I can find the distance between a point MyPoint and a polygon MyPolygon with
double dist = boost::geometry::distance(MyPoint, MyPolygon)
obviously the actual closest point on MyPolygon has to be computed somewhere. Is there an easy way to get that closest point? I can't find anything in the Boost Documentation and I'm sure others had that problem too.
According to source its iterating all points of polygon inside class distance_single_to_multi. Its not storing the iterator, so probably you should to the same.
You can find out how to do this in comparable_distance example.