增强几何：多边形定义

Question

Could you please tell me why this polygon definition don't work?

namespace bg = boost::geometry;

int main()
{
typedef bg::model::point<double, 2, bg::cs::cartesian> point_type;
typedef bg::model::polygon<point_type> polygon_type;

polygon_type P;

int xi[] = {0,100,100,0,0};
int yi[] = {0,0,100,100,0};

bg::append(P, bg::make<point_type>(*xi, *yi));

double area = bg::area(P);
std::cout << "Area:" << area << std::endl;

Return 0; }

This shows Area : 0

Thank you

Answer 1

Learn to use the library to diagnose your issues:

std::string reason;
bool ok = bg::is_valid(P, reason);
std::cout << "Polygon " << (ok?"valid":"invalid") << " (" << reason << ")\n";

Prints: Live On Coliru

Polygon invalid (Geometry has too few points)

You can also print the geometry in WKT/DSV (or even SVG): Live On Coliru

POLYGON((0 0)) invalid (Geometry has too few points)
Area:0

This makes the problem even more evident.

---

You don't want to add a single point, but a ring. The simplest way to achieve this is to explicitly make it a ring:

ring_type points {
    {   0,   0 },
    { 100,   0 },
    { 100, 100 },
    {   0, 100 },
    {   0,   0 },
};

bg::append(P, points);

Still not ok, but better: Live On Coliru

POLYGON((0 0,100 0,100 100,0 100,0 0)) invalid (Geometry has wrong orientation)
Area:-10000

As you can see we got the orientation wrong (should be clockwise):

ring_type points {
    {   0,   0 },
    {   0, 100 },
    { 100, 100 },
    { 100,   0 },
    {   0,   0 },
};

Prints: Live On Coliru

POLYGON((0 0,0 100,100 100,100 0,0 0)) valid (Geometry is valid)
Area:10000

Note You can use bg::correct to correct validity issues in straightforward cases, like this.

Style And Types

In fact the ring-type is the outer ring type of the polygon type:

static_assert(std::is_same<ring_type, polygon_type::ring_type>{}, "synonyms");
static_assert(bg::point_order<ring_type>::value == bg::order_selector::clockwise, "orientation");

Therefore, you can construct directly from the outer ring initializer:

polygon_type P { {
    {   0,   0 },
    {   0, 100 },
    { 100, 100 },
    { 100,   0 },
    {   0,   0 },
} };

Condensing the whole program to a single line: Live On Coliru

int main() {
    typedef bgm::polygon<bgm::d2::point_xy<double> > polygon_type;
    std::cout << "Area:" << bg::area(polygon_type { { {0, 0}, {0, 100}, {100, 100}, {100, 0}, {0, 0} } }) << std::endl;
}

Or you can, indeed read it from WKT/DSV: Live On Coliru

int main() {
    bgm::polygon<bgm::d2::point_xy<double> > P;
    bg::read_wkt("POLYGON((0 0,0 100,100 100,100 0,0 0))", P);
    std::cout << "Area:" << bg::area(P) << std::endl;
}

Still printing

Area:10000