Simple way to interpolate between points in 3D space to form a smooth surface

Question

I\'m trying to come up with a simple and efficient way to create a smooth surface which intersects a number of given \"sample\" points.

For any X,Y point on the surf

Answer 1

You can utilize bilinear/bicubic interpolation, but in three directions (trilinear/tricubic, respectively). It is quite trivial if you understand how these forms of interpolation work. See Tricubic Interpolation on Wikipedia for more information.