docs(plans): record the measured meteor curve from reference footage

plans/reports/research-261001-1404-genshin-meteor-curve.md

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+# Research: matching the gacha meteor to Genshin Impact's motion
+
+Conducted 2026-10-01. Target: `tiennm99/wheelofnames` `getMeteorState` in
+`src/remotion/gacha-timeline.js` and the trail in `GachaComposition.jsx`.
+
+## Outcome
+
+Genshin's meteor does **not** follow a gravity arc. Measured from reference
+footage, it sweeps in along a **straight line** from the upper left at about
+23° below horizontal and **decelerates exponentially** to a near hover just
+above the horizon, where the colour reveal and the 5★ rainbow ring play. The
+gravity parabola shipped earlier was replaced with this measured curve.
+
+## Method
+
+Reference: the single-pull wish videos (`3star-single.mp4`,
+`4star-single.mp4`, `5star-single.mp4`; 1920x1080, 60 fps, 6 s) from the
+public fan simulator
+[AguzzTN54/Genshin-Impact-Wish-Simulator](https://github.com/AguzzTN54/Genshin-Impact-Wish-Simulator).
+They were used only to measure motion; nothing from them is shipped. Frames
+were extracted with ffmpeg at 10 fps (timeline) and 30 fps (glide), and the
+head was tracked as the brightest cluster above the cloud line.
+
+## Findings
+
+Timeline of the in-game single pull: cloud portal (0–1.2 s), dive with a beam
+sweep (1.2–1.6 s), **glide and hover** (1.7–3.4 s), flash (3.5 s), a streak and
+a near-vertical drop, then the result card.
+
+Head position during the glide (5★, fraction of frame):
+
+| t (s) | 1.80 | 2.00 | 2.20 | 2.40 | 2.80 | 3.20 |
+|---|---|---|---|---|---|---|
+| x | 0.485 | 0.523 | 0.547 | 0.549 | 0.535 | 0.559 |
+| y | 0.509 | 0.531 | 0.540 | 0.536 | 0.543 | 0.560 |
+
+- **Path:** straight, about 23° below horizontal, from off-screen upper left to
+  about (0.56, 0.56).
+- **Easing:** exponential ease-out. About 88% of the distance is covered 0.5 s
+  after entry, then the head creeps and hovers; rate `k ≈ 4.2 /s`.
+- **Trail:** a long straight beam from beyond the frame edge that narrows into
+  the head and stays full length while the head hovers; several ribbons fan
+  out along it, with sparkles floating above it.
+- **Colour:** every tier starts blue. The 4★ beam turns purple around 2.5 s;
+  the 5★ head turns gold around 2.8 s and the rainbow ring forms by 3.1 s.
+
+## Formula now used
+
+```text
+s(t)   = D * (1 - e^(-k t)) / (1 - e^(-k T))      k = 4.2, T = 2.2 s
+p(t)   = hover - u * (D - s(t))                   u = (cos 23°, sin 23°)
+v(t)   = u * D * k * e^(-k t) / (1 - e^(-k T))
+```
+
+`D` reaches from 15% beyond the left edge to the hover point (0.55, 0.55);
+normalising by `1 - e^(-kT)` lands the head exactly on the hover point.
+
+## Not adopted
+
+- **Blue-first colour reveal** (all tiers start blue, then change): this is
+  the signature suspense beat in Genshin, but it changes how the tiers read,
+  so it is left as an option for the owner.
+- The cloud portal, beam dive, and final vertical drop do not fit the 7 s
+  clip without restructuring the timeline.
+
+## Unresolved questions
+
+- Should the meteor start blue for every tier and reveal its colour during
+  the hover, as Genshin does?