Gabor,
First make sure you are using a version newer than MapInfo 4.0.
In the old versions, the distances are right, but your area
calculations are dead
wrong.
This is because MapInfo's earlier area algorithm was flawed. In a
past message
(April '97), Joe Schwartz (from MapInfo) pointed out:
"In MapInfo 4.1, we changed the algorithm for calculating
spherical area. Whereas the old algorithm merely approximated
the
correct spherical area, the new algorithm (from Graphics Gems
IV,
pg. 132) purported to calculate it exactly.
Unfortunately, that algorithm appears to break down when
calculating the area of polygons with very short segments.
We've
fixed that problem in MapInfo 4.1.2 by modifying the
algorithm."
Here's how you can prove that version 4.0's algorithm is broken,
but that the new one is right (should convince a court, too):
First, note that the surface area of a sphere is 4*PI*R^2. The
radius of
the earth as used by MapInfo is 6370996.99 So, the surface area
of the
earth is 4*3.14159265359*6370996.99^2, or 510,063,990 sq km.
(that's
right--the World Factbook puts it at 510,072,000 sq km)
Now to test MapInfo, imagine a spherical triangle from the
equator along
the prime meridian to the north pole, then down the meridian at
90W and
back along the equator. So draw a polygon from (0,0) to (0,90) to
(-90,90) to (-90,0), and then double-click on it to get the area.
In
MapInfo 4.0, this is 70,817,331.4 sq km and if we multiply it by
8 to
cover the world, MapInfo thinks there's 566,538,651 sq km of
surface to
the earth. WRONG! However, in MapInfo 4.1 it's 63,757,999 sq km,
which
multiplied by 8 gives 510,063,992 sq km, which is as it should
be.
Also if you want to verify that MapInfo really is using a sphere,
and to
find out what radius it's using, try this in the MapBasic window:
print distance(0,0,90,0,"m")
print distance(0,0,0,90,"m")
This gives you identical values for a quarter of the
circumference along
the equator and along the prime meridian, so MapInfo assumes the
earth
is a sphere. Remembering the formula that relates radius to the
circumference (c = 2*PI*R), and that this value is a quarter of
the
circumference, the Radius is 6370996.99.
So, you have to use the latest version of MapInfo or at least
state the
version you are using when questioning results.
Also note that areas in MapInfo are spherical surface areas, and
their bounds are not the "straight" lines you see on your map but
segments of great circles drawn between the polygon vertices. For
small areas, there shouldn't be much difference, but there is
some. The world is not flat and your areas will be larger (and
more correct) than someone using a flat map and measuring off it
with a ruler.
If you want to duplicate their results, convert your data to some
equal-area projection, and dump it to a MIF file. Then change the
coordsys clause at the top of the MIF file to a non-earth system
and re-import that. In non-earth systems MapInfo assumes
everything is flat.
Finally the most legally indisputable measure of land is not
going to come from GIS software but from that other source (also
known as GIS... or Get It Surveyed).
- Bill Thoen
MapInfo is doing the right thing using great circle distances and
spherical surface areas, but I can see where there is going to be
a lot
of confusion over this. Basically, your line endpoints will be
accurate
in either projected or geographic coordinates, but any distances
or
areas calculated in a projected space using flatland software
(like
AutoCAD or ArcView) are only approximations with diminishing
accuracy
over smaller scales.
Gabor Vasarhelyi wrote:
>
> Dear Listers,
> Today I was summoned to court to give evidence relating to property areas I
>calculated on a non earth grid. I was only given an A1 plan which I scanned and
>digitised the property boundary onto. They fortunately had a grid on the map and it
>was that which I used for calculating areas.
>
> The reason I was in court was to explain why my area calculations were different
>(slightly higher 2.3%) than those of our opposition.
>
> Am I correct in assuming the areas calculated by MapInfo are good to the decimal
>places it gives? Your experience would be appreciated.
>
> The opposition were using a planimeter (which from my recolections is not as
>accurate as I assume Mapinfo to be.
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