G/sup 2/ planar spiral cubic interpolation to a spiral

We show that two-point G/sup 2/ Hermite cubic spline interpolation to a smooth spiral is a spiral. Its unit tangent matches given unit tangents and its signed curvature matches given signed curvatures at end points of the given spiral. Spiral segments are useful in the design of fair curves and have the advantages that there are no unplanned curvature maxima, curvature minima, or inflection points, and that loops and cusps are impossible within a segment.