I have come across this problem too and it seems to re-occur from time to
time.
Having discussed this with a my surveying colleague we'd offer the
following observations:
MapInfo doesn't calculate the area of a circle, it converts it to an
inscribed polygon with 101 sides which produces a underestimate as Vick points
out. We got a figure of 3,139,566.7
There are also problems with rectangles. Again MapInfo will not calculate
the area of a rectangle object it has to be converted to a polygon, but this
is less problematic. Nevertheless, even with a non-earth projection MapInfo
returns a value of 4,000,000.5 sq m for a square of side 2000m. My colleague
tells me a similar problem can occur with AutoCAD and suggests the cause of
the error is due to the method of triangulation. IF MapInfo uses
triangulation with isosceles triangles then there would be small excess
slithers at either end causing an overestimation this time. This method is
popular because the area of the triangles can be easily calculated with 0.5 *
base * height.
Hope this sheds a little more light on the subject.
Hello Cathy,
I'll bow to Clifford's extensive knowledge on this
subject, but in terms of
using MapInfo Pro, there are a few things to be
aware off.
The British national grid system is indeed a Transverse
Mercator projection
which give a Cartesian coordinate space to work with.
That is to say, it's
just a simple grid with parallels lines in x/y, or
Eastings/Northings, and
perpendicular axis. Assuming you're happy to accept
the errors associated
with this projection (which is a 2D simplification of
the 3D earth), then
distances and areas can just be calculated using
high/secondary school level
geometry. For a couple of major releases now (I
forget exactly when),
MapInfo Pro has distance and area functions which are
explicitly Cartesian.
As an experiment, I made a new table in British
NG with a "MyArea" integer
field, set MapInfo Pro to Cartesian (Map >
Options...), added a 1km radius
circle and then did a Table > Update
Column with CartesianArea(obj, "sq m").
Now, the results should be
3141592 sq m(rounded down) from pi * 1000^2, but
I get 3139553. This is
closer that you got - presumably because you did not
use Cartesian areas,
but is still about 0.65% off. I've noted a few problems
in Pro's
calculations over the years (especially with very large polygons),
but
there doesn't seem to be any reason why simple geometry in Cartesian
space
should be wrong.
If I recall correctly, didn't some MI-L/MapInfo user
in Sweden(?) end up in
court a few years ago to explain why an area
calculation (pre-Cartesian
support) from Pro was
wrong?
Regards,
Warren Vick
Europa Technologies Ltd., U.K.
http://www.europa-tech.com-----Original
Message-----
From: [EMAIL PROTECTED]
[
mailto:[EMAIL PROTECTED]]
On Behalf Of Clifford J
Mugnier
Sent: 24 August 2006 17:23
To:
COLDREY, Cathy (Bristol)
Cc:
[email protected]Subject:
Re: [MI-L] area calculation discrepancies
Dear
Cathy:
What you are experiencing is the distortion present in a
conformal
coordinate system. The British National Grid is based on
the
fully-conformal Gauss-Krueger Transverse Mercator projection.
That type of
projection preserves shapes and angles, but not areas.
There are two
sources of systematic error associated with a conformal
projection such as
the Transverse Mercator. Those two errors are the
"convergence angle"
correction needed to tranform between Grid Azimuth and
True Azimuth and the
"scale factor" correction to tranform between Grid
Distances and True
Distances.
Your current problem is related to the
latter of the two systematic errors
that involves the scale factor at a
point correction factor. This is solved
through an analytic function,
and I do not know if such a facility is
available in the MapInfo
package. It certainly is in the online as well as
the downloadable
free software available directly from the Ordnance Survey.
Recalling
that Area = Length X Width, note that the scale factor you obtain
for say,
a point near the center of your area of interest needs to be
divided by the
length as well as the width of your area. Since it is
circular, then
just divide the Grid Area by the SQUARE OF THE SCALE FACTOR.
That will
yield a "true" area as close as possible to theoretical without
computing
the whole process on the surface of the ellipsoid of revolution -
a most
difficult process.
This sort of correction process is a daily chore for
a Chartered Surveyor in
the UK. It's also why I insist that GIS
students under my guidance take
several courses in surveying ... it helps
one over the "humps" in
professional practice.
Professor Johathan
Iliffe, University College, London, has a marvellous book
entitled, "Datums
and Map Projections," Whittles Publishing, ISBN
1-870325-28-1 (UK).
It is a required text for my Advanced Surveying
students here at LSU, and
it should be on the bookshelf of every GIS
practitioner that can read
English. I recommend that you get a personal
copy and study it; it is
directly intended for the student in the UK, but is
so good I use it for my
own students here!
Good Luck,
Clifford J. Mugnier, C.P.,
C.M.S.
National Director (2006-2008),
Photogrammetric Applications
Division
American Society for Photogrammetry and Remote
Sensing
and
Chief of Geodesy,
CENTER FOR GEOINFORMATICS
Department
of Civil Engineering
CEBA 3223A
LOUISIANA STATE UNIVERSITY
Baton
Rouge, LA 70803
Voice and Facsimile: (225) 578-8536
[Academic]
Voice and Facsimile: (225) 578-4474 [Research]
Honorary
Life Member of the
Louisiana Society of Professional
Surveyors
======================================================
http://www.asprs.org/resources/GRIDS/http://appl003.lsu.edu/eng/ceeweb.nsf/$Content/Mugnier======================================================
Hi
List,
Does anyone have much experience in calculating areas of polygons
or circles
in MapInfo?
My problem is this. I have a 1 km
radius which has exactly a diameter of
2km, meaning a 1 km radius.
Now mathematically the area of theis would be
3136860 square m. But
if I use the update column option the number I get is
3118630 square
m
or double click on the object I get 3119000 square m.
I am
using British national grid projection.
Can anyone explain to me why I
get three differing numbers?
And also how will I find the correct areas of
several other polygons that
are not circular?
Thanks for any help
you can provide to this mystery.
:) cathy
Cathy
Coldrey
Geomatics Specialist, Europe
WorleyParsons Komex
Environment
& Water Resources
Tel: + 44 (0)117 9105 124
Fax: + 44 (0) 117
9105 139
3-8 Redcliffe Parade West
Bristol BS1 6SP
Registered No.
2718875
www.worleyparsons.com
Please note: effective immediately my
new e-mail address is
[EMAIL PROTECTED]
