Question

我正在尝试将Boost :: Geometry _union与整数一起用于性能和数值精度。为此，我将输入的坐标乘以10,000。因此创建最多9位数的坐标。我认为，因为我使用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（输出多边形包括一个远离输入中任何多边形的点）。研究Boost :: Geometry的代码让我得出结论：起源是文件cart_intersect.hpp中的一个环绕问题：

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

当所有三个（分子，dy_promoted和分母）都很大时，乘法的结果需要超过64位，因此整个结果是不正确的。

使用具有如此大整数的Boost :: Geometry是否有效？在保持正确性和精确度的同时，将Boost :: Geometry与整数一起使用的正确方法是什么？

修改 @sehe，谢谢你的回复。这是一个用VS2013和Boost 1.63

编译的SSCCE

#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);
}

该计划的输出是：

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),的 (3364230,-1372382) ,(-405129,1997709),(-405129,2010409),(3370580,2010409),(3370580,2004060),

请注意以粗体显示的坐标，Y值比输入中的任何Y坐标都要远。

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：

namespace mp = boost::multiprecision;

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

实际上，您可以使用任意精度的整数：

typedef mp::checked_cpp_int T;

注意如果要对cpp_int使用未经检查的算术，则必须确保禁用表达式模板以进行提升
typedef mp::number<mp::backends::cpp_int_backend<0, 0, mp::signed_magnitude, mp::unchecked>, mp::et_off> T;
参见例如Why does using boost::multiprecision::cpp_int affect tail call optimization here，How to use sqrt and ceil with Boost::multiprecision?等

通过以上所有，输出变为：

<强> 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

Answer 2

有点不相关，但是没有必要花费这么多代码来初始化或打印数据：

<强> Live On Wandbox

typedef bgm::polygon<bgm::d2::point_xy<mp::checked_int128_t, bg::cs::cartesian>> TPolygon;
typedef bgm::multi_polygon<TPolygon> TMultiPolygon;

int main() {
    std::cout << "BOOST_LIB_VERSION: " << BOOST_LIB_VERSION << "\n";
    TMultiPolygon 
        mpA{{{{ { -405129, 2010409 }, { 3370580, 2010409 }, { 3370580, 1997709 }, { -405129, 1997709 }, { -405129, 2010409 } }}}},
        mpB{{{{ { 3364230, -895349 }, { 3364230, 2004060 }, { 3376930, 2004059 }, { 3376930, -895350 }, { 3364230, -895349 } }}}},
        output;

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

    std::cout << "A : " << bg::wkt(mpA) << "\n";
    std::cout << "B : " << bg::wkt(mpB) << "\n";
    std::cout << "ouput : " << bg::wkt(output) << "\n";
}

打印

BOOST_LIB_VERSION: 1_64
A : POLYGON((-405129 2010409,3370580 2010409,3370580 1997709,-405129 1997709,-405129 2010409))
B : POLYGON((3364230 -895349,3364230 2004060,3376930 2004059,3376930 -895350,3364230 -895349))
ouput : MULTIPOLYGON(((3370580 2004060,3376930 2004059,3376930 -895350,3364230 -895349,3364230 1997709,-405129 1997709,-405129 2010409,3370580 2010409,3370580 2004060)))

请加入

#include <boost/geometry/io/io.hpp>

事实上，你真的不需要制作mpA / mpB多重多边形，所以你可以：

<强> Live On Wandbox

TPolygon 
    pA{{{ { -405129, 2010409 }, { 3370580, 2010409 }, { 3370580, 1997709 }, { -405129, 1997709 }, { -405129, 2010409 } }}},
    pB{{{ { 3364230, -895349 }, { 3364230, 2004060 }, { 3376930, 2004059 }, { 3376930, -895350 }, { 3364230, -895349 } }}};

TMultiPolygon output;
bg::union_(pA, pB, output);

打印：

BOOST_LIB_VERSION: 1_64
A : POLYGON((-405129 2010409,3370580 2010409,3370580 1997709,-405129 1997709,-405129 2010409))
B : POLYGON((3364230 -895349,3364230 2004060,3376930 2004059,3376930 -895350,3364230 -895349))
ouput : MULTIPOLYGON(((3370580 2004060,3376930 2004059,3376930 -895350,3364230 -895349,3364230 1997709,-405129 1997709,-405129 2010409,3370580 2010409,3370580 2004060)))

当然，阅读支持相同：

<强> Live On Wandbox

TPolygon pA, pB;
bg::read_wkt("POLYGON((-405129 2010409,3370580 2010409,3370580 1997709,-405129 1997709,-405129 2010409))", pA);
bg::read_wkt("POLYGON((3364230 -895349,3364230 2004060,3376930 2004059,3376930 -895350,3364230 -895349))", pB);

如何使用整数使用Boost :: Geometry _union

2 个答案: