关键词: 球面样条, 球面 Bézier 曲线, 插值, 参数连续, 刚体运动

Abstract: The high dimensional spherical spline curves fitting technology has received wide attention in computer animation and inertial navigation. In practical applications, spline curves are usually required to interpolate the given data points with certain continuity and local properties. Thus, the previous methods are limited in certain regards. For this reason, a new method, based on spherical Bézier curves, of constructing spherical spline in arbitrary dimensional space was proposed. Firstly, the higher order derivative vectors at the interpolation points were fitted by a reflection. Then, necessary and sufficient conditions for C2 Hermite interpolation were given. Finally, the C2 spherical Bézier spline was constructed, using only interpolation points. The proposed method exhibitslocal properties. The disturbance of some points will not impact other parts of the spline. The splines possess explicit expressions not involving nonlinear equations. Numerical experiments show that the method can be widely applicable and efficient. 

Key words:  , spherical spline, spherical Bézier curve, interpolation, parameter continuity, rigid body motion