The sphere as a rational Be´ier surface
Computer Aided Geometric Design
On the use of infinite control points in CAGD
Computer Aided Geometric Design - Special issue: Topics in CAGD
Curve and surface constructions using rational B-splines
Computer-Aided Design
Curvature continuity and offsets for piecewise conics
ACM Transactions on Graphics (TOG)
Good approximation of circles by curvature-continuous Be´zier curves
Computer Aided Geometric Design
Best approximation of circle segments by quadratic Be´zier curves
Curves and surfaces
Approximation of circular arcs by cubic polynomials
Computer Aided Geometric Design
Best approximations of parametric curves by splines
Mathematical methods in computer aided geometric design II
High accurate rational approximation of parametric curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
Geometric Hermite interpolation
Computer Aided Geometric Design
High-order approximation of conic sections by quadratic splines
Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
An O(h2n) Hermite approximation for conic sections
Computer Aided Geometric Design
Approximating a helix segment with a rational Be´zier curve
Computer Aided Geometric Design
Approximation of circular arcs by Bézier curves
Journal of Computational and Applied Mathematics
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Curve Fitting with Conic Splines
ACM Transactions on Graphics (TOG)
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
High accuracy approximation of helices by quintic curves
Computer Aided Geometric Design
Rational B-Splines for Curve and Surface Representation
IEEE Computer Graphics and Applications
High accuracy geometric Hermite interpolation
Computer Aided Geometric Design
On polynomial approximation of circular arcs and helices
Computers & Mathematics with Applications
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In this paper we present the error analysis for the approximation of a cylindrical helix by conic and quadratic Bezier curves. The approximation method yields G^1 conic spline and G^1 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 Bezier curves, we present the error bounds for the torus-like helicoid approximations by quadric surfaces and quadratic Bezier tensor product surfaces.