Rotasjonsvektorer

Rotasjonsvektorer, also known as rotation vectors or axis-angle representations, are a way to describe a rotation in three-dimensional space. They combine the axis around which a rotation occurs with the angle of that rotation. A rotation vector can be visualized as an arrow. The direction of the arrow indicates the axis of rotation, following the right-hand rule. The length of the arrow represents the angle of rotation in radians. For example, a rotation vector pointing along the z-axis with a length of pi/2 radians would describe a 90-degree rotation around the z-axis.

This representation offers several advantages. It is more intuitive than other methods like Euler angles, which can suffer from gimbal lock. It also provides a compact way to store rotation information. Mathematically, a rotation vector can be converted into a rotation matrix or a quaternion, which are other common representations for rotations. The conversion from a rotation vector (represented by a unit vector u and an angle theta) to a rotation matrix R typically involves the Rodrigues' rotation formula. The inverse operation, converting a rotation matrix or quaternion back to a rotation vector, is also well-defined.

Rotasjonsvektorer find applications in various fields, including computer graphics, robotics, and physics, wherever describing and manipulating 3D orientations is necessary. They are particularly useful in situations where interpolation between orientations is required, as interpolation along the rotation vector is often more straightforward and results in smoother transitions compared to other representations.