In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating...

possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a fixed axis. The special...

prescribed by the right-hand rule. The rotation axis is sometimes called the Euler axis. The axis–angle representation is predicated on Euler's rotation theorem...

space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications...

single rotation around a fixed axis. This gives one common way of representing the orientation using an axis–angle representation. Other widely used methods...

used as part of the representation of a more complicated object's orientation in physical space (e.g., axis–angle representation). Two directions are...

There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation). Here, we only describe the method based...

matrix in SO(3), the group of all rotation matrices, from an axis–angle representation. In terms of Lie theory, the Rodrigues' formula provides an algorithm...

3-dimensional rotation has the angle 2a about the axis r in axis–angle representation. In case a = π/2 (a right angle), then q = r {\displaystyle q=\mathbf...

[citation needed] 3D projection Rotation Axis-angle representation Conversion between quaternions and Euler angles Davenport chained rotations Euler's rotation...

called the origin; the polar angle θ between this radial line and a given polar axis; and the azimuthal angle φ, which is the angle of rotation of the radial...

this article the axis-angle representation is used for ρ. The rotation is about an axis in the direction of a unit vector e, through angle θ (positive anticlockwise...

eigenvalues. The angle θ which appears in the eigenvalue expression corresponds to the angle of the Euler axis and angle representation. The eigenvector...

axis–angle representation of rotations, the quaternion and dual quaternion representations of rotations and translations, the plücker representation of...

for rotations about a fixed point. Axis–angle representation (pictured at the right) specifies an angle with the axis about which the rotation takes place...

relative to each other according to either of two schemes: first-angle or third-angle projection. In each, the appearances of views may be thought of as...

similar method, called axis-angle representation, describes a rotation or orientation using a unit vector aligned with the rotation axis, and a separate value...

vectors, homogeneous transformations, roll-pitch-yaw and Euler angles, axis-angle representation, unit-quaternions, and twists, which are necessary to represent...

The axis of rotation is known as an Euler axis, typically represented by a unit vector ê. Its product by the rotation angle is known as an axis-angle vector...

of the magic angle is half of the opening angle formed when a cube is rotated from its space diagonal axis, which may be represented as arccos −⁠1/3⁠...

article the axis-angle representation is used, and θ = θe is the "axis-angle vector", the angle θ multiplied by a unit vector e parallel to the axis. Also,...

Fig. 3-2: the x-axis is drawn perpendicular to the ct′-axis, the x′ and ct-axes are added at angle φ; and the x′-axis is drawn at angle θ with respect...

about it; this is the axis angle representation of a rotation. The plane of rotation is the plane orthogonal to this axis, so the axis is a surface normal...

about an axis perpendicular to the relative velocities; The rotation is given by is a 4×4 rotation matrix R in the axis–angle representation, and coordinate...

that the horizontal x-axis, called the real axis, is formed by the real numbers, and the vertical y-axis, called the imaginary axis, is formed by the imaginary...

}\right)} , and rotation angle θ {\displaystyle \theta } (the angle from the positive horizontal axis to the ellipse's major axis) using the formulae: A...

The Axis powers, originally called the Rome–Berlin Axis and also Rome–Berlin–Tokyo Axis, was the military coalition which initiated World War II and fought...

angle, axis/angle, or Rodrigues vector space. Unit quaternions, while computationally convenient, do not lend themselves to graphical representation because...

pole, only one half. The solid angle subtended by a segment of a spherical cap cut by a plane at angle γ from the cone's axis and passing through the cone's...

\operatorname {\text{SO}} (3)\cong \mathbb {RP} ^{3}} (shown using the axis-angle representation). The proof uses known results in algebraic topology. The same...