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Pluto notebook adaptation of https://github.com/leios/simuleios/tree/master/raytracing
See https://www.youtube.com/watch?v=JwyQezsQkkw
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👀 Reading hidden code
begin
import Pkg
])
using Images
using Plots
using PlutoUI
using ThreadsX
end
Activating new project at `/tmp/jl_UC5bFu` Updating registry at `~/.julia/registries/General.toml` Resolving package versions... Installed ImageMagick ────── v1.3.0 Installed Accessors ──────── v0.1.41 Installed Referenceables ─── v0.1.3 Installed InitialValues ──── v0.3.1 Installed GR_jll ─────────── v0.72.8+0 Installed Images ─────────── v0.23.3 Installed DefineSingletons ─ v0.1.2 Installed SpecialFunctions ─ v1.8.8 Installed MicroCollections ─ v0.2.0 Installed StatsBase ──────── v0.33.21 Installed BangBang ───────── v0.4.3 Installed ArgCheck ───────── v2.4.0 Installed Libtiff_jll ────── v4.4.0+0 Installed ImageShow ──────── v0.2.3 Installed ColorVectorSpace ─ v0.8.7 Installed CompositionsBase ─ v0.1.2 Installed ThreadsX ───────── v0.1.12 Installed OpenSSL_jll ────── v1.1.23+1 Installed ColorTypes ─────── v0.10.12 Installed Transducers ────── v0.4.84 Installed Plots ──────────── v1.40.7 Installed WoodburyMatrices ─ v0.5.6 Installed SplittablesBase ── v0.1.15 Installed Baselet ────────── v0.1.1 Installed Interpolations ─── v0.13.6 Installed GR ─────────────── v0.72.8 Installed FFMPEG_jll ─────── v4.4.2+2 Updating `/tmp/jl_UC5bFu/Project.toml` [6218d12a] + ImageMagick v1.3.0 [916415d5] + Images v0.23.3 [91a5bcdd] + Plots v1.40.7 [7f904dfe] + PlutoUI v0.6.11 [ac1d9e8a] + ThreadsX v0.1.12 Updating `/tmp/jl_UC5bFu/Manifest.toml` [621f4979] + AbstractFFTs v1.5.0 [7d9f7c33] + Accessors v0.1.41 [79e6a3ab] + Adapt v4.3.0 [dce04be8] + ArgCheck v2.4.0 [13072b0f] + AxisAlgorithms v1.0.1 [39de3d68] + AxisArrays v0.4.7 [198e06fe] + BangBang v0.4.3 [9718e550] + Baselet v0.1.1 [d1d4a3ce] + BitFlags v0.1.9 [aafaddc9] + CatIndices v0.2.2 [d360d2e6] + ChainRulesCore v1.25.1 [9e997f8a] + ChangesOfVariables v0.1.10 [944b1d66] + CodecZlib v0.7.8 [35d6a980] + ColorSchemes v3.26.0 [3da002f7] + ColorTypes v0.10.12 [c3611d14] + ColorVectorSpace v0.8.7 [5ae59095] + Colors v0.12.11 [34da2185] + Compat v4.16.0 [a33af91c] + CompositionsBase v0.1.2 [ed09eef8] + ComputationalResources v0.3.2 [f0e56b4a] + ConcurrentUtilities v2.5.0 [187b0558] + ConstructionBase v1.5.8 [d38c429a] + Contour v0.6.3 [150eb455] + 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using LinearAlgebra
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using Test
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# TODO: get refraction to work without offsets in quadratic / inside_of fxs
# Also, use dot product to see if exiting lens
function Base.isapprox(n1::Nothing, n2::Nothing)
return true
end
# For now, all cameras are aligned on the z axis
struct Camera
# Set of all pixels, counts as scene resolution
pixels
# physical size of aperture
size::Vector{Float64}
# camera's distance from screen
focal_length::Float64
# camera's position
p::Vector{Float64}
end
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struct Ray
# Velocity vector
v::Vector{Float64}
# Position vector
p::Vector{Float64}
# Color
c::RGB
end
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struct Surface
# Reflectivity
r::Float64
# Transmission
t::Float64
# Color
c::RGBA
# index of refraction
ior::Float64
function Surface(in_r, in_t, in_c, in_ior)
if !isapprox(in_r+in_t+in_c.alpha, 1)
error("invalid surface definition, RTC < 1")
end
new(in_r,in_t,in_c, in_ior)
end
Surface(in_r, in_t, in_c::Float64, in_ior) =
new(in_r, in_t, RGBA(0,0,0,0), in_ior)
end
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abstract type Object end
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struct Sphere <: Object
# Lens position
p::Vector{Float64}
# Lens radius
r::Float64
s::Surface
end
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Lens (generic function with 1 method)function Lens(p, r, ior)
return Sphere(p, r, Surface(0,1,RGBA(0,0,0,0),ior))
end
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ReflectingSphere (generic function with 1 method)function ReflectingSphere(p, r)
return Sphere(p,r,Surface(1,0,RGBA(0,0,0,0),0))
end
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ColoredSphere (generic function with 1 method)function ColoredSphere(p, r, c::RGB)
return Sphere(p, r, Surface(0,0,RGBA(c), 0))
end
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mutable struct SkyBox <: Object
# Skybox position
p::Vector{Float64}
# Skybox radius
r::Float64
end
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sphere_normal_at (generic function with 1 method)function sphere_normal_at(ray, sphere)
n = normalize(ray.p .- sphere.p)
return n
end
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inside_of (generic function with 1 method)function inside_of(ray::Ray, sphere)
return inside_of(ray.p, sphere)
end
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inside_of (generic function with 2 methods)function inside_of(pos, sphere)
x = sphere.p[1] - pos[1]
y = sphere.p[2] - pos[2]
if (x^2 + y^2 <= sphere.r^2)
return true
else
return false
end
end
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refract (generic function with 1 method)function refract(ray, lens::Sphere, ior)
# note: light moves at a particular speed with respect to the medium it is
# moving through, so...
# n_2*v = n_1*l + (n_1*cos(theta_1) - n_2*cos(theta_2))*n
# Other approximations: ior = n_1/n_2, c = -n*l
n = sphere_normal_at(ray, lens)
if dot(n, ray.v) > 0
n .*= -1
end
c = dot(-n, ray.v);
d = 1.0 - ior^2 * (1.0 - c^2);
if (d < 0.0)
reflect!(ray, n)
return
end
ray_vel = ior * ray.v + (ior * c - sqrt(d)) * n;
return Ray(ray_vel, ray.p, ray.c)
end
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abstract type Wall <: Object end;
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mutable struct Mirror <: Wall
# Normal vector
n::Vector{Float64}
# Position of mirror
p::Vector{Float64}
# Mirror size
scale::Float64
Mirror(in_n, in_p) = new(in_n, in_p, 2.5)
end
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is_behind (generic function with 1 method)function is_behind(ray, mirror)
if dot(ray.p.-mirror.p, mirror.n) >= 0
return true
else
return false
end
end
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reflect (generic function with 1 method)# note: for reflection, l_x -> l_x, but l_y -> -l_y
# In this case, the y component of l = cos(theta)*n
# so new vector: v = l + 2cos(theta)*n
function reflect(ray, n)
ray_vel = ray.v .- 2*dot(ray.v, n).*n
ray_pos = ray.p .+ 0.001*ray.v
return Ray(ray_vel, ray_pos, ray.c)
end
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draw_circle (generic function with 1 method)👀 Reading hidden code
plot_rays (generic function with 1 method)👀 Reading hidden code
step (generic function with 1 method)function step(ray::Ray, dt)
ray.p .+= .+ ray.v.*dt
return ray
end
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10002.0
0.0
0.0
intersection(
Ray([1.0, 0.0, 0.0], [0.0, 0.0, 0.0], RGB(0,0,0)),
SkyBox([2.0,0,0], 10000)
)
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# begin
# function intersection(ray::Ray, skybox::SkyBox;
# threshold = 0.01)
# return skybox.r * ray.v
# end
# function intersection(ray::Ray, sphere::Sphere;
# threshold = 0.01)
# relative_dist = ray.p-sphere.p
# a = dot(ray.v, ray.v)
# b = 2.0 * dot(relative_dist, ray.v)
# c = dot(relative_dist, relative_dist) - sphere.r*sphere.r
# discriminant = b*b - 4*a*c
# if discriminant < 0
# return nothing
# elseif discriminant > 0
# roots = [(-b + sqrt(discriminant)) / (2*a),
# (-b - sqrt(discriminant)) / (2*a)]
# min = minimum(roots)
# max = maximum(roots)
# if min > threshold
# return (min)*ray.v
# elseif max > threshold
# return (max)*ray.v
# else
# return nothing
# end
# else
# # Returns nothing if tangential
# return nothing
# #return (-b/(2*a))*ray.v
# end
# end
# end
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intersection (generic function with 1 method)function intersection(ray::Ray, sphere::S;
threshold = 0.01) where
{S <: Union{Sphere, SkyBox}}
relative_dist = ray.p-sphere.p
a = dot(ray.v, ray.v)
b = 2.0 * dot(relative_dist, ray.v)
c = dot(relative_dist, relative_dist) - sphere.r*sphere.r
discriminant = b*b - 4*a*c
if discriminant < 0
return nothing
elseif discriminant > 0
roots = [(-b + sqrt(discriminant)) / (2*a),
(-b - sqrt(discriminant)) / (2*a)]
min = minimum(roots)
max = maximum(roots)
if min > threshold
return (min)*ray.v
elseif max > threshold
return (max)*ray.v
else
return nothing
end
else
# Returns nothing if tangential
return nothing
#return (-b/(2*a))*ray.v
end
end
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intersection (generic function with 2 methods)function intersection(ray::Ray, wall::W) where {W <: Wall}
intersection_pt = -dot((ray.p .- wall.p),wall.n)/dot(ray.v, wall.n)
if isfinite(intersection_pt) && intersection_pt > 0 &&
intersection_pt != NaN
return intersection_pt*ray.v
else
return nothing
end
end
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propagate (generic function with 1 method)function propagate(rays::Array{Ray}, objects::Vector{O},
num_intersections) where {O <: Object}
Threads.@threads for j = 1:length(rays)
rays[j] = propagate(rays[j], objects, num_intersections)
end
return rays
end
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propagate (generic function with 2 methods)function propagate(ray::Ray, objects::Vector{O},
num_intersections) where {O <: Object}
for i = 1:num_intersections
if ray.v != zeros(length(ray.v))
intersect_final = [Inf, Inf]
intersected_object = nothing
for object in objects
intersect = intersection(ray, object)
if intersect != nothing &&
sum(intersect[:].^2) < sum(intersect_final[:].^2)
intersect_final = intersect
intersected_object = object
end
end
if intersected_object != nothing
ray.p .+= intersect_final
if intersected_object isa Sphere
if !isapprox(intersected_object.s.t, 0)
ior = 1/intersected_object.s.ior
if dot(ray.v,
sphere_normal_at(ray,
intersected_object)) > 0
ior = intersected_object.s.ior
end
ray = refract(ray, intersected_object, ior)
elseif !isapprox(intersected_object.s.r, 0)
n = sphere_normal_at(ray, intersected_object)
ray = reflect(ray, n)
elseif !isapprox(intersected_object.s.c.alpha, 0)
ray_color = RGB(intersected_object.s.c)
ray_vel = zeros(length(ray.v))
ray = Ray(ray_vel, ray.p, ray_color)
end
elseif intersected_object isa Mirror
ray = reflect(ray, intersected_object.n)
elseif intersected_object isa SkyBox
ray_color = pixel_color(ray.p)
ray_vel = zeros(length(ray.v))
ray = Ray(ray_vel, ray.p, ray_color)
end
else
println("hit nothing")
end
end
end
return ray
end
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pixel_color (generic function with 1 method)function pixel_color(position)
extents = 1000.0
c = RGB(0)
if position[1] < extents && position[1] > -extents
c += RGB((position[1]+extents)/(2.0*extents), 0, 0)
else
println(position)
end
if position[2] < extents && position[2] > -extents
c += RGB(0,0,(position[2]+extents)/(2.0*extents))
else
println(position)
end
if position[3] < extents && position[3] > -extents
c += RGB(0,(position[3]+extents)/(2.0*extents), 0)
else
println(position)
end
return c
end
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convert_to_img (generic function with 1 method)function convert_to_img(rays::Array{Ray}, filename)
color_array = Array{RGB}(undef, size(rays)[2], size(rays)[1])
for i = 1:length(color_array)
color_array[i] = rays[i].c
end
save(filename, color_array)
end
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CartesianIndex(1, 2)CartesianIndex(1,2)
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init_rays (generic function with 1 method)function init_rays(cam::Camera)
res = size(cam.pixels)
dim = cam.size
pixel_width = dim ./ res
# create a set of rays that go through every pixel in our grid.
rays = map(CartesianIndices(cam.pixels)) do I
pixel_loc = [cam.p[1] + 0.5*dim[1] - I[1]*dim[1]/res[1] +
0.5*pixel_width[1],
cam.p[2] + 0.5*dim[2] - I[2]*dim[2]/res[2] +
0.5*pixel_width[2],
cam.p[3]+cam.focal_length]
l = normalize(pixel_loc - cam.p)
Ray(l, pixel_loc, RGB(0))
end
return rays
end
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ray_trace (generic function with 1 method)function ray_trace(objects::Vector{O}, cam::Camera; filename="check.png",
num_intersections = 10) where {O <: Object}
rays = init_rays(cam)
rays = propagate(rays, objects, num_intersections)
# convert_to_img(rays, filename)
return rays
end
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as_image (generic function with 1 method)function as_image(rays::Array{Ray})
[r.c for r in rays]
end
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0.0
0.0
0.0
1000.0
sky = [SkyBox([0.0, 0.0, 0.0], 1000)]
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objects (generic function with 1 method)objects(t) = vcat(sky, spheres(t))
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UndefVarError: t not defined
Here is what happened, the most recent locations are first:
- from This cell: line 1
t
C'est la vie !
t
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spheres (generic function with 1 method)spheres(t) = [
ReflectingSphere([0,0,-25], 10),
# ColoredSphere([0,0,-25], 5, RGB(0.75, .65, 0.1)),
# ReflectingSphere([50 * sin(t), 0, 50 * cos(t) - 25], 15),
Lens([50 * sin(t), 0, 50 * cos(t) - 25], 15, 1.5),
Lens([-50 * sin(t), 0, -50*cos(t) - 25], 15, 1.5),
Lens([-50 * sin(t + 2pi/3), 0, -50*cos(t + 2pi/3) - 25], 15, 1.5),
Lens([-50 * sin(t + 4pi/3), 0, -50*cos(t + 4pi/3) - 25], 15, 1.5),
]
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doit (generic function with 1 method)doit(T, highres) = let
# blank_img = Array{RGB}(undef, 1920,1080)
blank_img = if highres
Array{RGB}(undef, 800, 320)
else
Array{RGB}(undef, 200, 80)
end
repeat
blank_img[:] .= RGB(0)
cam = Camera(blank_img, [16,6], -10, [0,0,100])
ray_trace(objects(T / 100), cam) |> as_image
end |> transpose
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@bind T Slider(1:200)
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High resolution:
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doit(T, highres)
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