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The aim of this paper is to present a new method of approximation of planardata set using only arcs or segments. The first problem we are trying to solveis the following: the CNC machines can work only with simple curves (arcs orsegments, 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 curvecomposed by linear or circular paths only. Moreover, we want to minimize thenumber of these paths. The second problem is the following: the contour of anobject is detected by a specific laser, which collects a discrete data set. Thelaser detects a good approximation of a point if this point is not a corner ofthe 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 thirdpurpose 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 thefinal path.

Corner Detection and Arc Approximation of Planar Data Set