Meanderkurve

Meanderkurve, literally “meander curve” in German, is a term used to describe a curve that winds back and forth along a principal direction, creating a zigzag or serpentine path within a relatively narrow strip. In practice, a Meanderkurve can be constructed as a sequence of alternating straight segments connected by short bends, or as a smooth oscillatory curve such as a sine-like function restricted to a channel. The key feature is lateral displacement that increases with the number of turns while keeping the trajectory confined.

The geometry is characterized by parameters such as the bend length, segment length, and the width of the allowed strip. The curve can be designed to minimize crossing, to control curvature, or to approximate natural meanders in physical systems. In geomorphology, meandering rivers are often described using curves that shift position laterally over time; the Meanderkurve serves as a simple representation of such behavior.

Applications include modeling river paths, path planning in robotics where an area must be scanned in a back-and-forth pattern, and engineering contexts where compact lengthening of a trace is required without increasing footprint. Related concepts include meander lines in electronics, which use serpentine paths to achieve a desired electrical length.

There is no single canonical form for a Meanderkurve; researchers may use piecewise-linear, smooth, or fractal-like realizations depending on the context. The study of these curves focuses on length, curvature distribution, boundary confinement, and suitability as caricatures of more complex meandering phenomena.