𝔖 Bobbio Scriptorium
✦   LIBER   ✦

High accuracy approximation of helices by quintic curves

✍ Scribed by Xunnian Yang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
347 KB
Volume
20
Category
Article
ISSN
0167-8396

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we present methods for approximating a helix segment by quintic BΓ©zier curves or quintic rational BΓ©zier 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.

πŸ“œ SIMILAR VOLUMES

Accuracy of curve approximation by harmo
Accuracy of curve approximation by harmonically related vectors with elliptical loci
✍ Charles R. Giardina; Frank P. Kuhl πŸ“‚ Article πŸ“… 1977 πŸ› Elsevier Science βš– 330 KB

Closed contours ill two dimensions are approximated by h~rmonioally related rotating vectors wi~h elliptical loci. Aa easy to use method for determining the number of vectom needed in the approximation is given. Specification of b~ndwidtb\_ requirements for transmission of ,~ contour, either continu

Chebyshev Approximation of Plane Curves
Chebyshev Approximation of Plane Curves by Splines
✍ E.F. Eisele πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 552 KB

Given a parametric plane curve \(\mathbf{p}\) and any BΓ©zier curve \(\mathbf{q}\) of degree \(n\) such that \(\mathbf{p}\) and \(q\) have contact of order \(k\) at the common end points, we use the normal vector field of \(\mathbf{p}\) to measure the distance of corresponding points of \(\mathbf{p}\