### A Pluto.jl notebook ###
# v0.17.5

using Markdown
using InteractiveUtils

# ╔═╡ 8b6ec02e-adac-48d6-b7c9-60f736614a3c
begin
	using PlutoUI,SymPy,Plots,Parameters,Images

	
    PlutoUI.TableOfContents()
	
	
	
end

# ╔═╡ cf42bcec-d5bc-11ec-27bf-afe7c36b964b
md"# Simple  Geometry with Julia:part two  line and line segments plot"

# ╔═╡ 3d0ebd7d-b6c4-4dc8-9e65-0b800187764b
begin
	gr()
	theme(:bright)
	linecolor=:green
	linewidth=0.2
	size=(200,200)
	
	struct HomPoint
    x::Float64
    y::Float64
	h::Int
    end
	function vec(p)
	   return [p.x p.y ]
    end
	  function trans(p::HomPoint)
		return [p.x p.y p.h]
	  end
end

# ╔═╡ 0e16a745-f422-492b-b41d-9ffaec831acd
md"""
!!! notice "Abstract"
    1.**this part about line and vector**
    
    2.**given two points we can plot a line, if we use parametric equations,that is very clearly**
    
    3.**we will coumputing slope of line through tow points, and normalize it get norm vector, norm vector including  all information about line, we only need this params,we can scale the norm vector ,this is the simplest linear combination.**
    
"""

# ╔═╡ 6888211b-f064-4924-b084-5bf00dead7e8
md"## 1.plot with function expression
$$f1(x)=x-2$$
$$f2(x)=x$$
 $f1(x)$ is a affine line,has y-intercpt=-2, x-intercept=2,slope=1.
$f2(x)$ is a line through origin. 
if we only have data point,how can we get line function reversely?

"

# ╔═╡ 8c032c77-616a-436f-b8ae-784afa547497
let
	origin=[0 0]
	p1=[2 0]
	p2=[0 -2]
	sp=[origin;p1;p2]
	xs=-3:0.01:3
	fy(x)=x-2
	plot(fy,xs,framestyle=:origin,label=false,siz=size,draw_arrow=true,ylims=(-4,2),size=(300,300))
	scatter!(sp[:,1],sp[:,2],label=false,markersize = 4)
end

# ╔═╡ a673a28b-01cd-4197-a5e1-2ca3c65a2f68
md"""
 ## 2. line through two points

$$p1=\begin{bmatrix}
2\\ 
0\\
\end{bmatrix} ::::  p2=\begin{bmatrix}
0\\ 
-2\\
\end{bmatrix}$$


"""

# ╔═╡ c483fe19-2bc4-43f5-aa56-ba93eec20275
md"""
   we just need a vector to represent a line
    vector is $\overrightarrow{p1p2}$  
"""

# ╔═╡ c461a36d-8cd3-47c8-9c06-cfaf88f607ad
begin
	# define 2d point data structure
	struct  Point2d
	   x::Float64
	   y::Float64
    end
	struct  Point3d
	   x::Float64
	   y::Float64
	   z::Float64
    end

    #define  vector  through  two points(vectors)
	function vec(v1::Point2d,v2::Point2d)
	   return  [v2.x-v1.x  v2.y-v1.y]
	end
     #defing  distance of two points(vectors)
	function dist(v1::Point2d,v2::Point2d)
		 v1x=v1.x
		 v1y=v1.y
		 v2x=v2.x
		 v2y=v2.y
		 return sqrt((v2x-v1x)^2+(v2y-v1y)^2)
	end
	# normalize vector, 
   function normalvec(v1::Point2d,v2::Point2d)
	   vector=vec(v1,v2)
	   distance= dist(v1,v2)
	   return vector/distance
	end
	
end

# ╔═╡ 12f35dbd-3a42-4595-92e1-5f4e71c2be36
let
	p1=Point2d(2,0)
	p2=Point2d(0,-2)
	v12=vec(p1,p2)
	normVec=normalvec(p2,p1)
	affineline(t)=t*normVec+[p1.x p1.y]
	
	tspan=-10:1:10
	xs=[]
	ys=[]
	data=[affineline(t) for t in tspan]
	for  i in data
		push!(xs,i[1])
		push!(ys,i[2])
		
	end
	plot(xs,ys,framestyle=:origin,size=(300,300),label=false)
	
	
end

# ╔═╡ 52ef195b-eaeb-4139-b513-521f0a5d9904
md"""
  line not through origin, called affine line .actually it is not linear transformation cause of intercept. 

"""

# ╔═╡ fb1a3cbe-6949-48e0-9ab6-ee91f5bd0439
let
	p1=Point2d(2,0)
	p2=Point2d(0,-2)
	normVec=normalvec(p2,p1)
	affineline(t)=t*normVec+[p1.x p1.y] # it's not linear,cause last part 
	line(t)=t*normVec  #it's  linear system
	tspan=-10:1:10
	xs1=[]
	ys1=[]
	xs2=[]
	ys2=[]
	data1=[affineline(t) for t in tspan]
	data2=[line(t) for t in tspan]
	for  i in data1
		push!(xs1,i[1])
		push!(ys1,i[2])
		
	end
	for  i in data2
		push!(xs2,i[1])
		push!(ys2,i[2])
		
	end
	plot(xs1,ys1,framestyle=:origin,size=(300,300),label="affineline")
	plot!(xs2,ys2,framestyle=:origin,ls=:dash,color=:red,size=(300,300),label="line line")
	
	
end

# ╔═╡ 972775c8-86b6-4357-a971-f14446dc07cd
md"""
### what difference of $vec1-vec2$ and $vec2-vec1$ ?

$$vec1-vec2=\begin{bmatrix}
2\\ 
0\\
\end{bmatrix} -\begin{bmatrix}
0\\ 
-2\\
\end{bmatrix}=\begin{bmatrix}
2-0\\ 
0-(-2)\\
\end{bmatrix}=\begin{bmatrix}
2\\ 
2\\
\end{bmatrix}$$

$$vec2-vec1=\begin{bmatrix}
0\\ 
-2\\
\end{bmatrix} -\begin{bmatrix}
2\\ 
0\\
\end{bmatrix}=\begin{bmatrix}
0-2\\ 
-2-0\\
\end{bmatrix}=\begin{bmatrix}
-2\\ 
-2\\
\end{bmatrix}$$

seems they are different,but we can change a little

$$vec1-vec2=
\begin{bmatrix}
2\\ 
0\\
\end{bmatrix} -\begin{bmatrix}
0\\ 
-2\\
\end{bmatrix}=\begin{bmatrix}
2-0\\ 
0-(-2)\\
\end{bmatrix}=1\ast \begin{bmatrix}
2\\ 
2\\
\end{bmatrix}$$

$$vec2-vec1=\begin{bmatrix}
0\\ 
-2\\
\end{bmatrix} -\begin{bmatrix}
2\\ 
0\\
\end{bmatrix}=\begin{bmatrix}
0-2\\ 
-2-0\\
\end{bmatrix}=\begin{bmatrix}
-2\\ 
-2\\
\end{bmatrix}=-1\ast \begin{bmatrix}
2\\ 
2\\
\end{bmatrix}$$

they are all scaling vector $\begin{bmatrix}
2\\ 
2\\
\end{bmatrix}$

for convient we can change more

$$\begin{bmatrix}
-2\\ 
-2\\
\end{bmatrix}=-2\ast \begin{bmatrix}
1\\ 
1\\
\end{bmatrix}$$

**plot a line(not affine line)  we just need a vector execpt origin , then we can scaling it . cause they have same direction , they are living in a  one dimension world ,they are 1d creature**
"""

# ╔═╡ f31ad001-dbcb-442f-80dd-87643ef0c6d6
let
	

	θ=1/2pi
	pa=[2 1]
	pb=[3 1]
	pc=[3 2]
	pd=[2 2]
	s1=[pa;pb;pc;pd;pa]
	smatrix=[2 0;0 1.5]
	rotmatrix=[cos(θ) sin(θ);
		       -sin(θ) cos(θ)
	]
	s2=s1*smatrix
	s3=s1*rotmatrix
	#plot(s1[:,1],s1[:,2] ,label="origin rect")
	#plot!(s2[:,1],s2[:,2],label="scaling rect")		
	plot(s3[:,1],s3[:,2],label="rotating rect")	
	#@show s3
	#s3
end

# ╔═╡ 05082788-9ea0-4147-a158-34739dffd913
let
	#使用齐次坐标的绘图方法
	function vec(p)
	   return [p.x p.y ]
    end
	function trans(p::HomPoint)
	return [p.x p.y p.h]
    end
	p1=HomPoint(2.0,1.0,1)
	p2=HomPoint(3.0,1.0,1)
	p3=HomPoint(3.0,2.0,1)
	p4=HomPoint(2.0,2.0,1)
    
	matrix=[vec(p1);vec(p2);vec(p3);vec(p4);vec(p1)]
	hmatrix=[trans(p1);trans(p2);trans(p3);trans(p4);trans(p1)]
    smatrix=[ 2 0 0;
		      0 2 0;
		      0 0 1    
	         ]
    hs=hmatrix*smatrix
    
    plot(matrix[:,1],matrix[:,2])
    plot!(hs[:,1],hs[:,2])
	
end

# ╔═╡ b0c729e4-2ebc-4ac0-a508-fdb5660b0041
let
  
	p1=HomPoint(20,10,1)
	p2=HomPoint(22,10,1)
	p3=HomPoint(22,12,1)
	p4=HomPoint(20,12,1)
    origin=HomPoint(21,11,1)
    vorigin=vec(origin)
	matrix=[vec(p1);vec(p2);vec(p3);vec(p4);vec(p1)]
	hmatrix=[trans(p1);trans(p2);trans(p3);trans(p4);trans(p1)]
    tmatrix=[ 1 1 0;
		      -1 1 0;
		      11 -21 1  
	         ]
    hs=hmatrix*tmatrix
    scatter(vorigin[:,1],vorigin[:,2],label="(21,11)")
    plot!(matrix[:,1],matrix[:,2],size=(400,400))
    plot!(hs[:,1],hs[:,2])
    
end

# ╔═╡ 9d56da6a-f7e3-4bde-8702-9c3b9695ed7c
md"reflex transformation"

# ╔═╡ d3987d6f-96e6-4b6b-9514-916ecf8a631e
let
   
   p1=HomPoint(1,1,1)
   vecp1=vec(p1)
   homp1=trans(p1)
   reflexmatrix=[ -1 0 0;
	              0  -1 0;
	              0  0  1
   ]
   reflexp1=homp1*reflexmatrix
   scatter(vecp1[:,1],vecp1[:,2],framestyle=:origin ,label="origin",size=(300,300))
   scatter!(reflexp1[:,1],reflexp1[:,2],framestyle=:origin,label="reflex",size=(300,300))
	
end

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[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
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[[deps.SymPy]]
deps = ["CommonEq", "CommonSolve", "Latexify", "LinearAlgebra", "Markdown", "PyCall", "RecipesBase", "SpecialFunctions"]
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[[deps.TOML]]
deps = ["Dates"]
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[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
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[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits", "Test"]
git-tree-sha1 = "5ce79ce186cc678bbb5c5681ca3379d1ddae11a1"
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[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[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", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "f90022b44b7bf97952756a6b6737d1a0024a3233"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
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[[deps.TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "5683455224ba92ef59db72d10690690f4a8dc297"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
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[[deps.TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[deps.Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"

[[deps.URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

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

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[deps.VersionParsing]]
git-tree-sha1 = "58d6e80b4ee071f5efd07fda82cb9fbe17200868"
uuid = "81def892-9a0e-5fdd-b105-ffc91e053289"
version = "1.3.0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[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", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[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", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

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

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

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

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "78736dab31ae7a53540a6b752efc61f77b304c5b"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.8.6+1"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

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

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

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
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# ╠═6888211b-f064-4924-b084-5bf00dead7e8
# ╠═8c032c77-616a-436f-b8ae-784afa547497
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# ╠═c483fe19-2bc4-43f5-aa56-ba93eec20275
# ╠═c461a36d-8cd3-47c8-9c06-cfaf88f607ad
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# ╠═f31ad001-dbcb-442f-80dd-87643ef0c6d6
# ╠═05082788-9ea0-4147-a158-34739dffd913
# ╠═b0c729e4-2ebc-4ac0-a508-fdb5660b0041
# ╠═9d56da6a-f7e3-4bde-8702-9c3b9695ed7c
# ╠═d3987d6f-96e6-4b6b-9514-916ecf8a631e
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
