Changing orientation is the same as moving the coordinate axes.

The orientation of an object in space is the choice of positioning it with one point held in a fixed position. Since the object may still be rotated around its fixed point, position of the fixed point is not enough to completely describe the object. Thus the configuration space of a non-symmetrical object in n-dimensional space is SO(n) × Rⁿ. Orientation may be visualized by attaching a basis of tangent vectors to an object. The direction each vector attached to it points in determines its orientation. Image File history File links Axes_changes. ... Image File history File links Axes_changes. ... In mathematics, a function space is a set of functions of a given kind from a set X to a set Y. It is called a space because in most applications, it is a topological space or/and a vector space. ... The tangent space of a manifold is a concept which needs to be introduced when generalizing vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from one to the other. ...

Orientation of a rigid body

The orientation of a rigid body in the three dimensional space changes by rotation. In the case of rotation about an axis through the center of the body, only the orientation changes, otherwise also position. If the rigid body has any rotational symmetry, not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. In physics, a rigid body is an idealisation of a solid body of finite size in which deformation is neglected. ... Rotation of a plane, seen as the rotation of the terrain relative to the plane (exposure time 1. ... Rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. ...

In two dimensions the situation is similar. In one dimension a "rigid body" can not move (continuously change) from one orientation to the other.

This meaning of orientation should not be confused with the other meaning, where a different orientation means a change to the mirror image by an improper rotation, which includes a reflection, see orientation (mathematics). In geometry, the mirror image of an object or two-dimensional figure is the virtual image formed by reflection in a plane mirror; it is of the same size as the original object, yet different, unless the object or figure has reflection symmetry (also known in the terminology of modern... IT IS KNOWN AS MARK a lunitice insain int gw brain ... In mathematics, an orientation on a real vector space is a choice of which ordered bases are positively oriented (or right-handed) and which are negatively oriented (or left-handed). ...

Formally, for any dimension, the orientation of the image of an object under a direct isometry with respect to that object is the linear part of that isometry. Thus it is an element of SO(n), or, put differently, the corresponding coset in E⁺(n) / T, where T is the translation group. In mathematics, the Euclidean group is the symmetry group associated with Euclidean geometry. ...

See also gyroscope. This article or section does not cite its references or sources. ...