visualizations2.jl

### A Pluto.jl notebook ###
# v0.19.45

using Markdown
using InteractiveUtils

# ╔═╡ c4f087b6-64f6-4825-beef-d26b35192dc8
using DistanceTransforms: boolean_indicator, transform

# ╔═╡ e1123812-044c-4614-a1d0-b3ec54b88474
using PlutoUI: TableOfContents

# ╔═╡ 3aa5a142-4ea4-4397-95cf-0a505e532ba0
using GLMakie

# ╔═╡ 656849b1-cd13-462c-b839-5bfabf1e016c
using Random

# ╔═╡ 6ef1b663-351b-4896-a596-fc241140cca7
using Colors

# ╔═╡ 1bb5198f-4957-4d0a-8e23-5567840acc6e
using LinearAlgebra

# ╔═╡ bacf63dc-0bf3-4cc5-a6b6-b2439843976b
using GeometryBasics: Cylinder, Pyramid, Sphere, mesh

# ╔═╡ e6c3ca65-c68f-43ce-8408-f744778e27c8
TableOfContents()

# ╔═╡ f00a0ebc-9973-43e8-9161-d1272ca31746
md"""
## Various Distance Maps
"""

# ╔═╡ bc7070b6-2302-4b26-8d17-1f8f285c7bb5
Random.seed!(3)

# ╔═╡ 9ff0e3d6-95d0-4aa5-9e15-a53124195911
sphere = Sphere(Point3f(-0.5), 1)

# ╔═╡ 2bb54be3-f37d-4809-83a6-0c7cacd87808
begin
	# Define the grid dimensions 
	nx, ny, nz = 64, 64, 64  # Grid resolution
	
	# Define the grid bounds
	x_min, x_max = -2.0, 1.0  
	y_min, y_max = -2.0, 1.0
	z_min, z_max = -2.0, 1.0
	
	# Create grid arrays 
	x_vals = range(x_min, x_max, length=nx)
	y_vals = range(y_min, y_max, length=ny) 
	z_vals = range(z_min, z_max, length=nz)
	
	# Reshape to create 3D grids suitable for broadcasting
	xgrid = reshape(x_vals, nx, 1, 1)
	ygrid = reshape(y_vals, 1, ny, 1)
	zgrid = reshape(z_vals, 1, 1, nz)
	
	# Define the sphere's center and radius
	sphere_center = [-0.5, -0.5, -0.5]
	radius = 1.0
	
	# Compute the squared distances from the sphere's center  
	dx = xgrid .- sphere_center[1]
	dy = ygrid .- sphere_center[2]
	dz = zgrid .- sphere_center[3]
	dist2 = dx.^2 .+ dy.^2 .+ dz.^2
	
	# Create a boolean 3D array indicating points inside the sphere
	sphere_array = dist2 .<= radius^2  
end;

# ╔═╡ 8b150352-d2d5-48fc-9c02-73ea48876805
sphere_array_dt = transform(boolean_indicator(sphere_array));

# ╔═╡ 82248472-e0e5-4321-bef5-0c0dccaa3437
begin 
	rectmesh = Rect3(Point3f(-0.5), Vec3f(1))
	rectMesh = mesh(rectmesh)

	cmap = resample_cmap(:Spectral_11, length(rectMesh.position))
	colors1 = [cmap[i] for (i,v) in enumerate(rectMesh.position)]
end;

# ╔═╡ a1bc03c1-d334-4088-b243-17c1f3dd4132
pyr = Pyramid(Point3f(0), 1f0, 1f0)

# ╔═╡ f7d597cd-0a76-43cb-bae5-f9be2f75400b
# Rectangle grid setup
begin
	nx_r, ny_r, nz_r = 64, 64, 64
	x_min_r, x_max_r = -1.0, 1.0
	y_min_r, y_max_r = -1.0, 1.0 
	z_min_r, z_max_r = -1.0, 1.0
	
	x_vals_r = range(x_min_r, x_max_r, length=nx_r)
	y_vals_r = range(y_min_r, y_max_r, length=ny_r)
	z_vals_r = range(z_min_r, z_max_r, length=nz_r)
	
	xgrid_r = reshape(x_vals_r, nx_r, 1, 1)
	ygrid_r = reshape(y_vals_r, 1, ny_r, 1) 
	zgrid_r = reshape(z_vals_r, 1, 1, nz_r)
	
	rect_center = [0.0, 0.0, 0.0]
	rect_size = [1.0, 1.0, 1.0]
	
	# Create a boolean 3D array indicating points inside the rectangle
	rect_array = (abs.(xgrid_r .- rect_center[1]) .<= rect_size[1]/2) .&
	       (abs.(ygrid_r .- rect_center[2]) .<= rect_size[2]/2) .& 
	       (abs.(zgrid_r .- rect_center[3]) .<= rect_size[3]/2)
end;

# ╔═╡ 4904554b-718f-4ff8-b19a-9d1f69a09832
rect_array_dt = transform(boolean_indicator(rect_array));

# ╔═╡ 24990642-10b4-46aa-af0e-9351a627b57f
# Pyramid grid setup 
begin
	nx_p, ny_p, nz_p = 64, 64, 64
	x_min_p, x_max_p = -1.0, 1.0
	y_min_p, y_max_p = -1.0, 1.0
	z_min_p, z_max_p =  0.0, 2.0
	
	x_vals_p = range(x_min_p, x_max_p, length=nx_p)
	y_vals_p = range(y_min_p, y_max_p, length=ny_p)
	z_vals_p = range(z_min_p, z_max_p, length=nz_p)
	
	xgrid_p = reshape(x_vals_p, nx_p, 1, 1)
	ygrid_p = reshape(y_vals_p, 1, ny_p, 1)
	zgrid_p = reshape(z_vals_p, 1, 1, nz_p)
	
	pyr_center = [0.0, 0.0, 0.0]
	pyr_height = 1.0
	
	# Create a boolean 3D array indicating points inside the pyramid 
	pyr_array = (abs.(xgrid_p .- pyr_center[1]) .+ 
	        abs.(ygrid_p .- pyr_center[2])) .<= (1 .- zgrid_p ./ pyr_height)
end;

# ╔═╡ b95683f7-274f-4763-ae36-c9da26c79571
pyr_array_dt = transform(boolean_indicator(pyr_array));

# ╔═╡ 02f072f3-a837-4fb1-b01f-e24d35bfb0e3
let 
	fig = Figure(size = (1200, 800))
	axs = [
		Axis3(
			fig[i,j]; aspect = :data, perspectiveness = 0.7, xticklabelsvisible = false, yticklabelsvisible = false, zticklabelsvisible = false
		) 
		for j in 1:3, i in 1:2
	]
	
	mesh!(axs[1], sphere, color = :white)
	mesh!(axs[2], rectmesh, color = colors1)
	mesh!(axs[3], pyr; color = :dodgerblue)

	volume!(
		axs[4], 
		x_vals, 
		y_vals, 
		z_vals, 
		(sphere_array_dt .+ maximum(sphere_array_dt)) ./ (2 * maximum(sphere_array_dt)); 
		colormap = :Hiroshige,
		transparency = true
	) 
			
	volume!(
		axs[5],
		x_vals_r,
		y_vals_r,
		z_vals_r,
		(rect_array_dt .+ maximum(rect_array_dt)) ./ (2 * maximum(rect_array_dt));
		colormap = :Hiroshige,
		transparency = true
	)
			
	volume!(
		axs[6],
		x_vals_p,
		y_vals_p,
		z_vals_p,
		(pyr_array_dt .+ maximum(pyr_array_dt)) ./ (2 * maximum(pyr_array_dt)); 
		colormap = :Hiroshige,
		transparency = true
	)

	save(joinpath(pwd(), "plots/various_dts.png"), fig)
	fig
end

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[[deps.SpecialFunctions]]
deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
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deps = ["OffsetArrays"]
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[[deps.StaticArraysCore]]
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[[deps.SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
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[[deps.SuiteSparse_jll]]
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[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
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[[deps.Tables]]
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[[deps.Tar]]
deps = ["ArgTools", "SHA"]
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[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
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[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "ProgressMeter", "SIMD", "UUIDs"]
git-tree-sha1 = "bc7fd5c91041f44636b2c134041f7e5263ce58ae"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.10.0"

[[deps.TranscodingStreams]]
git-tree-sha1 = "e84b3a11b9bece70d14cce63406bbc79ed3464d2"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.11.2"

[[deps.Tricks]]
git-tree-sha1 = "7822b97e99a1672bfb1b49b668a6d46d58d8cbcb"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
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[[deps.TriplotBase]]
git-tree-sha1 = "4d4ed7f294cda19382ff7de4c137d24d16adc89b"
uuid = "981d1d27-644d-49a2-9326-4793e63143c3"
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[[deps.URIs]]
git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
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[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
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[[deps.Unitful]]
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git-tree-sha1 = "d95fe458f26209c66a187b1114df96fd70839efd"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
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    [deps.Unitful.extensions]
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    InverseFunctionsUnitfulExt = "InverseFunctions"

    [deps.Unitful.weakdeps]
    ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

[[deps.UnsafeAtomics]]
git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278"
uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
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[[deps.UnsafeAtomicsLLVM]]
deps = ["LLVM", "UnsafeAtomics"]
git-tree-sha1 = "2d17fabcd17e67d7625ce9c531fb9f40b7c42ce4"
uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
version = "0.2.1"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+1"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.31.0+0"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "1.0.0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "1165b0443d0eca63ac1e32b8c0eb69ed2f4f8127"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.13.3+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "a54ee957f4c86b526460a720dbc882fa5edcbefc"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.41+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.6+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.11+0"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "bcd466676fef0878338c61e655629fa7bbc69d8e"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.isoband_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.3+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.9.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.2+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.3+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "d7015d2e18a5fd9a4f47de711837e980519781a4"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.43+1"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "35976a1216d6c066ea32cba2150c4fa682b276fc"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.0+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "dcc541bb19ed5b0ede95581fb2e41ecf179527d2"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.6.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

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