Perspective affects ? (LOD)
Perspective means that we could possibly have a different mipmap for each fragment since W changes with each fragment.
New calculations for ?u/?x , ?u/?y , ?v/?x , ?v/?y are:
?u/?x = (ds/dx - S’’ * dw/dx) * width * (1/w’)
?u/?y = (ds/dy - S’’ * dw/dy) * width * (1/w’)
?v/?x = (dt/dx - T’’ * dw/dx) * height * (1/w’)
?v/?y = (dt/dy - T’’ * dw/dy) * height * (1/w’)
where width, height are the maximum size texture map (LOD = 0). The 1/w’ term will have already been computed during S’’ and T’’ computation.