Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Real rational curves are not “unit speed”
Computer Aided Geometric Design
Approximation of circular arcs by cubic polynomials
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
Circular arc approximation by quintic polynomial curves
Computer Aided Geometric Design
Accurate Parametrization of Conics by NURBS
IEEE Computer Graphics and Applications
A rational quartic Bézier representation for conics
Computer Aided Geometric Design
Helix approximations with conic and quadratic Bézier curves
Computer Aided Geometric Design
Helix approximations with conic and quadratic Bézier curves
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 methods for approximating a helix segment by quintic Bézier curves or quintic rational Bézier curves based on the geometric Hermite interpolation technique in space. The fitting curve interpolates the curvatures as well as the Frenet frames of the original helix at both ends. We achieve a high accuracy of the approximation by giving a proper parametrization of the curve, and the approximation order of the height function along the helix axis is 9 provided that the screw angle of the helix is fixed. Numerical examples are also presented to illustrate the efficiency of the new method.