Please refer to the example and corresponding image.
I would like to achieve the following: provide two locations (lat/lng), which are shown below as A and B. From this, a virtual line would be drawn and then the distance between this line and C would be calculated (in any measurement).
I have achieved this currently in Google Maps API v3 but would want to also be able to perform this behind the scenes in my language of choice. Any tips/ideas would be greatly appreciated!
Maybe I'm making it too complicated, but what you want is the distance from a point to a line. That is the distance from a point along AB that links AB with C with a line orthogonal to AB. This vector perpendicular to AB is given by
v=[x2-x1, -(y2-y1)] # Point A is [x1,y1] Point B is [x2,y2]
(I have used the square brackets to define a vector, or a two-element array). The distance between C [xp, yp] and point A is
u=[x1-xp, y1-xp]
The distance between the line and C is just the projection of u on to v. If we assume mod(v) = 1 (just normalise it), then
distance = u*v = abs( (x2-x1)*(y1-yp) - (x1-xp)*(y2-y1) )
The only complication is that you probably want to make sure your coordinates are not WGS84 lat/log pairs, but projected (or use geodetic coordinates). You can use OGR or Proj4 for this.
def get_perp( X1, Y1, X2, Y2, X3, Y3):
"""************************************************************************************************
Purpose - X1,Y1,X2,Y2 = Two points representing the ends of the line segment
X3,Y3 = The offset point
'Returns - X4,Y4 = Returns the Point on the line perpendicular to the offset or None if no such
point exists
'************************************************************************************************ """
XX = X2 - X1
YY = Y2 - Y1
ShortestLength = ((XX * (X3 - X1)) + (YY * (Y3 - Y1))) / ((XX * XX) + (YY * YY))
X4 = X1 + XX * ShortestLength
Y4 = Y1 + YY * ShortestLength
if X4 < X2 and X4 > X1 and Y4 < Y2 and Y4 > Y1:
return X4,Y4
return None
The shortest length is the distance you require, unless I am mistaken?
None when a legitimate solution exists. The problem is that the last conditional assumes X1 < X2 and Y1 < Y2, which cannot always be assured. A better test of betweenness is needed.
Being a bit averse to all this math as well, I would come at it from a different angle. I would make it an 'actual' line, rather than a virtual line, and then use existing tools.
If A and B share an attribute, you could connect them by drawing a line (Kosmo GIS has a tool that will create lines from points, and I believe there is also a QGIS plugin for this). Once you have the lines, a 'near' function on the 'C' point layer will give you the distance to the line. Let the software handle the math for you!
If you were using java on android, its only one line with the library function
import static com.google.maps.android.PolyUtil.distanceToLine;
distanceToLine:
public static double distanceToLine(LatLng p, LatLng start,LatLng end)
Computes the distance on the sphere between the point p and the line segment start to end.
Parameters: p - the point to be measured
start - the beginning of the line segment
end - the end of the line segment
Returns: the distance in meters (assuming spherical earth)
Just add library to your
dependencies {
compile 'com.google.maps.android:android-maps-utils:0.5+'
}
