CURVE INTERPOLATION WITH NONLINEAR SPIRAL SPLINES

Interpolating spiral splines are derived as an approximation to the cu rve of least energy. The defining equations, although nonlinear, are e asily solved because the Jacobian matrix has banded structure. A simpl e but effective iterative scheme for the solution of these equations i s described together with a useful scheme for determining initial appr oximations for nonlinear splines. The resulting curve is invariant wit h respect to translation and rotation of axes and is usually much smoo ther than is possible with polynomial splines because the curvature of the spiral spline varies linearly with respect to arc length.