🦇 三维 BOIDs 群飞、飞行限高与转向数学
📌 代码仓库源码免责声明：本维基文档反映了仓库当前的源代码状态，可能包含领先于 CurseForge 与 Modrinth 上公开发布版本的最新开发提交或未发布功能。
| 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 |
🧮 三维 BOIDs 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:
$$\vec{F}{\text{cohesion}} = \frac{1}{N}\sum^N (\vec{P}i - \vec{P}{\text{self}})$$ $$\vec{F}{\text{alignment}} = \frac{1}{N}\sum^N \vec{V}i - \vec{V}{\text{self}}$$ $$\vec{F}{\text{separation}} = \sum^M \frac{\vec{P}_{\text{self}} - \vec{P}j}{|\vec{P}{\text{self}} - \vec{P}_j|^2}$$
☕ 独立开发者寄语：如果你喜欢蝙蝠逼真的三维群飞和鸟粪为庄稼施肥的生态体验，欢迎在 Ko-fi 上支持我的独立开发！
📈 地表飞行限高计算
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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