# Rayons.jl : shortest optical path in 2D

Hi, I have made `Rayons.jl` public on github (not registered):

It was very fun and easy to develop with Julia and I guess that it would have been more difficult to implement efficiently with Python or Matlab (please prove me wrong).

This project simulates optical rays interacting with a 2D geometry composed of a set of rectangles with different optical velocities.

Minimal travel times from a given source to a set of sensors are computed.

The ray interacting with a (plane) boundary is split into two sub-rays (reflected and refracted) via the following recursive function :

``````function recursive_generate_rays_fluid!(reduce_ray!, state,celerity_domain, idx, time,
u::Point, pstart::Point, np::NumericalParameters, depth, power)
c₁,_,ρ₁ = cl_ct_rho(state)
u=normalize(u)
pend, pnext,uθ,state,next_state = advance_ds(pstart, u, np, state,celerity_domain)
c₂,_,ρ₂ = cl_ct_rho(next_state)

Δt = norm(pend - pstart) / c₁
time += Δt

reduce_ray!(pstart, pend, c₁, time, idx,power)

if depth <= np.maxdepth && time <= np.tmax  && power>np.power_threshold

uθr = maybeuθr(uθ, c₁, c₂) # refracted angle θr from incident angle θ
r,t = isnothing(uθr) ? (1.0,0.0) : rtpower_coeffs_fluid_fluid(uθr, uθ, c₁, c₂, ρ₁, ρ₂)
# reflection αf(α,θ,θ) =  π + α - θ - θᵣ
recursive_generate_rays_fluid!(reduce_ray!, state,celerity_domain, 2idx, time,
uαf(u,uθ,uθ), pend, np, depth+1, r*power)
# refraction α + θᵣ - θ
!isnothing(uθr) &&
recursive_generate_rays_fluid!(reduce_ray!, next_state,celerity_domain, 2idx+1, time,
uαr(u,uθ,uθr), pnext, np, depth+1, t*power)
end
end
``````

Note how different reduction functions (reduce_ray!) can be passed to the recursive function. In particular, we can pass a function computing the minimal arrival time of a given ray into each cell of a 2D Cartesian grid.

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