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...rt description|Geometric object used to describe rotation in any number of dimensions}} ...object used to describe or visualize [[rotation (mathematics)|rotation]]s in space. ...

...in a [[sensor]] plane (in two dimensions) to object coordinates (in three dimensions). The equations originate from the [[Projection (mathematics)|central proje [[File:NYW-CentralProjection02.png|thumb|300px|The three points P, Q and R are projected on the plane S through the projection centr ...

...]]s and non-uniform scaling are not. Conformal linear transformations come in two types, ''proper'' transformations preserve the [[Orientability|orientat * The transformation is conformal (angle preserving); in particular orthogonal vectors remain orthogonal after applying the transfor ...

...nal|last=Joseph|first=Toby|date=2020|title=An Alternative Proof of Euler's Rotation Theorem|url=http://link.springer.com/10.1007/s00283-020-09991-z|journal=The Euclidean geometry is expressed in the [[complex plane]] by points <math>p = x + y i</math> where i squared is ...

...sor" is fundamental for the definition of the subject, but nowhere defined in Wikipedia}} ...spherical basis closely relates to the description of [[angular momentum]] in quantum mechanics and [[spherical harmonic]] functions. ...

...[[Euclidean distance]]. For example, a radial function {{math|Φ}} in two dimensions has the form<ref>{{Cite news |date=2022-03-17 |title=Radial Basis Function A function is radial [[if and only if]] it is invariant under all [[rotation]]s leaving the origin fixed. That is, {{mvar|f}} is radial if and only if ...

...les because the general problem of decomposing a rotation in a sequence of three was studied first by Paul B. Davenport.<ref>[http://arc.aiaa.org/doi/abs/10 ...his case, it is sometimes called a ''local'' coordinate system. Given that rotation axes are solidary with the moving body, the generalized rotations can be di ...

{{Short description|Math formula for 3D vector rotation}} ...the rotation of a vector in three dimensions. It is based on [[Rodrigues' rotation formula]], but uses a different parametrization. ...

{{Short description|Geometric space with six dimensions}} ...erest is {{anchor|6D EUCLIDEAN SPACE}}six-dimensional [[Euclidean space]], in which 6-polytopes and the 5-sphere are constructed. Six-dimensional [[ellip ...

|bgcolor=#e7dcc3|[[Point groups in three dimensions#Rotation groups|Rotation group]]||D_''4'', [2,4]⁺, (224), order 8 The '''truncated square antiprism''' one in an infinite series of truncated antiprisms, constructed as a [[truncation ( ...

...10.1063/1.481289 | volume=112 | issue=16 | title=Solute molecular dynamics in a mesoscale solvent | year=2000 | journal=The Journal of Chemical Physics | ...he streaming step, interactions between the solvent particles are modelled in the collision step. The particles are sorted into collision cells with a la ...

...i>'</nowiki>'' of the new coordinate system has coordinates (''h'', ''k'') in the original system. The positive ''x<nowiki>'</nowiki>'' and ''y<nowiki>' ...''x'y<nowiki>'</nowiki>''-system . A translation of axes in more than two dimensions is defined similarly.<ref>{{harvtxt |Protter|Morrey|1970| pp=585–588}}</ref ...

...issajous-toric knot with parameters 5, 6 and 22 in braid form (with z-axis in horizontal direction)]] In [[knot theory]], a '''Lissajous-toric knot''' is a [[knot (mathematics)|kno ...

|bgcolor=#e7dcc3|[[Point groups in three dimensions#Rotation groups|Rotation group]]||I, [5,3]⁺, (532), order 60 The expansion operation from the [[rhombic triacontahedron]] can be seen in this animation: ...

In [[geometry]] of 4 dimensions, a '''3-4 duoprism''', the second smallest p-q [[duoprism]], is a [[4-polyt ...ists in some of the [[Uniform 5-polytope#The B5 family|uniform 5-polytopes in the B5 family]]. ...

{{Short description|Function in Chemistry}} In [[chemistry]], the '''rotational partition function''' relates the rotation ...

{{Short description|Type of symmetry in quantum theory}} ==In field theory== ...

...le]] only on one and two-dimensional [[Lattice model (physics)|lattices]], in several special cases. ...the spins assigned to each node of the <math>Z_N</math> model as pointing in any one of <math>N</math> equidistant directions. The [[Boltzmann factor|Bo ...

...rix]] between two coordinate systems from two sets of observations sampled in each system respectively. The key idea behind the algorithm is to find an e ...ref> and it is used for [[flight dynamics|attitude determination]] problem in fields such as [[robotics]] and [[avionics]].<ref>Psiaki (2000)</ref><ref>W ...

|bgcolor=#e7dcc3|[[Point groups in three dimensions#Rotation groups|Rotation group]]||O, [4,3]⁺, (432), order 24 The expansion operation from the [[rhombic dodecahedron]] can be seen in this animation: ...