"John D'Errico" <firstname.lastname@example.org> wrote in message <email@example.com>...
> > pchip in 2-d as a tensor product form has been shown > NOT to be adequate for the general desired behavior. > (It sometimes will produce an acceptable result, but in > general, it is not adequate.) >
John, I must admit that I don't know what is the adequate definition of shape preserving interpolation in 2D.
I just though at least the tensorial product would preserve at least the monotonic in any cut parallel to the two axis. Unless I'm mistaken, this also implies that the interpolation within a patch will necessary be bounded by the four corner data, thus never overshoot.
May be these characteristics are not enough for OP, but it is better than nothing. No?