initial

CwJ/makie-demos/tangent-line.jl

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+using AbstractPlotting
+using AbstractPlotting.MakieLayout
+using GLMakie
+
+using ForwardDiff
+Base.adjoint(f::Function) = x -> ForwardDiff.derivative(f, float(x))
+
+
+function tangent_line(f=nothing, a=0, b=pi)
+
+    if f == nothing
+        f = x -> sin(x)
+    end
+
+descr = """
+The tangent line has a slope approximated by the slope of secant lines. 
+This demo allows the points c and c+h to be adjusted to see the two lines"""
+
+## From http://juliaplots.org/MakieReferenceImages/gallery//edit_polygon/index.html:
+function add_move!(scene, points, pplot)
+    idx = Ref(0); dragstart = Ref(false); startpos = Base.RefValue(Point2f0(0))
+    on(events(scene).mousedrag) do drag
+        if ispressed(scene, Mouse.left)
+            if drag == Mouse.down
+                plot, _idx = mouse_selection(scene)
+                if plot == pplot
+                    idx[] = _idx; dragstart[] = true
+                    startpos[] = to_world(scene, Point2f0(scene.events.mouseposition[]))
+                end
+            elseif drag == Mouse.pressed && dragstart[] && checkbounds(Bool, points[], idx[])
+                pos = to_world(scene, Point2f0(scene.events.mouseposition[]))
+
+                # we work with components not vector
+                x,y = pos
+
+                x = clamp(x, a, b)
+                y = f(x)
+
+                points[][idx[]] = [x,y]
+                points[] = points[]
+            end
+        else
+            dragstart[] = false
+        end
+        return
+    end
+end
+
+
+c, h = pi/4, .5
+points = Node(Point2f0[(c, f(c)), (c+h, f(c+h))])
+
+
+# where we lay our scene:
+scene, layout = layoutscene()
+layout.halign = :left
+layout.valign = :top
+
+p = layout[1,1:2] = LScene(scene)
+
+rowsize!(layout, 1, Auto(1))
+colsize!(layout, 1, Auto(1))
+
+layout[2,1:2] = LText(scene, descr)
+
+
+secline = lift(points) do pts
+    c, ch = pts
+    x0, y0 = c
+    x1, y1 = ch
+    m = (y1 - y0)/(x1 - x0)
+    sl = x -> y0 + m * (x - x0)
+    Point2f0[(a, sl(a)), (b, sl(b))]
+end
+
+tangentline = lift(points) do pts
+    c, ch = pts
+    x0, y0 = c
+    m = f'(x0)
+    tl = x -> y0 + m * (x - x0)
+    Point2f0[(a, tl(a)), (b, tl(b))]
+end
+    
+
+lines!(p.scene, a..b, f, strokecolor=:red, strokewidth=15)
+lines!(p.scene, secline, color = :blue, strokewidth = 10, raw=true)
+lines!(p.scene, tangentline, color = :red, strokewidth = 10, raw=true)
+scatter!(p.scene, points, color = :white, strokewidth = 10, markersize = 0.05, strokecolor = :black, raw = true)
+xlims!(p.scene, (a, b))
+#ylims!(p.scene, (0, 1.5))
+
+
+add_move!(p.scene, points, p.scene[end])
+
+
+
+scene
+
+    end
+
+
+tangent_line()