Quintic generalized Hermite interpolation curves: construction and shape optimization using an improved GWO algorithm.

In the field of CAGD/CAD, interpolation curve plays an important role in shape representation and shape design. Based on the traditional quintic Hermite interpolation curve, this paper proposes a novel class of quintic generalized Hermite interpolation curve (QG-Hermite interpolation curve, for short) with local shape parameters, which can satisfy C² continuity automatically. Since each segment of the constructed curve has independent shape parameters, and its shape can be adjusted locally or globally by modifying the shape parameters. First, to obtain an interpolation curve satisfying certain specific geometric requirements such as the approximate shortest arc length, the strain energy minimization or the curvature variation energy minimization, etc., three shape optimization models of the QG-Hermite interpolation curve are established. Second, an improved gray wolf optimization (I-GWO) algorithm is used to solve the shape optimization models so as to determine the optimal shape parameters. Finally, the modeling examples show that the proposed method is effective and applicable in shape designing. [ABSTRACT FROM AUTHOR]