MinecraftMotionTools

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MinecraftMotionTools

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A library to compute entities' motion in Minecraft.

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# MinecraftMotionTools
MinecraftMotionTools is a collection of functions whose purpose is to ease prediction of the velocity and the position of entities simulated into Minecraft.
# How does it work?
Minecraft updates velocity in a different way from real-physics objects, plus it complicates everything just by being a video game and having to update the values in a finite unit of time (the tick).

Minecraft's Wiki got [some information](https://minecraft.wiki/w/Entity#Motion_of_entities) about how it works, but [here](https://hackmd.io/ySiQhr_SSUatNc6qAkbFcw) is the reasoning behind the velocity equations.

Another complication comes from what I, in the code, refer to as [acceleration drag](https://minecraft.wiki/w/Entity?oldid=3063842#cite_note-gravityBefore-5), which initially required forking the formulae for every different case (see [old sheet](https://hackmd.io/V9oMODQbT5mBA-o4OM76pA)), before I decided to generalize the formulae, introducing the coefficient `k`.

Acceleration drag works the following way:

$\text{position}\_{new}=\text{position}_{old}+\text{velocity}-k\cdot\text{acceleration}$

Having just 0 and 1 values, this turned out to simply swap the position updating order from P-A-D (position-acceleration-drag) to A-P-D. Still, I keep it this way to simplify the code and for flexibility, instead of having 4 different order cases (2 I didn't include can be solved by updating the velocity by 1 tick and considering that as initial velocity accordingly).

Finally, [here](https://hackmd.io/1t0ACyplTDKSgo-a1jA7nQ) is the formulae' sheet I wrote down. Take in mind that a fair amount of them make use of [Lambert's W function](https://en.wikipedia.org/wiki/Lambert_W_function).

For the acceleration's formulae refer to [this sheet](https://hackmd.io/vvFAdzekSn6R7vc9Mw8lxg?view) instead.
# Entities' parameter table
|Type|Acceleration|Vertical drag|Horizontal drag|Applies drag|k coefficient|
|-|-|-|-|-|-|
|Players, mobs and armor stands|0.08|0.02|0.09|After|0|
|Entities with slow falling|0.01|0.02|0.09|After|0|
|Items, falling blocks and TNTs|0.04|0.02|0.02|After|1|
|Minecarts|0.04|0.05|0.05|After|1|
|Boats|0.04|0|0.10|-|-|
|Thrown eggs, snowballs and ender pearls|0.03|0.01|0.01|Before|0|
|Thrown potions|0.05|0.01|0.01|Before|0|
|Thrown experience bottles|0.07|0.01|0.01|Before|0|
|Experience orbs|0.03|0.02|0.02|After|1|
|Thrown fishing bobbers|0.03|0.08|0.08|After|1|
|Llama spit|0.06|0.01|0.01|Before|0|
|Fired arrows and thrown tridents|0.05|0.01|0.01|Before|0|
|Fireballs, wither skulls and dragon fireballs|0.10|0.05|0.05|After|0|
|Dangerous wither skulls|0.10|0.27|0.27|After|0|
|Wind charges|0.10|0|0|-|-|

NOTES:
- For fireballs and alike, use negative acceleration (instead of being affected from gravity, fireballs accelerate on their own).
- Players, mobs and armor stands whose OnGround property is set to 1 have an horizontal drag force whose value depends on the slipperiness of the standing block. On most blocks, drag is 0.454 by default.
- The maximum general velocity value is 10. Any greater value is reset to 0.
- Even though 10 is the maximum velocity that can be set, entities with 0 drag force can gain infinite velocity due to acceleration (e.g. wind charges).
- Minecarts have a maximum horizontal velocity of 0.4. Any greater value is reset to that number.
- Boats (and since 1.21.2, throwables and fireball-like projectiles), are the only known entities to update the velocity before the position.
# Function list
v0: initial velocity 
t: ticks passed 
v: current velocity 
p: current relative position 
h: maximum height 
a: acceleration 
d: drag force 
after: whether drag is applied after or before gravity acceleration 
k: acceleration drag coefficient

Check some of the code examples for common use cases.

MinecraftMotionTools

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