This page presents Rodrigues rotation formula as a geometric construction rather than as a memorized identity. The first figure shows the step-by-step decomposition and reconstruction, and the second shows the same rotation dynamically around a fixed axis.
Start by decomposing the vector v into the part parallel to the axis and the part perpendicular to it. The axial component stays fixed, while the perpendicular component is expressed in plane coordinates, rotated in 2D and mapped back into 3D. This makes Rodrigues rotation formula a composition of projection, planar rotation and recombination.
The animation shows the same structure dynamically. The vector rotates around the fixed axis, the axial component remains unchanged and the perpendicular component sweeps through the rotation plane. This is the geometric content behind the formula.
Related work: GraphMath Linear Algebra
External reference: Wikipedia — Rodrigues' rotation formula, derivation section
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