Re: [Flightgear-devel] Quats from (lat,lon) to (0,0)

[Arnt K. <ar...@c2...>]

On Fri, 06 Nov 2009 09:43:25 -0700, John wrote in message 
<4AF...@av...>:

> On 11/06/2009 03:43 AM, Erik Hofman wrote:
> 
> > So what I basically need is:
> > 1. Orientate the Sun Position quad(lat,lon) to line op with
> >     SGQuatd::fromLonLat(SGGeod::fromRad(0,0))
> > 2. do the sunrise/sunset positioning math at (0,0)
> > 3. rotate the result back to SGQuatd::fromLonLat(geodViewPos);
> > 
> > But maybe I expect too much from quats?
> 
> Well, it is safe to say that there is more to celestial
> mechanics than just quaternions.  Some things are best
> done using quaternions, while other things are best
> done using plain old vectors, et cetera.
> 
> Here's how I would do the celestial mechanics:
> 
> This is simplest in the earth-centered nonrotating
> frame (ECN).
> 
>    Note: I couldn't find a decent reference defining
>    the various reference frames, so I wrote one:
>       http://www.av8n.com/physics/coords.htm
>    It's still somewhat drafty.  Suggestions are welcome.
> 
> We know where the sun is in the ECN frame.  
>  -- It is located at the point (declination, right ascension)
>   =(0,0) at the moment of the vernal equinox.
>  -- It goes around the ecliptic once per year.  This
>   is a rotation, well described by a quaternion.  The
>   rate of rotation is slightly nonuniform, as described 
>   by the so-called "equation of time".
> 
> Given the direction to the sun, we can easily calculate
> the position of the sun in absolute space.  This is a
> vector Rs from the center of the earth to the center of
> the sun.  This is a vector in the ECN system.
> 
> Given the (lan,lon) of the point of interest, we can 
> calculate the vector R1 from the center of the earth to
> that point.  This requires accounting for the lat,lon of
> the point of interest, as well as the rotation of the
> earth (elapsed time since the vernal equinox).
> 
> By adding vectors tip to tail (or in this case subtracting
> them) we can calculate the vector from the point of
> interest to the center of the sun.
> 
> It is then straightforward to find the elevation of
> this vector above the local horizontal plane.  This 
> is easily done using a projection operator, which 
> is constructed from the aforementioned R1 vector.
> 
> It may be tempting to use similar techniques to
> express the azimuth of the sun relative to the local
> north, but this scares me because it is guaranteed
> to fail at the poles.  The local vertical direction
> is always well defined, and the local horizontal is
> always well defined, but directions /within/ the
> horizontal plane are not so easily defined at the 
> poles.  That's why I'm always leery of using the NED
> frame (or ENU frame).  It's better to convert from 
> ECN (or ECEF) directly to the camera frame.
> 
> 
> That's a rather terse outline;  if anybody wants the
> next level of detail, let me know.

..just playing the Devil's advocate; Imagine an aircraft 
or "aerospacecraft" flying from KOSH to Mars the planet 
to fuel up for a few wee trips to those Earth-like planets 
we ought to find out there, before we need to get out of 
this smoking wreck? ;o)

-- 
..med vennlig hilsen = with Kind Regards from Arnt... ;o)
...with a number of polar bear hunters in his ancestry...
  Scenarios always come in sets of three: 
  best case, worst case, and just in case.