Helix approximations with conic and quadratic Bézier curves. (English) Zbl 1084.65015
An approach to the Hausdorff approximation of a cylindrical helix by Bézier curves is presented, taking into account \(G^1\) conic, quadratic, biconic and biquadratic splines. The order of the bound of the error is three. It is monotone increasing with respect to the length of the helix. The same method of approximation is used for representing the torus-like helicoid and it is suitable for any sweeping surface of a conic section along the helix. Also, the same type of bound analysis may be extended for the bi-quadratic rational/polynomial Hausdorff approximation.
Reviewer: Gabriela Cristescu (Arad)
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 65D07 | Numerical computation using splines |
Keywords:
helix; conic Bézier curve; quadratic Bézier curve; Hausdorff distance; helicoidal surface; \(G^{1}\) interpolation; \(G^1\) conic, quadratic, biconic and biquadratic splines; error boundReferences:
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