D3D11/C++ Inaccuracies in uv interpolation in pixel shader. How to avoid? - c++

Question

I'm trying to draw a quad with a texture onto the screen such that texels and pixels perfectly align. Sounds pretty easy. I draw 2 triangles (as TRIANGLE_LIST, so 6 vertices) using these shaders:
struct VSOutput
{
float4 position : SV_POSITION;
float2 uv : TEXCOORD0;
};
VSOutput VS_Draw(uint index : SV_VertexId)
{
uint vertexIndex = index % 6;
// compute face in [0,0]-[1,1] space
float2 vertex = 0;
switch (vertexIndex)
{
case 0: vertex = float2(0, 0); break;
case 1: vertex = float2(1, 0); break;
case 2: vertex = float2(0, 1); break;
case 3: vertex = float2(0, 1); break;
case 4: vertex = float2(1, 0); break;
case 5: vertex = float2(1, 1); break;
}
// compute uv
float2 uv = vertex;
// scale to size
vertex = vertex * (float2)outputSize;
vertex = vertex + topLeftPos;
// convert to screen space
VSOutput output;
output.position = float4(vertex / (float2)outputSize * float2(2.0f, -2.0f) + float2(-1.0f, 1.0f), 0, 1);
output.uv = uv;
return output;
}
float4 PS_Draw(VSOutput input) : SV_TARGET
{
uint2 pixelPos = (uint2)(input.uv * (float2)outputSize);
// output checker of 4x4
return (((pixelPos.x >> 2) & 1) ^ ((pixelPos.y >> 2) & 1) != 0) ? float4(0, 1, 1, 0) : float4(1, 1, 0, 0);
}
where outputSize and topLeftPos are constants and expressed in pixel units.
Now for outputSize = (102,12) and topLeftPos=(0,0) I get (what I would expect):
link to image (as i'm not allowed to post images)
But for outputSize = (102,12) and topLeftPos=(0,0.5) I get: Output for x=0, y=0.5
link to image (as i'm not allowed to post images)
As you can see there is a uv-discontinuity where the 2 triangles connect and interpolation of uv is inaccurate). This basically happens (in x and y) only at positions around the .5 (actually below .49 it correctly snaps to texel 0 and above .51 it snaps correctly to texel 1, but in between i get this artifact).
Now for the purpose I need this for it is essential to have pixel perfect mapping. Can anyone enlighten me why this happens ?

Answer 1

There are a two things you need consider to understand what is happening:
Pixel corners in window space have integer coordinates and pixel centers in windows space have half-integer coordinates.
When triangle is rasterized, D3D11 interpolates all attributes to pixel centers
So what is happening is that when topLeftPos=(0,0), the value of input.uv * (float2)outputSize is always half-integer, and it is consistently rounded down to closest integer. However, when topLeftPos=(0,0.5), the (input.uv * (float2)outputSize).y should always be exactly integer. However, due to unpredictable floating-point precision issues, it is sometimes little less than exact integer, and in this case it is rounded down too much. This is where you see your stretched squares.
So if you want perfect mapping, your source square should be aligned with the pixel boundaries and not pixel centers.