An interactive guide to sensor fusion with quaternions

12 comments

• mci 6 hours ago

  > a quaternion is a 4D representation of a rotation in 3D space

  A unit quaternion represents a rotation in R³.

  A quaternion represents the quotient of two vectors in R³. That's what Hamilton had in mind.

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  • xeonmc 5 hours ago

    in other words, dilation + rotation

• oneshtein 5 hours ago

    /* Produce a quaternion from an axis-angle representation.*/
    function quat_from_axis(theta: number, x: number, y: number, z: number) {    
      const halfcos = Math.cos(theta * 0.5);    
      const halfsin = Math.sin(theta * 0.5);    
  
      return new Quaternion(
          halfcos,
          axis[0] * halfsin,
          axis[1] * halfsin,
          axis[2] * halfsin,
      );    
    }
  

  Function is vibe coded.
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  • noodlejs 5 hours ago

    Hi! Author here. I hand wrote this website and the source code of the examples mostly comes from my own debugging tools. That method in particular is just a very minimal implementation of section 8.5.2 of this textbook (but I tried to make it friendly for the blog post).

    https://gamemath.com/book/orient.html#quaternion_geometry

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    • polishdude20 4 hours ago

      Sorry, but x,y and z are not even being used in that function...

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      • noodlejs 4 hours ago

        LOL ok yeah, that's a copy-paste issue. I'll fix it up here shortly.

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        • xeonmc 4 hours ago

          imo it's better to express the conversion relation as exp-log pairs:

              fn exp(q: Quat) -> Quat {
                  let ijk = sqrt(q.i*q.i + q.j*q.j + q.k*q.k);
                  Quat {
                      i: exp(q.l) * sin(ijk) * q.i / ijk,
                      j: exp(q.l) * sin(ijk) * q.j / ijk,
                      k: exp(q.l) * sin(ijk) * q.k / ijk,
                      l: exp(q.l) * cos(ijk),
                  }
              }
          
              fn log(q: Quat) -> Quat {
                  let ijk = sqrt(q.i*q.i + q.j*q.j + q.k*q.k);
                  Quat {
                      i: atan2(ijk, q.l) * q.i / ijk,
                      j: atan2(ijk, q.l) * q.j / ijk,
                      k: atan2(ijk, q.l) * q.k / ijk,
                      l: 0.5 * log(q.i*q.i + q.j*q.j + q.k*q.k + q.l*q.l),
                  }
              }

  • ARob109 4 hours ago

    I've been seeing "that's vibe coded" comments a lot lately on posts. Comments that call out code that may or may not be vibe-coded. At what point should these types of posts start getting down-voted? It's not constructive, and IMO imparts a negative connotation.

    HN: Show HN Awesome New LLM can Code!! Also HN: TFA is vibe coded angry pitchfork or ugh

  • feoren 5 hours ago

    What makes you so confident that you can tell that a 3-line function is AI? Especially given that the author denies it, with evidence.

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    • oneshtein 3 hours ago

      It cannot work, because x,y,z are not used at all.

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      • margalabargala 3 hours ago

        This looks more like a copy paste error, where the function signature requests xyz, but the function itself uses an undefined array "axis" of which xyz correspond to indexes 0-2.

        The code is correct aside from the obvious bug.

        Bugs predate the existence of AI by decades. This particular bug doesn't look like one an AI would write.

    • CamperBob2 4 hours ago

      Then again, that's just the AI would say...