Shape preserving interpolation on surfaces

We introduce a criterion for G2 shape-preserving interpolation of points on surfaces, based on the behaviour of the corresponding composite geodesic interpolant in the neighbourhood of the data points. Two alternative families of splines are proposed, combining appropriately nu- or non-uniform-degree splines with preimages of the geodesic segments, for conforming to the shape-preservation criterion for sufficiently large values of the nu or interval-degree parameters. Preliminary numerical results are given using the nu-splines-based interpolants for shape-preserving interpolation on cylinders, spheres and free-form surfaces