How to detect swipe direction between left/right and up/down

I wrote a simple class for this: it's well documented so I wont explain it here

public class OnSwipeListener extends GestureDetector.SimpleOnGestureListener {

    @Override
    public boolean onFling(MotionEvent e1, MotionEvent e2, float velocityX, float velocityY) {

        // Grab two events located on the plane at e1=(x1, y1) and e2=(x2, y2)
        // Let e1 be the initial event
        // e2 can be located at 4 different positions, consider the following diagram
        // (Assume that lines are separated by 90 degrees.)
        //
        //
        //         \ A  /
        //          \  /
        //       D   e1   B
        //          /  \
        //         / C  \
        //
        // So if (x2,y2) falls in region:
        //  A => it's an UP swipe
        //  B => it's a RIGHT swipe
        //  C => it's a DOWN swipe
        //  D => it's a LEFT swipe
        //

        float x1 = e1.getX();
        float y1 = e1.getY();

        float x2 = e2.getX();
        float y2 = e2.getY();

        Direction direction = getDirection(x1,y1,x2,y2);
        return onSwipe(direction);
    }

    /** Override this method. The Direction enum will tell you how the user swiped. */
    public boolean onSwipe(Direction direction){
        return false;
    }

    /**
     * Given two points in the plane p1=(x1, x2) and p2=(y1, y1), this method
     * returns the direction that an arrow pointing from p1 to p2 would have.
     * @param x1 the x position of the first point
     * @param y1 the y position of the first point
     * @param x2 the x position of the second point
     * @param y2 the y position of the second point
     * @return the direction
     */
    public Direction getDirection(float x1, float y1, float x2, float y2){
        double angle = getAngle(x1, y1, x2, y2);
        return Direction.fromAngle(angle);
    }

    /**
     *
     * Finds the angle between two points in the plane (x1,y1) and (x2, y2)
     * The angle is measured with 0/360 being the X-axis to the right, angles
     * increase counter clockwise.
     *
     * @param x1 the x position of the first point
     * @param y1 the y position of the first point
     * @param x2 the x position of the second point
     * @param y2 the y position of the second point
     * @return the angle between two points
     */
    public double getAngle(float x1, float y1, float x2, float y2) {

        double rad = Math.atan2(y1-y2,x2-x1) + Math.PI;
        return (rad*180/Math.PI + 180)%360;
    }


    public enum Direction{
        up,
        down,
        left,
        right;

        /**
         * Returns a direction given an angle.
         * Directions are defined as follows:
         *
         * Up: [45, 135]
         * Right: [0,45] and [315, 360]
         * Down: [225, 315]
         * Left: [135, 225]
         *
         * @param angle an angle from 0 to 360 - e
         * @return the direction of an angle
         */
        public static Direction fromAngle(double angle){
            if(inRange(angle, 45, 135)){
                return Direction.up;
            }
            else if(inRange(angle, 0,45) || inRange(angle, 315, 360)){
                return Direction.right;
            }
            else if(inRange(angle, 225, 315)){
                return Direction.down;
            }
            else{
               return Direction.left;
           }

        }

       /**
         * @param angle an angle
         * @param init the initial bound
         * @param end the final bound
         * @return returns true if the given angle is in the interval [init, end).
         */
        private static boolean inRange(double angle, float init, float end){
            return (angle >= init) && (angle < end);
        }
    }
 }

To use simply extend the OnSwipeListener and override the onSwipe method

Fernandour answer is perfect, I am writing this answer about how to use it with Activity and Fragment as many people are looking for it.

public class MyActivity extends Activity implements View.OnTouchListener{

     private RelativeLayout someLayout;
     //take any layout on which you want your gesture listener;

     @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
    gestureDetector=new GestureDetector(this,new OnSwipeListener(){

        @Override
        public boolean onSwipe(Direction direction) {
            if (direction==Direction.up){
               //do your stuff
                Log.d(TAG, "onSwipe: up");

            }

            if (direction==Direction.down){
               //do your stuff
                Log.d(TAG, "onSwipe: down");
            }
            return true;
        }


    });
    someLayout.setOnTouchListener(this);
}

    @Override
    public boolean onTouch(View v, MotionEvent event) {
      Log.d(TAG, "onTouch: ");
      gestureDetector.onTouchEvent(event);
      return true;
  }


}

You simply have to extend SimpleOnGestureListener class,

Declare this in your class,

private static final int SWIPE_MIN_DISTANCE = 120;
private static final int SWIPE_MAX_OFF_PATH = 250;
private static final int SWIPE_THRESHOLD_VELOCITY = 200;

As an example for horizontal swipe you can see the below code,

 class MyGestureDetector extends SimpleOnGestureListener {
    @Override
    public boolean onFling(MotionEvent e1, MotionEvent e2, float velocityX,
            float velocityY) {
        try {
            if (Math.abs(e1.getY() - e2.getY()) > SWIPE_MAX_OFF_PATH){
                return false;
            }
            // right to left swipe
            if (e1.getX() - e2.getX() > SWIPE_MIN_DISTANCE
                    && Math.abs(velocityX) > SWIPE_THRESHOLD_VELOCITY) {
                onLeftSwipe();
            } 
            // left to right swipe
            else if (e2.getX() - e1.getX() > SWIPE_MIN_DISTANCE
                    && Math.abs(velocityX) > SWIPE_THRESHOLD_VELOCITY) {
                onRightSwipe();
            }
        } catch (Exception e) {

        }
        return false;
      }
   }

You can do this similarly for vertical swipe purpose.