Abstract

It is known that if the degree of the typical plane Bezier curve is increased infinitely, the curve will converge to the logarithmic (equiangular) spiral. The logarithmic spiral is one of the log-aesthetic curves and they are formulated by α: the slope of the logarithmic curvature graph. In this paper we define the nonstationarily typical Bezier curve by making the transition matrix of the typical Bezier curve nonstationary and dependent on each side of the control polyline and defining the transition matrix in the Frenet frame. We propose a method that generates such a curve that it will converge to a log-aesthetic curve with arbitrary α, and β: the slope of the logarithmic torsion graph in case of space curves, by controlling the relationship between the rotation angle and the scaling factor if its degree of the curve is increased infinitely.