Animation helper functions

Luxor provides some functions to help you create animations—at least, it provides some assistance in creating lots of individual frames that can later be stitched together to form a moving animation, such as a GIF or MP4.

There are four steps to creating an animation.

1 Use Movie to create a Movie object which determines the title and dimensions.

2 Define some functions that draw the graphics for specific frames.

3 Define one or more Scenes that call these functions for specific frames.

4 Call the animate(movie::Movie, scenes) function, passing in the scenes. This creates all the frames and saves them in a temporary directory. Optionally, you can ask for ffmpeg (if it's installed) to make an animated GIF for you.

Example

demo = Movie(400, 400, "test")

function backdrop(scene, framenumber)
    background("black")
end

function frame(scene, framenumber)
    sethue(Colors.HSV(framenumber, 1, 1))
    eased_n = scene.easingfunction(framenumber, 0, 1, scene.framerange.stop)
    circle(polar(100, -π/2 - (eased_n * 2π)), 80, :fill)
    text(string("frame $framenumber of $(scene.framerange.stop)"),
        Point(O.x, O.y-190),
        halign=:center)
    text(scene.opts,
        boxbottomcenter(BoundingBox()),
        halign=:center,
        valign=:bottom)
end

animate(demo, [
    Scene(demo, backdrop, 0:359),
    Scene(demo, frame, 0:359,
        easingfunction=easeinoutcubic,
        optarg="made with Julia")
    ],
    creategif=true)

In this example, the movie uses two scenes, each specifying a function to draw frames from 0 to 359. For each frame numbered 0 to 359, the graphics are drawn by both the backdrop() and frame() functions, in that order. A drawing is automatically created (in PNG format) and centered (origin()) so you can start drawing immediately. The finish() function is automatically called when all the drawing functions in the scenes have completed, and the process starts afresh for the next frame. The second scene, calling the frame() function, shows how you can pass optional information to the function.

demo = Movie(400, 400, "test", 1:500)

bang = Movie(400, 100, "bang")

backdrop(scene, framenumber) =  background("black")

function frame1(scene, framenumber)
    background("white")
    sethue("black")
    eased_n = scene.easingfunction(framenumber, 0, 1, scene.framerange.stop)
    circle(O, 40 * eased_n, :fill)
end

animate(bang, [
    Scene(bang, backdrop, 0:200),
    Scene(bang, frame1, 0:200, easingfunction=easeinsine)],
    creategif=true,
    pathname="/tmp/animationtest.gif")

animate(movie::Movie, scenelist::Array{Scene, 1};
    creategif=false,
    framerate=30,
    pathname="",
    tempdirectory="",
    usenewffmpeg=true)

animate(bang, [
    Scene(bang, backdrop, 0:200),
    Scene(bang, frame1, 0:200, easingfunction=easeinsine)],
    creategif=true,
    pathname="/tmp/animationtest.gif")

animate(movie::Movie, scene::Scene; creategif=false, framerate=30)

Making the animation

For best results, you'll have to learn how to use something like ffmpeg, with its hundreds of options, which include codec selection, framerate adjustment and color palette tweaking. The creategif option for the animate function makes an attempt at running ffmpeg and assumes that it's already installed. Inside animate(), the first pass creates a GIF color palette, the second builds the file:

run(`ffmpeg -f image2 -i $(tempdirectory)/%10d.png -vf palettegen
    -y $(seq.stitle)-palette.png`)

run(`ffmpeg -framerate 30 -f image2 -i $(tempdirectory)/%10d.png
    -i $(seq.stitle)-palette.png -lavfi paletteuse -y /tmp/$(seq.stitle).gif`)

Many movie editing programs, such as Final Cut Pro, will also let you import sequences of still images into a movie timeline.

Using scenes

Sometimes you want to construct an animation that has different components, layers, or scenes. To do this, you can specify scenes that are drawn only for specific frames.

As an example, consider a simple example showing the sun for each hour of a 24 hour day.

sun24demo = Movie(400, 400, "sun24", 0:23)

The backgroundfunction() draws a background that's used for all frames (animated GIFs like constant backgrounds):

function backgroundfunction(scene::Scene, framenumber)
    background("black")
end

A nightskyfunction() draws the night sky:

function nightskyfunction(scene::Scene, framenumber)
    sethue("midnightblue")
    box(O, 400, 400, :fill)
end

A dayskyfunction() draws the daytime sky:

function dayskyfunction(scene::Scene, framenumber)
    sethue("skyblue")
    box(O, 400, 400, :fill)
end

The sunfunction() draws a sun at 24 positions during the day:

function sunfunction(scene::Scene, framenumber)
    i = rescale(framenumber, 0, 23, 2pi, 0)
    gsave()
    sethue("yellow")
    circle(polar(150, i), 20, :fill)
    grestore()
end

Finally a groundfunction() draws the ground:

function groundfunction(scene::Scene, framenumber)
    gsave()
    sethue("brown")
    box(Point(O.x, O.y + 100), 400, 200, :fill)
    grestore()
    sethue("white")
end

Now define a group of Scenes that make up the movie. The scenes specify which functions are to be used, and for which frames:

backdrop  = Scene(sun24demo, backgroundfunction, 0:23)   # every frame
nightsky  = Scene(sun24demo, nightskyfunction, 0:6)      # midnight to 06:00
nightsky1 = Scene(sun24demo, nightskyfunction, 17:23)    # 17:00 to 23:00
daysky    = Scene(sun24demo, dayskyfunction, 5:19)       # 05:00 to 19:00
sun       = Scene(sun24demo, sunfunction, 6:18)          # 06:00 to 18:00
ground    = Scene(sun24demo, groundfunction, 0:23)       # every frame

Finally, the animate function scans the scenes in the scenelist for a movie, and calls the functions for each frame to build the animation:

animate(sun24demo, [
   backdrop, nightsky, nightsky1, daysky, sun, ground
   ],
   framerate=5,
   creategif=true)

Notice that for some frames, such as frame 0, 1, or 23, three of the functions are called: for others, such as 7 and 8, four or more functions are called. Also notice that the order of scenes and the use of backgrounds is important.

An alternative approach is to use the incoming framenumber as the master parameter that determines the position and appearance of all the graphics.

function frame(scene, framenumber)
    background("black")
    n   = rescale(framenumber, scene.framerange.start, scene.framerange.stop, 0, 1)
    n2π = rescale(n, 0, 1, 0, 2π)
    sethue(n, 0.5, 0.5)
    box(BoundingBox(), :fill)
    if 0.25 < n < 0.75
        sethue("yellow")
        circle(polar(150, n2π + π/2), 20, :fill)
    end
    if n < 0.25 || n > 0.75
        sethue("white")
        circle(polar(150, n2π + π/2), 20, :fill)
    end
end

Passing information to the frame() function

If you want to pass information to the frame function, such as an array of values, try these:

function frame(scene, framenumber, datapoints)
...
end

somedata = Datapoints[...]

animate(demo, [
    Scene(demo, (s, f) -> frame(s, f, somedata),
        0:100,
        optarg=somedata)
    ],
    creategif=true,
    pathname="...")

Easing functions

Transitions for animations often use non-constant and non-linear motions, and these are usually provided by easing functions. Luxor defines some of the basic easing functions and they're listed in the (unexported) array Luxor.easingfunctions. Each scene can have one easing function.

Most easing functions have names constructed like this:

ease[in|out|inout][expo|circ|quad|cubic|quart|quint]

and there's an easingflat() linear transition.

using Luxor # hide
function draweasingfunction(f, pos, w, h)
    @layer begin
        translate(pos)
        setline(0.5)
        sethue("black")
        box(O, w, h, :stroke)
        sethue("purple")
        for i in 0:0.005:1.0
            circle(Point(-w/2, h/2) + Point(w * i, -f(i, 0, h, 1)), 1, :fill)
        end
        sethue("black")
        text(replace(string(f), "Luxor." => ""), Point(0, h/2 - 20), halign=:center)
    end
end

Drawing(650, 650, "assets/figures/easingfunctions.png") # hide
background("white") # hide
origin() # hide
t = Tiler(650, 650, 5, 5)
margin=5
fontsize(10)
fontface("Menlo")
for (pos, n) in t
    n > length(Luxor.easingfunctions) && continue
    draweasingfunction(Luxor.easingfunctions[n], pos,
        t.tilewidth-margin, t.tileheight-margin)
end

finish() # hide
nothing # hide

In these graphs, the horizontal axis is time (between 0 and 1), and the vertical axis is the parameter value (between 0 and 1).

One way to use an easing function in a frame-making function is like this:

function moveobject(scene, framenumber)
    background("white")
    ...
    easedframenumber = scene.easingfunction(framenumber, 0, 1, scene.framerange.stop)
    ...

This takes the current frame number, compares it with the end frame number of the scene, then adjusts it.

In the next example, the purple dot has sinusoidal easing motion, the green has cubic, and the red has quintic. They all traverse the drawing in the same time, but have different accelerations and decelerations.

fastandfurious = Movie(400, 100, "easingtests")
backdrop(scene, framenumber) =  background("black")
function frame1(scene, framenumber)
    sethue("purple")
    eased_n = scene.easingfunction(framenumber, 0, 1, scene.framerange.stop)
    circle(Point(-180 + (360 * eased_n), -20), 10, :fill)
end
function frame2(scene, framenumber)
    sethue("green")
    eased_n = scene.easingfunction(framenumber, 0, 1, scene.framerange.stop)
    circle(Point(-180 + (360 * eased_n), 0), 10, :fill)
end
function frame3(scene, framenumber)
    sethue("red")
    eased_n = scene.easingfunction(framenumber, 0, 1, scene.framerange.stop)
    circle(Point(-180 + (360 * eased_n), 20), 10, :fill)
end
animate(fastandfurious, [
    Scene(fastandfurious, backdrop, 0:200),
    Scene(fastandfurious, frame1,   0:200, easingfunction=easeinsine),
    Scene(fastandfurious, frame2,   0:200, easingfunction=easeinoutcubic),
    Scene(fastandfurious, frame3,   0:200, easingfunction=easeinoutquint)
    ],
    creategif=true)

Here's the definition of one of the easing functions:

function easeoutquad(t, b, c, d)
    t /= d
    return -c * t * (t - 2) + b
end

Here:

• t is the current time (framenumber) of the transition

• b is the beginning value of the property

• c is the change between the beginning and destination value of the property

• d is the total length of the transition

The easeinoutbezier() function accepts two additional arguments, two normalized control points of a normalized Bezier curve from Point(0, 0) to Point(1, 1). You can use these to define the shape of a custom easing transition. The Bezier curve's y coordinate determines the acceleration. [?]

easingflat(t, b, c, d)

easeinquad(t, b, c, d)

easeoutquad(t, b, c, d)

easeinoutquad(t, b, c, d)

easeincubic(t, b, c, d)

easeoutcubic(t, b, c, d)

easeinoutcubic(t, b, c, d)

easeinquart(t, b, c, d)

easeoutquart(t, b, c, d)

easeinoutquart(t, b, c, d)

easeinquint(t, b, c, d)

easeoutquint(t, b, c, d)

easeinoutquint(t, b, c, d)

easeinsine(t, b, c, d)

easeoutsine(t, b, c, d)

easeinoutsine(t, b, c, d)

easeinexpo(t, b, c, d)

easeoutexpo(t, b, c, d)

easeinoutexpo(t, b, c, d)

easeincirc(t, b, c, d)

easeoutcirc(t, b, c, d)

easeinoutcirc(t, b, c, d)

easeinoutinversequad(t, b, c, d)

easeinoutbezier(t, b, c, d, cpt1, cpt2)

...
lineareasing = rescale(framenumber, 1, scene.framerange.stop)
beziereasing = scene.easingfunction(lineareasing, 0, 1, 1,
    Point(0.25, 0.25), Point(0.75, 0.75))
...

lineareasing = rescale(framenumber, 1, scene.framerange.stop)
beziereasing = scene.easingfunction(lineareasing, 0, 1, 1,
    Point(0.01, 1.99), Point(0.99, -1.5))