5,337
edits
Quaternion: Difference between revisions
→Background
No edit summary |
|||
| Line 8: | Line 8: | ||
The conjugate is <math>\bar{q} = (q_0, -\mathbf{q})</math>. | The conjugate is <math>\bar{q} = (q_0, -\mathbf{q})</math>. | ||
===Multiplication=== | ===Multiplication=== | ||
Multiplication is <math>q * p = (q_0 p_0 - \mathbf{q} \cdot \mathbf{p}, q_0 \mathbf{p} + p_0 \mathbf{q} + \mathbf{q} \times \mathbf{p})</math>. | Multiplication is <math>q * p = (q_0 p_0 - \mathbf{q} \cdot \mathbf{p}, q_0 \mathbf{p} + p_0 \mathbf{q} + \mathbf{q} \times \mathbf{p})</math>. | ||
Similar to imaginary numbers, <math>i*i=j*j=k*k=-1</math>. | |||
Multiplication between bases follow cross product rules: <math>i * j = k</math>, <math>j * i = -k</math>. | |||
Intuition: Left multiplication by a quaternion is a 4D rotation plus a scaling operation. | Intuition: Left multiplication by a quaternion is a 4D rotation plus a scaling operation. | ||