WIP: Add demonstrative examples to documentation

.github/workflows/documentation.yml

@@ -19,7 +19,7 @@ jobs:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v2
         with:
-          version: '1.9'
+          version: '1.10'
       - uses: julia-actions/cache@v2
       - name: Install dependencies
         run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'

docs/Project.toml

@@ -1,12 +1,18 @@
 [deps]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 MeshIntegrals = "dadec2fd-bbe0-4da4-9dbe-476c782c8e47"
 Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
 BenchmarkTools = "1"
+CairoMakie = "0.15"
+Colors = "0.13"
+Distributions = "0.25"
 Documenter = "1"
 Meshes = "0.53, 0.54"
 Unitful = "1.19"

docs/make.jl

@@ -16,6 +16,9 @@ makedocs(
             "Support Status" => "support.md",
             "Tips" => "tips.md"
         ],
+        "Examples" => [
+            "Darts Strategy Analysis" => "examples/darts.md"
+        ],
         "Developer Notes" => [
             "Changelog" => "developer/CHANGELOG.md",
             "How it Works" => "developer/how_it_works.md",

docs/src/examples/darts.md

@@ -0,0 +1,138 @@
+# Darts (Draft)
+
+Steps
+- Construct a set of geometries representing a dartboard with individual sector scores
+- Develop a model of the dart trajectory with probability density distribution
+- Use integration over each geometry to determine the probabilities of particular outcomes
+- Calculate expected value for the throw, repeat for other distributions to compare strategies
+
+```@example darts
+using CairoMakie
+using Colors
+using Distributions
+using Meshes
+using MeshIntegrals
+using Unitful
+using Unitful.DefaultSymbols: mm, m
+
+red = colorant"red"
+black = colorant"black"
+white = colorant"white"
+green = colorant"green"
+
+# For containing any scored landing region on the dart board
+struct ScoredRegion{G, C}
+    geometry::G
+    points::Int64
+    color::C
+end
+
+# For defining an annular region
+struct Sector{L, A}
+    r_inner::L
+    r_outer::L
+    phi_a::A
+    phi_b::A
+end
+Sector(rs, phis) = Sector(rs..., phis...)
+
+# Sector -> Ngon
+function Ngon(sector::Sector; N=8)
+	ϕs = range(sector.phi_a, sector.phi_b, length=N)
+    arc_o = [point(sector.r_outer, ϕ) for ϕ in ϕs]
+    arc_i = [point(sector.r_inner, ϕ) for ϕ in reverse(ϕs)]
+    return Meshes.Ngon(arc_o..., arc_i...)
+end
+
+function _Point3f(p::Meshes.Point)
+    x, y, z = ustrip.(m, [p.coords.x, p.coords.y, p.coords.z])
+    return Point3f(x, y, z)
+end
+
+_poly(circle::Meshes.Circle; N=32) = [(_Point3f(circle(t)) for t in range(0, 1, length=N))...]
+_poly(ngon::Meshes.Ngon) = [(_Point3f(pt) for pt in ngon.vertices)...]
+```
+
+## Modeling the Dartboard
+
+Model the dartboard
+```@example darts
+dartboard_center = Meshes.Point(0m, 0m, 1.5m)
+dartboard_plane = Plane(dartboard_center, Meshes.Vec(1, 0, 0))
+
+function point(r::Unitful.Length, ϕ)
+    t = ustrip(m, r)
+    dartboard_plane(t * sin(ϕ), t * cos(ϕ))
+end
+
+# Scores on the Board
+ring1 = [20, 1, 18, 4, 13, 6, 10, 15, 2, 17, 3, 19, 7, 16, 8, 11, 14, 9, 12, 5]
+ring2 = 3 .* ring1
+ring3 = ring1
+ring4 = 2 .* ring1
+board_points = hcat(ring1, ring2, ring3, ring4)
+
+# Colors on the board
+ring1 = repeat([black, white], 10)
+ring2 = repeat([red, green], 10)
+ring3 = ring1
+ring4 = ring2
+board_colors = hcat(ring1, ring2, ring3, ring4)
+
+# Sector geometries
+sector_width = 2π/20
+phis_a = range(0, 2π, 20) .- sector_width/2
+phis_b = range(0, 2π, 20) .+ sector_width/2
+phis = Iterators.zip(phis_a, phis_b)
+rs = [ (16mm, 99mm), (99mm, 107mm), (107mm, 162mm), (162mm, 170mm) ]
+board_coords = Iterators.product(phis, rs)
+board_sectors = map(((phis, rs),) -> Sector(rs, phis), board_coords)
+board_ngons = Ngon.(board_sectors)
+
+# Consolidate the Sectors
+sector_data = Iterators.zip(board_ngons, board_points, board_colors)
+board_regions = map(args -> ScoredRegion(args...), sector_data)
+
+# Center region
+bullseye_inner = ScoredRegion(Meshes.Circle(dartboard_plane, 6.35mm), 50, red)
+bullseye_outer = ScoredRegion(Ngon(Sector((6.35mm, 16.0mm), (0.0, 2π)); N=32), 25, green)
+
+# Get set of all regions
+all_regions = vcat(vec(board_regions), bullseye_inner, bullseye_outer)
+
+# Initialize a 3D figure
+fig = Figure()
+#ax = LScene(fig[1, 1], scenekw=(show_axis=true,))
+ax = Axis3(fig[1, 1]; xlabel="X", ylabel="Y", zlabel="Z")
+limits!(ax, -0.1..0.1, -1.5..1.5, 0..3; fixed=true)
+
+# Populate the dart board scored regions
+for region in all_regions
+    poly!(ax, _poly(region.geometry), color=region.color)
+end
+
+fig
+```
+
+## Modeling the Dart Trajectory
+
+Define a probability distribution for where the dart will land
+```
+# TODO
+dist = MvNormal(μs, σs)
+```
+
+Integrand function is the distribution's PDF value at any particular point
+```
+# TODO
+function integrand(p::Point)
+    v_error = dist_center - p
+    pdf(dist, v_error)
+end
+```
+
+Example image of trajectory probability distribution on board
+
+## Strategy Evaluation
+
+Use these tools to evaluate different aiming/throwing parameters and their impact on expected scores.