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A reflection about a line or plane that does not go through the origin is not a linear transformation — it is an affine transformation — as a 4×4 affine transformation matrix, it can be expressed as follows (assuming the normal is a unit vector): [′ ′ ′] = [] [] where = for some point on the plane, or equivalently, + + + =.
Pygame version 2 was planned as "Pygame Reloaded" in 2009, but development and maintenance of Pygame completely stopped until the end of 2016 with version 1.9.1. After the release of version 1.9.5 in March 2019, development of a new version 2 was active on the roadmap. [11] Pygame 2.0 released on 28 October, 2020, Pygame's 20th anniversary. [12]
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 ...
The Hadamard transform H m is a 2 m × 2 m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2 m real numbers x n into 2 m real numbers X k.The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k.
The 2D Z-transform, similar to the Z-transform, is used in multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex frequency domain in which the 2D surface in 4D space that the Fourier transform lies on is known as the unit surface or unit bicircle.
The direct-quadrature-zero (DQZ, DQ0 [1] or DQO, [2] sometimes lowercase) or Park transformation (named after Robert H. Park) is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify analysis.
The multiplicative (or geometric) discrete wavelet transform [26] is a variant that applies to an observation model = involving interactions of a positive regular function and a multiplicative independent positive noise, with =.
In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space.