Differentiable Image Parameterizations

Hi colah3, I was wondering how you're able to propagate the gradient through the renderer. What I mean is:

f(X,Y,Z) = (x,y) (Mapping from 3D to 2D using renderer)

g(x,y) = (u,v) (mapping xy and uv)

h(x,y) = (r,g,b) (actual rendered image)

p(u,v) = (r,g,b) (texture map image)

gradient from upper layer is going to be wrt h(x,y) - dL/dh(x,y). How do you propagate this to get dL/dp ?

(Please let me know if this is explained in detail somewhere. Thanks!)