Create solid polygon in boost geometry

Question

I'm newbie at boost geometry, I have created polygon with boost::geometry::assign_points(). But I only create outer and inner of that polygon is empty. So I try test boost::geometry::overlaps() with two polygons A, B and A is inside B, result is not overlaps.

So, What can I do to create solid polygon (only know outer point of polygon and inside of polygon is valid) ?

Answer 1

Polygons are by definition solid until you subtract inner rings. From §6.1.11.1 from the standard¹:

A Polygon is a planar Surface defined by 1 exterior boundary and 0 or more interior boundaries. Each interior boundary defines a hole in the Polygon. A Triangle is a polygon with 3 distinct, non-collinear vertices and no interior boundary. ¹

Overlapping doesn't mean what you think it means.

From §6.1.15.3 (Named spatial relationship predicates based on the DE-9IM)

• Crosses
• Within

• Overlaps

  It is defined as

  a.Overlaps(b) ⇔ ( dim(I(a)) = dim(I(b)) = dim(I(a) ∩ I(b)))
                   ∧ (a ∩ b ≠ a) ∧ (a ∩ b ≠ b)
  

• Contains

  a.Contains(b) ⇔ b.Within(a)
  

• Intersects

  a.Intersects(b) ⇔ ! a.Disjoint(b) 
  

In your case you might be looking for !disjoint, within, contains or intersection:

Live On Coliru

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

namespace bg = boost::geometry;

template <typename Geo> void debug(std::string name, Geo const& g) {
    std::string reason;
    std::cout << name << ": " << bg::dsv(g) << " " << bg::is_valid(g, reason) << ", '" << reason << "'\n"; 
}

template <typename Geo, typename F>
void both_ways(std::string name, Geo const& a, Geo const& b, F f) {
    std::cout << name << "(a, b) -> " << f(a,b) << "\n";
    std::cout << name << "(b, a) -> " << f(b,a) << "\n";
}

int main() {
    std::cout << std::boolalpha;

    using Pt = bg::model::d2::point_xy<int>;
    using Poly = bg::model::polygon<Pt>;
    using Multi = bg::model::multi_polygon<Poly>;

    Poly const a {{ { 0,0 }, { 0,3 }, { 3,3 }, { 3,0 }, { 0,0 }} };
    Poly const b {{ { 1,1 }, { 1,2 }, { 2,2 }, { 2,1 }, { 1,1 }} };

    debug("a", a);
    debug("b", b);

#define TEST(algo) both_ways(#algo, a, b, [](auto& a, auto& b) { return bg::algo(a, b); })
    TEST(overlaps);
    TEST(intersects);
    TEST(within);
    //TEST(contains); // contains(a,b) ⇔ within(b,a)
    //TEST(crosses); // not implemented for polygons
    TEST(disjoint);

    both_ways("intersection", a, b, [](auto& a, auto& b) {
        Multi c; 
        bg::intersection(a, b, c);
        return boost::lexical_cast<std::string>(bg::dsv(c));
    });
}

Which prints

a: (((0, 0), (0, 3), (3, 3), (3, 0), (0, 0))) true, 'Geometry is valid'
b: (((1, 1), (1, 2), (2, 2), (2, 1), (1, 1))) true, 'Geometry is valid'
overlaps(a, b) -> false
overlaps(b, a) -> false
intersects(a, b) -> true
intersects(b, a) -> true
within(a, b) -> false
within(b, a) -> true
disjoint(a, b) -> false
disjoint(b, a) -> false
intersection(a, b) -> ((((1, 1), (1, 2), (2, 2), (2, 1), (1, 1))))
intersection(b, a) -> ((((1, 1), (1, 2), (2, 2), (2, 1), (1, 1))))

¹ The OGC Simple Feature / Common architecture