Interpolation using a fast spline transform (FST)

The problem of interpolating data points using a smooth function has many existing solutions. In particular, the use of piecewise polynomials (splines) has provided solutions with user control of smoothness. In this paper we examine the relationship between computational complexity and the degree of smoothness associated with particular spline solutions. We discuss new efficient computational algorithms for existing C₀, C₁ and C₂ continuity spline solutions. We also introduce a new interpolation procedure which utilizes multiple knot splines. The technique solves the inverse problem and renders the interpolating spline function, using fixed-point shifts and additions. In applications requiring parallel computation, the use of these simpler operations implies a significant reduction in hardware complexity