text: // Boost.Geometry (aka GGL, Generic Geometry Library)
  
  // Copyright (c) 2009-2012 Mateusz Loskot, London, UK.
  // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
  // Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
  
  // This file was modified by Oracle on 2016.
  // Modifications copyright (c) 2016, Oracle and/or its affiliates.
  // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
  
  // Use, modification and distribution is subject to the Boost Software License,
  // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  // http://www.boost.org/LICENSE_1_0.txt)
  
  #ifndef BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP
  #define BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP
  
  
  #include <cstddef>
  
  #include <boost/mpl/assert.hpp>
  #include <boost/mpl/size_t.hpp>
  
  #include <boost/geometry/core/access.hpp>
  #include <boost/geometry/core/coordinate_dimension.hpp>
  
  #include <boost/geometry/geometries/concepts/point_concept.hpp>
  
  
  namespace boost { namespace geometry
  {
  
  #ifndef DOXYGEN_NO_DETAIL
  namespace detail
  {
  
  template <std::size_t Dimension>
  struct cross_product
  {
      // We define cross product only for 2d (see Wolfram) and 3d.
      // In Math, it is also well-defined for 7-dimension.
      // Generalisation of cross product to n-dimension is defined as
      // wedge product but it is not direct analogue to binary cross product.
      BOOST_MPL_ASSERT_MSG((false),
                           NOT_IMPLEMENTED_FOR_THIS_DIMENSION,
                           (mpl::size_t<Dimension>));
  };
  
  template <>
  struct cross_product<2>
  {
      template <typename P1, typename P2, typename ResultP>
      static inline void apply(P1 const& p1, P2 const& p2, ResultP& result)
      {
          assert_dimension<P1, 2>();
          assert_dimension<P2, 2>();
          assert_dimension<ResultP, 2>();
  
          // For 2-dimensions, analog of the cross product U(x,y) and V(x,y) is
          // Ux * Vy - Uy * Vx
          // which is returned as 0-component (or X) of 2d vector, 1-component is undefined.
          set<0>(result, get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2));
      }
  };
  
  template <>
  struct cross_product<3>
  {
      template <typename P1, typename P2, typename ResultP>
      static inline void apply(P1 const& p1, P2 const& p2, ResultP& result)
      {
          assert_dimension<P1, 3>();
          assert_dimension<P2, 3>();
          assert_dimension<ResultP, 3>();
  
          set<0>(result, get<1>(p1) * get<2>(p2) - get<2>(p1) * get<1>(p2));
          set<1>(result, get<2>(p1) * get<0>(p2) - get<0>(p1) * get<2>(p2));
          set<2>(result, get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2));
      }
  };
  
  } // namespace detail
  #endif // DOXYGEN_NO_DETAIL
  
  
  /*!
  \brief Computes the cross product of two vectors.
  \details All vectors should have the same dimension, 3 or 2.
  \ingroup arithmetic
  \param p1 first vector
  \param p2 second vector
  \return the cross product vector
   */
  template <typename ResultP, typename P1, typename P2>
  inline ResultP cross_product(P1 const& p1, P2 const& p2)
  {
      BOOST_CONCEPT_ASSERT( (concepts::Point<ResultP>) );
      BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<P1>) );
      BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<P2>) );
  
      ResultP result;
      detail::cross_product<dimension<ResultP>::value>::apply(p1, p2, result);
      return result;
  }
  
  /*!
  \brief Computes the cross product of two vectors.
  \details All vectors should have the same dimension, 3 or 2.
  \ingroup arithmetic
  \param p1 first vector
  \param p2 second vector
  \return the cross product vector
  */
  template <typename P>
  inline P cross_product(P const& p1, P const& p2)
  {
      BOOST_CONCEPT_ASSERT((concepts::Point<P>));
      BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P>));
  
      P result;
      detail::cross_product<dimension<P>::value>::apply(p1, p2, result);
      return result;
  }
  
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP
  