Vendevinkler

Vendevinkler is a term used in Danish and Norwegian to denote the turning angle, the angular amount by which an object must rotate to change its direction from one heading to another. It can refer to an absolute amount of rotation or to an oriented rotation, depending on the convention used in a given field.

Definition and usage

The vendevinkel is the angular difference between two directions. In practical terms, it is the amount of rotation required to align with a new heading. The unsigned version is usually expressed in degrees (0° to 180°), while the oriented version carries a sign to indicate the direction of rotation (for example, positive for counterclockwise and negative for clockwise in a chosen convention).

Mathematical background

In planar geometry and kinematics, the concept corresponds to the angle between two direction vectors or two rays emanating from a common origin. If u and v are two 2D vectors, the unsigned angle is theta = arccos((u·v)/(|u||v|)). The oriented turning angle can be computed using a combination of dot and cross products, such as theta = atan2(det(u,v), dot(u,v)), which yields a signed angle capturing both magnitude and direction of rotation.

Applications

Vendevinkler appears in navigation and driving, where it describes the change in course, as well as in robotics, computer graphics, and animation, where systems rotate a model or camera from one orientation to another. In polygonal paths, the sum of exterior turning angles around a closed loop equals 360°, reflecting total rotation.

Etymology and terminology

The term derives from the Danish and Norwegian words for turning (vende) and angle (vinkel). Usage varies by language and field, and some contexts may prefer terms like turning angle or change in bearing.

See also

Bearing, azimuth, angle of rotation, exterior angle, orientation.