RE: MI-L A Mapping Puzzle for Savants

[Warren Vick, Europa Technologies Ltd.]

Hello Bill et al,

Having a good world map product at my disposal, I tried true radii around
the city centroids and found that there seemed to be no place where they all
intersect. Although a quick glance of the first two locations suggests
somewhere in North America, some of the distances do not reach (even if you
go via 180 degrees). From a scientific point of view, I would next explore
the notion that the point is not on the Earth's surface. i.e. it is below
the surface or up in space. I cannot think of non-brute force method to
calculate the puzzle if it is what it seems.

I noted that the distances given increment is more-or-less similar amounts
and wonder if this is a clue. Perhaps it is a word puzzle (rather than a
"world" one) and the names, increments or order are clues.

You're right about MapInfo buffers... it one of the things I really hate
about Pro. I first found this problem several years/releases ago when
calculating ETOPs circles - the range an aircraft can fly when an engine
fails. Although the distance tool uses a great circle calculation, buffers
do not use true 3D geometry and I have seen huge errors on many occasions.
The problem is very serious because users do have faith in MapInfo's
output - after all, it is a "Professional" product and has the maturity of
many releases. The problem has also cost me dearly... specifically a five
figure dollar sum where one of my clients gave erroneous figures to the
financial market community and I spent a long time unpaid clearing up the
mess. That one bug cost me more money than I have ever made reselling
MapInfo software (fortunately not from data too). I recall that a -L'er once
reported that they had to go to court to explain that a construction(?)
error was down to spherical rather than Cartesian area calculations. A
misunderstanding of coordinate systems is one thing but this is even worse
because it explicitly says "Spherical Buffer"... and that it is not.

The problem seems to root from Pro using a single sample point to convert
the required distance to a unit in degrees. While this may be fine for
latitude units, it's no good for longitude as a unit in this direction
changes with latitude (diminishing to zero at the poles). The errors can be
most seen with "latitude-rich" polygons... try using a polygon for the
country of Chile in tests. The error is the reason why buffers are always
circular/oval and do not spread out towards the poles. The lack of support
for 180 degrees is also a problem... Pro treats -180 and +180 longitude as
"a world apart".

The solution I used was to develop true 3D geometry for radii and, for
shortest paths, a proper Great Circle/Arc utility. I took the publicly
available PROJ4 code (fixed using WGS-84 datum) and made a MapBasic callable
DLL out of it. Great circle paths and radii are now no problem. I now make
large buffers by creating radii around each point in an object and combining
the results.

I'll intrigued to know the answer to the problem. I'm sure we will all kick
ourselves.

Regards,
Warren Vick
Europa Technologies Ltd, U.K.
http://www.europa-tech.com



> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED]]On Behalf Of Bill Thoen
> Sent: 24 April 2001 16:15
> To: [EMAIL PROTECTED]
> Subject: Re: MI-L A Mapping Puzzle for Savants
>
>
> Bill Huber wrote:
> > ... As the problem is phrased, there is no fast, simple
> procedure to get a practicably accurate answer.
>
> You may have put your finger on a clue here. I bet Jacques' observation
> about units was also a hint. Hendry Flavio is on target too. Stanley Ng
> also gets a nod for thinking outside the box (but I don't think "right
> in front of you" is the answer.) I don't believe it's in space, nor at
> the north pole. I think you can get the answer with simple deduction. I
> see two clues that eliminate everywhere else but one place.
>
> I think the answer Vos Savant is looking for is how you might deduce the
> location if you didn't have MapInfo (or Arc/Info, etc.) My guess is that
> "where" may not necessarily be precise. We'll just have to wait until
> she reveals the answer next Sunday.
>
> But I'm surprised that with all the GIS mapping power held by this group
> that few have tried the obvious: map the cities, and draw circular
> buffers around them at the specified distances. The precise place is the
> one place where all the circles intersect. Right? But it doesn't work in
> MapInfo because the distances are large  ...which reveals a subtle
> "Gotcha" that is lurking in MapInfo and probably most other mapping
> packages.
>
> The "circular" buffers are not what you may think they are when they
> would cross a pole. They compress, but this is not simple distortion due
> to map projection. Load in the following table and create points on the
> Lon/Lat columns with the "projection" set to Lat/Lon WGS 84. Then open
> just the cities in a map window. Select Paris and create a 4658 mile
> buffer around it. All the radii you can measure to the south are 4658
> miles, but to the north they are all short, with due north being the
> worst.
>
> City  Lon     Lat     Distance
> Paris 2.432778        48.881389       4658
> Moscow        37.938056       55.764167       5438
> Tel Aviv      34.480000       32.050000       6681
> Victoria (Hong Kong)  114.177222      22.274167       7878
> Sydney        151.028056      -33.889722      8746
> Johannesburg  28.004167       -26.178889      9092
>
> Begs the question, "What's the work-around?" I've also asked MI Tech
> Support.
>
> - Bill Thoen
> ------------------------------------------------------------
> GISnet, 1401 Walnut St., Suite C, Boulder, CO  80302
> tel: 303-786-9961, fax: 303-443-4856
> mailto:[EMAIL PROTECTED], http://www.ctmap.com/gisnet
> ------------------------------------------------------------
>
>
>
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