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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. 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.

4. 3D rotation group - Wikipedia

   en.wikipedia.org/wiki/3D_rotation_group

   Every non-trivial rotation is determined by its axis of rotation (a line through the origin) and its angle of rotation. Rotations are not commutative (for example, rotating R 90° in the x-y plane followed by S 90° in the y-z plane is not the same as S followed by R ), making the 3D rotation group a nonabelian group .

5. Möbius strip - Wikipedia

   en.wikipedia.org/wiki/Möbius_strip

   One way to embed the Möbius strip in three-dimensional Euclidean space is to sweep it out by a line segment rotating in a plane, which in turn rotates around one of its lines. [23] For the swept surface to meet up with itself after a half-twist, the line segment should rotate around its center at half the angular velocity of the plane's rotation.

6. Orientation (vector space) - Wikipedia

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

   The one-dimensional case deals with an oriented line or directed line, which may be traversed in one of two directions. In real coordinate space , an oriented line is also known as an axis . [ 3 ] There are two orientations to a line just as there are two orientations to an oriented circle (clockwise and anti-clockwise).

7. 3D projection - Wikipedia

   en.wikipedia.org/wiki/3D_projection

   This representation corresponds to rotating by three Euler angles (more properly, Tait–Bryan angles), using the xyz convention, which can be interpreted either as "rotate about the extrinsic axes (axes of the scene) in the order z, y, x (reading right-to-left)" or "rotate about the intrinsic axes (axes of the camera) in the order x, y, z ...