Rotation Conversion Tool:
Euler Angles, Quaternion, Axis-Angle & Rotation Matrix
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There are several ways to represent 3D rotations for computer graphics and other applications. Four of the most common are: Euler angles; quaternions; axis-angle; and rotation matrices. This tool converts Tait-Bryan Euler angles into each of the other three representations. It also rotates the input point by the specified amount. It works for all possible rotations, including the null rotation and gimbal lock (when pitch equals +90° or −90°). All angles are in degrees.
The following conventions are observed:
- Tait-Bryan Euler angles with rotation order yaw, pitch, roll, around the z, y and x axes respectively
- Intrinsic, active rotations
- Right-handed coordinate system with right-handed rotations
See this paper for a detailed explanation of Euler angles and rotation matrices.
See the main paper for a detailed explanation of quaternions, and the math used by this tool to perform the conversions.
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