Algorithm Research Based on an Elliptical Arc Fitting Curve

The fitting efficiency of lines or arcs fitting methods for various structural designs cannot meet the design requirements, and the fitting accuracy also needs to be improved. Therefore, this paper proposes a novel algorithm that uses a smaller number of elliptical arc segments to accurately fit the curve, while point-to-point continuity and a tangent relationship between all connected line segments of the curve can be maintained (G1 continuity). This algorithm uses elliptical arcs for curve fitting, and the advantage of using this conventional quadratic curve is that it does not require a higher-order equation to achieve that all connected line segments are tangent to each other, and its feature data is easily obtainable. In this paper, the novel elliptic arc fitting algorithm is used for the sine function curve, butterfly curve, parabola function curve, spiral line function curve and NURBS curve. The results show that this proposed method could be used to fit the curves with a smaller number of elliptical arc segments while satisfying the accuracy requirements. This algorithm with a simple solution method requires a significant reduction in the number of fitting segments while achieving the same fitting accuracy as other algorithms. It provides new ideas for the field of geometric modeling, tool path generation for numerical control (NC) machining and robot path planning.