Planar interpolation by second order spiral splines

Second order spiral splines are [Formula: see text] unit-speed planar curves that can be used to interpolate a finite list of points in the Euclidean plane. A fast algorithm is given for interpolation when the data comes from a strictly convex planar curve. The method uses a pair of tridiagonal systems of linear equations to find an approximate interpolant. Then the approximation is used with standard software to construct an exact interpolant. • The data should be planar and strictly convex. • The method is robust and extremely fast.