Arc-length preserving approximation of circular arcs by polynomial curves with lower degrees

Arc-length-preserving approximation of circular arcs by cubic Bézier and quartic PH curves was discussed. For cubic Bézier curves, the relation between the length of the curve and the distance of adjacent control points was explored. Hence, a robust numerical method was derived to determine the control points of the curve. Accurate solutions were also provided for quartic PH curves to approximate circular arcs. The results show that polynomial curves with lower degrees can approximate circular arcs with high precision with the requirement of preserving arc-length.