5,337
edits
Quaternion: Difference between revisions
→Orientation-Frame Alignment Problem
| Line 107: | Line 107: | ||
\mathbf{S}_{\text{chord}} = \sum_{k=1}^{N}\left( \min( \Vert (q*p_k) - r_k \Vert, \Vert (q*p_k)+r_k \Vert ) \right)^2 | \mathbf{S}_{\text{chord}} = \sum_{k=1}^{N}\left( \min( \Vert (q*p_k) - r_k \Vert, \Vert (q*p_k)+r_k \Vert ) \right)^2 | ||
</math> | </math> | ||
==Double Quaternions== | |||
{{main | Double quaternions}} | |||
These are different from dual quaternions. | |||
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== | |||
{{main | Dual quaternions}} | |||
==Combined Point + Frame Alignment Problem== | ==Combined Point + Frame Alignment Problem== | ||