Center of mass graphics

graphics/center_of_mass.jl

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+using Luxor
+using StaticArrays
+
+using ReCo: restrict_coordinate
+
+##
+
+function project(x, L)
+    φ = (x + L) * π / L
+    return Point(cos(φ), -sin(φ))
+end
+
+function project_back(θ, L)
+    return θ * L / π - L
+end
+
+##
+
+box_length = 100
+box_height = 100
+
+L = 0.35 * box_length
+
+R = 0.35 * box_length
+
+A = -0.9 * L
+B = 0.65 * L
+pr = 0.03 * L
+
+Ap = project(A, L)
+Bp = project(B, L)
+
+M = R * ((Ap + Bp) / 2)
+
+θ = atan(-M[2], M[1])
+
+COM = restrict_coordinate(project_back(θ, L); l=L)
+COMp = R * Point(cos(θ), -sin(θ))
+
+##
+
+graphics_export_dir = "exports/graphics"
+mkpath(graphics_export_dir)
+
+Drawing(box_length, box_height, "$graphics_export_dir/line.pdf")
+origin()
+
+setcolor("black")
+arrow(Point(-1.1 * L, 0), Point(1.2 * L, 0); arrowheadlength=0.1 * L, linewidth=0.8)
+
+green_orange = blend(Point(-1.5 * L, 0), Point(1.5 * L, 0))
+addstop(green_orange, 0.0, "orange")
+addstop(green_orange, (L) / (3 * L), "green")
+addstop(green_orange, (2 * L) / (3 * L), "orange")
+addstop(green_orange, 1.0, "green")
+setblend(green_orange)
+setline(0.8)
+line(Point(-L, 0), Point(L, 0), :stroke)
+
+setcolor("red")
+setline(0.5)
+for x in SVector(-L, L)
+    line(Point(x, 0.05 * L), Point(x, -0.05 * L), :stroke)
+end
+
+setcolor("cyan3")
+line(Point(0, 0.05 * L), Point(0, -0.05 * L), :stroke)
+
+setcolor("blue")
+for p in SVector(A, B)
+    circle(Point(p, 0), pr, :fill)
+end
+
+setcolor("brown")
+circle(Point(COM, 0), pr, :fill)
+
+setcolor("black")
+fontsize(5)
+text("x", Point(1.2 * L, 0.035 * L))
+text("-L", Point(-L - 0.08 * L, 0.18 * L))
+text("0", Point(0 - 0.035 * L, 0.18 * L))
+text("+L", Point(L - 0.08 * L, 0.18 * L))
+text("A", Point(A - 0.04 * L, -0.06 * L))
+text("B", Point(B - 0.04 * L, -0.06 * L))
+text("COM", Point(COM - 0.125 * L, -0.06 * L))
+
+finish()
+
+##
+
+Drawing(box_length, box_height, "$graphics_export_dir/circle.pdf")
+origin()
+
+arrow(Point(-1.2 * R, 0), Point(1.2 * R, 0); arrowheadlength=0.1 * R, linewidth=0.8)
+arrow(Point(0, 1.2 * R), Point(0, -1.2 * R); arrowheadlength=0.1 * R, linewidth=0.8)
+
+setcolor("black")
+fontsize(5)
+text("α", Point(1.22 * R, 0.035 * R))
+text("β", Point(-0.04 * R, -1.23 * R))
+
+orange_green = blend(Point(0, -R), Point(0, R), "green", "orange")
+setblend(orange_green)
+setline(0.8)
+circle(Point(0, 0), R, :stroke)
+
+setcolor("red")
+setline(0.5)
+line(Point(1.05 * R, 0), Point(0.95 * R, 0), :stroke)
+setcolor("cyan3")
+line(Point(-1.05 * R, 0), Point(-0.95 * R, 0), :stroke)
+
+setcolor("blue")
+for pp in SVector(Ap, Bp)
+    circle(R * pp, pr, :fill)
+end
+
+setcolor("black")
+setdash("dot")
+line(R * Ap, R * Bp, :stroke)
+line(Point(0, 0), COMp, :stroke)
+
+setcolor("purple1")
+circle(M, pr, :fill)
+
+setcolor("brown")
+circle(COMp, pr, :fill)
+
+finish()