Generalization of approximation of planar spiral segments by arc splines

Abstract

Spirals based on quadratic Bezier, cubic Bezier, Pythagorean hodogragh (PH) cubic, PH quintic and clothoid curves are suitable for CAD and computer-aided geometric design (CAGD) applications. The clothoidal spiral segments an widely used in highway design, railway design and robot trajectories. For CNC machining compared wi h polyline approximations, the suggested are spline approximations avoid sudden changes in the direction of the tool path, decrease the number of segments for approximation and lessen the need to polish objects. In this dissertation an existing method is generalized to approximate a planar spiral segment so that it can be applied to a large class of spiral segments. The properties of several spiral segments are analyzed and their approximations by the proposed method are presented.