As usual, denote by KW [a, b] the Sobolev class consisting of every function whose (r − 1)st derivative is absolutely continuous on the interval [a, b] and its rth derivative is bounded by K a.e. in [a, b]. For a function f ∈ KW [a, b], its values and derivatives up to r−1 order at a set of nodes x are known. These values are said to be given Hermite information. This work reports results on be...

e o A technique for limiting the knot slopes of hermite cubic splines in order to eliminat vershoot is proposed. It is proven that constraining each knot’s slope to lie between 0 and l three times the slope to the knot on either side forces all extrema to occur at knots. This al ows overshoot to be eliminated without sacrificing slope continuity. The technique has appli1 cations in keyframe int...