Given a set of points, build a quad mesh such that each point is in the center of a quad I have a complex grid of points in sort of an elliptical orientation.  I would like to make a 2D quad mesh such that each point is in the center of a quad.  

I had been trying to accomplish this programmatically with some difficulty, then I though maybe this functionality is already implemented in Blender.   

Is there some way that I can generate such a mesh given such a set of points with Blender?

EDIT

Here are a few images to better show what I am trying to do.  The given points are in blue.  I want to surround each point with a quad and have minimal gaps between them.
Use Dupli verts

1st mesh with center vertices, under Properties &gt; Object &gt; Duplication switch Verts:


2nd mesh a simple quad (add plane) and parent it under 1st mesh:


if you want to convert it to editable mesh, do it with Shift+Ctrl+A


Edit: To rotate them like in your picture, connect your points with edges so they form concentric ellipses. Extrude them so you have some polygons - this will give those verts proper normals:

Check the rotation in that Duplication tab and convert to geometry, delete the original plane, concentric ellipses and delete the bottom dupli-objects:

The spacing is determined by the position of your input vertices so this should end up in what you want..