이차 베지에 곡선의 합성곡선과 근사 곡선에 관한 연구

Abstract

In this thesis we study the geometric properties of the convolution curve of two quadratic Bezier curves. We present the necessary and sufficient condition for the existence of cusp on the convolution curve and the formular of the cusp point. Also, we characterize the behavior of convolution curve and quadratic approximation near . An unusual result was discovered that the one case does not occur among four cases of theorem. We present the necessary and sufficient conditions of that. Finally we approximate the convolution curve by the quadratic Bezier curve, and estimate the error bound between convolution curve and quadratic approximation. We also present method of reduce the error which apply the subdivision to convolution curve.