Add details

Author: mikeingold

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