
- Affine variety on Wikipedia.Wikipedia
- Complex affine space on Wikipedia.Wikipedia
- Anamorphosis on Wikipedia.Wikipedia
- Affine transformation on Encyclopedia of Mathematics