Rendering per-vertex data to texture (Direct3D 11) - directx

Question

I generate simple 2D grid with triangle strip representing water surface. First generated vertex has position [0,0] and the last one has [1,1]. For my water simulation I need to store current positions of vertices to a texture and then sample these values from the texture in the next frame to get the previous state of the water surface.
So, I created the texture in a size of vertices. For example if I will have a 10x10 vertices grid, I use a texture with 10x10 pixels (one pixel for one vertex data). And set this texture as a render target to render all vertex data into it.
According to this: MSDN Coordinate Systems, If I will use current positions of vertices in the grid (bottom-left at [0;0], top-right at [1;1]), rendered texture looks like this:
So I need to do some conversion to NDC. I convert it in a vertex shader like this:
[vertex.x * 2 - 1; vertex.y * 2 - 1]
Consider this 3x3 grid:
Now, grid is stretched to whole texture size. Texture coordinates are different from NDC and apparently I can use original coordinates of the grid (before conversion) to sample values from the texture and get previous values (positions) of vertices.
Here is a sample of my vertex/pixel shader code:
This vertex shader converts coordinates and sends it to pixel shader with SV_POSITION semantics (describes the pixel location).
struct VertexInput
{
float4 pos : POSITION;
float2 tex : TEXCOORD;
};
struct VertexOutput
{
float4 pos : SV_POSITION;
float2 tex : TEXCOORD;
};
// convertes coordinates from 0,0 origin to -1,-1, etc.
float2 toNDC(float2 px)
{
return float2(px.x * 2 - 1, px.y * 2 - 1);
}
VertexOutput main( VertexInput input )
{
VertexOutput output;
float2 ndc = toNDC(float2(input.pos.x, input.pos.z));
output.pos = float4(ndc, 1, 1);
output.tex = float2(input.pos.x, input.pos.z);
return output;
}
And here's the pixel shader saving values from vertex shader at defined pixel location (SV_POSITION).
struct PixelInput
{
float4 pos : SV_POSITION;
float2 tex : TEXCOORD;
};
float4 main(PixelInput input) : SV_TARGET
{
return float4(input.tex.x, input.tex.y, 0, 1);
}
And we're finally getting to my problem! I use graphics debugger in Visual Studio 2012 which allows me to look at the rendered texture and its values. I would expect that at the pixel location [0,1] (in texel coordinate system) should be value [0,0] (or [0,0,0,1] to be precise, for RGBA format) but it seems that value of final pixel is interpolated between 3 vertices and I have a wrong value for a given vertex.
Screenshot from VS graphics debugger:
Rendered 3x3 texture ([0;1] location in texel coordinate system):
Values from vertex and pixel shader:
How to render the exact value from vertex shader to texture for a given pixel?
I am pretty new to computer graphics and Direct3D 11, so please excuse my deficiencies.