Splitting Surfaces with Multiple Nodes Question

Hi,

I have a surface as shown below where I have created nodes where I want to split the surface. The desired output is such that the vertices of the quad from split lies on the nodes.

 

So I tried splitting the surfaces using Multiple Nodes option as shown below:

 

<?xml version="1.0" encoding="UTF-8"?>

 

But the resulting output is as follows:

 

 

Totally not what I am expecting. Is there anyway I can get the surfaces to split like how it is on the extreme right? Rectangles or quads only with vertices lying on nodes? Hopefully it should be done in one execution rather than multiple ones like I am having to do.

 

Thanks...