GSM cell (longitude, latitude), it's sector and some object (with longitude, latitude)

Question

I have rather simple task and I would like to ask you for recommendation. I hope there is a Java library which can help me.

Description

Given

GSM cell with longitude, latitude, azimuth, max and min distance. With the help of these parameters I can describe a sector (a part of circle)
longitude, latitude and a radious of an object.

Meaning

Each GSM cell consists of several sectors (they start from one point). Each object is represented as a circle (longitude, latitude, radius). A circle can

touch one sector
intercept one sector
intercept several sectors of a given GSM cell

Task: I get a list of GSM cells and an object. I need to find all iterceptions/touches of an object with some sectors. I need to order by resulting list of interceptions by square of interception.

Look like typical math/geometry task. Is there any library in Java which can help me?

Looks like pure domain related use-case you want to implement. I don't think, you'll get a fairly free to use library for this. — R Kaja Mohideen, Feb 04 '13 at 06:52
It can be generalized to: find intersection of some sectors with geographical coordinates and circle with geographical coordinates. It doesn't look like something domain-related. — Capacytron, Feb 04 '13 at 06:59
after transform lat lon to x,y itbis simple school mathematics — AlexWien, Feb 04 '13 at 12:35

score 0 · Answer 1 · answered Feb 04 '13 at 12:42

1) tranform all latitude, lomgitude coordinates to cartesian x,y in meters. ( you can use the simple EuqiDistant Projection) serach here or on wiki, google

2) once all are in x,y coords, it is school mathematics:
point is inside circle? : distance between point and circle center < radius
point in circle segment? point is inside circle and angle from point to center point is within sector azimut range.

Calculate the angle from point1 to point2 using

angleRad = atan2(dy/dx);

where dy = p2.y - p1.y
dx analog

score 0 · Accepted Answer · answered Feb 07 '13 at 12:55

So here is my solution. We deciced that "center" of 2D projection should be relative. It does fit our task. Here are some code samples:

public final class GeometryUtil {
    /**
        https://www.cfa.harvard.edu/~dfabricant/huchra/ay145/constants.html
        1 Earth Radius = 6.37814x108 cm = 6.37814x10^6 m (Equatorial)
     */
    public static final double EARTH_RADIUS_IN_METERS = 6.37814e+6;

    private GeometryUtil(){}

    /**
     * @param geoPoint is a point of some object you want to translate to Cartesian.
     * @param geoPointRelative is a point of relative center.
     *                         We suppose that this relative GeoPoint is a center for the first parameter.
     * */
    public static Coordinate toCoordinate(GeoPoint geoPoint, GeoPoint geoPointRelative){
        return new Coordinate(toX(geoPoint, geoPointRelative.getLongitude()),
                              toY(geoPoint, geoPointRelative.getLatitude()));
    }

    public static double toX(GeoPoint geoPoint, double relativeLongitude){
        return  EARTH_RADIUS_IN_METERS *
                cos(toRadians(geoPoint.getLatitude()))  *
                toRadians(geoPoint.getLongitude()- relativeLongitude);
    }

    public static double toY(GeoPoint geoPoint, double relativeLatitude){
        return  EARTH_RADIUS_IN_METERS * toRadians(geoPoint.getLatitude() - relativeLatitude);
    }

}

Here is a builder for Geometry figures:

public final class GeometryBuilder {

    private static final int DIAMETER_MULTIPLIER = 2;
    private static final int TURN_LEFT = 90;    //We should start to roll to the right from "North"/"Up"/12 o'clock

    private GeometryBuilder(){}


    public static Circle buildCirlce(GeoPoint centerOfCircle, GeoPoint relativeCenter, Distance radiusDistance){
        GeometricShapeFactory geometricShapeFactory = new GeometricShapeFactory();
        geometricShapeFactory.setCentre(GeometryUtil.toCoordinate(centerOfCircle, relativeCenter));
        geometricShapeFactory.setSize(radiusDistance.getMeters() * DIAMETER_MULTIPLIER);
        return new Circle(geometricShapeFactory.createEllipse());
    }


     public static Sector buildGSMCellSector(GSMCellLocation gsmCellLocation, GeoPoint relativeCenter){
        GeometricShapeFactory geometricShapeFactory = new GeometricShapeFactory();
        geometricShapeFactory.setCentre(GeometryUtil.toCoordinate(gsmCellLocation.getGeoPoint(), relativeCenter));
        geometricShapeFactory.setSize(gsmCellLocation.getMidDist() * DIAMETER_MULTIPLIER);
        return new Sector(geometricShapeFactory.createArcPolygon(-toRadians(gsmCellLocation.getEndAngle()- TURN_LEFT),
                                                                  toRadians(gsmCellLocation.getAngleWidth())));
    }
}

I should mention that TURN_LEFT is specific. Angles of my object starts at 12 o'clock. Geometry library starts to count from 3 o'clock. That it why I have to turn it 3 hours (90 degrees) back.

The problem is solved. I've also used LiteShape to draw some images to PNG file. Everythng is ok.

GSM cell (longitude, latitude), it's sector and some object (with longitude, latitude)

2 Answers2