I have a 3D point cloud, which I can reconstruct back the 3D surface easily by using any existing 3D interpolation algorithm.

The question now is, let's say I have only a small neighbourhood of the 3D point cloud, and I am required to reconstruct back the 3D surface for that particular neighbourhood, how influential is the 3D points not in the neighbourhood contribute to the 3D surface shape of that particular chosen neighbourhood?

Obviously, the answer would depend on how densely populated the 3D points are, and how big the neighbourhood is. But is it possible to quantify those?

~~My question is algorithm independent. I just want to know the general characteristics of the influence of points from afar on a neighbourhood .~~

I am aiming to compare the following interpolation method:

- Triangle-based linear interpolation
- Triangle-based cubic interpolation
- Nearest neighbor interpolation

Note: when I say 3D surface, I mean a 2-manifold embedded in 3D.

That depends on how you do the reconstruction.Different methods will give you different reconstructions for the same point set and can behave very differently. – Darsh Ranjan Dec 11 '09 at 8:42