Rotation representation: Matrix

\( \left\{ \begin{array}{l} \mathrm{R}= \left( \begin{array}{ccc} r_{00} & r_{01} & r_{02} \\ r_{10} & r_{11} & r_{12} \\ r_{20} & r_{21} & r_{22} \\ \end{array} \right) \\ \\ \mathrm{R}^T\,\mathrm{R}= \mathrm{Id} \end{array} \right. \)

Pro.

• - Standard structure (storage,manipulate)
• - Simple application to vector: \(v'=\mathrm{R}v\)
• - Composition b/w rotations: \(\mathrm{R} = \mathrm{R}_1\,\mathrm{R}_2\)

Cons.

• - Large redundancy (9 coefficients for 3 dof).
• - Rotation parameters don't appear explicitely
• - Unclear interpolation