Communications of the
Korean Mathematical Society CKMS

In this paper we approximate a cylindrical helix by bi-conic and bi-quadratic \Bezier curves. Each approximation method is $G^1$ end-points interpolation of the helix. We present a sharp upper bound of the Hausdorff distance between the helix and each approximation curve. We also show that the error bound has the approximation order three and monotone increases as the length of the helix increases. As an illustration we give some numerical examples.

Keywords: helix, bi-conic, bi-quadratic, Bezier curve, helicoid surface, $G^1$ end-points interpolation

MSC numbers: 65D05, 65D07, 65D17