C++ 如何使用Boost:：Geometry\u与整数的并集

我尝试使用Boost:：Geometry与整数的并集，以提高性能和数值精度。为此，我将输入的坐标乘以10000。从而创建最多9位的坐标。我想既然我用的是64位整数，那就应该很好了

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）。通过研究Boost:：Geometry的代码，我得出结论，原点是文件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));

set（点，get（段）+boost:：numeric\u cast
<
配位
>（分子*dy_/分母））；

当所有三个（分子、dy_和分母）都很大时，乘法的结果超过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有效吗？在保持正确性和精度的同时，使用Boost:：Geometry和整数的正确方法是什么

---

编辑 @谢谢你的回复。这是一个SSCCE，使用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);
}

#包括
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使用名称空间std；
名称空间bg=boost:：geometry；
typedef bg:：model:：d2:：point_xy TPoint；
typedef bg:：model:：环字符串；
typedef bg:：model:：polygon TPolygon；
typedef bg:：model:：multi_polygon t multi polygon；
无效打印环（常量字符串和标记）
{
用于（常数自动和版本：rng）
{
确实可以使用
-fsanitize=undefined
打印运行

 /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;

注意如果您想对
cpp_int
使用未经检查的算术，则必须确保禁用表达式模板进行boost

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

查看更多信息：
实际上，使用
-fsanize=undefined打印运行

 /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;

注意如果您想对
cpp_int
使用未经检查的算术，则必须确保禁用表达式模板进行boost

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

查看更多信息：
有点不相关，但无需花费太多代码初始化或打印数据：


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),

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";
}

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);

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);

包括

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

印刷品：

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，同样支持阅读：


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),

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";
}

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);

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);

有点不相关，但无需花费太多代码初始化或打印数据：


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),

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";
}

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);

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);

包括

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

印刷品：

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，同样支持阅读：


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),

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";
}

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);

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);

您可以使用防止溢出的整数类型和/或boost:：multiprecision中的大容量整数。如果您发布了SSCCE，我们可以向您展示一个示例。现在我们无法给出更有用的答案，因为问题中缺少所有有用的代码。@sehe，谢谢您的回答。我已经相应地更新了帖子。您可以使用inte防止boost:：multiprecision溢出和/或大容量整数的ger类型。如果您发布SSCCE，我们可以向您展示一个示例。现在我们无法给出更有用的答案，因为问题中缺少所有有用的代码。@sehe，感谢您的回复。我已相应地更新了帖子。感谢您提供的详细信息和建议我尝试用我的1_63 boost库编译这段代码，但得到以下编译错误：1>C:\Workspace\ThirdParty\boost\ver_1_63\u 0\boost/geometry/po‌​licies/robustness/se‌​水电站发电量比率（152）‌​: 错误C2679:二进制“=”：未找到接受类型为“double”的右操作数的运算符（或没有可接受的转换）有什么想法吗？哦..我建议升级。谢谢你详细而专业的回答。我尝试用我的1\u 63 boost库编译这段代码，但得到了以下编译错误：1>C:\Workspace\ThirdParty\boost\ver\u 1\u 63\u 0\boost/geometry/po‌​licies/robustness/se‌​水电站发电量比率（152）‌​: 错误C2679:二进制“=”：找不到接受“double”类型右操作数的运算符（或没有可接受的转换）。有什么想法吗？哦..我建议升级。