Collocating spiral splines are derived as an approximation to the curve of least energy. The defining equations, although nonlinear, are easily solved because the Jacobian matrix has banded structure. A simple but effective iterative scheme for the solution of these equations is described together with a useful scheme for determining initial approximations for nonlinear splines. The resulting curve is invariant with respect to translation and rotation of axes and is usually much smoother than is possible with polynomial splines because the curvature of the spiral spline varies linearly with respect to arc length.