### A Pluto.jl notebook ###
# v0.20.17

using Markdown
using InteractiveUtils

# ╔═╡ 0fea38f6-2c9e-43c6-bfc1-267ff220a0cc
begin
	using Drifters, PlutoUI, CairoMakie
	"done with loading packages"
end

# ╔═╡ abdcae13-40fe-495a-bf6c-dba5549c558a
TableOfContents()

# ╔═╡ 5c7e4e72-3f69-11ec-258b-6bcfdc7b1d65
md"""# Simple Three Dimensional Flow Field

Simulate the trajectory of an individual point, first in a perfectly circular flow (a.k.a. solid body rotation). Then add a convergent term to obtain a spiraling trajectory, and a constant vertical velocity for the third dimension. These simple flow configurations can be thought of as idealized models e.g. ocean meso-scale eddies.

For additional documentation e.g. see :
[1](https://JuliaClimate.github.io/Drifters.jl/dev/),
[2](https://JuliaClimate.github.io/MeshArrays.jl/dev/),
[3](https://docs.juliadiffeq.org/latest/solvers/ode_solve.html),
[4](https://en.wikipedia.org/wiki/Displacement_(vector))

### Exercise examples: 

- make the sinking velocity decrease with time (hint: it increases in the original notebook) 
- change the number of times the particle goes around the origin
- flow field parameters (e.g. intensity and sign of the convergent term)
"""

# ╔═╡ aadd082a-3ed9-41b7-ba5e-7c5f77d59508
md"""## 1. Problem Configuration

### 1.1 Gridded Flow Fields

Set up an idealized flow field which consists of 
[rigid body rotation](https://en.wikipedia.org/wiki/Rigid_body), 
plus a convergent term, plus a sinking term.
"""

# ╔═╡ 2200503c-605c-4dfd-878f-ffea2431f7ba
begin
	(np,nz)=(24,16) #gridded domain size (horizontal and vertical)
	u,v,w=Drifters.vortex_flow_field(np=np,nz=nz) #staggered velocity arrays
	F=FlowFields(u,u,v,v,0*w,1*w,[0,19.95*2*pi]); #FlowFields data structure
	"Done with defining the flow fields."
end

# ╔═╡ bde49eaf-3747-4edf-b712-3ee6f08ffe20
md"""### 1.2 Initialize Individuals

Here just one individual is initialized at [np*1/3,np*1/3,nz*1/3] in the three-dimensional space of the flow fields."""

# ╔═╡ c60a48e0-6f51-44b0-bd6e-332e04d2d332
begin
	(x,y,z)=(np*1/3,np*1/3,nz*1/3)
	I=Individuals(F,x,y,z)
end

# ╔═╡ 45762eb1-7404-4524-8d1d-788a70f8f5ef
md"""### 1.3 A Closer Look

The above `Individuals` constructor wraps up F, the initial position, and other needed components within I. **At this point, you can either jump to section 2 or read through the next code cell**
to learn more about how the details as needed e.g. if you wanted to overide default options 
that were selected for you by the section 1.2 constructor.
"""

# ╔═╡ b70d76d1-09f3-462a-b550-8fa51cb90c2c
begin
	# Initial position is 
	
	📌=[x,y,z] 
	
	# and the data structure ([DataFrame](http://juliadata.github.io/DataFrames.jl/stable/)) 
	# to record properties along the individual's path accordingly. 
	
	🔴 = DataFrame(ID=Int[], x=Float64[], y=Float64[], z=Float64[], t=Float64[])

	# It is the postprocessing function's responsibility to provide the record. It is thus 
	# important that this intermediary (`postproc`) be consistent with the solver setup (`sol`) 
	# and the expected record format (`🔴`).
	
	function postproc(sol,F::FlowFields;id=missing,T=missing)
	    df=postprocess_xy(sol,F,id=id,T=T)
	    #add third coordinate
	    z=sol[3,:]
	    df.z=z[:]
	    return df
	end
	
	# The velocity function `🚄` relies only on flow fields obtained from
	# `F` (which is defined above) to interpolate velocity at the specified
	# space-time position (e.g. those of individuals). 
	
	🚄 = dxdt!
	
	# Now that every thing needed to carry out the computation is in place, 
	# we wrap up the problem configuration in a struct (`Individuals`) which 
	# links to the initial positions, flow fields, etc. all that will be 
	# necessary to compute trajectories over time (`∫!(I,T)`).
	
	#assemble as a NamedTuple:
	I0=(position=📌,record=🔴,velocity=🚄,
	postprocessing=postproc,parameters=F)
	
	#construct Individuals from NamedTuple:
	𝐽=Individuals(I0)
end

# ╔═╡ 8cc54cc2-5284-40b1-9a30-0ad6f725053f
md"""## 2 Trajectory Simulations

The `∫!` function call below returns the final positions & updates `I.📌` accordingly. It also records properties observed along the trajectory in `I.🔴`. 
Simple methods to visualize the individual trajectory (plot or movie) are provided at the end.

### 2.1 Compute Trajectory
"""

# ╔═╡ 503c8702-df0b-4495-8245-4ba6608431e3
begin
	T=(0.0,I.P.T[2])
	∫!(I,T)
end

# ╔═╡ 32a8b0ee-e61d-495b-ba53-56a6c6126950
md"""### 2.2 Visualize Trajectory"""

# ╔═╡ dd62433c-2274-4c6f-9e27-34bc2c620df1
f=plot( DriftersDataset( data=(I=I,), options=(plot_type=:simple_plot2,) ) )

# ╔═╡ 250d011e-57db-4d80-b16e-dbc28fec9fba
begin
	#plt=myplot(nt)
	#scatter!(plt,[📌[1]],[📌[2]],[📌[3]])
	#scatter!(plt,[I.🔴.x[end]],[I.🔴.y[end]],[I.🔴.z[end]])
	#scatter!(plt,[I.🔴.x[1]],[I.🔴.y[1]],[I.🔴.z[1]])
end

# ╔═╡ a0bf6d10-5d42-481b-8720-dadd3f727e8b
md"""### 2.3 Animation example"""

# ╔═╡ 2b8ee43d-1225-4475-91c9-161cf612bfb2
begin
	if false
		p=Int(ceil(nt/50))
		tt=1:p:nt
		tt=tt.+(nt-maximum(tt))
	
		fil=joinpath(tempdir(),"solid_body_rotation.mp4")
		record(f,fil, tt; framerate = 20) do t
			time[] = t
		end
		LocalResource(fil)
	else
		"""try code in this cell to generate animation"""
	end
end



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version = "0.18.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.1+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.6.0+0"

[[deps.ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "f492b7fe1698e623024e873244f10d89c95c340a"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.10.1"

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

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.7+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.libaec_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1aa23f01927b2dac46db77a56b31088feee0a491"
uuid = "477f73a3-ac25-53e9-8cc3-50b2fa2566f0"
version = "1.1.4+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "4bba74fa59ab0755167ad24f98800fe5d727175b"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.12.1+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "125eedcb0a4a0bba65b657251ce1d27c8714e9d6"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.17.4+0"

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

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "07b6a107d926093898e82b3b1db657ebe33134ec"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.50+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "libpng_jll"]
git-tree-sha1 = "c1733e347283df07689d71d61e14be986e49e47a"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.5+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.libwebp_jll]]
deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"]
git-tree-sha1 = "4e4282c4d846e11dce56d74fa8040130b7a95cb3"
uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2"
version = "1.6.0+0"

[[deps.libzip_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "OpenSSL_jll", "XZ_jll", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "86addc139bca85fdf9e7741e10977c45785727b7"
uuid = "337d8026-41b4-5cde-a456-74a10e5b31d1"
version = "1.11.3+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2022.0.0+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 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "4.1.0+0"
"""

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