The first line of the main function within the fragment shader expands the texture coordinates to a 3D (homogeneous) value with a z coordinate of zero (s, t, 0, 1), and then transforms the value via the Slice matrix. This matrix can scale, translate, and/or rotate the texture coordinates to define the 2D region of the virtual log.
One way to visualize this is to think of the slice as a 2D unit square embedded in the log with its lower-left corner at the origin. The matrix is then used to transform that square within the log to define a slice through the log. For example, I might just translate the square by (-0.5, -0.5, -0.5) and scale by 20 in x and y to get a slice through the middle of the log.
Next, the distance from the ...
