Planar interpolation by second order spiral splines.

Second order spiral splines are C2 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.