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#Actualquasar3d

Posted 13 August 2014 - 11:11 AM

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

 

The reason why the error gets so big, is that the inverse cosine function is very steep around 1. This has the effect that the (even exact) inverse cosine of a dot product which is only a tiny bit off, will give a pretty big angle difference.

 

For example, the cosine of 0.1 degree is 0.99999847691, and so if your dot product would give 0.99999847691 (which is a pretty good approximation of 1), the angle you get will be around 0.1

 

I bet that the reason why, after renormalizing your quaternions, you did get the correct result, was that this gave a dot product of exactly 1, but I don't think this will work for all quaternions. There will certainly be normalized quaternions, which give a dot product with themselves not exactly equal to 1.

 

The good news is that it's only this bad when you're computing the angle between quaternions which are almost parallel. For quaternions which are not nearly parallel, the result will be more accurate.


#1quasar3d

Posted 13 August 2014 - 10:58 AM

The main reason why it was so inaccurate is that the inverse cosine function is very steep around 1, and so a relatively small error introduced by your dot product will give an 

 

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

 

The reason why the error gets so big, is that the inverse cosine function is very steep around 1. This has the effect that the (even exact) inverse cosine of a dot product which is only a tiny bit off, will give a pretty big angle difference.

 

For example, the cosine of 0.1 degree is 0.99999847691, and so if your dot product would give 0.99999847691 (which is a pretty good approximation of 1), the angle you get will be around 0.1

 

I bet that the reason why, after renormalizing your quaternions, you did get the correct result, was that this gave a dot product of exactly 1, but I don't think this will work for all quaternions. There will certainly be normalized quaternions, which give a dot product with themselves not exactly equal to 1.

 

The good news is that it's only this bad when you're computing the angle between quaternions which are almost parallel. For quaternions which are not nearly parallel, the result will be more accurate.


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