Rotation

glRotate()

Rotation is setup in the top left part of a matrix so only the 3x3 part is shown here for each matrix.

Rotation θ around a axis

x =| 1 0 0 |

| 0 cos(θ) -sin(θ) |

| 0 sin(θ) cos(θ) |

y =| cos(θ) 0 sin(θ) |

| 0 1 0 |

| -sin(θ) 0 cos(θ) |

z =| cos(θ) -sin(θ) 0 |

| sin(θ) cos(θ) 0 |

| 0 0 1 |

Rotation θ around a arbitrary axis R

c = cos(θ) and s = sin(θ). R is the normalized axis of rotation.

r = | c+(1-c)R_x² (1-c)R_xR_y-sR_z (1-c)R_xR_z+sR_y |

| (1-c)R_xR_y+sR_z c+(1-c)R_y² (1-c)R_yR_z-sR_x |

| (1-c)R_xR_z-sR_y (1-c)R_yR_z+sR_x c+(1-c)R_z² |