Re: Radius of a zip code

On Fri, Dec 26, 2003 at 05:42:08PM -0600, Andy Lewis wrote:
> I was trying to find all zip codes within a given zip code or radius.
>  
> I have map points and Latitude and Longitude in my zip table.
>  
> I remember seeing a post or two referencing this but can't see to find
> it.

The code in contrib/earthdistance in the PostgreSQL source code might
be what you're looking for.  I haven't used it myself, as I had already
written a function I needed for another DBMS and ported it to PostgreSQL.

> I've tried the following with no luck:
>  
> -- 20 Miles
> --select 20 * 360.0 / (7900.0 * atan2(1,1) * 4.0);
> select * from zip_code where map_loc @
> circle(map_point('dallas','tx','75201'), .290105212724467 ) order by
> city

This isn't related to the problem, but is there a reason your map_point
function requires city, state, and zip code?  If you know the zip code
then you shouldn't need the city and state.

> Anyone that has this experience, can you validate this for correctness?

I have several databases with lat/lon coordinates and frequently make
"show me all records within a certain distance of this point" queries.
I wrote a haversine() function that uses the Haversine Formula to
calculate the great circle distance between two points on a sphere
(assuming the earth is a perfect sphere is accurate enough for my uses).
Here's a web site with related info:

http://www.census.gov/cgi-bin/geo/gisfaq?Q5.1

Here's an example of how I use the haversine() function.  I'm not using
PostgreSQL's geometric types -- latitude and longitude are stored in
separate fields.  The function takes two lat/lon coordinates in degrees
and optionally a radius (the default is 3956.0, the approximate radius
of the earth in miles); it returns the distance in whatever units the
radius is in.

SELECT a.zipcode, a.city, a.state,      haversine(a.latitude, a.longitude, b.latitude, b.longitude) AS dist
FROM zipcode AS a, zipcode AS b
WHERE b.zipcode = 75201 AND haversine(a.latitude, a.longitude, b.latitude, b.longitude) <= 20
ORDER BY dist;
zipcode |     city      | state |       dist        
---------+---------------+-------+-------------------75201   | Dallas        | TX    |                 075270   |
Dallas       | TX    | 0.46057679577955575202   | Dallas        | TX    |  0.62326173788043 . . .76012   | Arlington
| TX    |   19.64413257306875126   | Forney        | TX    |  19.896325372353675024   | Plano         | TX    |
19.9884653971924
(106 rows)

As for validating the function's correctness, I'm using a well-known
formula and I've compared the function's output to distances measured on
a map.  I wouldn't use it for missile targeting, but it's sufficiently
accurate for "show me all stores within 20 miles of my home."

Here's the meat of the function (written in C); the coordinates have by
now been converted to radians:
 dlat = lat2 - lat1; dlon = lon2 - lon1;
 a1 = sin(dlat / 2.0); a2 = sin(dlon / 2.0);
 a = (a1 * a1) + cos(lat1) * cos(lat2) * (a2 * a2); c = 2.0 * atan2(sqrt(a), sqrt(1.0 - a));
 dist = radius * c;

If anybody's interested I'll post the entire file.

-- 
Michael Fuhr
http://www.fuhr.org/~mfuhr/