bouncing ball

#!/usr/bin/env julia

# inspired by http://stackoverflow.com/questions/40031913/simulate-a-bouncing-ball
# and the inspired Chris Rackauckas

using DifferentialEquations, ParameterizedFunctions, NLsolve, Luxor

f = @ode_def BallBounce begin
  dy =  v
  dv = -g
end g=9.81

function event_f(t, u) # Event when event_f(t, u, k) == 0
  u[1]
end

function apply_event!(u,cache)
  u[2] = -u[2] - 3.5
end

# You put these functions together to build the callback using the macros:

function condition(t,u,integrator) # Event when event_f(t,u) == 0
  u[1]
end

function affect!(integrator)
  integrator.u[2] = -integrator.u[2]
end

cb = ContinuousCallback(condition, affect!)

#Now you solve as usual. You define the ODEProblem using f and the initial condition, and
#you call solve on a timespan. The only thing extra is you pass the callback along with the
#solver:

u0 = [30.0,0.0]
tspan = (0.0,15.0)
prob = ODEProblem(f,u0,tspan)
sol = solve(prob, Tsit5(), callback=cb)

# create animation
width, height = 300, 300
ballradius = 20
ground = 100

demomovie = Movie(width, height, "test", 1:100)

function backdrop_f(scene::Scene, framenumber)
    background("skyblue")
    sethue("darkgreen")
    box(Point(-width/2,  ground), Point(width/2, height/2), :fill)
end

function frame_f(scene::Scene, framenumber)
    ballsize = 10
    yvals = sol(rescale(framenumber, 0, scene.movie.movieframerange.stop, 0, 15))
    ypos = rescale(yvals[1], 0, 50, ground - ballradius, -height/2)
    xpos = rescale(framenumber, 0, scene.movie.movieframerange.stop, -width/2, width/2)
    translate(xpos, ypos + 1.5ballsize)
    juliacircles(ballsize)
end

Luxor.animate(demomovie, [Scene(demomovie, backdrop_f), Scene(demomovie, frame_f)], framerate=20, creategif=true)