Real (Great Circle) distance in PostGIS with lat/long SRID? - gis

Question

I'm using a lat/long SRID in my PostGIS database (-4326). I would like to find the nearest points to a given point in an efficient manner. I tried doing an
ORDER BY ST_Distance(point, ST_GeomFromText(?,-4326))
which gives me ok results in the lower 48 states, but up in Alaska it gives me garbage. Is there a way to do real distance calculations in PostGIS, or am I going to have to give a reasonable sized buffer and then calculate the great circle distances and sort the results in the code afterwards?

Answer 1

You are looking for ST_distance_sphere(point,point) or st_distance_spheroid(point,point).
See:
http://postgis.refractions.net/documentation/manual-1.3/ch06.html#distance_sphere
http://postgis.refractions.net/documentation/manual-1.3/ch06.html#distance_spheroid
This is normally referred to a geodesic or geodetic distance... while the two terms have slightly different meanings, they tend to be used interchangably.
Alternatively, you can project the data and use the standard st_distance function... this is only practical over short distances (using UTM or state plane) or if all distances are relative to a one or two points (equidistant projections).

Answer 2

PostGIS 1.5 handles true globe distances using lat longs and meters. It is aware that lat/long is angular in nature and has a 360 degree line

Answer 3

This is from SQL Server, and I use Haversine for a ridiculously fast distance that may suffer from your Alaska issue (can be off by a mile):
ALTER function [dbo].[getCoordinateDistance]
(
#Latitude1 decimal(16,12),
#Longitude1 decimal(16,12),
#Latitude2 decimal(16,12),
#Longitude2 decimal(16,12)
)
returns decimal(16,12)
as
/*
fUNCTION: getCoordinateDistance
Computes the Great Circle distance in kilometers
between two points on the Earth using the
Haversine formula distance calculation.
Input Parameters:
#Longitude1 - Longitude in degrees of point 1
#Latitude1 - Latitude in degrees of point 1
#Longitude2 - Longitude in degrees of point 2
#Latitude2 - Latitude in degrees of point 2
*/
begin
declare #radius decimal(16,12)
declare #lon1 decimal(16,12)
declare #lon2 decimal(16,12)
declare #lat1 decimal(16,12)
declare #lat2 decimal(16,12)
declare #a decimal(16,12)
declare #distance decimal(16,12)
-- Sets average radius of Earth in Kilometers
set #radius = 6366.70701949371
-- Convert degrees to radians
set #lon1 = radians( #Longitude1 )
set #lon2 = radians( #Longitude2 )
set #lat1 = radians( #Latitude1 )
set #lat2 = radians( #Latitude2 )
set #a = sqrt(square(sin((#lat2-#lat1)/2.0E)) +
(cos(#lat1) * cos(#lat2) * square(sin((#lon2-#lon1)/2.0E))) )
set #distance =
#radius * ( 2.0E *asin(case when 1.0E < #a then 1.0E else #a end ) )
return #distance
end
Vicenty is slow, but accurate to within 1 mm (and I only found a javascript imp of it):
/*
* Calculate geodesic distance (in m) between two points specified by latitude/longitude (in numeric degrees)
* using Vincenty inverse formula for ellipsoids
*/
function distVincenty(lat1, lon1, lat2, lon2) {
var a = 6378137, b = 6356752.3142, f = 1/298.257223563; // WGS-84 ellipsiod
var L = (lon2-lon1).toRad();
var U1 = Math.atan((1-f) * Math.tan(lat1.toRad()));
var U2 = Math.atan((1-f) * Math.tan(lat2.toRad()));
var sinU1 = Math.sin(U1), cosU1 = Math.cos(U1);
var sinU2 = Math.sin(U2), cosU2 = Math.cos(U2);
var lambda = L, lambdaP = 2*Math.PI;
var iterLimit = 20;
while (Math.abs(lambda-lambdaP) > 1e-12 && --iterLimit>0) {
var sinLambda = Math.sin(lambda), cosLambda = Math.cos(lambda);
var sinSigma = Math.sqrt((cosU2*sinLambda) * (cosU2*sinLambda) +
(cosU1*sinU2-sinU1*cosU2*cosLambda) * (cosU1*sinU2-sinU1*cosU2*cosLambda));
if (sinSigma==0) return 0; // co-incident points
var cosSigma = sinU1*sinU2 + cosU1*cosU2*cosLambda;
var sigma = Math.atan2(sinSigma, cosSigma);
var sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;
var cosSqAlpha = 1 - sinAlpha*sinAlpha;
var cos2SigmaM = cosSigma - 2*sinU1*sinU2/cosSqAlpha;
if (isNaN(cos2SigmaM)) cos2SigmaM = 0; // equatorial line: cosSqAlpha=0 (§6)
var C = f/16*cosSqAlpha*(4+f*(4-3*cosSqAlpha));
lambdaP = lambda;
lambda = L + (1-C) * f * sinAlpha *
(sigma + C*sinSigma*(cos2SigmaM+C*cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)));
}
if (iterLimit==0) return NaN // formula failed to converge
var uSq = cosSqAlpha * (a*a - b*b) / (b*b);
var A = 1 + uSq/16384*(4096+uSq*(-768+uSq*(320-175*uSq)));
var B = uSq/1024 * (256+uSq*(-128+uSq*(74-47*uSq)));
var deltaSigma = B*sinSigma*(cos2SigmaM+B/4*(cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)-
B/6*cos2SigmaM*(-3+4*sinSigma*sinSigma)*(-3+4*cos2SigmaM*cos2SigmaM)));
var s = b*A*(sigma-deltaSigma);
s = s.toFixed(3); // round to 1mm precision
return s;
}