For people trying to understand quaternions, the faster way to intuition is understanding axis-angle first. I think axis-angle is totally intuitive. First pick

For people trying to understand quaternions, the faster way to intuition is understanding axis-angle first. I think axis-angle is totally intuitive. First pick a direction (some 3d unit vector) and then rotate around that direction by some amount (so some scalar). Then convert those four numbers to quaternions qx = ax * sin(angle/2) qy = ay * sin(angle/2) qz = az * sin(angle/2) qw = cos(angle/2) where (ax, ay, az) is the unit direction (ax^2 + ay^ + az^2 = 1) and angle is the amount you want to rotate. http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/ http://www.euclideanspace.com/maths/geometry/rotations/conve... http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/ http://www.euclideanspace.com/maths/geometry/rotations/conve...