In a method and apparatus for determining the curvature of a curve passing through a plurality of points, the shape of which is defined by a line connecting these points, curvature is assigned to the individual points by determining the position of adjacent points relative to the individual points. The curvature of a point (B) is determined by further taking into account two additional points (A, C), one of which (A) lies on the connecting line forward of the respective point (B) and the other (C) on the connecting line behind the respective point (B). The points (A, C) are determined such that they are as remote as possible from the respective point (B) and, at the same time, no points exist which lie between the respective point (B) and one of the additional points (A, C), and which are farther than a set distance from the connecting lines between the respective point (B) and each of the two additional points (A, C).