The fairing and G1 continuity of quartic C‐Bézier curves

Quartic C‐Bézier curves possess similar properties with the traditional Bézier curves including terminal property, convex hull property, affine invariance, and approaching the shape of their control polygons as the shape parameter α decreases. In this paper, by adjusting the shape parameter α on the basis of the utilization of the least square approximation and nonlinear functional minimization together with fairing of a quartic C‐Bézier curve with G¹ continuity of quartic C‐Bézier curve segments, we develop a fairing and G¹ continuity algorithm for any given stitching coefficients λ_k(k = 1,2,…,n ? 1). The shape parameters α_i(i=1, 2, …, n) can be adjusted by the value of control points. The curvature of the resulting quartic C‐Bézier curve segments after fairing is more uniform than before. Moreover, six examples are provided in the paper to demonstrate the efficacy of the algorithm and illustrate how to apply this algorithm to the computer‐aided design/computer‐aided manufacturing modeling systems. Copyright © 2015 John Wiley & Sons, Ltd.