Is the computation of Snell's law correct?

[ligoudaner377]

mitsuba3/include/mitsuba/render/fresnel.h

Line 160 in a946691

dr::fnmadd(dr::fnmadd(cos_theta_i, cos_theta_i, 1.f), eta_ti * eta_ti, 1.f);

I have difficulty understanding the above code for computing the cos value of the transmitted light.
To me,
Float cos_theta_t_sqr = dr::fnmadd(dr::fnmadd(cos_theta_i, cos_theta_i, -1.f), eta_ti * eta_ti, 1.f);
is more meaningful.

Sorry in advance. if I asked a too-naive question

[njroussel]

Hi @ligoudaner377

By definition we have sin_theta_t = et_ti * sin_theta_i
The current code translates to:

-(-sqr(cos_theta_i) + 1) * sqr(eta_ti) + 1 =  # which we'll rewrite as
1 - (1 - sqr(cos_theta_i)) * sqr(eta_ti) =    # using trigonometric identities we get
1 - sqr(sin_theta_i) * sqr(eta_ti) =          # if we take the square of our definition and subsitute it in this formula we get
1 - sqr(sin_theta_t) =                        # again with the trigonometric identity:
sqr(cos_theta_t)

Do you agree?

[ligoudaner377]

I see, I confused the functions fnmadd and fmadd.
Thank you!!