Colour Mesh from Multiple Mesh Points

I have been trying to colour a simple mesh from multiple points and I feel I I’ve just been going in circles.

I take the vertices from A and find the closest point B. I want to colour these points with the colours C and interpolate the rest to give a nice contoured mesh as the end product.

Any help would be greatly appreciated.

MESH (19.2 KB)

Something like this?

MESH (18.5 KB)