Design and Implementation of the Stone Elliptical Arc Contour Fitting Algorithm

Abstract

Elliptical arcs have been widely used in stone contours, but the circular saw of the existing stone bridge cutting machine can only cut stone contours which compose of long lines and large radius arcs. The elliptical arc is often fitted by small line segments or small arc segments, and the circular saw cannot be used to process the stone elliptical arc contour. Therefore, a better choice of fitting the elliptical arc in the stone contour is the four-arc fitting algorithm. The traditional four-arc fitting ellipse algorithm can only fit the whole ellipse, in order to fit elliptical arcs, a new fitting algorithm of four-arc fitting elliptical arc is designed. Firstly, identify the stone contour and analyze the elliptical entities section from the DXF file, and divide the elliptical arc curve into several arcs according to the angular relationship. Then adopting the Chebyshev approximation theory of four-arc fitting ellipse, the preliminary fitting of the elliptical arc is performed, and re-fit the start section and end section of the elliptical arc curve, the elliptical arc fitting algorithm is designed. In addition, the maximum value of fitting error has been calculated. Finally, by using the Visual C++ as the developing software, the stone elliptical arc contour fitting algorithm and its processing trajectory simulation are realized. Testing results show that the fitting algorithm can meet the requirements of the circular saw cutting the stone elliptical arc contour.