Abstract
This paper presents an algorithm for approximating planar curves with conjugated circular arcs and straight-line segments. Approximation of digital planar curves using line segments and analytic curve pieces is a problem of fundamental importance in image analysis and pattern recognition. A specific variation of this problem is approximation by conjugated arcs and line segments, which also arises in robotics, particularly in motion planning. We propose an algorithmic solution to this problem, designed for the automatic generation of programs for robotic manipulators in the AS language. The originality of the method lies in employing a special representation of planar curves that is invariant under translation, rotation, and scaling. Such a representation enables the development of an optimal algorithm that automatically determines the number and placement of conjugated arcs and line segments approximating a given curve with a prescribed accuracy. The simplicity, flexibility with respect to input data, and low computational requirements of the proposed method make it suitable not only for image recognition tasks but also for robotic trajectory planning.