5,321
edits
Computer Graphics: Difference between revisions
→Rotation Matrix
| Line 35: | Line 35: | ||
\end{bmatrix} | \end{bmatrix} | ||
</math> | </math> | ||
To formulate a rotation about a specific axis, we use [[Wikipedia:Rodrigues' rotation formula]].<br> | |||
Suppose we want to rotate by angle <math>\theta</math> around axis <math>\mathbf{k}=(k_x, k_y, k_z)</math>.<br> | |||
Let <math> | |||
\mathbf{K} = [\mathbf{k}]_{\times} = | |||
\begin{bmatrix} | |||
0 & -k_z & k_y\\ | |||
k_z & 0 & -k_x\\ | |||
-k_y & k_x & 0 | |||
\end{bmatrix}</math><br> | |||
Then the rotation matrix is <math>\mathbf{R} = \mathbf{I}_{3} + (\sin \theta)\mathbf{K} + (1 - \cos \theta)\mathbf{K}^2</math> | |||
===Scaling Matrix=== | ===Scaling Matrix=== | ||