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Miloslav Ciz 2023-07-25 20:55:42 +02:00
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quaternion.md
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@ -12,7 +12,7 @@ where *a*, *b*, *c* and *d* are real numbers and *i*, *j* and *k* are the basic
**Why four components and not three?** Simply put, numbers with three components don't have such nice properties, it just so happens that with four dimensions we get this nice system that's useful.
Operations with quaternions such as their multiplication can simply be derived using basic algebra and the above given axioms. Note that **quaternion multiplication is non-commutative** (*q1 * q2 != +2 * q1*), but it is still associative (*q1 * (q2 * q3) = (q1 * q2) * q3*).
Operations with quaternions such as their multiplication can simply be derived using basic algebra and the above given axioms. Note that **quaternion multiplication is non-commutative** (*q1 * q2 != q2 * q1*), but it is still associative (*q1 * (q2 * q3) = (q1 * q2) * q3*).
A **unit quaternion** is a quaternion in which *a^2 + b^2 + c^2 + d^2 = 1*.
@ -28,4 +28,6 @@ Rotating point *p* by quaternion *q* is done as
Rotation quaternion can be obtained from axis (*v*) and angle (*a*) as
*q = cos(a/2) + sin(a/2) * (v.x i + v.y j + v.z k)*
*q = cos(a/2) + sin(a/2) * (v.x i + v.y j + v.z k)*
TODO: compare to euler angles, exmaples