Quaternion angle with itself > 0.001

Stephany Bowman · 2014-08-13T17:30:04

Hey guys, I'm in the process of working out my math library, and so I was testing out a function that returns the angle between two quaternions.. { return 2.0f * acos( Abs( Dot4( qa, qb ) ) ); } .. but for some reason, I'm either getting a lot of floating point error in the result, or I'm not checking for a situation that I should be. While testing a quaternion (which was generated by a random axis+angle rotation and appears to be very close to normalized).. { x=0.0172970667 y=-0.0245058369 z=0.0205858145, w=-0.999337912 } .. with itself, I'm getting a result angle of 0.00138106791 (or almost 0.1 degrees).. I'm just wondering if this is acceptable error when working with float variables? And is there anything I can do to improve this issue other than switching to double type or something else as drastic? edit note: After testing some more, the highest "error angle" I've been able to generate (through random axis-angles) is 0.001953125. And that was getting the angle (from itself) of a quaternion generated by the axis @ angle: { -0.833756,0.551120,-0.033417 @ 2.960138559341 } (quaternion result: { -0.830327,0.548853,-0.033279,0.090603 } ) Thank you

Math and Physics Programming

Started by Stephany August 03, 2014 04:55 PM

19 comments, last by alvaro 10 years, 6 months ago

alvaro

21,610

August 13, 2014 05:30 PM

You can also compute the angle between quaternions using

  dot_product = dot4(qa, qb);
  dot_product_squared = dot_product * dot_product;
  denominator = dot4(qa, qa) * dot4(qb, qb);
  return 2.0f * acos(sqrt(abs(dot_product_squared / denominator)));

I haven't tried it, so there could be mistakes. The idea is to not rely on the inputs being normalized, and write the expression in such a way that you are guaranteed to get exactly 0 if you qa==qb.

Quaternion angle with itself > 0.001

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Quaternion angle with itself > 0.001

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