Q-Ferguson curves

Lan-Yin Sun,Chun-Gang Zhu

doi:10.1177/1687814018809295

Q-Ferguson curves

Lan-Yin Sun, Chun-Gang Zhu

Open Access

https://doi.org/10.1177/1687814018809295

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Abstract

Ferguson’s curves are widely used in airfoil design. We present a kind of Ferguson’s curves with a shape parameter by integrating the classical Ferguson’s curves with the q-derivatives, called q-Ferguson curves. This kind of curves not only preserves the interpolation properties of classical Ferguson’s curves but also has a shape parameter which provides a freedom variable to construct the desired curves satisfying the interpolation or length constraint.

Highlights

The problem of defining a curve through an array of points in space is a fundamental problem in mechanical design and computer-aided geometric design (CAGD), and several methods have been proposed
The resolution of generalized problem is applicable to a variety of questions, such as airship aeroelasticity[2] and airfoil design[3]
In section ‘‘Ferguson curves,’’ we briefly summarize the relevant definitions and results about Ferguson’s curves

Summary

Introduction

The problem of defining a curve through an array of points in space is a fundamental problem in mechanical design and computer-aided geometric design (CAGD), and several methods have been proposed. In 1963, Ferguson[1] generalized the problem to a much broader class of permissible points and presented the resulting curve in a smooth composite of curve segments. Zhu and Wang[4] provided a new method for fitting C1 piecewise algebraic curves to the given scattered data. Juttler and Felis[7] presented an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. Some results on q-derivatives are recalled in section ‘‘qderivative.’’ In section ‘‘q-Ferguson curves,’’ we construct a q-Ferguson curve R(u) interpolating the given points and tangent at endpoints. The h-B-splines are limits of the q-B-splines.[14,20] The q-derivative is known as the Jackson derivative It has the analogous linear and product rules to the ordinary derivative.

À qd 1Àq or in the matrix form

Conclusion