enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    A basic 3D rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle θ about the x-, y-, or z-axis, in three dimensions, using the right-hand rule—which codifies their alternating signs.

  3. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    Rotation matrices have a determinant of +1, and reflection matrices have a determinant of −1. The set of all orthogonal two-dimensional matrices together with matrix multiplication form the orthogonal group: O(2). The following table gives examples of rotation and reflection matrix :

  4. Active and passive transformation - Wikipedia

    en.wikipedia.org/wiki/Active_and_passive...

    A rotation of the vector through an angle θ in counterclockwise direction is given by the rotation matrix: = (⁡ ⁡ ⁡ ⁡), which can be viewed either as an active transformation or a passive transformation (where the above matrix will be inverted), as described below.

  5. Rotation (mathematics) - Wikipedia

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

    That it is an orthogonal matrix means that its rows are a set of orthogonal unit vectors (so they are an orthonormal basis) as are its columns, making it simple to spot and check if a matrix is a valid rotation matrix. Above-mentioned Euler angles and axis–angle representations can be easily converted to a rotation matrix.

  6. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    However, both the definition of the elemental rotation matrices X, Y, Z, and their multiplication order depend on the choices taken by the user about the definition of both rotation matrices and Euler angles (see, for instance, Ambiguities in the definition of rotation matrices). Unfortunately, different sets of conventions are adopted by users ...

  7. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axis–angle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

  8. Givens rotation - Wikipedia

    en.wikipedia.org/wiki/Givens_rotation

    For the same reason, any rotation matrix in 3D can be decomposed in a product of three of these rotation operators. The meaning of the composition of two Givens rotations g ∘ f is an operator that transforms vectors first by f and then by g, being f and g rotations about one axis of basis of the space

  9. 3D rotation group - Wikipedia

    en.wikipedia.org/wiki/3D_rotation_group

    An infinitesimal rotation matrix or differential rotation matrix is a matrix representing an infinitely small rotation. While a rotation matrix is an orthogonal matrix = representing an element of () (the special orthogonal group), the differential of a rotation is a skew-symmetric matrix = in the tangent space (the special orthogonal Lie ...