quaternion.hpp

CGAL is a collaborative effort of several sites in Europe and Israel. The goal is to make the most i

            // (this is taken care of by the compiler itself)
            
            // converting copy constructors
            
            explicit                    quaternion(quaternion<float> const & a_recopier)
            {
                *this = detail::quaternion_type_converter<long double, float>(a_recopier);
            }
            
            explicit                    quaternion(quaternion<double> const & a_recopier)
            {
                *this = detail::quaternion_type_converter<long double, double>(a_recopier);
            }
            
            // destructor
            // (this is taken care of by the compiler itself)
            
            // accessors
            //
            // Note:    Like complex number, quaternions do have a meaningful notion of "real part",
            //            but unlike them there is no meaningful notion of "imaginary part".
            //            Instead there is an "unreal part" which itself is a quaternion, and usually
            //            nothing simpler (as opposed to the complex number case).
            //            However, for practicallity, there are accessors for the other components
            //            (these are necessary for the templated copy constructor, for instance).
            
            BOOST_QUATERNION_ACCESSOR_GENERATOR(long double)
            
            // assignment operators
            
            BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double)
            
            // other assignment-related operators
            //
            // NOTE:    Quaternion multiplication is *NOT* commutative;
            //            symbolically, "q *= rhs;" means "q = q * rhs;"
            //            and "q /= rhs;" means "q = q * inverse_of(rhs);"
            
            BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double)
            
            
        protected:
            
            BOOST_QUATERNION_MEMBER_DATA_GENERATOR(long double)
            
            
        private:
            
        };
        
        
#undef    BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR
#undef    BOOST_QUATERNION_MEMBER_ADD_GENERATOR
#undef    BOOST_QUATERNION_MEMBER_SUB_GENERATOR
#undef    BOOST_QUATERNION_MEMBER_MUL_GENERATOR
#undef    BOOST_QUATERNION_MEMBER_DIV_GENERATOR
#undef    BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1
#undef    BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2
#undef    BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3
#undef    BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1
#undef    BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2
#undef    BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3
#undef    BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1
#undef    BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2
#undef    BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3
#undef    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1
#undef    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2
#undef    BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3
        
#undef    BOOST_QUATERNION_CONSTRUCTOR_GENERATOR
        
        
#undef    BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR
        
#undef    BOOST_QUATERNION_MEMBER_DATA_GENERATOR
        
#undef    BOOST_QUATERNION_ACCESSOR_GENERATOR
        
        
        // operators
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)      \
        {                                                    \
            quaternion<T>    res(lhs);                       \
            res op##= rhs;                                   \
            return(res);                                     \
        }
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op)                                                  \
        template<typename T>                                                                            \
        inline quaternion<T>    operator op (T const & lhs, quaternion<T> const & rhs)                  \
        BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op)                                                  \
        template<typename T>                                                                            \
        inline quaternion<T>    operator op (quaternion<T> const & lhs, T const & rhs)                  \
        BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op)                                                  \
        template<typename T>                                                                            \
        inline quaternion<T>    operator op (::std::complex<T> const & lhs, quaternion<T> const & rhs)  \
        BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op)                                                  \
        template<typename T>                                                                            \
        inline quaternion<T>    operator op (quaternion<T> const & lhs, ::std::complex<T> const & rhs)  \
        BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR_3(op)                                                    \
        template<typename T>                                                                            \
        inline quaternion<T>    operator op (quaternion<T> const & lhs, quaternion<T> const & rhs)      \
        BOOST_QUATERNION_OPERATOR_GENERATOR_BODY(op)
        
#define    BOOST_QUATERNION_OPERATOR_GENERATOR(op)     \
        BOOST_QUATERNION_OPERATOR_GENERATOR_1_L(op)    \
        BOOST_QUATERNION_OPERATOR_GENERATOR_1_R(op)    \
        BOOST_QUATERNION_OPERATOR_GENERATOR_2_L(op)    \
        BOOST_QUATERNION_OPERATOR_GENERATOR_2_R(op)    \
        BOOST_QUATERNION_OPERATOR_GENERATOR_3(op)
        
        
        BOOST_QUATERNION_OPERATOR_GENERATOR(+)
        BOOST_QUATERNION_OPERATOR_GENERATOR(-)
        BOOST_QUATERNION_OPERATOR_GENERATOR(*)
        BOOST_QUATERNION_OPERATOR_GENERATOR(/)


#undef    BOOST_QUATERNION_OPERATOR_GENERATOR
        
#undef    BOOST_QUATERNION_OPERATOR_GENERATOR_1_L
#undef    BOOST_QUATERNION_OPERATOR_GENERATOR_1_R
#undef    BOOST_QUATERNION_OPERATOR_GENERATOR_2_L
#undef    BOOST_QUATERNION_OPERATOR_GENERATOR_2_R
#undef    BOOST_QUATERNION_OPERATOR_GENERATOR_3

#undef    BOOST_QUATERNION_OPERATOR_GENERATOR_BODY
        
        
        template<typename T>
        inline quaternion<T>                    operator + (quaternion<T> const & q)
        {
            return(q);
        }
        
        
        template<typename T>
        inline quaternion<T>                    operator - (quaternion<T> const & q)
        {
            return(quaternion<T>(-q.R_component_1(),-q.R_component_2(),-q.R_component_3(),-q.R_component_4()));
        }
        
        
        template<typename T>
        inline bool                                operator == (T const & lhs, quaternion<T> const & rhs)
        {
            return    (
                        (rhs.R_component_1() == lhs)&&
                        (rhs.R_component_2() == static_cast<T>(0))&&
                        (rhs.R_component_3() == static_cast<T>(0))&&
                        (rhs.R_component_4() == static_cast<T>(0))
                    );
        }
        
        
        template<typename T>
        inline bool                                operator == (quaternion<T> const & lhs, T const & rhs)
        {
            return    (
                        (lhs.R_component_1() == rhs)&&
                        (lhs.R_component_2() == static_cast<T>(0))&&
                        (lhs.R_component_3() == static_cast<T>(0))&&
                        (lhs.R_component_4() == static_cast<T>(0))
                    );
        }
        
        
        template<typename T>
        inline bool                                operator == (::std::complex<T> const & lhs, quaternion<T> const & rhs)
        {
            return    (
                        (rhs.R_component_1() == lhs.real())&&
                        (rhs.R_component_2() == lhs.imag())&&
                        (rhs.R_component_3() == static_cast<T>(0))&&
                        (rhs.R_component_4() == static_cast<T>(0))
                    );
        }
        
        
        template<typename T>
        inline bool                                operator == (quaternion<T> const & lhs, ::std::complex<T> const & rhs)
        {
            return    (
                        (lhs.R_component_1() == rhs.real())&&
                        (lhs.R_component_2() == rhs.imag())&&
                        (lhs.R_component_3() == static_cast<T>(0))&&
                        (lhs.R_component_4() == static_cast<T>(0))
                    );
        }
        
        
        template<typename T>
        inline bool                                operator == (quaternion<T> const & lhs, quaternion<T> const & rhs)
        {
            return    (
                        (rhs.R_component_1() == lhs.R_component_1())&&
                        (rhs.R_component_2() == lhs.R_component_2())&&
                        (rhs.R_component_3() == lhs.R_component_3())&&
                        (rhs.R_component_4() == lhs.R_component_4())
                    );
        }
        
        
#define    BOOST_QUATERNION_NOT_EQUAL_GENERATOR  \
        {                                        \
            return(!(lhs == rhs));               \
        }
        
        template<typename T>
        inline bool                                operator != (T const & lhs, quaternion<T> const & rhs)
        BOOST_QUATERNION_NOT_EQUAL_GENERATOR
        
        template<typename T>
        inline bool                                operator != (quaternion<T> const & lhs, T const & rhs)
        BOOST_QUATERNION_NOT_EQUAL_GENERATOR
        
        template<typename T>
        inline bool                                operator != (::std::complex<T> const & lhs, quaternion<T> const & rhs)
        BOOST_QUATERNION_NOT_EQUAL_GENERATOR
        
        template<typename T>
        inline bool                                operator != (quaternion<T> const & lhs, ::std::complex<T> const & rhs)
        BOOST_QUATERNION_NOT_EQUAL_GENERATOR
        
        template<typename T>
        inline bool                                operator != (quaternion<T> const & lhs, quaternion<T> const & rhs)
        BOOST_QUATERNION_NOT_EQUAL_GENERATOR
        
#undef    BOOST_QUATERNION_NOT_EQUAL_GENERATOR
        
        
        // Note:    we allow the following formats, whith a, b, c, and d reals
        //            a