View Full Version : Conversion of Quaternions to Euler angles

Dr. Chris Kirtley
01-23-2003, 03:23 AM
Dear all,

Following on from all the angle calculation stuff, someone just brought
my attention to another problem:

In this page that I made some time ago, I provide a method for
conversion between quaternion representation and Euler angles (from
Kuipers JB 1999):


tan(yaw) = 2(q1q2+q4q3) / (q42 + q12 - q22 - q32)
sin(pitch) = -2(q1q3-q4q2)
tan(roll) = 2(q4q1+q2q3)/ (q42 - q12 - q22 + q32)

These equations fail when, e.g., the pitch angle is 90 degrees. Is this
just the inherent problem of Euler angle gimbal lock, or is there a way
round it?

Dr. Chris Kirtley MD PhD
Associate Professor
Dept. of Biomedical Engineering
Catholic University of America
620 Michigan Ave NE, Washington, DC 20064
Tel. 202-319-6247, fax 202-319-4287
Email: kirtley@cua.edu

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