CODEWITHSUNDEEP
javagoogle-mapsrotationcoordinatespoint
anonymous
anonymous

Reputation: 1161

Java: Rotate a Point around an other using Google Maps Coordinates

From Google Earth I got a Box with coordinates for a picture, like following:

    <LatLonBox>
        <north>53.10685</north>
        <south>53.10637222222223</south>
        <east>8.853144444444444</east>
        <west>8.851858333333333</west>
        <rotation>-26.3448</rotation>
    </LatLonBox>

Now I want to test weather a point intersect with this LatLonBox. My base idea to check, whether a point intersect with the LatLonBox was, to rotate the point back by the given angle, and then to test whether the point intersect with a regular (not rotated) rectangle.

I tried to calculate the rotation manually:

public static MyGeoPoint rotatePoint(MyGeoPoint point, MyGeoPoint origion, double degree)
{
double x = origion.getLatitude() + (Math.cos(Math.toRadians(degree)) * (point.getLatitude() - origion.getLatitude()) - Math.sin(Math.toRadians(degree)) * (point.getLongitude() - origion.getLongitude()));
double y =  origion.getLongitude()  + (Math.sin(Math.toRadians(degree)) * (point.getLatitude() - origion.getLatitude()) + Math.cos(Math.toRadians(degree))  * (point.getLongitude() - origion.getLongitude()));

return new MyGeoPoint(x, y);

}

public boolean intersect(MyGeoPoint geoPoint)
{   
    geoPoint = MyGeoPoint.rotatePoint(geoPoint, this.getCenter(), - this.getRotation());
    
    return (geoPoint.getLatitude() < getTopLeftLatitude()
            && geoPoint.getLatitude() > getBottomRightLatitude()
                && geoPoint.getLongitude() > getTopLeftLongitude()
                    && geoPoint.getLongitude() < getBottomRightLongitude());
}

And it seems that the results are wrong.

    LatLonBox box = new LatLonBox(53.10685, 8.851858333333333, 53.10637222222223, 8.853144444444444, -26.3448);
    
    MyGeoPoint point1 = new MyGeoPoint(53.106872, 8.852311);
    MyGeoPoint point2 = new MyGeoPoint(53.10670378322918, 8.852967186822669);   
    MyGeoPoint point3 = new MyGeoPoint(53.10652664993972, 8.851994565566875);
    MyGeoPoint point4 = new MyGeoPoint(53.10631650700605, 8.85270995172055);
    
    System.out.println(box.intersect(point1));
    System.out.println(box.intersect(point2));
    System.out.println(box.intersect(point3));
    System.out.println(box.intersect(point4));

The result is true, false, false, true. But it should be 4x true. Probably I´, making some kind of error in reasoning. Maybe because the latitude values are getting bigger upwards. But I don´t knwo how to change the formular.

I need some help ...

EDIT: I think my basic idea and formular is right. Also I found similar solutions eg. link and couldn´t find any difference.

So I think the only possible error source is, that the axis are not proportional. So the problem is how to take account of this.

I hope someone has got an idea.

Upvotes: 2

Views: 2377

Answers (3)

anonymous
anonymous

Reputation: 1161

The problem was indeed that the axis were not proportional.

The following method takes care of it.

public static MyGeoPoint rotatePoint(MyGeoPoint point, MyGeoPoint origion, double degree)
{
double x =  origion.longitude   + (Math.cos(Math.toRadians(degree)) * (point.longitude - origion.longitude) - Math.sin(Math.toRadians(degree))  * (point.latitude - origion.latitude) / Math.abs(Math.cos(Math.toRadians(origion.latitude)));
double y = origion.latitude + (Math.sin(Math.toRadians(degree)) * (point.longitude - origion.longitude) * Math.abs(Math.cos(Math.toRadians(origion.latitude))) + Math.cos(Math.toRadians(degree))   * (point.latitude - origion.latitude));
return new MyGeoPoint(x, y);
}

Upvotes: 3

Gene
Gene

Reputation: 46960

The problem appears to be that the data structure LatLonBox doesn't make any sense as a description for the boundary of a picture. A box in lat-lon coordinates is not a geometric rectangle. (Think about a box near or including the north pole.) You need to re-think your application to deal in a lat/lon coordinate for the center of the picture and then deal with the rotation as an angle with respect to lines of latitude (parallel to the equator). (Even then, a picture with center on the north or south pole will be a degenerate case that must be handled separately.) So a box should properly be something like:

<geobox>
  <center_lat>41</center_lat>
  <center_lon>-74</center_lon>
  <rotation_degrees_ccw>-23</rotation_degrees_ccw>
  <width>1000</width> <!-- in pixels or meters, but not in degrees! -->
  <height>600</height> <!-- same as above -->
</geobox>

Having said all that, suppose you have a true geometric box centered at (x0,y0), width w, height h, rotated angle T about its center. Then you can test a point P(x,y) for membership in the box with the following. You need the transformation that takes the box to the origin and aligns it with the axes. This is Translate(-x0,-y0) then Rotate(-T). This transformation as a matrix is 

[cos(-T) -sin(-T) 0][1 0 -x0]   [ cos(T)  sin(T) -x0*cos(T)-y0*sin(T)]
[sin(-T)  cos(-T) 0][0 1 -y0] = [-sin(T)  cos(T)  x0*sin(T)-y0*cos(T)]
[0        0       1][0 0   1]   [  0        0                  1     ]

You want to apply this transformation to the point to be tested and then see if it lies in the desired box:

// Transform the point to be tested.
ct = cos(T);
st = sin(T);
xp =  ct * x + st * y - x0 * ct - y0 * st;
yp = -st * x + ct * y + x0 * st - y0 * ct;
// Test for membership in the box.
boolean inside = xp >= -w/2 && xp <= w/2 && yp >= -h/2 && yp <= h/2;

It's late and I haven't checked this arithmetic, but it's close. Say if it doesn't work.

Upvotes: 0

LadyWoodi
LadyWoodi

Reputation: 496

if I understand correctly you want to check if these four points are in rotated rectangle.

I would recommend checking not by corner points because your rectangle is rotated but:

if you have rotated rectangle ABCD then calculate lines |AB|, |BC|,|CD| and |DA|. If you have two points then use y=ax+b (you will calculate a,b by by giving [x,y] of both coordinates that gives you two easy equatations).

Finally function intersect will check

  if point <= line |CD| 
      AND point >= line |AB|
          AND point <= line |BC|
             AND point >= |DA|

then it is inside rect.

This can be done when your point P[x,y] you put in ax+y+b (a>0 or -ax-y-b). If it is zero it is lying on the line, if it is < than it is under line or "on the left side". Hope I helped..

BTW why are you using -degree value, which you multiply by -1 , is it necessary?

Upvotes: 0

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