Сглаживание ломаных линий составными сплайнами Безье

Abstract

The paper considers a new iterative method for constructing a smooth spline on a plane, consisting of cubic Bezier curves and repeating the shape of a given polyline with the required accuracy. At each iteration of the method, the following operations are performed: choosing the number of spline interpolation nodes, placing them on a given polyline according to certain rule, constructing a smooth compound Bezier spline passing through these nodes, and estimating the approximation accuracy, that is, the proximity of the constructed spline to a given polyline. The choice of the position of the spline interpolation nodes on a given polyline is performed by comparing the proximity measures of adjacent Bezier curves that make up the spline and the segments of the polyline that approximate these curves. The examples of smoothing polylines of varying complexity, including polylines with self-intersections, are given, confirming the effectiveness of the proposed method. The results of the work can be used in various applications, for example, when constructing the trajectory of automatic vehicles and mobile robots, when designing technical objects in computer-aided design systems, when performing cartographic generalization of linear cartographic objects, when designing fonts, etc.