Dual quaternion: Difference between revisions
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These can be combined as <math>\mathbf{q} = \mathbf{q}_t * \mathbf{q}_r = \mathbf{q}_r + \frac{\epsilon}{2}\mathbf{t}\mathbf{q}_r</math>. | These can be combined as <math>\mathbf{q} = \mathbf{q}_t * \mathbf{q}_r = \mathbf{q}_r + \frac{\epsilon}{2}\mathbf{t}\mathbf{q}_r</math>. | ||
Applying the transformation to a point <math>\mathbf{ | Applying the transformation to a point <math>\mathbf{v} \in \mathbb{R}^3</math> is: | ||
<math>\mathbf{p}' = \mathbf{q}\mathbf{ | <math>\mathbf{p}' = \mathbf{q}(1 + \epsilon\mathbf{v})\mathbf{q}^*</math> | ||
==Resources== | ==Resources== | ||
* [https://cs.gmu.edu/~jmlien/teaching/cs451/uploads/Main/dual-quaternion.pdf A Beginners Guide to Dual-Quaternions by Ben Kenwright] | * [https://cs.gmu.edu/~jmlien/teaching/cs451/uploads/Main/dual-quaternion.pdf A Beginners Guide to Dual-Quaternions by Ben Kenwright] | ||