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Quaternion: Difference between revisions
→Rotations
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===Rotations=== | ===Rotations=== | ||
Quadratically conjugating a quaternion as follows is equivalent to applying a rotation on <math>\mathbf{x}=(x,y,z)</math>: | Quadratically conjugating a quaternion as follows is equivalent to applying a rotation on <math>\mathbf{x}=(x,y,z)</math>: | ||
<math display="block">q * (c,x,y,z)*\bar{q} = (c, R(q) \cdot \mathbf{x})</math> | <math display="block">\mathbf{q} * (c,x,y,z)*\bar{\mathbf{q}} = (c, R(\mathbf{q}) \cdot \mathbf{x})</math> | ||
Here, <math>R(q)=R(-q)</math> is a two-to-one mapping from quaternions to 3x3 rotation matrices. | Here, <math>R(q)=R(-q)</math> is a two-to-one mapping from quaternions to 3x3 rotation matrices. | ||