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Dual quaternion: Difference between revisions
→Background
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Here, <math>\epsilon^2=0</math>. | Here, <math>\epsilon^2=0</math>. | ||
Multiplication | ;Scalar Multiplication | ||
<math>s\mathbf{q} = s\mathbf{q}_r + s \mathbf{q}_d \epsilon</math> | |||
;Addition | |||
<math>\mathbf{q}_1 + \mathbf{q}_2 = \mathbf{q}_{r1} +\mathbf{q}_{r2} + (\mathbf{q}_{d1} + \mathbf{q}_{d2}) \epsilon</math> | |||
;Multiplication | |||
<math>\mathbf{q}_1 \mathbf{q}_2 = \mathbf{q}_{r1} \mathbf{q}_{r2} + (\mathbf{q}_{r1}\mathbf{q}_{d2} + \mathbf{q}_{d1} \mathbf{q}_{r2})\epsilon</math>. | <math>\mathbf{q}_1 \mathbf{q}_2 = \mathbf{q}_{r1} \mathbf{q}_{r2} + (\mathbf{q}_{r1}\mathbf{q}_{d2} + \mathbf{q}_{d1} \mathbf{q}_{r2})\epsilon</math>. | ||
;Conjugate | |||
<math>\mathbf{q}^* = \mathbf{q}_{r}^* + \mathbf{q}_{d}^*\epsilon</math> | |||
;Magnitude | |||
<math>\Vert \mathbf{q} \Vert = \mathbf{q}\mathbf{q}^*</math> | |||
===Rotations and Translations=== | ===Rotations and Translations=== | ||