Search results
Results from the WOW.Com Content Network
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 ...
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
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 ...
For example, to study the equations of ellipses and hyperbolas, the foci are usually located on one of the axes and are situated symmetrically with respect to the origin. If the curve (hyperbola, parabola , ellipse, etc.) is not situated conveniently with respect to the axes, the coordinate system should be changed to place the curve at a ...
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 ...
Transformations with reflection are represented by matrices with a determinant of −1. This allows the concept of rotation and reflection to be generalized to higher dimensions. In finite-dimensional spaces, the matrix representation (with respect to an orthonormal basis ) of an orthogonal transformation is an orthogonal matrix .
In geometry, isomorphisms and automorphisms are often called transformations, for example rigid transformations, affine transformations, projective transformations. Category theory , which can be viewed as a formalization of the concept of mapping between structures, provides a language that may be used to unify the approach to these different ...
The group Λ consists of all modular transformations for which a and d are odd and b and c are even. Another important family of congruence subgroups are the modular group Γ 0 (N) defined as the set of all modular transformations for which c ≡ 0 (mod N), or equivalently, as the subgroup whose matrices become upper triangular upon reduction ...