fullseye

traj_tau_dot — FLYVISION trajectory op

• データ種: points × signal → table
• 呼び出し: import fullseye as fs; fs.ledger.traj_tau_dot(points, t_s, target=(0.0, 0.0, 0.0), normal=None) (実装を直接呼ぶなら import flyvision; flyvision.traj_tau_dot(points, t_s, target=(0.0, 0.0, 0.0), normal=None)、台帳から引くなら opsflyvision.get("traj_tau_dot"))

使い方

Distance, approach speed, tau and tau-dot along a measured 3-D trajectory.

The quantity a looming detector is supposed to deliver, computed from the true path so that an eye’s estimate can be scored against it. With d(t) the distance to target (a point, or — with normal — the signed distance to the plane through target), the approach speed is v = -dd/dt, the time-to-contact tau = d/v and its rate tau-dot = d tau/dt. Lee’s (1976) sign convention: tau-dot = -1 at constant speed, tau-dot = -0.5 under the constant deceleration that stops exactly at the target (the braking law), and a value between them means the agent is braking enough to stop short.

points: (N, 3) positions, metres, N >= 3. t_s: (N,) strictly increasing sample times, seconds. target: the point approached (3,), metres. normal: None for the Euclidean distance to target, or a (3,) plane normal: the distance is then (p - target) . normal / |normal|.

Returns a dict {"t_s", "distance_m", "speed_m_s", "tau_s", "tau_dot", "closest_m", "t_closest_s", "n"}. Samples where the agent is not approaching (v <= 0) carry NaN in tau_s and tau_dot — a documented non-finite: a receding agent has no time-to-contact.

Ground truth (pinned in the tests): for d = v0 t toward the target at constant speed tau-dot == -1, and for d = v0 t - a t^2 / 2 with v0^2 = 2 a d0 (stops exactly at the target) tau-dot == -0.5 — both to 1e-9 on a uniform grid, where central differences are exact for a quadratic.

Raises ValueError: points not (N, 3) with N >= 3 (an empty points is refused), a t_s that is not (N,) strictly increasing, non-finite entries, a malformed target / normal, and a zero normal.

詳しい使い方ガイド

• fly_vision ファミリ ガイド

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• poc_zebra_stripes_fly_eye — py -3.11 examples/poc_zebra_stripes_fly_eye.py

型が繋がる次の op(table を入力に取れる)

fly_t4t5_field · fly_flow_from_directions · fly_matched_filter · fly_egomotion_from_flow · fly_eye_merge · fly_view_plane_texture · fly_hex_resample · fly_expansion_readout

同カテゴリ(trajectory)

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Provenance: flyvision.py — FLYVISION operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.

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