An approximation approach of the clothoid curve defined in the interval [0, π/2] and its offset by free-form curves

摘要

We propose an algorithm to approximate the clothoid curve defined in the interval [0, π/2] and its offset curves with Bezier curves and the approximation errors converge to zero as the degree of the Bezier curves is increased. Secondly, we discuss how to approximate the clothoid curve by B-spline curves of low degrees. By employing our method, the clothoid curve and its offset can be efficiently incorporated into CAD/CAM systems, which are important for the development of 3D civil engineering CAD systems, especially for 3D highway road design systems. The proposed method has been implemented on AutoCAD R14.