aksiskulmaesitys

Aksiskulmaesitys is a Finnish term that translates to "axis angle representation" or "axis-angle representation" in English. It is a mathematical concept used to describe a rotation in three-dimensional space. Instead of using a sequence of rotations around standard axes (like Euler angles) or a single matrix, the axis-angle representation defines a rotation by specifying a unit vector that represents the axis of rotation and an angle that represents the magnitude of the rotation around that axis.

This representation is often considered more intuitive and less prone to issues like gimbal lock, which can occur with Euler angles. The axis is typically represented as a 3D vector (x, y, z) where x² + y² + z² = 1. The angle is a scalar value, usually measured in radians. To perform a rotation using this representation, one would rotate a point or vector around the specified axis by the given angle. This is commonly achieved using Rodrigues' rotation formula. The axis-angle representation is widely used in fields such as computer graphics, robotics, and aerospace engineering for representing and manipulating orientations and transformations. While it is conceptually simple, converting it to other representations like rotation matrices or quaternions is a common operation in practical applications.