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An area-preserving affine transformation. Equiaffinities include the crossed hyperbolic rotation, elliptic rotation, hyperbolic rotation, and parabolic rotation.

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

An angle theta drawn on the coordinate plane is said to be in standard position if its initial side lies on the positive x-axis so that its vertex coincides with the origin ...

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

A translation along a straight line L and a rotation about L such that the angle of rotation is proportional to the translation at each instant. Also known as a twist.

The symmetry operation (x,y,z)->(-x,-y,-z). When used in conjunction with a rotation, it becomes an improper rotation.