Arbitrary Rotations Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering Georgia Institute of TechnologyRotation along an arbitrary axis 1. Transform the axis to cross origin (0,0,0) 2. Transform the axis around X onto the XZ plane 3. Transform the axis around Y onto the Z axis 4. Perform rotation (angle=θ) 5. Inverse transform of 3. 6. Inverse transform of 2. 7. Inverse transform of 1.Step 1: Translate to (0, 0, 0) • For easier viewing, I use RHS. x y z Rotating axisStep 2: Rotate around X, project to XZ x y z z y x (into the screen) θ (a, b, c) c b • Let’s pick up a random point (a, b, c) on the axis to figure out cosθStep 3: Transform around Y onto the Z axis x y z ω x z y (into the screen) a (a’, 0, c’) ωStep 4: Perform Rotation (angle=θ) on ZCombine all matrices with steps 5, 6,
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