c++ - 如何使用 Boost::Geometry _union 与整数

Question

我正在尝试将 Boost::Geometry _union 与整数一起使用，以 boost 性能和数值准确性。为此，我将输入的坐标乘以 10,000。从而创建最多 9 位的坐标。我认为由于我使用 64 位整数，所以应该可以正常工作。

不幸的是，当我运行代码时，我得到了奇怪的结果(输出多边形包含一个远离输入中任何多边形的点)。调查 Boost::Geometry 的代码使我得出结论，起源是文件 cart_intersect.hpp 中的环绕问题:

set<1>(point, get<0, 1>(segment) + boost::numeric_cast
            <
                CoordinateType
            >(numerator * dy_promoted / denominator));

当三个(分子、d​​y_promoted 和分母)都很大时，乘法结果占用超过 64 位，因此整个结果不正确。

使用具有如此大整数的 Boost::Geometry 是否有效？在保持正确性和精度的同时使用带有整数的 Boost::Geometry 的正确方法是什么？

---

编辑@sehe，感谢您的回复。这是一个 SSCCE，用 VS2013 和 Boost 1.63 编译

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

using namespace std;
namespace bg = boost::geometry;

typedef bg::model::d2::point_xy<long long, bg::cs::cartesian> TPoint;
typedef bg::model::ring<TPoint> TRing;
typedef bg::model::polygon<TPoint> TPolygon;
typedef bg::model::multi_polygon<TPolygon> TMultiPolygon;

void PrintRing(const TRing& rng)
{
  for (const auto& ver : rng)
  {
    cout << "(" << ver.x() << "," << ver.y() << "),";
  }
}

void PrintPolygon(const TPolygon& pol)
{
  cout << "Outer: ";
  PrintRing(pol.outer());
  cout << endl;

  for (const auto& rng : pol.inners())
  {
    cout << "Inner: ";
    PrintRing(rng);
    cout << endl;
  }
}

void PrintMultiPolygon(const string name, const TMultiPolygon& mp)
{
  cout << "Multi-Polygon " << name << " : " << endl;
  for (const auto& pol : mp)
  {
    PrintPolygon(pol);
  }
  cout << endl;
}

int main()
{
  cout << "BOOST_LIB_VERSION: " << BOOST_LIB_VERSION << endl;
  const vector<TPoint> verticesA{ { -405129, 2010409 }, { 3370580, 2010409 }, { 3370580, 1997709 }, { -405129, 1997709 }, { -405129, 2010409 } };
  const TRing rngA(verticesA.cbegin(), verticesA.cend());
  TPolygon polA;
  polA.outer() = rngA;
  TMultiPolygon mpA;
  mpA.push_back(polA);

  const vector<TPoint> verticesB{ { 3364230, -895349 }, { 3364230, 2004060 }, { 3376930, 2004059 }, { 3376930, -895350 }, { 3364230, -895349 } };
  const TRing rngB(verticesB.cbegin(), verticesB.cend());
  TPolygon polB;
  polB.outer() = rngB;
  TMultiPolygon mpB;
  mpB.push_back(polB);

  TMultiPolygon output;

  bg::union_(mpA, mpB, output);

  PrintMultiPolygon("A", mpA);
  PrintMultiPolygon("B", mpB);
  PrintMultiPolygon("output", output);
}

---

程序的输出是:

BOOST_LIB_VERSION: 1_63

Multi-Polygon A :
Outer: (-405129,2010409),(3370580,2010409),(3370580,1997709),(-405129,1997709),(-405129,2010409),

Multi-Polygon B :
Outer: (3364230,-895349),(3364230,2004060),(3376930,2004059),(3376930,-895350),(3364230,-895349),

Multi-Polygon output :
Outer: (3370580,2004060),(3376930,2004059),(3376930,-895350),(3364230,-895349),(3364230,-1372382),(-405129,1997709),(-405129,2010409),(3370580,2010409),(3370580,2004060),

请注意粗体坐标，Y 值比输入中的任何 Y 坐标都远。

Answer 1

确实，使用-fsanitize=undefined 打印

 /home/sehe/custom/boost/boost/geometry/strategies/cartesian/intersection.hpp:190:18: runtime error: signed integer overflow: 10923345128122 * 2899409 cannot be represented in type 'long long int'

相反，您可以使用供应商定义的 128 位扩展，或使用 Boost 的:

namespace mp = boost::multiprecision;

typedef mp::checked_int128_t T;
typedef bg::model::d2::point_xy<T, bg::cs::cartesian> TPoint;

事实上，您可以使用任意精度的整数:

typedef mp::checked_cpp_int T;

Note If you want to use unchecked arithmetic with cpp_int you will have to make sure that expression-templates are disabled for boost

typedef mp::number<mp::backends::cpp_int_backend<0, 0, mp::signed_magnitude, mp::unchecked>, mp::et_off> T;

See e.g. Why does using boost::multiprecision::cpp_int affect tail call optimization here, How to use sqrt and ceil with Boost::multiprecision?, etc.

有了上面所有的输出就变成了:

Live On Wandbox

BOOST_LIB_VERSION: 1_64
Multi-Polygon A : 
Outer: (-405129,2010409),(3370580,2010409),(3370580,1997709),(-405129,1997709),(-405129,2010409),

Multi-Polygon B : 
Outer: (3364230,-895349),(3364230,2004060),(3376930,2004059),(3376930,-895350),(3364230,-895349),

Multi-Polygon output : 
Outer: (3370580,2004060),(3376930,2004059),(3376930,-895350),(3364230,-895349),(3364230,1997709),(-405129,1997709),(-405129,2010409),(3370580,2010409),(3370580,2004060),

查看更多:Boost Geometry and exact point types