5 messages---------------------------------Johnnie
-----------------------------------------
>From: "dimitriou eleni" <[log in to unmask]>
>Date: Tue, 14 May 1996 19:01:50 +0200
>Help! A man just called and wants to know if there is a formula
>for computing the distance in meters between "Point A" and "Point
>B" if he knows the coordinates for each point. Does anyone know?
>This is beyond me.
>Jane "BA in Literature; MLS; 11 yrs. children's librarian" Carlson
>Map Collection Assistant
>University of Iowa
---------------------------------------------------------------------
If the coordinates are cartesian then the formula would be
d=squareroot(dx^2+dy^2)
dx=Xa-Xb
dy=Ya-Yb
if the coordinates are geographic (longitude-latitude) then you will have to
calculate the lentgh of the geodesic line between those 2 points which is quite
complicated and you should refer to a book having to do with geodetic and
cartographic computations.
--
Christopher Vradis
National Technical University Of Athens
Rural and Surveying Engineering Department
Cartography Laboratory
9, Hroon Polytexneiou St.
Zografou
Athens, GREECE
------------------------------------------------------------
>Date: Tue, 14 May 1996 15:59:28 -0400 (EDT)
>From: william j thornton <[log in to unmask]>
>Subject: Re: Formula for computing distance?
There is a web site, "http://www.indo.com/distance/," which will compute
the distance between two coordinates.
---------------------------------------------------------------
>Date: 14 May 1996 09:39:24 U
>From: "Joe Crotts" <[log in to unmask]>
>Subject: Distance from Coordinates
The "arc" or great circle distance between two points, the coordinates of
which are known, can be calculated as follows:
cos d = (sin a) (sin b) + (cos a) (cos b) (cos P)
in which
d = arc distance between points A and B
a = latitude of A
b = latitude of B
P = degrees of longitude between A and B
The arc distance will be in degrees of latitude, which then can be converted
to miles, for instance, by multiplying by the number of miles in a degree of
latitude--ca. 69 miles with slight variation.
I haven't done this in years and hope I've got it right. Please don't be to
hard on me if I'm off a bit.
-------------------------------------------------------
>Date: Wed, 15 May 1996 11:22:19 +0000
>From: [log in to unmask] (Mike Shand)
>Subject: Re: Formula for computing distance?
>----------------------------Original message----------------------------
>Help! A man just called and wants to know if there is a formula
>for computing the distance in meters between "Point A" and "Point
>B" if he knows the coordinates for each point. Does anyone know?
>This is beyond me.
>
>Jane "BA in Literature; MLS; 11 yrs. children's librarian" Carlson
>Map Collection Assistant
>University of Iowa
I'm no mathematician, but is it not a simple case of using the Pythagoras
Theorm i.e. that the sum of the square of the length of the hypotenuse
equals the square of the sum of the other two sides.
Using point A and point B as the hypotenuse of a right-angled triangle.
The vertical height of the triangle (AC) is the difference between the two
Northing values and the horizontal distance (BC) is the difference between
the two Easting values.
C ------- B
| /
| /
| / AB2 = AC2 + BC2
| /
| /
|/
A
The Formula would then be :
Distance AB =
square root [ (northing A - northing B)2 + (easting A - easting B)2 ]
Maybe I'm missing the point !!
Hope this helps,
MIke
************************************************************************
Mike Shand, Tel: Direct 0141-330-4780
Senior Cartographer, E-mail: [log in to unmask]
Dept. of Geography & Topographic Science, Fax: 0141-330-4894
University of Glasgow.
GLASGOW, Honorary Secretary:
G12 8QQ, SOCIETY OF CARTOGRAPHERS
Scotland, U.K.
http://www.geog.gla.ac.uk/staff/tech/mshand/mshand.htm
************************************************************************
---------------------------------------------------------
>Date: 15 May 96 01:17:22 EDT
>From: "Frank E. Reed" <[log in to unmask]>
>Subject: RE: Formula for computing distance?
A FEW NUMERICAL RECIPES FOR CALCULATING DISTANCES:
0) Assume you start out with the latitudes and longitudes of two
points expressed in decimal degrees (lat1,lon1),(lat2,lon2).
--------------------------------------------------------------------
GREAT CIRCLE DISTANCE ON A SPHERICAL EARTH:
1) Convert the latitudes to co-latitudes and all angles to radians:
phi1 = (90-lat1)*pi/180
phi2 = (90-lat2)*pi/180
theta = (lon2-lon1)*pi/180
[NOTE: do NOT multiply by pi/180 if you are using a handheld
calculator since they usually let you do trig functions in degrees.
If you're doing calcs in a spreadsheet or programming language,
keep the pi/180].
2) Get the standard great circle angular distance in radians:
a = arccos[cos(phi1)*cos(phi2)+sin(phi1)*sin(phi2)*cos(theta)].
Many programming languages do not include the arccos function. In
that case, use
arccos(x) = pi/2 - arctan(x/sqrt(1-x*x)).
3) Multiply by the radius of the Earth to convert radians to
statute miles:
d = 3955*a.
------------------------------------------------------------------
SHORTCUT FOR POINTS SEPARATED BY LESS THAN ~250 MILES:
1) Convert to radians:
lat1 = lat1*pi/180
lat2 = lat2*pi/180
theta = (lon2-lon1)*pi/180
2) Get the angular separation in radians using the Pythagorean
Theorem:
a = sqrt((theta*cos(lat1))^2+(cos(lat2-lat1))^2).
3) Convert to miles:
d = 3955*a.
------------------------------------------------------------------
MORE ACCURATE DISTANCE ACCOUNTING FOR THE EARTH'S
ELLIPSOIDAL SHAPE:
0) Use e = 1/298.26 for the flattening of the Earth.
1) Convert the latitudes to co-latitudes and all angles to
radians as usual:
phi1' = pi*(90-lat1)/180
phi2' = pi*(90-lat2)/180
theta = pi*(lon2-lon1)/180
2) Calculate adjusted colatitudes:
phi1 = phi1'+(3/4)*e*sin(2*phi1')
phi2 = phi2'+(3/4)*e*sin(2*phi2')
3) Get the standard great circle angular distance:
a' = arccos[cos(phi1)*cos(phi2)+sin(phi1)*sin(phi2)*cos(theta)]
4) Calculate the geodesic distance on the ellipsoid:
a = a'*[1+(1/2)*e*(sin(phi1)*sin(phi2)*sin(theta)/sin(a'))^2]
5) Convert to miles
D = 3955.5*a.
If you skip steps 2 and 4, this is just the great circle distance
on a spherical Earth again. It's important to note that the
distance calculated above is the shortest distance between two
points on the Earth's surface at sea level. It is not properly
a "great circle" distance anymore since the geodesics on the
surface of an ellipsoid are not circles. Note that the ellipsoidal
distances are always within 1% of the great circle distances,
but that can mean 20 miles or so for widely separated points. This
ellipsoidal distance calculation is something I derived. It
seems to work correctly, but there still might be a problem in
there somewhere.
-Frank E. Reed
Clockwork Software, Inc.
[log in to unmask]
Visit
http://www.clockwk.com
for info on the CENTENNIA Historical Atlas.
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