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Affine transformation (Euclidean geometry) Bäcklund transform; Bilinear transform; Box–Muller transform; Burrows–Wheeler transform (data compression) Chirplet transform; Distance transform; Fractal transform; Gelfand transform; Hadamard transform; Hough transform (digital image processing) Inverse scattering transform; Legendre ...
Download as PDF; Printable version ... are generalized in transformation geometry, ... of calculus and linear algebra to study problems in geometry. [95]
Geometric transformations can be distinguished into two types: active or alibi transformations which change the physical position of a set of points relative to a fixed frame of reference or coordinate system (alibi meaning "being somewhere else at the same time"); and passive or alias transformations which leave points fixed but change the ...
In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them.
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
Under the projective transformations, the incidence structure and the relation of projective harmonic conjugates are preserved. A projective range is the one-dimensional foundation. Projective geometry formalizes one of the central principles of perspective art: that parallel lines meet at infinity, and therefore are drawn that way. In essence ...