🦇 三維 BOIDs 群飛、飛行限高與轉向數學
📌 代碼倉庫原始碼免責聲明：本維基文件反映了倉庫當前的原始碼狀態，可能包含領先於 CurseForge 與 Modrinth 上公開發布版本的最新開發提交或未發布功能。
| Math Parameter | Symbol | Value / Formula | Description |
|---|---|---|---|
| Separation Radius | $r_{\text{sep}}$ | 1.5 blocks | Minimum distance before repulsion force triggers |
| Neighbor Radius | $r_{\text{nbr}}$ | 8.0 blocks | Bounding sphere for cohesion and alignment |
| Cohesion Weight | $W_{\text{coh}}$ | 0.02 | Force pulling towards average flock centroid |
| Alignment Weight | $W_{\text{ali}}$ | 0.05 | Force matching average velocity vector of neighbors |
| Separation Weight | $W_{\text{sep}}$ | 0.08 | Force pushing away from overlapping bats |
| Max Acceleration | $a_{\text{max}}$ | 0.05 blocks/tick² | Maximum steering delta applied per tick |
🧮 三維 BOIDs 演算法公式
The composite steering force applied to each bat per tick is governed by the classic Reynolds BOIDs vector equation:
$$\vec{F}{\text{steer}} = W{\text{coh}}\vec{F}{\text{cohesion}} + W{\text{ali}}\vec{F}{\text{alignment}} + W{\text{sep}}\vec{F}_{\text{separation}}$$
Where each component vector is evaluated against the set of $N$ visible flock neighbors:
$$\vec{F}{\text{cohesion}} = \frac{1}{N}\sum^N (\vec{P}i - \vec{P}{\text{self}})$$ $$\vec{F}{\text{alignment}} = \frac{1}{N}\sum^N \vec{V}i - \vec{V}{\text{self}}$$ $$\vec{F}{\text{separation}} = \sum^M \frac{\vec{P}_{\text{self}} - \vec{P}j}{|\vec{P}{\text{self}} - \vec{P}_j|^2}$$
☕ 獨立開發者寄語：如果你喜歡蝙蝠逼真的三維群飛和鳥糞為莊稼施肥的生態體驗，歡迎在 Ko-fi 上支持我的獨立開發！
📈 地表飛行限高計算
To prevent bats from soaring into upper atmospheric void or despawn ceilings, BatFlightHelper samples the terrain height $Y_{\text{surface}}$ directly below the bat and applies a downward restoration force when $Y > Y_{\text{surface}} + 12$:
$$F_y = -0.04 \times \frac{Y - (Y_{\text{surface}} + 12)}{4.0}$$
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