Helix approximations with conic and quadratic Bézier curves

In this paper we present the error analysis for the approximation of a cylindrical helix by conic and quadratic Bézier curves. The approximation method yields G1 conic spline and G1 quadratic spline, respectively. We give 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 angle subtended to helix increases. Furthermore, using the error bound analysis for the helix approximation by conic and quadratic Bézier curves, we present the error bounds for the torus-like helicoid approximations by quadric surfaces and quadratic Bézier tensor product surfaces.