// Boost.Geometry (aka GGL, Generic Geometry Library)
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// Copyright (c) 2009-2012 Mateusz Loskot, London, UK.
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// Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
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// Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
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// This file was modified by Oracle on 2016-2020.
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// Modifications copyright (c) 2016-2020, Oracle and/or its affiliates.
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// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
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// Use, modification and distribution is subject to the Boost Software License,
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// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP
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#define BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP
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#include <cstddef>
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#include <type_traits>
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#include <boost/geometry/core/access.hpp>
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#include <boost/geometry/core/make.hpp>
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#include <boost/geometry/core/coordinate_dimension.hpp>
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#include <boost/geometry/core/static_assert.hpp>
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#include <boost/geometry/geometries/concepts/point_concept.hpp>
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namespace boost { namespace geometry
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{
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#ifndef DOXYGEN_NO_DETAIL
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namespace detail
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{
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template <std::size_t Dimension>
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struct cross_product
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{
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// We define cross product only for 2d (see Wolfram) and 3d.
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// In Math, it is also well-defined for 7-dimension.
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// Generalisation of cross product to n-dimension is defined as
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// wedge product but it is not direct analogue to binary cross product.
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BOOST_GEOMETRY_STATIC_ASSERT_FALSE(
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"Not implemented for this Dimension.",
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std::integral_constant<std::size_t, Dimension>);
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};
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template <>
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struct cross_product<2>
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{
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template <typename P1, typename P2, typename ResultP>
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static void apply(P1 const& p1, P2 const& p2, ResultP& result)
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{
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assert_dimension<P1, 2>();
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assert_dimension<P2, 2>();
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assert_dimension<ResultP, 2>();
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// For 2-dimensions, analog of the cross product U(x,y) and V(x,y) is
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// Ux * Vy - Uy * Vx
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// which is returned as 0-component (or X) of 2d vector, 1-component is undefined.
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set<0>(result, get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2));
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}
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};
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template <>
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struct cross_product<3>
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{
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template <typename P1, typename P2, typename ResultP>
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static void apply(P1 const& p1, P2 const& p2, ResultP& result)
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{
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assert_dimension<P1, 3>();
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assert_dimension<P2, 3>();
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assert_dimension<ResultP, 3>();
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set<0>(result, get<1>(p1) * get<2>(p2) - get<2>(p1) * get<1>(p2));
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set<1>(result, get<2>(p1) * get<0>(p2) - get<0>(p1) * get<2>(p2));
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set<2>(result, get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2));
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}
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template <typename ResultP, typename P1, typename P2>
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static constexpr ResultP apply(P1 const& p1, P2 const& p2)
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{
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assert_dimension<P1, 3>();
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assert_dimension<P2, 3>();
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assert_dimension<ResultP, 3>();
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return traits::make<ResultP>::apply(
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get<1>(p1) * get<2>(p2) - get<2>(p1) * get<1>(p2),
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get<2>(p1) * get<0>(p2) - get<0>(p1) * get<2>(p2),
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get<0>(p1) * get<1>(p2) - get<1>(p1) * get<0>(p2));
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}
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};
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} // namespace detail
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#endif // DOXYGEN_NO_DETAIL
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/*!
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\brief Computes the cross product of two vectors.
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\details All vectors should have the same dimension, 3 or 2.
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\ingroup arithmetic
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\param p1 first vector
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\param p2 second vector
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\return the cross product vector
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*/
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template
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<
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typename ResultP, typename P1, typename P2,
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std::enable_if_t
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<
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dimension<ResultP>::value != 3
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|| ! traits::make<ResultP>::is_specialized,
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int
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> = 0
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>
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inline ResultP cross_product(P1 const& p1, P2 const& p2)
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{
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BOOST_CONCEPT_ASSERT( (concepts::Point<ResultP>) );
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BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<P1>) );
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BOOST_CONCEPT_ASSERT( (concepts::ConstPoint<P2>) );
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ResultP result;
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detail::cross_product<dimension<ResultP>::value>::apply(p1, p2, result);
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return result;
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}
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template
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<
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typename ResultP, typename P1, typename P2,
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std::enable_if_t
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<
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dimension<ResultP>::value == 3
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&& traits::make<ResultP>::is_specialized,
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int
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> = 0
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>
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// workaround for VS2015
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#if !defined(_MSC_VER) || (_MSC_VER >= 1910)
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constexpr
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#endif
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inline ResultP cross_product(P1 const& p1, P2 const& p2)
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{
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BOOST_CONCEPT_ASSERT((concepts::Point<ResultP>));
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BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P1>));
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BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P2>));
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return detail::cross_product<3>::apply<ResultP>(p1, p2);
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}
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/*!
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\brief Computes the cross product of two vectors.
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\details All vectors should have the same dimension, 3 or 2.
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\ingroup arithmetic
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\param p1 first vector
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\param p2 second vector
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\return the cross product vector
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\qbk{[heading Examples]}
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\qbk{[cross_product] [cross_product_output]}
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*/
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template
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<
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typename P,
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std::enable_if_t
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<
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dimension<P>::value != 3
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|| ! traits::make<P>::is_specialized,
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int
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> = 0
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>
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inline P cross_product(P const& p1, P const& p2)
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{
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BOOST_CONCEPT_ASSERT((concepts::Point<P>));
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BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P>));
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P result;
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detail::cross_product<dimension<P>::value>::apply(p1, p2, result);
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return result;
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}
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template
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<
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typename P,
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std::enable_if_t
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<
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dimension<P>::value == 3
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&& traits::make<P>::is_specialized,
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int
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> = 0
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>
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// workaround for VS2015
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#if !defined(_MSC_VER) || (_MSC_VER >= 1910)
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constexpr
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#endif
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inline P cross_product(P const& p1, P const& p2)
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{
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BOOST_CONCEPT_ASSERT((concepts::Point<P>));
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BOOST_CONCEPT_ASSERT((concepts::ConstPoint<P>));
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return detail::cross_product<3>::apply<P>(p1, p2);
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}
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}} // namespace boost::geometry
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#endif // BOOST_GEOMETRY_ARITHMETIC_CROSS_PRODUCT_HPP
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