The classical de Casteljau algorithm for constructing B
xe9;zier curves can be generalised to a sphere of arbitrary dimension by replacing line segments with shortest great circle arcs. The resulting
spherical Bxe9;zier curves are
C∞ and interpolate the endpoints of their control polygons. In the present paper, we address the problem of piecing these curves together into
e981f" title="Click to view the MathML source">C2 splines. For this purpose, we compute the endpoint velocities and accelerations of a spherical B
xe9;zier curve of arbitrary degree and use the formulae to define control points that give the curve a desired initial velocity and acceleration. In addition, for uniform splines we establish a simple relationship between the control points of neighbouring curve segments that is necessary and sufficient for
C2 continuity. As illustration, we solve an interpolation problem involving sparse data using both the present method and a normalised polynomial interpolant. The normalised spline exhibits large variations in speed and magnitude of acceleration, whilst the spherical B
xe9;zier spline is far better behaved. These considerations are important in applications where velocities and accelerations need to moderated or estimated, notably computer animation and rigid body trajectory planning, where interpolation in the 3-sphere is a fundamental task.