5,337
edits
Quaternion: Difference between revisions
no edit summary
No edit summary |
|||
| Line 1: | Line 1: | ||
Quaternions are a number system which can be used to represent [[rotations]] in 3D space. | Quaternions are a number system which can be used to represent [[rotations]] in 3D space. | ||
Double quaternion allows representing 4D rotations using two quaternions. | |||
[[Dual quaternion]] allows represent both rotations and translations in 3D space. | |||
The algebra of quaternions, double quaternions, and dual quaternions is called Clifford algebras. | |||
==Background== | ==Background== | ||
| Line 109: | Line 112: | ||
==Double Quaternions== | ==Double Quaternions== | ||
Note that double quaternions are different from dual quaternions. | |||
Double quaternions are written as <math>q_1 + \epsilon q_2</math> with <math>\epsilon^2 = 1</math>. | Double quaternions are written as <math>q_1 + \epsilon q_2</math> with <math>\epsilon^2 = 1</math>. | ||
Dual quaternions are written as <math>q_1 + \varepsilon q_2</math> with <math>\varepsilon^2 = 0</math>. | Dual quaternions are written as <math>q_1 + \varepsilon q_2</math> with <math>\varepsilon^2 = 0</math>. | ||
==Dual Quaternions== | ==Dual Quaternions== | ||