Smooth orientation interpolation using parametric quintic-polynomial-based quaternion spline curve

In this paper, a G2continuous quintic-polynomial-based unit quaternion interpolation spline curve with tension parameters is presented to interpolate a given sequence of solid orientations. The curve in unit quaternion space S3 is an extension of the quintic polynomial interpolation spline curve in Euclidean space. It preserves the interpolatory property and G2 continuity. Meanwhile, the unit quaternion interpolation spline curve possesses the local shape adjustability due to the presence of tension parameters. The change of one tension parameter will only affect the adjacent two pieces of curves. Compared with the traditional B-spline unit quaternion interpolation curve and v-spline unit quaternion interpolation curve, the proposed curve can automatically interpolate the given data points, without solving the nonlinear system of equations over quaternions to obtain the control points, which greatly improves the computational efficiency. Simulation results demonstrate the effectiveness of the proposed scheme.