Combining two polygons into one polygon in Boost.Geometry: Exterior points only, no holes

Question

I have two polygons. I want to combine them into one polygon such that it includes the exterior points only without any holes.
How can I do that? Code with little explanation would be very helpful. Thank you.
See the picture for better understanding.

Answer 1

I think you can just use the union_ algorithm

polygon a, b;
bg::read_wkt("POLYGON((0 0, 5 5, 9 0, 0 0))", a);
bg::read_wkt("POLYGON((5 1, 10 5, 10 -2, 5 1))", b);

std::string reason;
std::cout << std::boolalpha;
std::cout << bg::is_valid(a, reason) << " (" << reason << ")\n";
std::cout << bg::is_valid(b, reason) << " (" << reason << ")\n";

multi_polygon ab;
bg::union_(a, b, ab);

write_svg("union.svg", a, b, ab);

Creates

Trouble

Of course, replacing with your second example

bg::read_wkt("POLYGON((0 0, 0 5, 3 5, 1 2, 3 0, 0 0))", a);
bg::read_wkt("POLYGON((5 0, 10 5, 14 0, 5 0))", b);

Just results in the polygons separately. This is the correct answer:

It's correct because there is no overlap. Slapping together the polygons by force as you did is

• arbitrary (you could join them by different artifical lines)
• invalid (the resulting polygon is self intersecting)

See e.g.

for (auto wkt : {
    "POLYGON((0 0, 0 5, 3 5, 1 2, 3 0, 5 0, 10 5, 14 0, 5 0, 3 0, 0 0))",
    "POLYGON((0 0, 0 5, 3 5, 1 2, 3 0, 5 0, 10 5, 14 0, 5 0, 0 0))",
    "POLYGON((0 0, 0 5, 3 5, 1 2, 3 0, 5 0, 10 5, 14 0, 0 0))",
}) {
    polygon invalid;
    bg::read_wkt(wkt, invalid);
    std::cout << bg::is_valid(invalid, reason) << " (" << reason << ")\n";
}

Prints

false (Geometry has invalid self-intersections. A self-intersection point was found at (3, 0); method: t; operations: x/i; segment IDs {source, multi, ring, segment}: {0, -1, -1, 3}/{0, -1, -1, 8})
false (Geometry has invalid self-intersections. A self-intersection point was found at (3, 0); method: m; operations: x/i; segment IDs {source, multi, ring, segment}: {0, -1, -1, 3}/{0, -1, -1, 8})
false (Geometry has invalid self-intersections. A self-intersection point was found at (3, 0); method: m; operations: x/i; segment IDs {source, multi, ring, segment}: {0, -1, -1, 3}/{0, -1, -1, 7})

Forcing The Issue

Doesn't work, e.g.:

polygon force_combine;
bg::append(force_combine, a.outer());
bg::append(force_combine, b.outer());
force_fix(force_combine);

With

template <typename G> void force_fix(G& g) {
    G previous;
    std::string reason;
    do {
        if (bg::is_valid(g, reason))
            return;

        std::cout << "Invalid: " << reason << "\n";
        previous = g;
        bg::correct(g);
    } while (!bg::equals(previous, g));
    std::cout << "Warning: could not force_fix\n";
}

Prints

Invalid: Geometry is defined as closed but is open
Warning: could not force_fix

Full Demo Code

Live On Coliru

#include <boost/geometry/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp>
#include <boost/geometry/geometries/polygon.hpp>
#include <boost/geometry/geometries/multi_polygon.hpp>
#include <iostream>

namespace bg        = boost::geometry;
namespace bgm       = bg::model;

using point         = bgm::d2::point_xy<double>;
using polygon       = bgm::polygon<point>;
using multi_polygon = bgm::multi_polygon<polygon>;

template <typename G>
    void write_svg(std::string fname, polygon const& a, polygon const& b, G const& g);
template <typename G>
    void force_fix(G& g);

struct { std::string a,b; } const examples[] = {
    { "POLYGON((0 0, 5 5, 9 0, 0 0))",
      "POLYGON((5 1, 10 5, 10 -2, 5 1))" },
    { "POLYGON((0 0, 0 5, 3 5, 1 2, 3 0, 0 0))",
      "POLYGON((5 0, 10 5, 14 0, 5 0))" } };

int main() {
    int n = 0;
    for (auto example : examples) {
        ++n;
        polygon a, b;
        bg::read_wkt(example.a, a);
        bg::read_wkt(example.b, b);

        force_fix(a); // input sanitation if needed
        force_fix(b);

        multi_polygon ab;
        bg::union_(a, b, ab);

        write_svg("example" + std::to_string(n) + ".svg", a, b, ab);
        std::cout << "Example " << n << " is compound? " << (ab.size() > 1) << "\n";
    }
}

#include <fstream>

template <typename G>
void write_svg(std::string fname, polygon const& a, polygon const& b, G const& g) {
    std::ofstream ofs(fname);
    bg::svg_mapper<point> mapper(ofs, 400, 400);

    mapper.add(g);
    mapper.map(g, "fill-opacity:0.1;fill:rgb(100,0,0);stroke:rgb(200,0,0);stroke-width:2", 5);

    mapper.add(a);
    mapper.map(a, "fill-opacity:0.01;fill:rgb(0,100,0);stroke:rgb(0,200,0);stroke-width:1;stroke-dasharray:4", 5);

    mapper.add(b);
    mapper.map(b, "fill-opacity:0.01;fill:rgb(0,0,100);stroke:rgb(0,0,200);stroke-width:1;stroke-dasharray:4", 5);
}

template <typename G> void force_fix(G& g) {
    G previous;
    std::string reason;
    do {
        if (bg::is_valid(g, reason))
            return;

        std::cout << "Invalid: " << reason << "\n";
        previous = g;
        bg::correct(g);
    } while (!bg::equals(previous, g));
    std::cout << "Warning: could not force_fix\n";
}

Prints

Example 1 is compound? 0
Example 2 is compound? 1

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