View Matrix to Texture Matrix

Question

I'm converting view coordinates to texture coordinates for both my shadow maps and Screen space reflections. I keep seeing this conversion in examples:

            var T = new Matrix
            {
                M11 = 0.5f,
                M22 = -0.5f,
                M33 = 1.0f,
                M41 = 0.5f,
                M42 = 0.5f,
                M44 = 1.0f
            };

            Matrix m = view * projection * T;

What is T and why does this "work"? I'm saying "work" because I not satisfied with the result but the problem may not lie here.

I would like to use and inverted view and projection and then adjust the coordinates from -1,1 to 0,1. But that doesn't work at all. What have I misunderstood?

Answer 1

It's transforming the range from [-1 : 1] to [0 : 1] and inverting the y/u component for texture coords.

The standard formula is:

u = (x / 2) + 0.5

v = (y / -2) + 0.5.

There's a negative 2 here because tex coords are often vertically inverted. That is, the top left coord is (0,0). See here.

T = [ 0.5, 0.0, 0.0, 0.0 ] [ 0.0, -0.5, 0.0, 0.0 ] [ 0.0, 0.0, 1.0, 0.0 ] [ 0.5, 0.5, 0.0, 1.0 ]

M11 and M22 are the scaling for the X and Y coords, and inversion of the Y component. The range changes from [-1 : 1] to [-0.5 : 0.5] in X and [-1 : 1] to [0.5 : -0.5] in Y.

M41 and M42 is translation required to go from [-0.5 : 0.5] to [0 : 1] in X and [0.5, -0.5] to [1 : 0] in Y.