axi2.jl

### A Pluto.jl notebook ###
# v0.18.0

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 17a6af91-6978-4878-af60-d619c44e6363
begin
	import Pkg
	eval(quote
		Pkg.add(url="https://github.com/paulgb/PenPlots.jl")
	end)
	using PenPlots
end

# ╔═╡ c065248a-25cb-4f4b-a048-482344e80b7a
using Triangulate

# ╔═╡ 3027890b-196b-4a65-9f17-0180d21f6beb
using HypertextLiteral

# ╔═╡ 42b04181-4784-4906-b869-dea036f1afb7
using CoordinateTransformations

# ╔═╡ 440e84f1-b479-4b63-a869-27d74930b08f
using Rotations

# ╔═╡ 017246d7-756f-4e06-b5fb-eabe28c0683e
using Interpolations

# ╔═╡ d9f51e7e-bcab-4fbb-87ca-b5e7fd06bde4
using LinearAlgebra

# ╔═╡ ba23cd4b-9c51-4b3b-888f-e170fd4edbdd
using BenchmarkTools

# ╔═╡ dc30e200-edd3-457c-9cb9-56a34f6a112c
using PlutoUI

# ╔═╡ 264dad85-32a2-42f5-80b6-6644112ab8a1
using Printf

# ╔═╡ e6d06f83-18d1-4bbe-8e12-15814316441b
using StaticArrays

# ╔═╡ e9010ab3-cdb4-49f9-b2c3-705437ea5ebf
points = [
	0.0 0
	1.0 0
	0.0 1
]

# ╔═╡ 034c5094-f107-4ed2-bd9d-b964b4ad669d
let n=10,raster=10
    triin=Triangulate.TriangulateIO()
    triin.pointlist=hcat(unique([ Cdouble[rand(1:raster)/raster, rand(1:raster)/raster] for i in 1:n])...)
    display(triin)
    (triout, vorout)=Triangulate.triangulate("Q", triin)
end

# ╔═╡ 4b89fc14-755d-4df3-a800-05c5a089b3db
let n=10,raster=10
    hcat(unique([ Cdouble[rand(1:raster)/raster, rand(1:raster)/raster] for i in 1:n])...)
end

# ╔═╡ 288decf2-88ca-4a74-bde0-7b39ddb7f88a
function to_triangulate_mat(ps::AbstractVector{<:SVector})
	# const output_type = eltype(eltype(ps))
	# output_type = Float64
	A = Matrix{Float64}(undef, length(eltype(ps)), length(ps))
	for (i,p) in enumerate(ps)
		@inbounds A[:,i] .= p
	end
	A
end

# ╔═╡ 6eb00ffe-9b67-4ad5-a00e-86d02f673664
aa = rand(2,10)

# ╔═╡ cff314d6-7e2d-42d7-b4ab-30b76cac82bc
reinterpret(10, SVector{Float64,2}, aa)

# ╔═╡ 976d9aa3-bf54-4630-980b-bfa063a56819
function triangulate_raw(ps::AbstractVector{<:SVector}; switches::String="Q")
	mat = to_triangulate_mat(ps)
    triin=Triangulate.TriangulateIO()
    triin.pointlist=mat
    Triangulate.triangulate(switches, triin)
end

# ╔═╡ 83fee9f6-106a-4ca7-b93f-15b9038cde8b
function triangulate(args...; kwargs...)
	t, v = triangulate_raw(args...; kwargs...)

	z = t.trianglelist
	[
		SVector{4,Int}(z[1,j], z[2,j], z[3,j], z[1,j] )
		for j in 1:size(z,2)
	]
end

# ╔═╡ a97e2c01-2245-479f-8d1f-bf660f23d767
n(prefix::String, value::Float64) = "$(prefix)$(@sprintf("%.15f",value))"

# ╔═╡ a223cf19-8dc7-4e74-8a30-48475b2c8196
n(prefix::String, value::Bool) = prefix

# ╔═╡ e4275a7e-a03d-4181-91e8-06361fc80d96
n(prefix::String, value::Nothing) = ""

# ╔═╡ 00549702-11c7-49c0-a928-88251eb7d186
# let n=10,raster=10
#     triin=Triangulate.TriangulateIO()
#     triin.pointlist=hcat(unique([ Cdouble[rand(1:raster)/raster, rand(1:raster)/raster] for i in 1:n])...)
#     display(triin)
#     Triangulate.triangulate("Qa38.986q18.986037025490717", triin)[1].trianglelist
# end

# ╔═╡ 84d06013-be32-4722-ab5b-61ff9ef84fbe
function build_switches(; 
		max_area::Union{Float64,Nothing}=nothing, 
		min_angle::Union{Float64,Nothing}=nothing,
		quiet::Bool=true,
	)
	@assert isnothing(min_angle) || min_angle < 28.6 "Oh ohhh"

	string(
		n("Q", quiet),
		n("a", max_area),
		n("q", min_angle),
	)
end

# ╔═╡ bd7b2e9f-205f-4999-b6b7-288f448c70bf
function triangulate_true(args...; kwargs...)
	t, v = triangulate_raw(args...; switches=build_switches(;kwargs...))

	pl = t.pointlist
	new_pl = [
		SVector{2,Float64}(pl[1,j], pl[2,j] )
		for j in 1:size(pl,2)
	]
	tl = t.trianglelist
	new_tl = [
		SVector{4,Int}(tl[1,j], tl[2,j], tl[3,j], tl[1,j] )
		for j in 1:size(tl,2)
	]
	new_pl, new_tl
end

# ╔═╡ 19da2136-a5e4-476e-95a9-853960e3a50f
macro label_bind(name::Symbol, ex::Expr)
	quote
		@htl("""
		<code style='font-weight: bold'>$($(String(name)))</code>: $(@bind $(name) $(esc(ex)))
		""")
	end
end

# ╔═╡ 8e4955bb-59cd-4f15-91af-c6ccf675f1b3
@label_bind max_area PlutoUI.Experimental.transformed_value(
					x -> 10^x, 
					Slider(LinRange(-0.5,4,100); default=4)
			)

# ╔═╡ 5d1c8f91-f0b9-4a5d-9463-0438c57b271f
@label_bind min_angle Slider(0:.1:28)

# ╔═╡ ce02fd38-a690-426e-a10e-e768fc222981
xx = 30 .* randn(SVector{2,Float64},10)

# ╔═╡ 4c755e8a-3568-43a9-b730-aa1f3eea353c
triangulate_raw(xx; switches="Q")[1]

# ╔═╡ 4ba3975c-a449-4c6d-8ef2-d3106f091efd
Path([
	SVector(1,2),
	SVector(2,2),
	SVector(1.2,1),
	SVector(1,1.9),
])

# ╔═╡ f49f35fc-5005-4baf-be54-cb3a46fc2479
# xx = [10000*SVector(p...) for p in small_dot.points[20:end]]

# ╔═╡ 17c2953f-96ff-409c-949e-561158bcf6c2
const fillable_tri = 20*randn(SVector{2,Float64},3)

# ╔═╡ f63083d5-eb82-4f65-8799-c2cc59385ab0
@bind fill_angle Slider(LinRange(0,2π,500))

# ╔═╡ 90c00e90-13ba-4b32-a85c-d6fd5394164b
rotate_90(p::SVector{2,<:Real}) = SVector(-p[2], p[1])

# ╔═╡ d235e2f7-47c0-49e3-b000-1027413dd6a5
dot([1,1], rotate_90(SVector(0.5,0.5)))

# ╔═╡ 9c72e77e-7cd3-4dc0-9e98-d2a4101329ac
dot([1,0], rotate_90(SVector(0.5,0.5)))

# ╔═╡ ebb7519b-97b9-4a24-bd43-dec89a93fab4


# ╔═╡ 6e23ba2a-ceff-411c-94c1-c16e293a5b9b
minabs(a,b) = abs(a) < abs(b) ? a : b

# ╔═╡ 28162e97-0166-45d4-b07d-0ecf228e9707
function fill_with_pattern(triangle_corners; step::Real=1.5, direction)
	a, b, c = triangle_corners

	AB = b - a
	AC = c - a
	BC = c - b

	crossAB = rotate_90(AB)

	z1, z2 = dot(rotate_90(direction), AC), dot(rotate_90(direction), BC)
	# @info "asdf" z1 z2

	# if z1 == 0
	# 	if 
	# 	return fill_with_pattern((b,c,a); step, direction)
	# end
	# if z2 == 0
	# 	# that's fine
	# end
	if z1 < 0
		return fill_with_pattern((c,b,a); step, direction)
	end
	if z2 > 0
		return fill_with_pattern((a,c,b); step, direction)
	end

	# direction = @something(direction, crossAB)
	
	
	# if dot(AB,AC) < 0
	# 	return fill_with_pattern((b,a,c))
	# end
	# if dot(-AB,BC) < 0
	# 	return fill_with_pattern((a,c,b))
	# end
	ABlength = norm(AB)
	AClength = norm(AC)
	BClength = norm(BC)

	direction *= ABlength / norm(direction)

	step_AB = step / abs(dot(crossAB,direction)) * ABlength
	map(step_AB/2:step_AB:1) do x
		s = a + x * AB

		yAC = x * dot(AC,crossAB) / dot(direction,rotate_90(AC))
		yBC = -(1-x) * dot(BC,crossAB) / dot(direction,rotate_90(BC))
		
		eAC = s + (
			z1 == 0 ? yBC : 
			z2 == 0 ? yAC : 
			minabs(yAC, yBC)
		) * direction
		# eAC = s + yAC * direction
		Path([s,eAC])
	end
end

# ╔═╡ 61e0b87d-e07c-4e4e-a9e3-889dc865d0dd
LinRange(fillable_tri[1], fillable_tri[2], 10)

# ╔═╡ 8407ef41-63ed-4cf6-a069-33010f1914cb
"Split a `Path` into the single-line paths that it consists of, but check the return type..."
split_lines(p::Path)::Vector{Tuple{Point,Point}} = [
	# Use `extrema` to "sort" the two points (which just works apparently!). This will canonalize the result.
	extrema((p.points[i], p.points[i+1]))
	for i in 1:length(p.points)-1
]

# ╔═╡ abe6e1b4-ccf0-4abd-81c5-4f0b0df7fe94
flatmap(args...) = vcat(map(args...)...)

# ╔═╡ b294fc41-eb86-44dc-b608-96d538189a10
function without_duplicate_lines(paths::MultiPath)::MultiPath
	original_lines = flatmap(split_lines, paths)
	unique_lines = Set(original_lines)

	sort([Path([l...]) for l in unique_lines])
end

# ╔═╡ d1820c35-6acd-41fd-9138-ca37bdbb8126
result = let
	pl, tl = triangulate_true(xx; max_area, min_angle)
	
		
	[
		without_duplicate_lines([
			Path(pl[t])
			for t in tl
		])...,
		# [
		# 	Path(200 .* (degree_rotation(rand(0:359)),) .* (small_dot.points) .+ (x,))
		# 	for x in xx
		# ]...,
		flatmap(tl) do t
			fill_with_pattern(
				pl[t]; 
				step=rand(.5:.1:5), 
				direction=degree_rotation(rand(0:359)) * SVector(1,0)
			)
			
		end...
	]
end

# ╔═╡ 84da64fc-a35e-45bf-bcdc-83a7f163621b
result .|> length |> sum

# ╔═╡ 21b0614e-ba9f-4301-a622-6f07fcb9583f
without_duplicate_lines(result) .|> length |> sum

# ╔═╡ 4c5f697c-6ec9-492f-9fda-03aa31ec7362


# ╔═╡ 798f75b7-cfb9-4bf3-bb0c-9a8d063d1c9c
random_subset(xs) = xs[rand(Bool, length(xs))]

# ╔═╡ 667feb4c-d64f-4cf3-b454-8612a09dfdb4
small_triangle = Path([
	SVector(-.1, -.1),
	SVector(0, .07),
	SVector(.1, -.1),
	SVector(-.1, -.1),
] .* .2)

# ╔═╡ f107a173-ebbb-45b9-967f-a99f010cb3fb
small_dot = Path([
	0.01 * x * SVector(cos(x*2π), sin(x*2π))
	for x in LinRange(0,2,100)
])

# ╔═╡ fa475a5f-280d-4d80-ba1d-502ede1ce971
[
	fill_with_pattern(
		fillable_tri; 
		step=2, 
		direction=SVector(cos(fill_angle),sin(fill_angle))
	)...,
	[
		Path(200 .* (degree_rotation(rand(0:0)),) .* (small_dot.points) .+ (x,))
		for x in fillable_tri
	]...,
]

# ╔═╡ 2874c51f-bdee-4070-b129-a40d5f674a1a
[
	[
		Path(xx[t])
		for t in triangulate(xx; switches="Q")
	]...,
	[
		Path(small_dot.points .+ (x,))
		for x in xx
	]...,
]

# ╔═╡ d2a13df5-abed-4bde-b5b9-ccd1dd0818ba
xx

# ╔═╡ daaecfe6-f443-468b-a176-e631b75d5ddd
triangulate_raw(xx; switches="QiC")

# ╔═╡ 7021d17f-5710-4faf-a1cf-54b37ce0bbc7


# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
CoordinateTransformations = "150eb455-5306-5404-9cee-2592286d6298"
HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
PenPlots = "61246389-3d51-4c70-b82d-266223a1b313"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
Rotations = "6038ab10-8711-5258-84ad-4b1120ba62dc"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
Triangulate = "f7e6ffb2-c36d-4f8f-a77e-16e897189344"

[compat]
BenchmarkTools = "~1.3.1"
CoordinateTransformations = "~0.6.2"
HypertextLiteral = "~0.9.3"
Interpolations = "~0.13.5"
PenPlots = "~0.1.0"
PlutoUI = "~0.7.34"
Rotations = "~1.2.0"
StaticArrays = "~1.3.4"
Triangulate = "~2.1.1"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

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uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.3"

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uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

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uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

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uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

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uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

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deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
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version = "0.3.6"

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deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "547aedc234db13379e3c9f9528a3ff8f1a232e9f"
repo-rev = "master"
repo-url = "https://github.com/paulgb/PenPlots.jl"
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uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[deps.PlutoUI]]
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git-tree-sha1 = "8979e9802b4ac3d58c503a20f2824ad67f9074dd"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
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uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[deps.Random]]
deps = ["SHA", "Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

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git-tree-sha1 = "01d341f502250e81f6fec0afe662aa861392a3aa"
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[[deps.Zlib_jll]]
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[[deps.nghttp2_jll]]
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[[deps.p7zip_jll]]
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"""

# ╔═╡ Cell order:
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