Query to get records based on Radius in SQLite? - sql

Question

I have this query which does work fine in MySQL
SELECT ((ACOS(SIN(12.345 * PI() / 180) * SIN(lat * PI() / 180) +
COS(12.345 * PI() / 180) * COS(lat * PI() / 180) * COS((67.89 - lon) *
PI() / 180)) * 180 / PI()) * 60 * 1.1515 * 1.609344) AS distance, poi.*
FROM poi
WHERE lang='eng'
HAVING distance<='30'
distance is in Kilometers, the input is lat=12.345 and lon=67.89
The SQLite is 3, and I can't run custom functions with it as it's on Android. I also don't have acos() etc... as that is not part of the standard SQLite.
How would be the above query in SQLite?

Answer 1

Here is an implementation in Java for building a location based query on an Android device.
The idea comes from KennyTM (see accepted response) and implies the addition of 4 columns in your table to store values of sinus and cosinus of latitude and longitudes.
Here is the code preparing the data for a "Shop" table at insert time:
public static void injectLocationValues(ContentValues values, double latitude, double longitude) {
values.put(LocationColumns.LATITUDE, latitude);
values.put(LocationColumns.LONGITUDE, longitude);
values.put(LocationColumns.COSLAT, Math.cos(MathUtil.deg2rad(latitude)));
values.put(LocationColumns.SINLAT, Math.sin(MathUtil.deg2rad(latitude)));
values.put(LocationColumns.COSLNG, Math.cos(MathUtil.deg2rad(longitude)));
values.put(LocationColumns.SINLNG, Math.sin(MathUtil.deg2rad(longitude)));
}
public static double deg2rad(double deg) {
return (deg * Math.PI / 180.0);
}
You can then build your projection using the following function:
/**
* Build query based on distance using spherical law of cosinus
*
* d = acos(sin(lat1).sin(lat2)+cos(lat1).cos(lat2).cos(long2−long1)).R
* where R=6371 and latitudes and longitudes expressed in radians
*
* In Sqlite we do not have access to acos() sin() and lat() functions.
* Knowing that cos(A-B) = cos(A).cos(B) + sin(A).sin(B)
* We can determine a distance stub as:
* d = sin(lat1).sin(lat2)+cos(lat1).cos(lat2).(cos(long2).cos(long1)+sin(long2).sin(long1))
*
* First comparison point being fixed, sin(lat1) cos(lat1) sin(long1) and cos(long1)
* can be replaced by constants.
*
* Location aware table must therefore have the following columns to build the equation:
* sinlat => sin(radians(lat))
* coslat => cos(radians(lat))
* coslng => cos(radians(lng))
* sinlng => sin(radians(lng))
*
* Function will return a real between -1 and 1 which can be used to order the query.
* Distance in km is after expressed from R.acos(result)
*
* #param latitude, latitude of search
* #param longitude, longitude of search
* #return selection query to compute the distance
*/
public static String buildDistanceQuery(double latitude, double longitude) {
final double coslat = Math.cos(MathUtil.deg2rad(latitude));
final double sinlat = Math.sin(MathUtil.deg2rad(latitude));
final double coslng = Math.cos(MathUtil.deg2rad(longitude));
final double sinlng = Math.sin(MathUtil.deg2rad(longitude));
//#formatter:off
return "(" + coslat + "*" + LocationColumns.COSLAT
+ "*(" + LocationColumns.COSLNG + "*" + coslng
+ "+" + LocationColumns.SINLNG + "*" + sinlng
+ ")+" + sinlat + "*" + LocationColumns.SINLAT
+ ")";
//#formatter:on
}
It will inject a response column with the distance on which you need to apply the following formula to convert in kilometers:
public static double convertPartialDistanceToKm(double result) {
return Math.acos(result) * 6371;
}
If you want to order your query using the partial distance, you need to order DESC and not ASC.

Answer 2

Had the same issue while working on sqlite3 for ios, after playing a little with the formula here is a way to do it without using function from the sql side (pseudo-code):
Pre-calculate these value for each item you store in the database (and store them):
cos_lat = cos(lat * PI / 180)
sin_lat = sin(lat * PI / 180)
cos_lng = cos(lng * PI / 180)
sin_lng = sin(lng * PI / 180)
Pre-calculate these value at the search time (for a given position cur_lat,cur_lng)
CUR_cos_lat = cos(cur_lat * PI / 180)
CUR_sin_lat = sin(cur_lat * PI / 180)
CUR_cos_lng = cos(cur_lng * PI / 180)
CUR_sin_lng = sin(cur_lng * PI / 180)
cos_allowed_distance = cos(2.0 / 6371) # This is 2km
Your SQL query will look like this (replace CUR_* by the values you just calculated)
SELECT * FROM position WHERE CUR_sin_lat * sin_lat + CUR_cos_lat * cos_lat * (cos_lng* CUR_cos_lng + sin_lng * CUR_sin_lng) > cos_allowed_distance;

Answer 3

You can create 4 new columns, being sin and cos of lat and lon. Since cos(a+b) = cos a cos b - sin a sin b, and other appearances of sin and cos like SIN(12.345 * PI() / 180) can be calculated in the program before running the query, the big "distance" expression reduces to something of the form P * SIN_LAT + Q * COS_LAT + ... that can be handled by SQLite3.
BTW, see also Sqlite on Android: How to create a sqlite dist db function - to be used in the app for distance calculation using lat, long.