# SCION 13 · Nora Willett — Secondary Motion · PAE-02 threshold

**Swarm language.** Secondary Motion for Performed 2D Animation (Willett, Li, Popović, Berthouzoz, Finkelstein 2017), as a
studio: performed *primary trajectories* of rigid paper pieces, and *secondary rig links* hung from them, each an
*inertial spring-damper* with *collision masks* under *wind and gravity*. Here the dog is made of its own secondary links: a
long-coated dog of crepe- and tissue-paper fringe, so that material and intention are carried by the coat, ears, tail plume
and dewlap rather than by a silhouette.

**Thesis.** The viewer should read the dog's state from how its paper moves: the coat flattens and the tail tucks when it
is called; the ears flick to the soft voice before the head comes round; the coat swings, lags and settles as it lies down;
in the last seconds the wind lifts a few fringe tips while the dog stays still. What would make it bland: a generic
oscillation on everything (see `proof/compare_none_generic_tuned.mp4`).

## How the dog is built (build/scene.js, build/draw.js)

- **Primary pieces (performed trajectories).** Six torso discs on a spine whose height bends for crouch (rear lower) and
  lying (front first, rear 0.13 s later); two neck discs, a skull, two muzzle discs and a nose; four two-bone legs with
  paws. Performed curves, keyed to the score's choice times: body heading (turns its back 3.44–3.78 s through facing the
  viewer, turns back 8.05–8.80 s), head heading (leads the body: 3.40–3.70 s; over the shoulder to the door 7.44–7.68 s with
  the body still lying; into the room, away from the camera, 26.45–26.95 s), lie, chin-rest, head height (low on the
  approach), fear. x, crouch, ears, tail, wag and "moving" come from the score. Stance feet stay planted: their offset
  falls exactly as distance travelled grows (stride 0.56 m, the score's own walk-phase rate); swing feet lift.
- **Secondary links (264 on the dog).** 180 body strips (15 rings × 12 rows, jittered), 20 neck-ruff, 10 head (forelock,
  cheeks, beard), 3 dewlap, 2 five-node ear flaps with 16 feather strips hung from the moving ear links (second order), a
  six-node tail with 20 feather strips, 12 leg feathers. Elsewhere: 8 curtain strips, 34 reeds, the person's 7 hair strands,
  2 scarf tails, 3 coat tails. The door leaf is a driven spring-damper hinge.
- **Solver.** Per node: a = k(r − p) − c(v − v_r) + g·grav + drag(w − v), semi-implicit Euler, 4 substeps per frame
  (dt = 1/96 s), inextensible links by follow-the-leader projection, then collisions, then a speed clamp. r is the rest
  shape the primary piece carries this substep (interpolated between frames), v_r its velocity, w the wind.
- **Material presets** (k 1/s², c 1/s, gravity scale, drag 1/s): crepe fur 80 / 9 / 0.35 / 1.4, rising to 230 / 17 when
  afraid (the coat is held flat, sleek and back along the body); ruff 60 / 6.5; ear 120 / 7.5 / 0.55 / 0.6; feathers 45 / 6;
  tail 95 / 8; dewlap 22 / 3.2 / 0.8 (loose, it lags); curtain 6 / 2.2 / 1 / 2.4; reed 140 / 2.6 (springy, little damping,
  stiffer at the root); hair 28 / 4.2; scarf 9 / 4.2; coat tails 30 / 6. Tip nodes are softer (k × 0.35–0.7).
- **Collision masks.** Fur, ears, tail: the floor and the dog's own discs (torso, neck, skull, muzzle). Curtain: floor,
  the dog, the person's arm, torso and head. Reeds: the dog. Hair: her head and torso. Scarf: her torso. Coat tails: the
  floor and her legs.
- **Forces.** Gravity; a gust field from the yard toward the house (named gusts at 5.4, 12.8, 19.6, 30.4 s), none indoors;
  a draft out of the doorway when the door opens (6.15–8.2 s).
- **Where intention is carried.** Rest-shape targets change with the dog's state: fear blends the coat's rest direction from
  "hanging, a little fluffed" to "pressed back along the body" and stiffens it (refusal, retreat); the tail's rest angle
  follows the score's tail value (tucked under on the refusal); ears move from flat to semi-pricked, and receive an
  impulse 60 ms after each soft-voice onset (the flick); lying turns the coat's rest direction out and back so it spreads on
  the boards. The coat, ear and tail motions are not keyed: they are what the solver does with those targets.
- **Drawing.** Orthographic diorama camera (yaw +16°, pitch 12°) from the porch side, house cut in section at the door's
  near edge. Each strip is a torn ribbon with a glued rounded top, a crease line and a torn tip; rows overlap like shingles
  (sort key = view depth + height above the spine), discs are torn tissue circles, everything shaded by a cool dusk ambient
  plus the warm lamp wedge through the doorway. Paper-fibre overlay.

## Staging of the hard moments

- Refusal: a turn through a front view (every frame a dog: `stills`, frames 3.40–3.90 s were looked at one by one); the
  coat flattens and the tail tucks; it lies down facing away (4.25–4.95 s), chin down.
- 7.46: ears flick at the soft voice, the head comes round over the near shoulder to the door (muzzle level, 3/4 toward
  us), the body still down; it rises at 7.86 and turns its body 8.05–8.80.
- Approach: head held below the back line for the whole walk (measured 100 % of frames 15.2–23.6 s).
- Lying across the sill: torso on the porch side, neck over the sill, skull, muzzle and forepaws inside the room, tail out
  on the boards; legs folded (forelegs forward, hind legs out to the side under the coat).
- Looking in (26.4): the neck stretches in and the head turns into the room's depth, away from the camera: the back of the
  skull (dark crown) between the two ears, inside the lit room; the person sits nearer the camera, so it is not a look at her.

## Measured (from the encoded film's own render pass; build/cache/summary.json, trace.json)

Onsets measured from the dog's mask pass (score time → measured): retreat 1.000 → 1.125 (centroid moves away > 2 cm);
watch 2.333 → 2.375 (head starts to rise); refuse 3.417 → 3.542 (head starts to turn), back shown (snout right of skull)
3.583; turn back 7.458 → 7.542 (head moves toward the door), muzzle toward the door 7.583; approach 14.708 → 14.792;
lie down 23.792 → 23.958 (torso drops > 2 cm); looks in 26.4 → 26.5 (head moves 2 cm further in). End: lying, head
centroid at x = −0.10 m (inside the threshold at x = 0); while looking in −0.30 m. Checker: ALL OK (I3 r = 1.0 on
x_world_measured, I4 share turned 0.93). Voices: calls −16.8/−16.4 dBFS RMS, soft −27.3/−27.8/−29.7 dBFS (10.5 dB under),
room tone −42.6 dBFS; each voice starts 40 ms before the dog's reaction. Film 912 frames, 38.0 s, 4.7 MB, H.264 + AAC,
faststart. Numeric assertions (`proof/assertions.json`, 8/8): the coat's energy peaks after the lying onset (24.13 s) and
is below 15 % of that peak by 25.0 s (the pose stops at 24.55 s); ear-energy peaks 0.10–0.22 s after each soft voice; fur-tip distance from
the spine drops 0.248 → 0.197 m on the refusal; tail tip drops 0.32 → 0.24 m.

## What failed and what changed

See `ledger.jsonl`. In short: a picket-fence/mop coat → overlapping shingles; a room-side camera would have turned "looking
in" into looking at us → camera moved to the porch side; the near jamb cut the lying dog in two → house cut at the door's
edge; the curtain hid the head → drawn to the far half; the facing measure (head vs torso centroid) was late for the
over-the-shoulder look → measured from snout vs skull; a nose drawn over the back of the skull → depth-ordered muzzle.

## Repair round 1

After the critic's round 1: ears hang down beside the skull while looking in (no strip streams into the room), the folded forepaws are drawn and visible while lying, the belly fringe is shorter so the legs and feet show on the walk, the cards load and fit the credited fonts, the curtain stays behind the dog once it lies, and the cheek strips no longer read as fangs. See ledger entry 12.

## What is weak (looked at, not fixed)

- At the wide framing (0–14 s) the standing dog is about 170–210 px tall (ears included) and its head about 60 px; the ear flick and the coat's lag read, but small.
- Crouched and flattened on the refusal, the dog can read as a hedgehog for a few frames.
- The back of the head when looking in is legible but small and busy (cheek fringe and ruff in front of it).
- Lying, the near-side coat still hangs a little like a skirt rather than spreading flat.
- The voices are formant-synthesized and only roughly intelligible; the person is a simple paper puppet.
- The camera moves (pull back 4.6–6.4 s, push in 14.8–24.2 s); x_world_measured unprojects through it.

## What I did not do

No kit footage, Quick, Draw! drawing or archive frame is used; no maquette; no text on screen during the scene; no
independent critic was run by me (the builder does not approve its own work); no mobile operator page. The solver is not
a reproduction of the 2017 paper's system; it is the same primitives built here.

## Rebuild

`bash build/make.sh` (≈3 min): render.js (scene + measurements) → sound.py → assemble.py (film, trace, stills, checker)
→ test_motion.py → comparison clip. `build/look.py` extracts frames from the encoded film for looking.