Corner Detection and Arc Approximation of Planar Data Set

Abstract: The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or segments, indeed). So, if we have a contour of an object and we want to cut, for example, glass or metal following that profile, we need a continuous curve composed by linear or circular paths only. Moreover, we want to minimize the number of these paths. The second problem is the following: the contour of an object is detected by a specific laser, which collects a discrete data set. The laser detects a good approximation of a point if this point is not a corner of the object. So in many cases our data set will not contain the real corners. Our task is to present a method on how to find these particular points. A third purpose is to study the regularity of the approximating curve, which can be $G^1$ or $C^0$ continuous. The entire method is developed using single arcs, segments and in certain cases biarcs, in order to ensure the smoothness of the final path.