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  2. Rotation formalisms in three dimensions - Wikipedia

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

    The Rodrigues vector (sometimes called the Gibbs vector, with coordinates called Rodrigues parameters) [3] [4] can be expressed in terms of the axis and angle of the rotation as follows: = ^ ⁡ This representation is a higher-dimensional analog of the gnomonic projection , mapping unit quaternions from a 3-sphere onto the 3-dimensional pure ...

  3. Three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Three-dimensional_space

    A sphere in 3-space (also called a 2-sphere because it is a 2-dimensional object) consists of the set of all points in 3-space at a fixed distance r from a central point P. The solid enclosed by the sphere is called a ball (or, more precisely a 3-ball). The volume of the ball is given by

  4. 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 ...

  5. Pinhole camera model - Wikipedia

    en.wikipedia.org/wiki/Pinhole_camera_model

    Note: the x 1 x 2 x 3 coordinate system in the figure is left-handed, that is the direction of the OZ axis is in reverse to the system the reader may be used to. The geometry related to the mapping of a pinhole camera is illustrated in the figure. The figure contains the following basic objects: A 3D orthogonal coordinate system with its origin ...

  6. Right-hand rule - Wikipedia

    en.wikipedia.org/wiki/Right-hand_rule

    In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.

  7. Point groups in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_three...

    In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices.

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