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  2. Orientation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Orientation_(geometry)

    Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]

  3. Orientation (vector space) - Wikipedia

    en.wikipedia.org/wiki/Orientation_(vector_space)

    The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space , right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also ...

  4. Orientability - Wikipedia

    en.wikipedia.org/wiki/Orientability

    A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]

  5. Rotation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rotation_(mathematics)

    A motion of a Euclidean space is the same as its isometry: it leaves the distance between any two points unchanged after the transformation. But a (proper) rotation also has to preserve the orientation structure. The "improper rotation" term refers to isometries that reverse (flip) the

  6. Quaternions and spatial rotation - Wikipedia

    en.wikipedia.org/wiki/Quaternions_and_spatial...

    The square of a quaternion rotation is a rotation by twice the angle around the same axis. More generally q n is a rotation by n times the angle around the same axis as q. This can be extended to arbitrary real n, allowing for smooth interpolation between spatial orientations; see Slerp.

  7. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. [1]They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in three dimensional linear algebra.

  8. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.

  9. Geometric terms of location - Wikipedia

    en.wikipedia.org/wiki/Geometric_terms_of_location

    Collinear – in the same line; Parallel – in the same direction. Transverse – intersecting at any angle, i.e. not parallel. Orthogonal (or perpendicular) – at a right angle (at the point of intersection). Elevation – along a curve from a point on the horizon to the zenith, directly overhead.

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