partial derivatives of spherical angles w.r.t surface u, v. which is calculated in this method
Basically given a normalized vector
w(x,y,z)and it's partial derivatives
dw/dvvectors, how do you calculate:
dphi/dv? (theta and phi are spherical coords of w)
partial derivatives of refracted ray w.r.t surface u, v implemented here. ie. Given an incoming ray, surface normal and their partial derivative vectors w.r.t to surface u,v, what are partial derivatives of the refracted ray w.r.t u and v?
I guess it's using chain rule but I don't fully understand the math behind these two.
For example for the first case :
dtheta/du = dtheta/dz . dz/du and
dtheta/dz comes from derivative of
theta = cos^-1(z) w.r.t
z. But I don't understand how
dphi/du is calculated.