Krökningsriktning

Krökningsriktning is a Swedish term that denotes the local direction in which a curve or an object bends at a given point. It is used in mathematics, physics, and engineering to describe the orientation of curvature, i.e., how the shape changes as one moves along the curve or surface.

In plane geometry, curvature κ(s) measures how quickly the tangent direction changes with arc length s. The direction of bending at a point is given by the normal vector toward the center of curvature, which lies at the center of the osculating circle. If the curve is traversed with a chosen orientation, the sign of κ can indicate whether the turn is to the left or to the right, depending on the convention used. Magnitude alone is sometimes used as absolute curvature, ignoring direction.

In three dimensions, curvature is part of the Frenet–Serret framework. The curvature κ and the unit normal N describe how a space curve departs from a straight line, with the curvature vector κN pointing toward the center of curvature. Torsion measures how the curve twists out of the plane, complementing the bending described by κ and N.

Applications of krökningsriktning include engineering (designing bends in beams and pipes), biomechanics (shape of bones and vessels), and computer graphics (path shaping and animation). When modelling a trajectory or a curved feature, specifying both the bending magnitude and the bending direction provides a complete local geometric description. For common examples, a circle has constant κ with N toward the circle center, while a straight line has κ = 0 and no defined bending direction. Sign conventions for κ depend on the chosen orientation.