Boost-geometry：多边形定义

Question

你能告诉我为什么这个多边形定义不起作用吗？

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; }

这显示区域：0

谢谢

Answer 1

学习使用该库来诊断您的问题：

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

印刷品：Live On Coliru

Polygon invalid (Geometry has too few points)

您还可以在WKT / DSV（甚至SVG）中打印几何体：Live On Coliru

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

这使问题更加明显。

---

您不想添加单个点，而是添加一个环。实现这一目标的最简单方法是明确地使它成为一个环：

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

bg::append(P, points);

还不行，但更好：Live On Coliru

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

你可以看到我们的方向错误（应该是顺时针方向）：

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

印刷品：Live On Coliru

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

注意您可以使用bg::correct在简单的情况下纠正有效性问题，如下所示。

风格和类型

实际上，ring-type是多边形类型的外环类型：

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");

因此，您可以直接从外环初始化器构造：

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

将整个程序缩小为一条线：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;
}

或者你可以，确实从WKT / DSV中读到它：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;
}

还在打印

Area:10000