Two shape preserving lagrangeC 2-interpolants

Summary We present a LagrangeC²-interpolant to scattered convex data which preserves convexity. We also present a LagrangeC²-interpolant to uniformly spaced monotone data sites which preserves monotonicity. In both cases no further conditions are required on the data values. These interpolants are explicitely described and local. Error isO(h³) when the function to be interpolated isC³.