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.