Query to get records based on Radius in SQLite?

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

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.

Answer 2

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 3

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):

1. 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)
   

2. 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
   

3. 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;