Solid color for each face in cycles when using image textures? I'm trying to create a polygonal art background, based on an image texture, like this penguin picture at this link: http://www.polygenapp.com/ 
That image was generated using this method, How can I do something like it using cycles. Note, I already have a mesh, I just want to texture it.

Ideally I prefer OSL, but anything that is one or two click to update will fly.

The method works by finding the color at the center of the face. I believe the is better then averaging vertexes in many instances.

Note: It would mean a lot if I didn't have to apply any modifiers on the mesh in order for this to work, just heads up.

Here is a practice file with modifiers:



This is not a duplicate of this: Is there a smart way to apply a better transition between colours while maintaining one solid colour per face?, That is not applicable to any textures, just gradients.
Here is one way to do this :


duplicate the final mesh (modifiers applied )
UV unwrap the new object using this method :


select all face
hit Ctrl+E and select Edges Split
resize all faces to Zero with Individual origins as a pivot 
U and select Project from View Bounds






copy this map to the original object, using CtrlL>Transfer UV map


After that all points on the same face will have the same UV coordinates meaning they will have the same color in render.
You can adjust the UVmap for more precise output.



For the workflow of setting up a good mesh  :


Add the Image as a background in the view
Add a plane (or simply import the same image as plane to skip setting up materials)
Delete the face (in Edit mode Select All and X and select Only Faces)
Start doing a loose tracing of the image by adding vertices in Edit mode (Ctrl+LMB, don't worry about crossing edges!)





Delete all edges (Select All and X and select Only Edges&amp;Faces)
For this step you need the Delaunay/voronoi Addon it will create a triangulated mesh from the points 





The rest is described in the first part above 


And here is a sweet penguin render :