Knickpunkter

Knickpunkter is a Swedish term used to describe points on a curve where the direction or rate of change changes abruptly, commonly referred to in English as kink points or elbow points. The word is formed from knick, meaning bend or kink, and punkt, meaning point. In mathematical and technical literature, knickpunkter designate non-smooth points on a graph or curve where the tangent may be undefined or the slope changes discontinuously, such as at a vertex of a polyline or at a junction in a piecewise-defined function.

In practice, knickpunkter are used to identify structural changes in data or models. They can mark transitions between different linear regimes in a piecewise model, serve as feature points in computer graphics or geographic information systems, and aid in curve fitting and change-point analysis by signaling where a single model should be split into separate segments. A classic example is the absolute value function, f(x) = |x|, which has a knickpunkt at x = 0 where the slope changes from -1 to 1.

Knickpunkter are related to, but distinct from, cusps (points where a curve has a pointed tip) and from general points of non-differentiability. They are also connected to concepts like knee points in data analysis, which similarly denote notable changes in the behavior of a curve or dataset.