Useful Formulae

Ordinary Objects

An ordinary object is any object that does not fall withing any of the other categories described below.

Let the 3D vectors \(p_d\) and \(p_s\) represent the object’s position and the warp’s origin, respectively; and \(\vec{v}\) the directional vector from \(p_s\) to \(p_d\). Let \(r\) be the object’s radius.

The object’s warp-in point is the vector \(p_s + \vec{v} - r\hat{v}\).

Large Objects

A large object is any celestial body whose radius exceeds 90 kilometres (180 kilometres in diameter), except planets.

Let \(x\), \(y\), and \(z\) represent the object’s coordinates. Let \(r\) be the object’s radius.

The object’s warp-in point is the vector \(\left(x + (r + 5000000)\cos{r} \\, y + 1.3r - 7500 \\, z - (r + 5000000)\sin{r} \\ \right).\)

Planets

The warp-in point of a planet is determined by the planet's ID, its location, and radius.

Let \(x\), \(y\), and \(z\) represent the planet's coordinates. Let \(r\) be the planet's radius.

The planet's warp-in point is the vector \(\left(x + d \sin{\theta}, y + \frac{1}{2} r \sin{j}, z - d \cos{\theta}\right)\) where:

\[ d = r(s + 1) + 1000000 \]

\[ \theta = \sin^{-1}\left(\frac{x}{|x|} \cdot \frac{z}{\sqrt{x^2 + z^2}}\right) + j \]

\[ s|_{0.5 \leq s \leq 10.5} = 20\left(\frac{1}{40}\left(10\log_{10}\left(\frac{r}{10^6}\right) - 39\right)\right)^{20} + \frac{1}{2} \]

Now, \(j\) is a special snowflake. Its value is the Python equivalent of (random.Random(planetID).random() - 1.0) / 3.0.

Example

Python

import math
import random


def warpin(id, x, y, z, r):
    j = (random.Random(id).random() - 1.0) / 3.0
    t = math.asin(x / abs(x) * (z / math.sqrt(x**2 + z**2))) + j
    s = 20.0 * (1.0 / 40.0 * (10 * math.log10(r / 10**6) - 39)) ** 20.0 + 1.0 / 2.0
    s = max(0.5, min(s, 10.5))
    d = r * (s + 1) + 1000000

    return (x + d * math.sin(t), y + 1.0 / 2.0 * r * math.sin(j), z - d * math.cos(t))

Skillpoints needed per level

The skillpoints needed for a level depend on the skill rank.

\(y_{skillpoints} = 2^{2.5(x_{skilllevel}-1)} \cdot 250 \cdot r_{skillrank}\)

Skillpoints for common ranks

Rank	Level 1	Level 2	Level 3	Level 4	Level 5
1	250	1.414	8000	45,254	256,000
2	500	2,828	16,000	90,509	512,000
3	750	4,242	24,000	135,764	768,000
4	1000	5,656	32,000	181,019	1,024,000
5	1250	7,071	40,000	226,274	1,280,000
6	1500	8,485	48,000	271,529	1,536,000
7	1750	9,899	56,000	316,784	1,792,000
8	2000	11,313	64,000	362,039	2,048,000
9	2250	12,727	72,000	407,293	2,304,000
10	2500	14,142	80,000	452,548	2,560,000
11	2750	15,556	88,000	497,803	2,816,000
12	3000	16,970	96,000	543,058	3,072,000
13	3250	18,384	104,000	588,312	3,328,000
14	3500	19,798	112,000	633,567	3,584,000
15	3750	21,213	120,000	678,822	3,840,000
16	4000	22,627	128,000	724,077	4,096,000

Skillpoints per minute

The skillpoints generated each minute depend on the primary \((a_{primary})\) and secondary attribute \((a_{secondary})\) of the skill.

\[ y_{skillpointsPerMinute} = a_{primary} + {a_{secondary} \over 2} \]

Target lock time

The target lock time (\(t_{targetlock}\)) in seconds depends on the ship's scan resolution (\(s\)) and the target's signature radius (\(r\))

\[ t_{targetlock} = {40000 \over s \cdot asinh(r)^2} \]

Alignment time

The ship alignment time (\(t_{align}\)) depends on the ship's inertia modifier (\(i\)) and the ships mass (\(m\))

\[ t_{align} = { ln(2) \cdot i \cdot m \over 500000 } \]