提升几何和精确的点类型

Question

我目前正致力于一个处理几何问题的项目。由于这个项目将在商业上使用，我不能使用像CGAL这样的库。

我目前正在使用不精确类型的boost :: geometry，但我遇到了数字问题。 我试图简单地使用boost :: multiprecision中的精确点类型，但是当我调用boost :: geometry函数时它不会编译。

我发现this page显示了如何使用numeric_adaptor来使用具有确切数字类型的boost :: geometry。但是，它似乎过时了，我无法使其发挥作用。

boost :: geometry可以与精确数字类型一起使用吗？怎么样？

#include <vector>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp> 
#include <boost/geometry/geometries/segment.hpp>
#include <boost/geometry/algorithms/intersection.hpp>

#include <boost/multiprecision/gmp.hpp>

namespace bg = boost::geometry;
namespace bm = boost::multiprecision;

typedef bg::model::d2::point_xy<bm::mpq_rational> point;
typedef boost::geometry::model::segment<point> segment;

int main(void)
{
    point a(0,0);
    point b(1,0);
    point c(1,1);
    point d(0,1);

    segment s1(a,c);
    segment s2(b,d);

    std::vector<point> ip;
    bg::intersection(s1, s2, ip); // Doesn't compile

    return 0;
}

clang ++ 3.4.2输出：

In file included from boost_geom_intersect.cpp:3:
In file included from /usr/include/boost/geometry.hpp:17:
In file included from /usr/include/boost/geometry/geometry.hpp:36:
In file included from /usr/include/boost/geometry/core/radian_access.hpp:21:
In file included from /usr/include/boost/numeric/conversion/cast.hpp:33:
In file included from /usr/include/boost/numeric/conversion/converter.hpp:14:
/usr/include/boost/numeric/conversion/converter_policies.hpp:187:69: error: cannot convert 'const
      boost::multiprecision::detail::expression<boost::multiprecision::detail::divides,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::multiply_immediates,
      boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      void, void>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, void, void>' to 'result_type' (aka 'double') without a conversion
      operator
  static result_type low_level_convert ( argument_type s ) { return static_cast<result_type>(s) ; }
                                                                    ^~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/boost/numeric/conversion/detail/converter.hpp:524:32: note: in instantiation of member function
      'boost::numeric::raw_converter<boost::numeric::conversion_traits<double, boost::multiprecision::detail::expression<boost::multiprecision::detail::divides,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::multiply_immediates,
      boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      void, void>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, void, void> > >::low_level_convert' requested here
      return RawConverterBase::low_level_convert(s);
                               ^
/usr/include/boost/numeric/conversion/cast.hpp:53:27: note: in instantiation of member function
      'boost::numeric::convdetail::non_rounding_converter<boost::numeric::conversion_traits<double,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::divides,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::multiply_immediates,
      boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      void, void>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, void, void> >,
      boost::numeric::convdetail::dummy_range_checker<boost::numeric::conversion_traits<double,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::divides,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::multiply_immediates,
      boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      void, void>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, void, void> > >,
      boost::numeric::raw_converter<boost::numeric::conversion_traits<double, boost::multiprecision::detail::expression<boost::multiprecision::detail::divides,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::multiply_immediates,
      boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      void, void>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, void, void> > > >::convert' requested here
        return converter::convert(arg);
                          ^
/usr/include/boost/geometry/policies/robustness/segment_ratio.hpp:146:22: note: in instantiation of function template specialization 'boost::numeric_cast<double,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::divides,
      boost::multiprecision::detail::expression<boost::multiprecision::detail::multiply_immediates,
      boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      void, void>, boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, void, void> >' requested here
            : boost::numeric_cast<double>
                     ^
/usr/include/boost/geometry/policies/robustness/segment_ratio.hpp:129:9: note: in instantiation of member function
      'boost::geometry::segment_ratio<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1> >::initialize' requested here
        initialize();
        ^
/usr/include/boost/geometry/strategies/cartesian/cart_intersect.hpp:207:33: note: in instantiation of member function
      'boost::geometry::segment_ratio<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1> >::assign' requested here
                sinfo.robust_ra.assign(robust_da, robust_da0);
                                ^
/usr/include/boost/geometry/algorithms/detail/overlay/intersection_insert.hpp:114:47: note: in instantiation of function template specialization
      'boost::geometry::strategy::intersection::relate_cartesian_segments<boost::geometry::policies::relate::segments_intersection_points<boost::geometry::segment_intersection_points<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian>, boost::geometry::segment_ratio<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1> > > >,
      void>::apply<boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >, boost::geometry::detail::no_rescale_policy,
      boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::geometry::cs::cartesian> >' requested
      here
        intersection_return_type is = policy::apply(segment1, segment2,
                                              ^
/usr/include/boost/geometry/algorithms/intersection.hpp:51:12: note: in instantiation of function template specialization
      'boost::geometry::detail::intersection::intersection_segment_segment_point<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian>
      >::apply<boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >, boost::geometry::detail::no_rescale_policy,
      std::back_insert_iterator<std::vector<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian>, std::allocator<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian> > > >, boost::geometry::strategy_intersection<boost::geometry::cartesian_tag,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >, boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian>, boost::geometry::detail::no_rescale_policy, void> >' requested here
        >::apply(geometry1, geometry2, robust_policy, std::back_inserter(geometry_out), strategy);
           ^
/usr/include/boost/geometry/algorithms/intersection.hpp:148:12: note: in instantiation of function template specialization
      'boost::geometry::dispatch::intersection<boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >, boost::geometry::segment_tag, boost::geometry::segment_tag, false>::apply<boost::geometry::detail::no_rescale_policy,
      std::vector<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>, boost::geometry::cs::cartesian>,
      std::allocator<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> > >, boost::geometry::strategy_intersection<boost::geometry::cartesian_tag,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >, boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian>, boost::geometry::detail::no_rescale_policy, void> >' requested here
        >::apply(geometry1, geometry2, robust_policy, geometry_out, strategy());
           ^
/usr/include/boost/geometry/algorithms/intersection.hpp:308:21: note: in instantiation of function template specialization
      'boost::geometry::resolve_variant::intersection<boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >
      >::apply<std::vector<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian>, std::allocator<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian> > > >' requested here
        >::template apply
                    ^
boost_geom_intersect.cpp:27:9: note: in instantiation of function template specialization
      'boost::geometry::intersection<boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian> >,
      boost::geometry::model::segment<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> >, std::vector<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational,
      1>, boost::geometry::cs::cartesian>,
      std::allocator<boost::geometry::model::d2::point_xy<boost::multiprecision::number<boost::multiprecision::backends::gmp_rational, 1>,
      boost::geometry::cs::cartesian> > > >' requested here
    bg::intersection(s1, s2, ip); // Doesn't compile
        ^
1 error generated.

Answer 1

Boost Geometry被从表达式模板返回的代理类型感到困惑，它期望具体的数字结果：documentation

  

Multiprecision库有两个不同的部分：

     

  
• 支持表达式模板的前端编号，用于处理所有操作符重载，表达式评估优化和代码缩减。
  
• 一系列实现实际算术运算的后端，只需要符合前端​​减少的接口要求。
  

元编程在那里停滞不前。

幸运的是，您只需使用已修改的mpq_rational来禁用表达式模板：

typedef bm::number<bm::gmp_rational, bm::et_off> my_rational;

这将编译没有问题。

---

Coliru对此嗤之以鼻，但现在是：http://coliru.stacked-crooked.com/a/232d98bfbb430468

#include <vector>

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/point_xy.hpp> 
#include <boost/geometry/geometries/segment.hpp>
#include <boost/geometry/algorithms/intersection.hpp>

#include <boost/multiprecision/gmp.hpp>
#include <boost/multiprecision/number.hpp>

namespace bg = boost::geometry;
namespace bm = boost::multiprecision;

typedef bm::number<bm::gmp_rational, bm::et_off> my_rational;
typedef bg::model::d2::point_xy<my_rational > point;
typedef boost::geometry::model::segment<point> segment;

int main(void)
{
    point a(0,0);
    point b(1,0);
    point c(1,1);
    point d(0,1);

    segment s1(a,c);
    segment s2(b,d);

    std::vector<point> ip;
    bg::intersection(s1, s2, ip); // Doesn't compile

    return 0;
}