This constraint computes the relative rotation between AnchorOrientationALocal fixed on the first body and AnchorOrientationBLocal fixed on the second body. It computes the three Euler angles for the relative orientation (see GetEulerAngles(Matrix33F)).

Euler Angles: The Euler angles are computed for following order of rotations: The first rotation is about the x-axis. The second rotation is about the rotated y-axis after the first rotation. The last rotation is about the final z-axis.

The Euler angles are unique if the second angle is less than +/- 90°. The limits for the rotation angles are [-180°, 180°] for the first and the third angle. And the limit for the second angle is ]-90°, 90°[. Important: For Minimum and Maximum these angles must be specified in radians not degrees.

Each rotation of the three Euler angle rotations can be restricted using Minimum and Maximum. Important: The second rotation must be fixed in the range ]-90°, 90°[ (otherwise a Gimbal Lock situation occurs).

This constraint can be used to create custom constraints. For example using a minimum and maximum limits of (0, 0, 0) creates a NoRotationConstraint. Combining the AngularLimit with a BallJoint and using a minimum and maximum of (-∞, 0, 0) and (+∞, 0, 0) creates a HingeJoint. Combining the AngularLimit with a BallJoint and using a minimum and maximum of (-π/4, 0, -∞) and (+π/4, 0, +∞) creates a Hinge2Joint where the first rotation axis is the limited steering axis and the third axis is the rolling axis.

Reference