R³ 中的旋轉

🚧 under construction

Last updated 2 years ago

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🚧 under construction

⟩ ⟩ ⟩ R³ 中的旋轉

A rotation in $\mathbb{R}^3$ is a function $\rho:\mathbb{R}^3 \to \mathbb{R}^3$ that preserves lengths, angles, and handedness：

保長： $\|\rho(\mathbf{v})\| = \|\mathbf{v}\|$
保角： $\rho(\mathbf{u}) \cdot \rho(\mathbf{v}) = \mathbf{u} \cdot \mathbf{v}$ (保)
保方向性： $\rho(\mathbf{u}) \times \rho(\mathbf{v}) = \rho(\mathbf{u} \times \mathbf{v})$ (保)

(註：「保」即可「保長」，所以第一個條件是多餘的)

Last updated 2 years ago

Was this helpful?

⟩ ⟩ ⟩ R³ 中的旋轉

A rotation in $\mathbb{R}^3$ is a function $\rho:\mathbb{R}^3 \to \mathbb{R}^3$ that preserves lengths, angles, and handedness：

保長： $\|\rho(\mathbf{v})\| = \|\mathbf{v}\|$
保角： $\rho(\mathbf{u}) \cdot \rho(\mathbf{v}) = \mathbf{u} \cdot \mathbf{v}$ (保)
保方向性： $\rho(\mathbf{u}) \times \rho(\mathbf{v}) = \rho(\mathbf{u} \times \mathbf{v})$ (保)

(註：「保」即可「保長」，所以第一個條件是多餘的)