This is a list of some of the most commonly used coordinate transformations. Let ( x , y ) {\displaystyle (x,y)} be the standard Cartesian coordinates...

composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different...

frequencies. Mathematics portal Curvilinear coordinates List of common coordinate transformations Log-polar coordinates Polar decomposition Unit circle...

Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely by a pair of real...

are nn transformations and (n+1)n partial transformations. Coordinate transformation Data transformation (statistics) Geometric transformation Infinitesimal...

an axis of rotation. Each coordinate system is named after its choice of fundamental plane. The following table lists the common coordinate systems in...

hyperplane at infinity of a projective space, the affine transformations are the projective transformations of that projective space that leave the hyperplane...

of coordinate systems have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between...

In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates...

{\varphi }}}+{\ddot {z}}\,{\hat {\boldsymbol {z}}}} List of canonical coordinate transformations Vector fields in cylindrical and spherical coordinates...

the real coordinate space or real coordinate n-space, of dimension n, denoted Rn or R n {\displaystyle \mathbb {R} ^{n}} , is the set of all ordered...

A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude...

also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation...

orthogonal transformations. Area is invariant under linear maps which have determinant ±1 (see Equiareal map § Linear transformations). Some invariants of projective...

symplectic geometry and canonical transformations are generalized by contact transformations, so the 19th century definition of canonical coordinates in classical...

analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic...

a public registry of geodetic datums, spatial reference systems, Earth ellipsoids, coordinate transformations and related units of measurement, originated...

that direction. This type of mapping is also called shear transformation, transvection, or just shearing. The transformations can be applied with a shear...

defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots ,q^{d})} in which the coordinate hypersurfaces...

called a regular coordinate transformation or regular variable substitution, where regular refers to the C r {\displaystyle C^{r}} -ness of Φ {\displaystyle...

_{a}^{b}{\sqrt {(dx)^{2}+(dy)^{2}}}\,.} The Euclidean metric in some other common coordinate systems can be written as follows. Polar coordinates (r, θ): x = r...

example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including...

(Bogoliubov) transformations of a quantum state of light. In turn, the Bloch-Messiah decomposition (2) means that such an arbitrary Gaussian transformation can...

respect to restricted coordinate transformations. Strictly speaking, such objects are not tensors at all. A famous example of such a pseudotensor is...

group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly...

products. This pathway runs along the reaction coordinate, which is a parametric curve that follows the pathway of the reaction and indicates its progress;...

astronomy are celestial coordinate systems and time. The coordinates of objects on the sky are listed using the equatorial coordinate system, which is based...

linear transformation, and a special case of homothetic transformation (scaling about a point). In most cases, the homothetic transformations are non-linear...

automorphism of a set. In geometry, isomorphisms and automorphisms are often called transformations, for example rigid transformations, affine transformations, projective...

primitive. Model space Coordinate system in which a 3D model is created and stored. Model transformation matrix A transformation matrix producing world...