Talk:Conversion between quaternions and Euler angles: Difference between revisions

Revision as of 14:31, 18 December 2022

Revision as of 16:41, 18 December 2022

Line 84:

2) The page [[Quaternions and spatial rotation]] makes very valid points on why Hamilton quaternions should be favored, so using only Hamilton quaternions here should be preferred. [[User:Ebernardes|Ebernardes]] ([[User talk:Ebernardes|talk]]) 14:31, 18 December 2022 (UTC)

== Changed the quaternion to Euler angles conversion formula ==

This new one has no numerical problems for the pitch. For anyone interested, I'll leave here a simple Python snippet that test both expressions to show they are equivalent:

<syntaxhighlight lang="python">

import numpy as np

from itertools import product

for w, x, y, z in product([-1, 0, 1], repeat=4):

n = np.sqrt(w**2 + x**2 + y**2 + z**2)

if n > 10e-7:

w /= n

x /= n

y /= n

z /= n

sinp = np.sqrt(1 + 2 * (w * x - y * z));

cosp = np.sqrt(1 - 2 * (w * x - y * z));

pitch1 = 2 * np.arctan2(sinp, cosp) - np.pi / 2;

pitch2 = np.arcsin(2 * (w * x - y * z))

assert (pitch1 - pitch2) < 10e-7

</syntaxhighlight>[[User:Ebernardes|Ebernardes]] ([[User talk:Ebernardes|talk]]) 16:41, 18 December 2022 (UTC)