From 65dbde4c97d8bc6062b7dffbc249725e9087d02d Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Sun, 31 Aug 2025 09:05:41 -0400
Subject: [PATCH 01/31] Add Examples

---
 docs/make.jl | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/docs/make.jl b/docs/make.jl
index 0cb480e7..e018a62f 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -16,6 +16,9 @@ makedocs(
             "Support Status" => "support.md",
             "Tips" => "tips.md"
         ],
+        "Examples" => [
+            "Changelog" => "examples/darts.md"
+        ],
         "Developer Notes" => [
             "Changelog" => "developer/CHANGELOG.md",
             "How it Works" => "developer/how_it_works.md",

From da49d180c341816e14b3dff4fbee8cc80da9df93 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Sun, 31 Aug 2025 09:17:37 -0400
Subject: [PATCH 02/31] Create darts.md

---
 docs/src/examples/darts.md | 11 +++++++++++
 1 file changed, 11 insertions(+)
 create mode 100644 docs/src/examples/darts.md

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
new file mode 100644
index 00000000..80ba6328
--- /dev/null
+++ b/docs/src/examples/darts.md
@@ -0,0 +1,11 @@
+# Darts (Draft)
+
+Steps
+- Comstruct a set of geomtries representimg 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
+
+## Modeling the Datboard
+
+## Modeling the Dart Trajectory

From a4b128a8a5fc7994a4b857a105ec752ec4e0ef8e Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Mon, 1 Sep 2025 22:23:00 -0400
Subject: [PATCH 03/31] Add details

---
 docs/src/examples/darts.md | 43 ++++++++++++++++++++++++++++++++++++--
 1 file changed, 41 insertions(+), 2 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 80ba6328..e2b61381 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -1,11 +1,50 @@
 # Darts (Draft)
 
 Steps
-- Comstruct a set of geomtries representimg a dartboard with individual sector scores
+- Comstruct a set of geometries representimg 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
 
-## Modeling the Datboard
+```@example darts
+using Meshes
+using MeshIntegrals
+using Unitful
+```
+
+## Modeling the Dartboard
+
+Model the geometries
+```@example darts
+center = Point(0u"m", 0u"m", 1.5u"m")
+point(r, ϕ) = center + Meshes.Vec(0u"m", r*sin(ϕ)*u"m", r*cos(ϕ)*u"m")
+
+struct Sector{L, A}
+    r_inner::L
+    r_outer::L
+    phi_a::A
+    phi_b::A
+    points::Int64
+end
+
+function to_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 Ngon(arc_o..., arc_i...)
+end
+```
+
+Point system
+```@example darts
+sector_width = 2pi/20
+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
+
+bullseye_inner = (points=50,)
+bullseye_outer = (points=25,)
+```
 
 ## Modeling the Dart Trajectory

From 15ed2b85fc76bdeb47a8c97f3497ac220d9ce251 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Tue, 2 Sep 2025 22:17:34 -0400
Subject: [PATCH 04/31] Update page name

---
 docs/make.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/make.jl b/docs/make.jl
index e018a62f..fd2311ba 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -17,7 +17,7 @@ makedocs(
             "Tips" => "tips.md"
         ],
         "Examples" => [
-            "Changelog" => "examples/darts.md"
+            "Darts Strategy Analysis" => "examples/darts.md"
         ],
         "Developer Notes" => [
             "Changelog" => "developer/CHANGELOG.md",

From 39834d9a3a50f66796a3731c764b7a024a87c395 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 5 Sep 2025 21:26:39 -0400
Subject: [PATCH 05/31] Add more details

---
 docs/src/examples/darts.md | 64 +++++++++++++++++++++++++++++---------
 1 file changed, 50 insertions(+), 14 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index e2b61381..f0786713 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -1,12 +1,15 @@
 # Darts (Draft)
 
 Steps
-- Comstruct a set of geometries representimg a dartboard with individual sector scores
+- 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
 
+Note: can use `@setup darts` block to hide some implementation code
+
 ```@example darts
+# using Distributions
 using Meshes
 using MeshIntegrals
 using Unitful
@@ -14,11 +17,43 @@ using Unitful
 
 ## Modeling the Dartboard
 
-Model the geometries
+Define a dartboard coordinate system
+```@example darts
+dartboard_center = Point(0u"m", 0u"m", 1.5u"m")
+dartboard_plane = Plane(dartboard_center, Meshes.Vec(1, 0, 0))
+
+function point(r::Unitful.Length, ϕ)
+    t = ustrip(r, u"m")
+    dartboard_plane(t * sin(ϕ), t * cos(ϕ))
+end
+```
+
+Model the bullseye region
+```@example darts
+bullseye_inner = (geometry = Circle(dartboard_plane, 6.35u"mm"), points = 50)
+bullseye_outer = (geometry = Circle(dartboard_plane, 16u"mm"), points = 25)
+# TODO subtract center circle region from outer circle region -- or replace with another annular geometry
+```
+
+Model the sectors
 ```@example darts
-center = Point(0u"m", 0u"m", 1.5u"m")
-point(r, ϕ) = center + Meshes.Vec(0u"m", r*sin(ϕ)*u"m", r*cos(ϕ)*u"m")
+# 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)
 
+# Locations
+sector_width = 2π/20
+phis_a = range(0, 2π, 20) .- sector_width/2
+phis_b = range(0, 2π, 20) .+ sector_width/2
+rs_inner = [16, 99, 107, 162]u"mm"
+rs_outer = [99, 107, 162, 170]u"mm"
+```
+
+Define a struct to manage sector data
+```@example darts
 struct Sector{L, A}
     r_inner::L
     r_outer::L
@@ -35,16 +70,17 @@ function to_ngon(sector::Sector; N=8)
 end
 ```
 
-Point system
-```@example darts
-sector_width = 2pi/20
-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
+## Modeling the Dart Trajectory
 
-bullseye_inner = (points=50,)
-bullseye_outer = (points=25,)
+Define a probability distribution for where the dart will land
+```
+dist = MvNormal(μs, σs)
 ```
 
-## Modeling the Dart Trajectory
+Integrand function is the distribution's PDF value at any particular point
+```
+function integrand(p::Point)
+    v_error = dist_center - p
+    pdf(dist, v_error)
+end
+```

From d0792062a845a0fd9c53327b74e850615728ccda Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 5 Sep 2025 22:01:44 -0400
Subject: [PATCH 06/31] Update darts.md

---
 docs/src/examples/darts.md | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index f0786713..7a194415 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -13,25 +13,26 @@ Note: can use `@setup darts` block to hide some implementation code
 using Meshes
 using MeshIntegrals
 using Unitful
+using Unitful.DefaultSymbols: mm, m
 ```
 
 ## Modeling the Dartboard
 
 Define a dartboard coordinate system
 ```@example darts
-dartboard_center = Point(0u"m", 0u"m", 1.5u"m")
+dartboard_center = Point(0m, 0m, 1.5m)
 dartboard_plane = Plane(dartboard_center, Meshes.Vec(1, 0, 0))
 
 function point(r::Unitful.Length, ϕ)
-    t = ustrip(r, u"m")
+    t = ustrip(r, m)
     dartboard_plane(t * sin(ϕ), t * cos(ϕ))
 end
 ```
 
 Model the bullseye region
 ```@example darts
-bullseye_inner = (geometry = Circle(dartboard_plane, 6.35u"mm"), points = 50)
-bullseye_outer = (geometry = Circle(dartboard_plane, 16u"mm"), points = 25)
+bullseye_inner = (geometry = Circle(dartboard_plane, 6.35mm), points = 50)
+bullseye_outer = (geometry = Circle(dartboard_plane, 16mm), points = 25)
 # TODO subtract center circle region from outer circle region -- or replace with another annular geometry
 ```
 
@@ -48,8 +49,9 @@ board_points = hcat(ring1, ring2, ring3, ring4)
 sector_width = 2π/20
 phis_a = range(0, 2π, 20) .- sector_width/2
 phis_b = range(0, 2π, 20) .+ sector_width/2
-rs_inner = [16, 99, 107, 162]u"mm"
-rs_outer = [99, 107, 162, 170]u"mm"
+phis = Iterators.zip(phis_a, phis_b)
+rs = [ (16mm, 99mm), (99mm, 107mm), (107mm, 162mm), (162mm, 170mm) ]
+grid = Iterators.product(phis, rs)
 ```
 
 Define a struct to manage sector data

From 55f403f34cb2ba1bf3066229304c8c5e27a7a176 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Sat, 6 Sep 2025 11:04:21 -0400
Subject: [PATCH 07/31] Update darts.md

---
 docs/src/examples/darts.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 7a194415..985ba080 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -52,6 +52,9 @@ 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) ]
 grid = Iterators.product(phis, rs)
+
+# Collect sector data (points, coordinates)
+sector_data = Iterators.zip(grid, board_points)
 ```
 
 Define a struct to manage sector data
@@ -64,12 +67,17 @@ struct Sector{L, A}
     points::Int64
 end
 
+Sector(points, (phis, rs)) = Sector(rs[1], rs[2], phis[1], phis[2], points)
+
 function to_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 Ngon(arc_o..., arc_i...)
 end
+
+# Convert sector data to geometries
+sector_geometries = map(to_ngon, sector_data)
 ```
 
 ## Modeling the Dart Trajectory

From 2a15296af12f72abb30527e6942337ab874c30ba Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Sat, 6 Sep 2025 16:39:29 -0400
Subject: [PATCH 08/31] Bugfix

---
 docs/src/examples/darts.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 985ba080..2286d2bf 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -77,7 +77,7 @@ function to_ngon(sector::Sector; N=8)
 end
 
 # Convert sector data to geometries
-sector_geometries = map(to_ngon, sector_data)
+sector_geometries =  sector_data .|> Sector .|> to_ngon
 ```
 
 ## Modeling the Dart Trajectory

From d2429c55a54c41169e46de1ca17e1b2ee0099b0d Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Thu, 11 Sep 2025 12:45:40 -0400
Subject: [PATCH 09/31] Add colors and new struct [skip ci]

---
 docs/src/examples/darts.md | 25 ++++++++++++++++++++++---
 1 file changed, 22 insertions(+), 3 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 2286d2bf..838087af 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -9,7 +9,8 @@ Steps
 Note: can use `@setup darts` block to hide some implementation code
 
 ```@example darts
-# using Distributions
+using Colors
+using Distributions
 using Meshes
 using MeshIntegrals
 using Unitful
@@ -32,12 +33,12 @@ end
 Model the bullseye region
 ```@example darts
 bullseye_inner = (geometry = Circle(dartboard_plane, 6.35mm), points = 50)
-bullseye_outer = (geometry = Circle(dartboard_plane, 16mm), points = 25)
+bullseye_outer = (geometry = Circle(dartboard_plane, 16mm), points = 25, color=)
 # TODO subtract center circle region from outer circle region -- or replace with another annular geometry
 ```
 
 Model the sectors
-```@example darts
+```@setup darts
 # 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
@@ -45,6 +46,17 @@ ring3 = ring1
 ring4 = 2 .* ring1
 board_points = hcat(ring1, ring2, ring3, ring4)
 
+# Colors on the board
+red = colorant"red"
+black = colorant"black"
+white = colorant"white"
+green = colorant"green"
+ring1 = repeat([black, white], 10)
+ring2 = repeat([red, green], 10)
+ring3 = ring1
+ring4 = ring2
+board_colors = hcat(ring1, ring2, ring3, ring4)
+
 # Locations
 sector_width = 2π/20
 phis_a = range(0, 2π, 20) .- sector_width/2
@@ -59,6 +71,12 @@ sector_data = Iterators.zip(grid, board_points)
 
 Define a struct to manage sector data
 ```@example darts
+struct ScoredRegion{G, C}
+    geometry::G
+    points::Int64
+    color::C
+end
+
 struct Sector{L, A}
     r_inner::L
     r_outer::L
@@ -77,6 +95,7 @@ function to_ngon(sector::Sector; N=8)
 end
 
 # Convert sector data to geometries
+sectors = 
 sector_geometries =  sector_data .|> Sector .|> to_ngon
 ```
 

From 2bcf0d4d72b5223cd39d6f8d370bd8452618ab45 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Thu, 11 Sep 2025 20:31:33 -0400
Subject: [PATCH 10/31] Add Colors and Distributions to docs Project toml [skip
 ci]

---
 docs/Project.toml | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/docs/Project.toml b/docs/Project.toml
index 8a11b5a1..4acc651a 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,5 +1,7 @@
 [deps]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+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"
@@ -7,6 +9,8 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
 BenchmarkTools = "1"
+Colors = "0.13"
+Distributions = "0.25"
 Documenter = "1"
 Meshes = "0.53, 0.54"
 Unitful = "1.19"

From 701d93096a89dd8b71f7e4346221bb7fbd0b5bf0 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Thu, 11 Sep 2025 21:10:47 -0400
Subject: [PATCH 11/31] Update code

---
 docs/src/examples/darts.md | 90 +++++++++++++++++++-------------------
 1 file changed, 45 insertions(+), 45 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 838087af..e2d2d382 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -6,8 +6,6 @@ Steps
 - 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
 
-Note: can use `@setup darts` block to hide some implementation code
-
 ```@example darts
 using Colors
 using Distributions
@@ -15,6 +13,35 @@ 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 to_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 Ngon(arc_o..., arc_i...)
+end
 ```
 
 ## Modeling the Dartboard
@@ -25,20 +52,13 @@ dartboard_center = Point(0m, 0m, 1.5m)
 dartboard_plane = Plane(dartboard_center, Meshes.Vec(1, 0, 0))
 
 function point(r::Unitful.Length, ϕ)
-    t = ustrip(r, m)
+    t = ustrip(m, r)
     dartboard_plane(t * sin(ϕ), t * cos(ϕ))
 end
 ```
 
-Model the bullseye region
+Model the dart board's sectors
 ```@example darts
-bullseye_inner = (geometry = Circle(dartboard_plane, 6.35mm), points = 50)
-bullseye_outer = (geometry = Circle(dartboard_plane, 16mm), points = 25, color=)
-# TODO subtract center circle region from outer circle region -- or replace with another annular geometry
-```
-
-Model the sectors
-```@setup darts
 # 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
@@ -47,67 +67,47 @@ ring4 = 2 .* ring1
 board_points = hcat(ring1, ring2, ring3, ring4)
 
 # Colors on the board
-red = colorant"red"
-black = colorant"black"
-white = colorant"white"
-green = colorant"green"
 ring1 = repeat([black, white], 10)
 ring2 = repeat([red, green], 10)
 ring3 = ring1
 ring4 = ring2
 board_colors = hcat(ring1, ring2, ring3, ring4)
 
-# Locations
+# 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) ]
-grid = Iterators.product(phis, rs)
+board_coords = Iterators.product(phis, rs)
+board_sectors = map(((phis, rs),) -> Sector(rs, phis), board_coords)
+board_ngons = to_ngon.(board_sectors)
 
-# Collect sector data (points, coordinates)
-sector_data = Iterators.zip(grid, board_points)
+# Consolidate the board's sector data
+sector_data = Iterators.zip(board_ngons, board_points, board_colors)
 ```
 
-Define a struct to manage sector data
+Collect dart board data into `ScoredRegion`s
 ```@example darts
-struct ScoredRegion{G, C}
-    geometry::G
-    points::Int64
-    color::C
-end
-
-struct Sector{L, A}
-    r_inner::L
-    r_outer::L
-    phi_a::A
-    phi_b::A
-    points::Int64
-end
-
-Sector(points, (phis, rs)) = Sector(rs[1], rs[2], phis[1], phis[2], points)
-
-function to_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 Ngon(arc_o..., arc_i...)
-end
+# Sectors
+board_regions = map(args -> ScoredRegion(args...), sector_data)
 
-# Convert sector data to geometries
-sectors = 
-sector_geometries =  sector_data .|> Sector .|> to_ngon
+# Center region
+bullseye_inner = ScoredRegion(Circle(dartboard_plane, 6.35mm), 50, red)
+bullseye_outer = ScoredRegion(to_ngon(Sector((6.35mm, 16.0mm), (0.0, 2π)); N=32), 25, green)
 ```
 
 ## 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)

From 205261d99b52faaf4b9197a92997dca13fd85635 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 07:12:27 -0400
Subject: [PATCH 12/31] Add CairoMakie

---
 docs/Project.toml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/docs/Project.toml b/docs/Project.toml
index 4acc651a..9c5932d8 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,5 +1,6 @@
 [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"
@@ -9,6 +10,7 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
 BenchmarkTools = "1"
+CairoMakie = "0.5"
 Colors = "0.13"
 Distributions = "0.25"
 Documenter = "1"

From 4cc2406cb0c048f333375a5848dda9b48c2bd2ed Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 07:15:27 -0400
Subject: [PATCH 13/31] Update version

---
 docs/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 9c5932d8..e6c9f5b9 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -10,7 +10,7 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
 BenchmarkTools = "1"
-CairoMakie = "0.5"
+CairoMakie = "0.15"
 Colors = "0.13"
 Distributions = "0.25"
 Documenter = "1"

From 24801498ea1c9de19cee5259a09733a403d1beb1 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 07:20:26 -0400
Subject: [PATCH 14/31] Add some illustration code

---
 docs/src/examples/darts.md | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index e2d2d382..7c9cd4d1 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -7,6 +7,7 @@ Steps
 - Calculate expected value for the throw, repeat for other distributions to compare strategies
 
 ```@example darts
+using CairoMakie
 using Colors
 using Distributions
 using Meshes
@@ -42,6 +43,14 @@ function to_ngon(sector::Sector; N=8)
     arc_i = [point(sector.r_inner, ϕ) for ϕ in reverse(ϕs)]
     return Ngon(arc_o..., arc_i...)
 end
+
+function to_makie_poly(circle::Meshes.Circle)
+    return nothing # TODO
+end
+
+function to_makie_poly(ngon::Meshes.Ngon)
+    return nothing # TODO
+end
 ```
 
 ## Modeling the Dartboard
@@ -95,6 +104,21 @@ board_regions = map(args -> ScoredRegion(args...), sector_data)
 # Center region
 bullseye_inner = ScoredRegion(Circle(dartboard_plane, 6.35mm), 50, red)
 bullseye_outer = ScoredRegion(to_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)
+```
+
+Illustration
+```@example darts
+fig = Figure()
+ax = LScene(fig[1, 1], scenekw=(show_axis=true,))
+
+for region in all_regions
+    poly!(ax, to_makie_poly(region.geometry), color=region.color)
+end
+
+fig
 ```
 
 ## Modeling the Dart Trajectory

From 8ffa33c21d8d7c9511ed51b260f457685912064d Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 07:41:02 -0400
Subject: [PATCH 15/31] Update Project.toml

---
 docs/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index e6c9f5b9..1598b3ea 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -10,7 +10,7 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
 BenchmarkTools = "1"
-CairoMakie = "0.15"
+CairoMakie = "0.15 - 0.24"
 Colors = "0.13"
 Distributions = "0.25"
 Documenter = "1"

From 94fe86af019579843fefa7473e0a64bfd501f44d Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 08:04:05 -0400
Subject: [PATCH 16/31] Update Julia version to current LTS

---
 .github/workflows/documentation.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml
index c1f6550f..9704582f 100644
--- a/.github/workflows/documentation.yml
+++ b/.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()'

From c466dbd2660b34e6e265742d92663b5e5fb1cd58 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 08:04:30 -0400
Subject: [PATCH 17/31] Update version bounds

---
 docs/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 1598b3ea..e6c9f5b9 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -10,7 +10,7 @@ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
 
 [compat]
 BenchmarkTools = "1"
-CairoMakie = "0.15 - 0.24"
+CairoMakie = "0.15"
 Colors = "0.13"
 Distributions = "0.25"
 Documenter = "1"

From 07fc306e5be148e5a981408bb0b1716603cfeb26 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 08:17:06 -0400
Subject: [PATCH 18/31] Update ref

---
 docs/src/examples/darts.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 7c9cd4d1..41683231 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -57,7 +57,7 @@ end
 
 Define a dartboard coordinate system
 ```@example darts
-dartboard_center = Point(0m, 0m, 1.5m)
+dartboard_center = Meshes.Point(0m, 0m, 1.5m)
 dartboard_plane = Plane(dartboard_center, Meshes.Vec(1, 0, 0))
 
 function point(r::Unitful.Length, ϕ)

From 3f76ec7429b4c716375f8513b690c989d672959c Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 17:55:25 -0400
Subject: [PATCH 19/31] Combine code blocks (for now)

---
 docs/src/examples/darts.md | 15 ++-------------
 1 file changed, 2 insertions(+), 13 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 41683231..6e64847d 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -55,7 +55,7 @@ end
 
 ## Modeling the Dartboard
 
-Define a dartboard coordinate system
+Model the dartboard
 ```@example darts
 dartboard_center = Meshes.Point(0m, 0m, 1.5m)
 dartboard_plane = Plane(dartboard_center, Meshes.Vec(1, 0, 0))
@@ -64,10 +64,7 @@ function point(r::Unitful.Length, ϕ)
     t = ustrip(m, r)
     dartboard_plane(t * sin(ϕ), t * cos(ϕ))
 end
-```
 
-Model the dart board's sectors
-```@example darts
 # 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
@@ -92,13 +89,8 @@ board_coords = Iterators.product(phis, rs)
 board_sectors = map(((phis, rs),) -> Sector(rs, phis), board_coords)
 board_ngons = to_ngon.(board_sectors)
 
-# Consolidate the board's sector data
+# Consolidate the Sectors
 sector_data = Iterators.zip(board_ngons, board_points, board_colors)
-```
-
-Collect dart board data into `ScoredRegion`s
-```@example darts
-# Sectors
 board_regions = map(args -> ScoredRegion(args...), sector_data)
 
 # Center region
@@ -107,10 +99,7 @@ bullseye_outer = ScoredRegion(to_ngon(Sector((6.35mm, 16.0mm), (0.0, 2π)); N=32
 
 # Get set of all regions
 all_regions = vcat(vec(board_regions), bullseye_inner, bullseye_outer)
-```
 
-Illustration
-```@example darts
 fig = Figure()
 ax = LScene(fig[1, 1], scenekw=(show_axis=true,))
 

From 68ca4e41ba5e996b3ae36ce6deaea98b1c028249 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 19:11:20 -0400
Subject: [PATCH 20/31] Fill in prior todos

---
 docs/src/examples/darts.md | 23 +++++++++++++++++------
 1 file changed, 17 insertions(+), 6 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 6e64847d..1339c6eb 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -37,19 +37,24 @@ end
 Sector(rs, phis) = Sector(rs..., phis...)
 
 # Sector -> Ngon
-function to_ngon(sector::Sector; N=8)
+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 Ngon(arc_o..., arc_i...)
 end
 
-function to_makie_poly(circle::Meshes.Circle)
-    return nothing # TODO
+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
+
+function to_makie_poly(circle::Meshes.Circle; N=32)
+    return [Point3f(circle(t)) for t in range(0, 1, length=N)]
 end
 
 function to_makie_poly(ngon::Meshes.Ngon)
-    return nothing # TODO
+    return [Point3f(pt) for pt in ngon.vertices]
 end
 ```
 
@@ -94,8 +99,8 @@ sector_data = Iterators.zip(board_ngons, board_points, board_colors)
 board_regions = map(args -> ScoredRegion(args...), sector_data)
 
 # Center region
-bullseye_inner = ScoredRegion(Circle(dartboard_plane, 6.35mm), 50, red)
-bullseye_outer = ScoredRegion(to_ngon(Sector((6.35mm, 16.0mm), (0.0, 2π)); N=32), 25, green)
+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)
@@ -126,3 +131,9 @@ function integrand(p::Point)
     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.

From a9241039d5d05abb66f871888df4cb81b3a44008 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 20:15:13 -0400
Subject: [PATCH 21/31] Bugfix

---
 docs/src/examples/darts.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 1339c6eb..d34fbad6 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -92,7 +92,7 @@ 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 = to_ngon.(board_sectors)
+board_ngons = Ngon.(board_sectors)
 
 # Consolidate the Sectors
 sector_data = Iterators.zip(board_ngons, board_points, board_colors)

From ac5e67de4e476fd755b4ef4ddc0ea9ea82243177 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 20:59:55 -0400
Subject: [PATCH 22/31] Bugfix

---
 docs/src/examples/darts.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index d34fbad6..669dedac 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -41,7 +41,7 @@ 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 Ngon(arc_o..., arc_i...)
+    return Meshes.Ngon(arc_o..., arc_i...)
 end
 
 function Point3f(p::Meshes.Point)

From d71a0781035ae73a03bf0796eaad213956326f63 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 21:18:12 -0400
Subject: [PATCH 23/31] Bugfix

---
 docs/src/examples/darts.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 669dedac..1b7760f8 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -45,7 +45,7 @@ function Ngon(sector::Sector; N=8)
 end
 
 function Point3f(p::Meshes.Point)
-    x, y, z = ustrip(m, [p.coords.x, p.coords.y, p.coords.z])
+    x, y, z = ustrip.(m, [p.coords.x, p.coords.y, p.coords.z])
     return Point3f(x, y, z)
 end
 

From 3dad74a0880d470ec13c833ba859a74885bc7ab3 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 21:31:05 -0400
Subject: [PATCH 24/31] Bugfix

---
 docs/src/examples/darts.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 1b7760f8..fdd5def1 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -44,17 +44,17 @@ function Ngon(sector::Sector; N=8)
     return Meshes.Ngon(arc_o..., arc_i...)
 end
 
-function Point3f(p::Meshes.Point)
+function to_Point3f(p::Meshes.Point)
     x, y, z = ustrip.(m, [p.coords.x, p.coords.y, p.coords.z])
     return Point3f(x, y, z)
 end
 
 function to_makie_poly(circle::Meshes.Circle; N=32)
-    return [Point3f(circle(t)) for t in range(0, 1, length=N)]
+    return [to_Point3f(circle(t)) for t in range(0, 1, length=N)]
 end
 
 function to_makie_poly(ngon::Meshes.Ngon)
-    return [Point3f(pt) for pt in ngon.vertices]
+    return [to_Point3f(pt) for pt in ngon.vertices]
 end
 ```
 

From 08a00f07ebcc3b8d5bd7b84ad3f5469771a101cc Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 21:51:48 -0400
Subject: [PATCH 25/31] Bugfix - generate non-svector

---
 docs/src/examples/darts.md | 9 ++-------
 1 file changed, 2 insertions(+), 7 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index fdd5def1..6d53a224 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -49,13 +49,8 @@ function to_Point3f(p::Meshes.Point)
     return Point3f(x, y, z)
 end
 
-function to_makie_poly(circle::Meshes.Circle; N=32)
-    return [to_Point3f(circle(t)) for t in range(0, 1, length=N)]
-end
-
-function to_makie_poly(ngon::Meshes.Ngon)
-    return [to_Point3f(pt) for pt in ngon.vertices]
-end
+to_makie_poly(circle::Meshes.Circle; N=32) = Point3f[to_Point3f(circle(t)) for t in range(0, 1, length=N)]
+to_makie_poly(ngon::Meshes.Ngon) = Point3f[to_Point3f(pt) for pt in ngon.vertices]
 ```
 
 ## Modeling the Dartboard

From a72924db2e1d8f88bd4ff348b95bda8e2a810276 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 22:44:55 -0400
Subject: [PATCH 26/31] Bugfix the bugfix

---
 docs/src/examples/darts.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 6d53a224..d97eb204 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -44,13 +44,13 @@ function Ngon(sector::Sector; N=8)
     return Meshes.Ngon(arc_o..., arc_i...)
 end
 
-function to_Point3f(p::Meshes.Point)
+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
 
-to_makie_poly(circle::Meshes.Circle; N=32) = Point3f[to_Point3f(circle(t)) for t in range(0, 1, length=N)]
-to_makie_poly(ngon::Meshes.Ngon) = Point3f[to_Point3f(pt) for pt in ngon.vertices]
+_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
@@ -104,7 +104,7 @@ fig = Figure()
 ax = LScene(fig[1, 1], scenekw=(show_axis=true,))
 
 for region in all_regions
-    poly!(ax, to_makie_poly(region.geometry), color=region.color)
+    poly!(ax, _poly(region.geometry), color=region.color)
 end
 
 fig

From dec7ea9a858c17969a6643502d8dfd00fda1b09f Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 23:34:04 -0400
Subject: [PATCH 27/31] Set axes limits for LScene

---
 docs/src/examples/darts.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index d97eb204..8f4a50d8 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -107,6 +107,8 @@ for region in all_regions
     poly!(ax, _poly(region.geometry), color=region.color)
 end
 
+limits!(ax, -0.1 .. 0.1, -1.5 .. 1.5, 0 .. 3)
+
 fig
 ```
 

From c9a97c028a14cde9180fef20ae24210fb9dad6ac Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Fri, 12 Sep 2025 23:39:45 -0400
Subject: [PATCH 28/31] Switch from LScene to Axis3

---
 docs/src/examples/darts.md | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index 8f4a50d8..e286ea3d 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -100,15 +100,17 @@ bullseye_outer = ScoredRegion(Ngon(Sector((6.35mm, 16.0mm), (0.0, 2π)); N=32),
 # 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 = 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
 
-limits!(ax, -0.1 .. 0.1, -1.5 .. 1.5, 0 .. 3)
-
 fig
 ```
 

From ffcdcfd65e8b495d25a7b779f1901d17eb58bf8b Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Tue, 23 Sep 2025 20:16:48 -0400
Subject: [PATCH 29/31] Switch to 2D viz of dartboard

---
 docs/src/examples/darts.md | 35 +++++++++++++++++++++--------------
 1 file changed, 21 insertions(+), 14 deletions(-)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index e286ea3d..f87d0cf0 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -10,6 +10,7 @@ Steps
 using CairoMakie
 using Colors
 using Distributions
+using GeometryBasics
 using Meshes
 using MeshIntegrals
 using Unitful
@@ -37,7 +38,7 @@ end
 Sector(rs, phis) = Sector(rs..., phis...)
 
 # Sector -> Ngon
-function Ngon(sector::Sector; N=8)
+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)]
@@ -51,6 +52,9 @@ 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)...]
+
+_poly2d(circle::Meshes.Circle; N=32) = [(_Point2f(circle(t)) for t in range(0, 1, length=N))...]
+_poly2d(ngon::Meshes.Ngon) = [(_Point2f(pt) for pt in ngon.vertices)...]
 ```
 
 ## Modeling the Dartboard
@@ -81,13 +85,14 @@ 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
+sector_centers = [n * sector_width for n in 0:19]
+phis_a = sector_centers .- sector_width/2
+phis_b = sector_centers .+ 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)
+board_ngons = _Ngon.(board_sectors)
 
 # Consolidate the Sectors
 sector_data = Iterators.zip(board_ngons, board_points, board_colors)
@@ -95,22 +100,24 @@ 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)
+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)
+ax = Axis(fig[1, 1], xlabel="y [m]", ylabel="z [m]")
+ax.aspect = DataAspect()
+
+for region in board_regions
+    pts = _poly2d(region.geometry)
+    poly!(ax, pts, color=region.color)
+	
+    centerPt = centroid(region.geometry)
+    center = ustrip.(u"m", [centerPt.coords.y, centerPt.coords.z])
+    text!(ax, string(region.points), position=Point2f(center...), align=(:center,:center), color=:blue, fontsize=10)
 end
-
+	
 fig
 ```
 

From f41836cf7430a17892901347b240db016f1a35a8 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Tue, 23 Sep 2025 20:30:51 -0400
Subject: [PATCH 30/31] Add GeometryBasics

---
 docs/Project.toml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/docs/Project.toml b/docs/Project.toml
index e6c9f5b9..744745e3 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -4,6 +4,7 @@ CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
 MeshIntegrals = "dadec2fd-bbe0-4da4-9dbe-476c782c8e47"
 Meshes = "eacbb407-ea5a-433e-ab97-5258b1ca43fa"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
@@ -14,6 +15,7 @@ CairoMakie = "0.15"
 Colors = "0.13"
 Distributions = "0.25"
 Documenter = "1"
+GeometryBasics = "0.5"
 Meshes = "0.53, 0.54"
 Unitful = "1.19"
 julia = "1.9"

From 5a5eec994e51d93ac68dab6a34657c3df1b20739 Mon Sep 17 00:00:00 2001
From: Michael Ingold <mike.ingold@gmail.com>
Date: Tue, 23 Sep 2025 21:42:47 -0400
Subject: [PATCH 31/31] Add _Point2f method

---
 docs/src/examples/darts.md | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/docs/src/examples/darts.md b/docs/src/examples/darts.md
index f87d0cf0..a221855d 100644
--- a/docs/src/examples/darts.md
+++ b/docs/src/examples/darts.md
@@ -45,6 +45,11 @@ function _Ngon(sector::Sector; N=8)
     return Meshes.Ngon(arc_o..., arc_i...)
 end
 
+function _Point2f(p::Meshes.Point)
+    x, y, z = ustrip.(m, [p.coords.x, p.coords.y, p.coords.z])
+    return Point2f(y, z)
+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)