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Quaternion: Difference between revisions
→Multiplication
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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 | Similar to imaginary numbers, <math>\mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=\mathbf{i}\mathbf{j}\mathbf{k}=-1</math>. | ||
Multiplication between bases follow cross product rules: <math>i * j = k</math>, <math>j * i = -k</math>. | Multiplication between bases follow cross product rules: <math>\mathbf{i} * \mathbf{j} = \mathbf{k}</math>, <math>\mathbf{j} * \mathbf{i} = -\mathbf{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. | ||