boost geometry polygon distance for inside point - c++

Question

I am using boost::geometry to handle some geometrical tasks. I have two requirements that I need to cover:
Handle point -> polygon intersection (inside or not). This works great with boost::geometry::within so thats good
Get the distance of an arbitrary point to the closest edge of the polygon. While points outside of the polygon are handled correctly by boost::geometry::distance, however it seems that it considers polygons solid. So every point inside the polygon obviously has a distance of 0 to the polygon.
I tried experimenting with inner/outer stuff and was wondering if there is a possbility to get the distance for both inside and outside points of a polygon.

Answer 1

In case where point is inside polygon you may speed your code up using comparable_distance instead of distance algorithm. You don't need to calculate the exact distance for every segment-point pair. Find the nearest segment of polygon to the given point using comparable_distance and then calculate the real distance using distance algorithm.
auto distance = std::numeric_limits<float>::max();
if(boost::geometry::within(pt, mPolygon))
{
Segment nearestSegment;
boost::geometry::for_each_segment(mPolygon,
[&distance, &pt, &nearestSegment](const auto& segment)
{
double cmpDst = boost::geometry::comparable_distance(segment,pt);
if (cmpDst < distance)
{
distance = cmpDst;
nearestSegment = segment; // UPDATE NEAREST SEGMENT
}
});
// CALCULATE EXACT DST
distance = boost::geometry::distance(nearestSegment,pt);
} else {
distance = boost::geometry::distance(pt, mPolygon);
}

Answer 2

I have decided to use the following approach which seems to provide the right results so far:
const TPolygonPoint pt{ x, y };
auto distance = std::numeric_limits<float>::max();
if(boost::geometry::within(pt, mPolygon)) {
boost::geometry::for_each_segment(mPolygon, [&distance, &pt](const auto& segment) {
distance = std::min<float>(distance, boost::geometry::distance(segment, pt));
});
} else {
distance = boost::geometry::distance(pt, mPolygon);
}
return distance;
If anyone knows a faster or nicer way, please leave a comment :)

Answer 3

For best performances you should use an RTree with boost::geometry::index. Creating the RTree has a cost, but then computing the ditance of a point to any of the (multi)polygon ring will be much fast. Example code:
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
#include <boost/geometry/index/rtree.hpp>
#include <iostream>
#include <vector>
int main()
{
namespace bg = boost::geometry;
namespace bgi = boost::geometry::index;
typedef bg::model::point<double, 2, bg::cs::cartesian> point;
typedef bg::model::polygon<point> polygon;
point p{ 0, 0 };
// create some polygon and fill it with data
polygon poly;
double a = 0;
double as = bg::math::two_pi<double>() / 100;
for (int i = 0; i < 100; ++i, a += as)
{
double c = cos(a);
double s = sin(a);
poly.outer().push_back(point{10 * c, 10 * s});
poly.inners().resize(1);
poly.inners()[0].push_back(point{5 * c, 5 * s});
}
// make sure it is valid
bg::correct(poly);
// create rtree containing objects of type bg::model::pointing_segment
typedef bg::segment_iterator<polygon const> segment_iterator;
typedef std::iterator_traits<segment_iterator>::value_type segment_type;
bgi::rtree<segment_type, bgi::rstar<4> > rtree(bg::segments_begin(poly),
bg::segments_end(poly));
// get 1 nearest segment
std::vector<segment_type> result;
rtree.query(bgi::nearest(p, 1), std::back_inserter(result));
BOOST_ASSERT(!result.empty());
std::cout << bg::wkt(result[0]) << ", " << bg::distance(p, result[0]) << std::endl;
return 0;
}

Answer 4

You can directly use boost::geometry::distance if you add an inner boundary to the polygon coinciding with the outer boundary [Polygon Concept].
#include <iostream>
#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
namespace bg = boost::geometry;
int main() {
typedef bg::model::point<int, 2, bg::cs::cartesian> point_t;
typedef bg::model::polygon<point_t> polygon_t;
polygon_t poly1;
bg::append (poly1.outer(), point_t (1, -1));
bg::append (poly1.outer(), point_t (1, 1));
bg::append (poly1.outer(), point_t (-1, 1));
bg::append (poly1.outer(), point_t (-1, -1));
bg::append (poly1.outer(), point_t (1, -1));
poly1.inners().resize (1);
bg::append (poly1.inners()[0], point_t (1, -1));
bg::append (poly1.inners()[0], point_t (1, 1));
bg::append (poly1.inners()[0], point_t (-1, 1));
bg::append (poly1.inners()[0], point_t (-1, -1));
bg::append (poly1.inners()[0], point_t (1, -1));
point_t myPoint (0, 0);
std::cout << "Minimal distance: " << bg::distance (poly1, myPoint) << std::endl;
std::cout << "Is within: " << bg::within (myPoint, poly1) << std::endl;
return 0;
}
-> Will return:
Minimal distance: 1
Is within: 0
However, if you do that, points strictly inside the polygon will be considered to lie 'outside' the polygon by boost::geometry::within. If you want both functionalities, you can maintain two separate polygons- one with an inner boundary and one without.