Rodrigues Rotation Formula Calculator
Rotate 3D vectors using Rodrigues' rotation formula
Rotation Axis
Normalized: (0.0000, 0.0000, 1.0000)
Rotation Angle
90° = 1.570796 radians
Vector to Rotate (v)
Rotated Vector
v_rotated =
(0.000000, 1.000000, 0.000000)
Formula Breakdown
v_rot = v*cos(theta) + (k x v)*sin(theta) + k*(k.v)*(1-cos(theta))
v*cos(0.0000) = (0.0000, 0.0000, 0.0000)
(k x v)*sin(1.0000) = (0.0000, 1.0000, 0.0000)
k*(k.v)*(1-cos) = (0.0000, 0.0000, 0.0000)
Rotation Matrix
0.000000-1.0000000.000000
1.0000000.0000000.000000
0.0000000.0000001.000000
Rodrigues Rotation Formula
The Rodrigues rotation formula provides an efficient method to rotate a vector v around an axis k by angle theta:
v_rot = v*cos(theta) + (k x v)*sin(theta) + k*(k.v)*(1-cos(theta))
This is equivalent to the rotation matrix formula: R = I + sin(theta)*K + (1-cos(theta))*K^2
where K is the skew-symmetric cross-product matrix of k.