Approximation of straight segments and circular arcs by the minimax method

For graphics and image processing, the minimax method is useful to approximate given points by a straight line or segment. This method minimizes the maximum value of the perpendicular length (Euclidian distance) between given points and the line. In this paper, a minimax method approximating given points to a circular arc is defined and some iterative algorithms to obtain the numeric solution are described. Examples and problems are shown for the minimax approximated circular arc. The minimax approximation of a straight segment and that of a circular arc have a close relation. A new proposal is introduced. It shows that the minimax approximation by two straight segments gives a good estimation for that by a circular arc. Hence, for practical purposes, the minimax method is effective to approximate given points by straight segments and/or circular arcs. [In Japanese.]