RE: [Re: calculating distance based on zip/postal codes]

I totally agree - I am impressed.

A great reason to keep tuning in...

regards,
Cathy Favre
IDON EAST Corporation
cfavre(at)idon.com

> -----Original Message-----
> From: owner-hwg-business(at)hwg.org [mailto:owner-hwg-business(at)hwg.org]On
> Behalf Of Manewell, Brett
> Sent: Monday, May 15, 2000 6:08 PM
> To: 'Jan Theodore Galkowski'
> Cc: hwg-business
> Subject: RE: [Re: calculating distance based on zip/postal codes]
>
>
> OK, I'm impressed already.
>
> I knew there was a good reason I subscr1bed to the hwg-business
> mail list ;)
>
> It's been 10 years since I did any heavy duty engineering maths at Uni and
> this is way beyond me getting my head around during my working
> day.  I think
> I'll just archive this discussion thread for later consideration.
>
> Thanks for the insight!
>
> regards
> Brett Manewell
> CSR Timber Products ISD
> BManewell(at)csr.com.au
>
>
> -----Original Message-----
> From: Jan Theodore Galkowski [mailto:jtgalkowski(at)alum.mit.edu]
> Sent: Tuesday, 16 May 2000 10:09
> Subject: Re: [Re: calculating distance based on zip/postal codes]
>
> >D= 6,370,997*arcos(sin(LAT1)*sin(LAT2) +
> cos(LAT1)*cos(LAT2)*cos(LONG1-LONG2))
> [snip]
>
> >Though I believe that this is the arc-cosine rule that Galkowski advised
> >against.
> Just to confirm Capt Ron's suspicion, yes, this is the problematic
> arccosine rule.  All's fine except that nasty cosine of the
> difference between two longitudes:  As the distance between the
> longitudes halves, you need more than double the amount of precision
> to get the same accuracy out of the expression.
>
> In general, folks who do a lot of 3-dimensional work on the sphere
> represent positions by unit vectors in 3-space and use their dot
> products as a reciprocal measure of distance between the points.
> To change that into a length, one can use a number of gimmicks
> which avoid having to push the quantity through a trig function.
> Indeed, most real-time 3-or-greater-space work avoids trig functions
> altogether, trying to reduce the calculation to +, -, *, /, and
> SQRT operations only.  Vector analysis is good for this.  There
> are also more numerically stable representations, such as
> quaternions (although, apart from religious considerations, it's
> hard to make a case for them versus, say, spin matrices, or
> rotation matrices themselves) or Rodrigues parameters (a favorite
> of mine).
>
> In serious work, error analysis on the sphere is an important
> consideration and, if the standard angular deviations are anything
> but tiny, involves some non-standard stuff which is the subject
> of spherical statistics and spherical regression, eg, paleomagnetic
> calculations.
>   --jtg
> [snip]
>

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