Three Parametrizations of Rotations

progress

1

method

EulerZYZ

axis/angle

roll pitch yaw

Euler ZYZ

ϕ

0

θ

0

ψ

0

axis angle

axislat/long

	0.
0.

angle

0.

roll

γ

pitch

β

yaw

α

R

x

0, α

0.

R

y

0, β

0.

R

z

0, γ

0.

A rotation can be parameterized in several ways. This Demonstration compares three popular parametrizations:

• Euler angles about the

ZYZ

axes

• the angle of rotation about an arbitrary axis

• the roll, pitch and yaw about the world

XYZ

axes

The progress slider rotates a teapot shape through these rotations, from an initial orientation in green to a final orientation in red. The intermediate configurations of the teapot depend on the parametrization chosen, but the final configuration is always the same.