12.1 Build the plotted Visuals🔗ℹ

(define coordinate-axes

(axes #:id 'coordinate-axes

#:x-range (axis-range -4 4 1)

#:y-range (axis-range -3 3 1)

#:x-length 8

#:y-length 6

#:stroke "navy"))

(define loop-curve

(parametric-curve

coordinate-axes

(lambda (parameter)

(define x (- (* parameter parameter) 2))

(vec2 x (/ (* parameter x) 2)))

#:id 'loop-curve

#:parameter-range (parameter-range -2 2)

#:sample-count 181

#:interpolation 'smooth

#:stroke "crimson"))

(define observations

(data-plot

coordinate-axes

(list (vec2 -3 -3/2)

(vec2 -2 1/2)

(vec2 -1 1)

(vec2 0 1/4)

(vec2 1 -1)

(vec2 2 -1/2)

(vec2 3 3/2))

#:id 'observations

#:interpolation 'smooth

#:stroke "seagreen"))

parametric-curve calls its procedure while constructing the Visual. The resulting path stores immutable geometry, not the sampling procedure.

12.2 Animate the plots and camera together🔗ℹ

(define initial-camera

(make-camera #:world-width 14 #:center origin))

(define animation

(scene-wait

(scene-play (make-scene #:camera initial-camera)

(fade-in coordinate-axes)

(create loop-curve)

(create observations)

(camera-pan-to (vec2 1 0))

(camera-zoom-by 3/2)

#:duration 2)

1/2))

At two seconds the paths have been created and the camera has reached its new position and zoom:

> (scene->pict animation 2)

> (scene-duration animation)

5/2

The camera center and visible width are sampled from the same Scene clip as the Visual animations.

12.3 Render explicitly🔗ℹ

Media output is effectful, so the manual shows these calls but substitutes (void) during documentation evaluation. This is the same show-one-form/evaluate-another technique used in the Racket manuals for environment-dependent examples.

(eval:alts

(render-frames! animation "frames" #:fps 30)

(void))

(eval:alts

(encode-mp4! "frames" "animation.mp4" #:fps 30)

(void))

Run those displayed forms yourself when you want files. The MP4 step requires FFmpeg.