Re: [Plib-users] Problem with rotations results

[Ben W. <za...@ec...>]

----- Original Message -----
From: "Steve Baker" <sjb...@ai...>
To: <pli...@li...>
Sent: Tuesday, September 10, 2002 11:46 PM
Subject: Re: [Plib-users] Problem with rotations results


> Ben Woodhead wrote:
>
> > Wow, I had no idea the results returning from a matrix were that like
that.. I
> > understood what you meant, when you said h <> h, and so on. But I didn't
> > realise just how off they would actually be.
>
> Yes - well, it's a mathematical fact.  There are an infinite number of
ways
> to represent an arbitary rotation matrix in terms of Euler angles - and
the
> code has no way to know which one you wanted - so it just picks one.
>
> It's hard to know what else we could do.
>
> > Anyway back to the point, I was
> > wrong about the 0 and 180, its at 90 degrees that cause the problem.
Here is
> > the header, pitch and role from the 3 different rotations. Take a close
look
> > at the pitch.
>
> (BTW: The word is "Roll" - not "Role" and "Heading" - not "Header")
>
> > Pitch
> > Header: -0.000000, Pitch: 88.002075, Role: -0.000000
> > Header: -0.000000, Pitch: 89.004166, Role: -0.000000
> > Header: 0.000000, Pitch: 90.000000, Role: 90.000000
>
> Eh?  Are you sure the heading was zero?  I'd expect it to
> be -90 or something.

No, that was actually the log from the program running, that I copied into
here.. That was what was causing me the greef.

> But anyway - this *is* classic 'Gymbal Lock'.

Ah, I always thought gymbal lock was only when rotating around all 3 axes at
the same time.

> As Norman suggested, you can visualise it in these
> terms:
>
>      "A hunter walks South one mile from his tent, then
>       he is chased due East for one mile by a ferocious Bear.
>       Having escaped, he walks North for one mile and finds
>       himself back at his tent.  What colour was the Bear?"
>
>      (White!)

What? I don't get it..

> > As you can see in pitch when it hits 90 on pitch, role also goes to 90.
The
> > one thing that I just noticed is that non of the other rotations get to
> > exactly 90.0.
>
> It's not so much that Roll or Pitch is special, it actually comes
> about that way because of the order of rotational operations.
>
> The bottom line is that Mat-to-Coord is working OK - it's just
> that you have to understand it's limitations.

Well, thanks everybody.. I rewrote all the code to have not use coord and
everything is good..
Thanks Ben

> ----------------------------- Steve Baker -------------------------------
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