152 lines
3.9 KiB
Julia
152 lines
3.9 KiB
Julia
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using AbstractPlotting
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using AbstractPlotting.MakieLayout
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using GLMakie
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using LinearAlgebra
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using Roots
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using ForwardDiff
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D(f) = x -> ForwardDiff.derivative(f, float(x))
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descr = """
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An old optimization problem is to find the shortest distance between two
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points when the rate of travel differs due to some medium (darker means slower).
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In this example, the relative rate can be adjusted (with the slider), and the
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various points (by clicking on and dragging a point). From there, the
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user can adjust the crossing point to identify the time.
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"""
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## From http://juliaplots.org/MakieReferenceImages/gallery//edit_polygon/index.html:
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function add_move!(scene, points, pplot)
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idx = Ref(0); dragstart = Ref(false); startpos = Base.RefValue(Point2f0(0))
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on(events(scene).mousedrag) do drag
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if ispressed(scene, Mouse.left)
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if drag == Mouse.down
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plot, _idx = mouse_selection(scene)
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if plot == pplot
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idx[] = _idx; dragstart[] = true
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startpos[] = to_world(scene, Point2f0(scene.events.mouseposition[]))
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end
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elseif drag == Mouse.pressed && dragstart[] && checkbounds(Bool, points[], idx[])
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pos = to_world(scene, Point2f0(scene.events.mouseposition[]))
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# very wierd, but we work with components
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# not vector
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z = zero(eltype(pos))
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x,y = pos
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ptidx = idx[]
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x = clamp(x, 0, 5)
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if ptidx == 1
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y = clamp(y, z, 5)
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elseif ptidx == 2
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y = z
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elseif ptidx == 3
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y = clamp(y, -5, z)
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end
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points[][idx[]] = [x,y]
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points[] = points[]
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end
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else
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dragstart[] = false
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end
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return
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end
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end
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upperpoints = Point2f0[(0,0), (5, 0), (5, 5), (0,5)]
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lowerpoints = (Point2f0[(0,0), (5, 0), (5, -5), (0,-5)])
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points = Node(Point2f0[(1, 4), (3, 0), (4,-4.0)])
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# where we lay our scene:
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scene, layout = layoutscene()
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layout.halign = :left
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layout.valign = :top
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p = layout[1:3, 1] = LScene(scene)
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rowsize!(layout, 1, Auto(1))
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colsize!(layout, 1, Auto(1))
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flayout = GridLayout()
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layout[1,2] = flayout
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flayout[1,1] = LText(scene, chomp(descr))
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details = flayout[2, 1] = LText(scene, "...")
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λᵣ = flayout[3,1] = LText(scene, "λ = v₁/v₂ = 1")
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λ = flayout[4,1] = LSlider(scene, range = -3:0.2:3, startvalue = 0.0)
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tm = lift(λ.value, points) do λ, pts
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x0,y0 = pts[1]
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x, y = pts[2]
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x1, y1 = pts[3]
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v1 = 1
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v2 = v1/2.0^λ
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t(x) = sqrt((x-x0)^2 + y0^2)/v1 + sqrt((x1-x)^2 + y1^2)/v2
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val = t(x)
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details.text[] = "Time: $(round(val, digits=2)) units"
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val
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end
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a = lift(λ.value, points) do λ, pts
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x0,y0 = pts[1]
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x1, y1 = pts[3]
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v1 = 1
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v2 = v1/2.0^λ
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t(x) = sqrt((x-x0)^2 + y0^2)/v1 + sqrt((x1-x)^2 + y1^2)/v2
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x′ = fzero(D(t), x0, x1)
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t(x′)
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end
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λcolor = lift(λ.value) do val
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# val = v1/v2 ∈ [1/8, 8]
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n = floor(Int, 50 - val/3 * 25)
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Symbol("gray" * string(n))
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end
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linecolor = lift(a) do val
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abs(val - tm[]) <= 1e-2 ? :green : :white
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end
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on(λ.value) do val
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v = round(2.0^(val), digits=2)
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txt = "λ = v₁/v₂ = $v"
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λᵣ.text[] = txt
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end
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poly!(p.scene, upperpoints, color = :gray50) # neutral color
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poly!(p.scene, lowerpoints, color = λcolor) # color depends on λ
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lines!(p.scene, Point2f0[(0,0), (5, 0)], color=:black, strokewidth=5, strokecolor=:black, raw=true)
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lines!(p.scene, points, color = linecolor, strokewidth = 10, markersize = 0.05, strokecolor = :black, raw = true)
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scatter!(p.scene, points, color = linecolor, strokewidth = 10, markersize = 0.05, strokecolor = :black, raw = true)
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xlims!(p.scene, (0,5))
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ylims!(p.scene, (-5,5))
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add_move!(p.scene, points, p.scene[end])
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scene
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