1774 lines
81 KiB
Plaintext
1774 lines
81 KiB
Plaintext
// boost quaternion.hpp header file
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// (C) Copyright Hubert Holin 2001.
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// Distributed under the Boost Software License, Version 1.0. (See
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// 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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// See http://www.boost.org for updates, documentation, and revision history.
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#ifndef BOOST_QUATERNION_HPP
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#define BOOST_QUATERNION_HPP
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#include <complex>
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#include <iosfwd> // for the "<<" and ">>" operators
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#include <sstream> // for the "<<" operator
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#include <boost/config.hpp> // for BOOST_NO_STD_LOCALE
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#include <boost/detail/workaround.hpp>
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#ifndef BOOST_NO_STD_LOCALE
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#include <locale> // for the "<<" operator
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#endif /* BOOST_NO_STD_LOCALE */
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#include <valarray>
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#include <boost/math/special_functions/sinc.hpp> // for the Sinus cardinal
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#include <boost/math/special_functions/sinhc.hpp> // for the Hyperbolic Sinus cardinal
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namespace boost
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{
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namespace math
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{
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#define BOOST_QUATERNION_ACCESSOR_GENERATOR(type) \
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type real() const \
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{ \
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return(a); \
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} \
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\
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quaternion<type> unreal() const \
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{ \
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return(quaternion<type>(static_cast<type>(0),b,c,d)); \
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} \
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\
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type R_component_1() const \
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{ \
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return(a); \
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} \
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\
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type R_component_2() const \
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{ \
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return(b); \
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} \
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\
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type R_component_3() const \
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{ \
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return(c); \
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} \
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\
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type R_component_4() const \
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{ \
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return(d); \
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} \
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\
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::std::complex<type> C_component_1() const \
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{ \
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return(::std::complex<type>(a,b)); \
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} \
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\
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::std::complex<type> C_component_2() const \
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{ \
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return(::std::complex<type>(c,d)); \
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}
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#define BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \
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template<typename X> \
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quaternion<type> & operator = (quaternion<X> const & a_affecter) \
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{ \
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a = static_cast<type>(a_affecter.R_component_1()); \
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b = static_cast<type>(a_affecter.R_component_2()); \
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c = static_cast<type>(a_affecter.R_component_3()); \
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d = static_cast<type>(a_affecter.R_component_4()); \
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\
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return(*this); \
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} \
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\
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quaternion<type> & operator = (quaternion<type> const & a_affecter) \
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{ \
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a = a_affecter.a; \
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b = a_affecter.b; \
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c = a_affecter.c; \
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d = a_affecter.d; \
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\
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return(*this); \
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} \
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\
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quaternion<type> & operator = (type const & a_affecter) \
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{ \
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a = a_affecter; \
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\
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b = c = d = static_cast<type>(0); \
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\
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return(*this); \
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} \
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\
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quaternion<type> & operator = (::std::complex<type> const & a_affecter) \
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{ \
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a = a_affecter.real(); \
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b = a_affecter.imag(); \
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\
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c = d = static_cast<type>(0); \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_DATA_GENERATOR(type) \
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type a; \
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type b; \
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type c; \
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type d;
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template<typename T>
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class quaternion
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{
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public:
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typedef T value_type;
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// constructor for H seen as R^4
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// (also default constructor)
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explicit quaternion( T const & requested_a = T(),
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T const & requested_b = T(),
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T const & requested_c = T(),
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T const & requested_d = T())
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: a(requested_a),
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b(requested_b),
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c(requested_c),
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d(requested_d)
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{
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// nothing to do!
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}
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// constructor for H seen as C^2
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explicit quaternion( ::std::complex<T> const & z0,
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::std::complex<T> const & z1 = ::std::complex<T>())
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: a(z0.real()),
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b(z0.imag()),
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c(z1.real()),
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d(z1.imag())
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{
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// nothing to do!
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}
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// UNtemplated copy constructor
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// (this is taken care of by the compiler itself)
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// templated copy constructor
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template<typename X>
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explicit quaternion(quaternion<X> const & a_recopier)
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: a(static_cast<T>(a_recopier.R_component_1())),
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b(static_cast<T>(a_recopier.R_component_2())),
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c(static_cast<T>(a_recopier.R_component_3())),
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d(static_cast<T>(a_recopier.R_component_4()))
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{
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// nothing to do!
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}
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// destructor
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// (this is taken care of by the compiler itself)
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// accessors
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//
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// Note: Like complex number, quaternions do have a meaningful notion of "real part",
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// but unlike them there is no meaningful notion of "imaginary part".
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// Instead there is an "unreal part" which itself is a quaternion, and usually
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// nothing simpler (as opposed to the complex number case).
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// However, for practicallity, there are accessors for the other components
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// (these are necessary for the templated copy constructor, for instance).
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BOOST_QUATERNION_ACCESSOR_GENERATOR(T)
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// assignment operators
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BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T)
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// other assignment-related operators
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//
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// NOTE: Quaternion multiplication is *NOT* commutative;
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// symbolically, "q *= rhs;" means "q = q * rhs;"
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// and "q /= rhs;" means "q = q * inverse_of(rhs);"
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quaternion<T> & operator += (T const & rhs)
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{
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T at = a + rhs; // exception guard
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a = at;
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return(*this);
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}
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quaternion<T> & operator += (::std::complex<T> const & rhs)
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{
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T at = a + rhs.real(); // exception guard
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T bt = b + rhs.imag(); // exception guard
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a = at;
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b = bt;
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return(*this);
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}
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template<typename X>
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quaternion<T> & operator += (quaternion<X> const & rhs)
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{
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T at = a + static_cast<T>(rhs.R_component_1()); // exception guard
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T bt = b + static_cast<T>(rhs.R_component_2()); // exception guard
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T ct = c + static_cast<T>(rhs.R_component_3()); // exception guard
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T dt = d + static_cast<T>(rhs.R_component_4()); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator -= (T const & rhs)
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{
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T at = a - rhs; // exception guard
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a = at;
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return(*this);
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}
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quaternion<T> & operator -= (::std::complex<T> const & rhs)
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{
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T at = a - rhs.real(); // exception guard
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T bt = b - rhs.imag(); // exception guard
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a = at;
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b = bt;
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return(*this);
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}
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template<typename X>
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quaternion<T> & operator -= (quaternion<X> const & rhs)
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{
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T at = a - static_cast<T>(rhs.R_component_1()); // exception guard
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T bt = b - static_cast<T>(rhs.R_component_2()); // exception guard
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T ct = c - static_cast<T>(rhs.R_component_3()); // exception guard
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T dt = d - static_cast<T>(rhs.R_component_4()); // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator *= (T const & rhs)
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{
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T at = a * rhs; // exception guard
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T bt = b * rhs; // exception guard
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T ct = c * rhs; // exception guard
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T dt = d * rhs; // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator *= (::std::complex<T> const & rhs)
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{
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T ar = rhs.real();
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T br = rhs.imag();
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T at = +a*ar-b*br;
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T bt = +a*br+b*ar;
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T ct = +c*ar+d*br;
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T dt = -c*br+d*ar;
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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template<typename X>
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quaternion<T> & operator *= (quaternion<X> const & rhs)
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{
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T ar = static_cast<T>(rhs.R_component_1());
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T br = static_cast<T>(rhs.R_component_2());
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T cr = static_cast<T>(rhs.R_component_3());
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T dr = static_cast<T>(rhs.R_component_4());
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T at = +a*ar-b*br-c*cr-d*dr;
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T bt = +a*br+b*ar+c*dr-d*cr; //(a*br+ar*b)+(c*dr-cr*d);
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T ct = +a*cr-b*dr+c*ar+d*br; //(a*cr+ar*c)+(d*br-dr*b);
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T dt = +a*dr+b*cr-c*br+d*ar; //(a*dr+ar*d)+(b*cr-br*c);
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator /= (T const & rhs)
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{
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T at = a / rhs; // exception guard
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T bt = b / rhs; // exception guard
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T ct = c / rhs; // exception guard
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T dt = d / rhs; // exception guard
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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quaternion<T> & operator /= (::std::complex<T> const & rhs)
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{
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T ar = rhs.real();
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T br = rhs.imag();
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T denominator = ar*ar+br*br;
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T at = (+a*ar+b*br)/denominator; //(a*ar+b*br)/denominator;
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T bt = (-a*br+b*ar)/denominator; //(ar*b-a*br)/denominator;
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T ct = (+c*ar-d*br)/denominator; //(ar*c-d*br)/denominator;
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T dt = (+c*br+d*ar)/denominator; //(ar*d+br*c)/denominator;
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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template<typename X>
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quaternion<T> & operator /= (quaternion<X> const & rhs)
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{
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T ar = static_cast<T>(rhs.R_component_1());
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T br = static_cast<T>(rhs.R_component_2());
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T cr = static_cast<T>(rhs.R_component_3());
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T dr = static_cast<T>(rhs.R_component_4());
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T denominator = ar*ar+br*br+cr*cr+dr*dr;
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T at = (+a*ar+b*br+c*cr+d*dr)/denominator; //(a*ar+b*br+c*cr+d*dr)/denominator;
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T bt = (-a*br+b*ar-c*dr+d*cr)/denominator; //((ar*b-a*br)+(cr*d-c*dr))/denominator;
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T ct = (-a*cr+b*dr+c*ar-d*br)/denominator; //((ar*c-a*cr)+(dr*b-d*br))/denominator;
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T dt = (-a*dr-b*cr+c*br+d*ar)/denominator; //((ar*d-a*dr)+(br*c-b*cr))/denominator;
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a = at;
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b = bt;
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c = ct;
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d = dt;
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return(*this);
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}
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protected:
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BOOST_QUATERNION_MEMBER_DATA_GENERATOR(T)
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private:
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};
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// declaration of quaternion specialization
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template<> class quaternion<float>;
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template<> class quaternion<double>;
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template<> class quaternion<long double>;
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// helper templates for converting copy constructors (declaration)
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namespace detail
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{
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template< typename T,
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typename U
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>
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quaternion<T> quaternion_type_converter(quaternion<U> const & rhs);
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}
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// implementation of quaternion specialization
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#define BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(type) \
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explicit quaternion( type const & requested_a = static_cast<type>(0), \
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type const & requested_b = static_cast<type>(0), \
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type const & requested_c = static_cast<type>(0), \
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type const & requested_d = static_cast<type>(0)) \
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: a(requested_a), \
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b(requested_b), \
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c(requested_c), \
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d(requested_d) \
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{ \
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} \
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\
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explicit quaternion( ::std::complex<type> const & z0, \
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::std::complex<type> const & z1 = ::std::complex<type>()) \
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: a(z0.real()), \
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b(z0.imag()), \
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c(z1.real()), \
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d(z1.imag()) \
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{ \
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}
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#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
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quaternion<type> & operator += (type const & rhs) \
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{ \
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a += rhs; \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
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quaternion<type> & operator += (::std::complex<type> const & rhs) \
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{ \
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a += rhs.real(); \
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b += rhs.imag(); \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \
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template<typename X> \
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quaternion<type> & operator += (quaternion<X> const & rhs) \
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{ \
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a += static_cast<type>(rhs.R_component_1()); \
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b += static_cast<type>(rhs.R_component_2()); \
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c += static_cast<type>(rhs.R_component_3()); \
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d += static_cast<type>(rhs.R_component_4()); \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
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quaternion<type> & operator -= (type const & rhs) \
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{ \
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a -= rhs; \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
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quaternion<type> & operator -= (::std::complex<type> const & rhs) \
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{ \
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a -= rhs.real(); \
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b -= rhs.imag(); \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \
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template<typename X> \
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quaternion<type> & operator -= (quaternion<X> const & rhs) \
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{ \
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a -= static_cast<type>(rhs.R_component_1()); \
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b -= static_cast<type>(rhs.R_component_2()); \
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c -= static_cast<type>(rhs.R_component_3()); \
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d -= static_cast<type>(rhs.R_component_4()); \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
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quaternion<type> & operator *= (type const & rhs) \
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{ \
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a *= rhs; \
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b *= rhs; \
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c *= rhs; \
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d *= rhs; \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
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quaternion<type> & operator *= (::std::complex<type> const & rhs) \
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{ \
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type ar = rhs.real(); \
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type br = rhs.imag(); \
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\
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type at = +a*ar-b*br; \
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type bt = +a*br+b*ar; \
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type ct = +c*ar+d*br; \
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type dt = -c*br+d*ar; \
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\
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a = at; \
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b = bt; \
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c = ct; \
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d = dt; \
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\
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return(*this); \
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}
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#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \
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template<typename X> \
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quaternion<type> & operator *= (quaternion<X> const & rhs) \
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{ \
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type ar = static_cast<type>(rhs.R_component_1()); \
|
|
type br = static_cast<type>(rhs.R_component_2()); \
|
|
type cr = static_cast<type>(rhs.R_component_3()); \
|
|
type dr = static_cast<type>(rhs.R_component_4()); \
|
|
\
|
|
type at = +a*ar-b*br-c*cr-d*dr; \
|
|
type bt = +a*br+b*ar+c*dr-d*cr; \
|
|
type ct = +a*cr-b*dr+c*ar+d*br; \
|
|
type dt = +a*dr+b*cr-c*br+d*ar; \
|
|
\
|
|
a = at; \
|
|
b = bt; \
|
|
c = ct; \
|
|
d = dt; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
// There is quite a lot of repetition in the code below. This is intentional.
|
|
// The last conditional block is the normal form, and the others merely
|
|
// consist of workarounds for various compiler deficiencies. Hopefuly, when
|
|
// more compilers are conformant and we can retire support for those that are
|
|
// not, we will be able to remove the clutter. This is makes the situation
|
|
// (painfully) explicit.
|
|
|
|
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
|
|
quaternion<type> & operator /= (type const & rhs) \
|
|
{ \
|
|
a /= rhs; \
|
|
b /= rhs; \
|
|
c /= rhs; \
|
|
d /= rhs; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
|
|
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
|
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
|
quaternion<type> & operator /= (::std::complex<type> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
using ::std::abs; \
|
|
\
|
|
valarray<type> tr(2); \
|
|
\
|
|
tr[0] = rhs.real(); \
|
|
tr[1] = rhs.imag(); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(4); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]; \
|
|
tt[2] = +c*tr[0]-d*tr[1]; \
|
|
tt[3] = +c*tr[1]+d*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#else
|
|
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
|
quaternion<type> & operator /= (::std::complex<type> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<type> tr(2); \
|
|
\
|
|
tr[0] = rhs.real(); \
|
|
tr[1] = rhs.imag(); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(4); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]; \
|
|
tt[2] = +c*tr[0]-d*tr[1]; \
|
|
tt[3] = +c*tr[1]+d*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP)
|
|
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
|
|
template<typename X> \
|
|
quaternion<type> & operator /= (quaternion<X> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
using ::std::abs; \
|
|
\
|
|
valarray<type> tr(4); \
|
|
\
|
|
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
|
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
|
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
|
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(4); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
|
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
|
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#else
|
|
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
|
|
template<typename X> \
|
|
quaternion<type> & operator /= (quaternion<X> const & rhs) \
|
|
{ \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<type> tr(4); \
|
|
\
|
|
tr[0] = static_cast<type>(rhs.R_component_1()); \
|
|
tr[1] = static_cast<type>(rhs.R_component_2()); \
|
|
tr[2] = static_cast<type>(rhs.R_component_3()); \
|
|
tr[3] = static_cast<type>(rhs.R_component_4()); \
|
|
\
|
|
type mixam = static_cast<type>(1)/(abs(tr).max)(); \
|
|
\
|
|
tr *= mixam; \
|
|
\
|
|
valarray<type> tt(4); \
|
|
\
|
|
tt[0] = +a*tr[0]+b*tr[1]+c*tr[2]+d*tr[3]; \
|
|
tt[1] = -a*tr[1]+b*tr[0]-c*tr[3]+d*tr[2]; \
|
|
tt[2] = -a*tr[2]+b*tr[3]+c*tr[0]-d*tr[1]; \
|
|
tt[3] = -a*tr[3]-b*tr[2]+c*tr[1]+d*tr[0]; \
|
|
\
|
|
tr *= tr; \
|
|
\
|
|
tt *= (mixam/tr.sum()); \
|
|
\
|
|
a = tt[0]; \
|
|
b = tt[1]; \
|
|
c = tt[2]; \
|
|
d = tt[3]; \
|
|
\
|
|
return(*this); \
|
|
}
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
#define BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
|
|
BOOST_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
|
|
BOOST_QUATERNION_MEMBER_ADD_GENERATOR_3(type)
|
|
|
|
#define BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
|
|
BOOST_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
|
|
BOOST_QUATERNION_MEMBER_SUB_GENERATOR_3(type)
|
|
|
|
#define BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
|
|
BOOST_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
|
|
BOOST_QUATERNION_MEMBER_MUL_GENERATOR_3(type)
|
|
|
|
#define BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
|
|
BOOST_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
|
|
BOOST_QUATERNION_MEMBER_DIV_GENERATOR_3(type)
|
|
|
|
#define BOOST_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_ADD_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_SUB_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_MUL_GENERATOR(type) \
|
|
BOOST_QUATERNION_MEMBER_DIV_GENERATOR(type)
|
|
|
|
|
|
template<>
|
|
class quaternion<float>
|
|
{
|
|
public:
|
|
|
|
typedef float value_type;
|
|
|
|
BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(float)
|
|
|
|
// UNtemplated copy constructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// explicit copy constructors (precision-loosing converters)
|
|
|
|
explicit quaternion(quaternion<double> const & a_recopier)
|
|
{
|
|
*this = detail::quaternion_type_converter<float, double>(a_recopier);
|
|
}
|
|
|
|
explicit quaternion(quaternion<long double> const & a_recopier)
|
|
{
|
|
*this = detail::quaternion_type_converter<float, long 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(float)
|
|
|
|
// assignment operators
|
|
|
|
BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float)
|
|
|
|
// 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(float)
|
|
|
|
|
|
protected:
|
|
|
|
BOOST_QUATERNION_MEMBER_DATA_GENERATOR(float)
|
|
|
|
|
|
private:
|
|
|
|
};
|
|
|
|
|
|
template<>
|
|
class quaternion<double>
|
|
{
|
|
public:
|
|
|
|
typedef double value_type;
|
|
|
|
BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(double)
|
|
|
|
// UNtemplated copy constructor
|
|
// (this is taken care of by the compiler itself)
|
|
|
|
// converting copy constructor
|
|
|
|
explicit quaternion(quaternion<float> const & a_recopier)
|
|
{
|
|
*this = detail::quaternion_type_converter<double, float>(a_recopier);
|
|
}
|
|
|
|
// explicit copy constructors (precision-loosing converters)
|
|
|
|
explicit quaternion(quaternion<long double> const & a_recopier)
|
|
{
|
|
*this = detail::quaternion_type_converter<double, long 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(double)
|
|
|
|
// assignment operators
|
|
|
|
BOOST_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(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(double)
|
|
|
|
|
|
protected:
|
|
|
|
BOOST_QUATERNION_MEMBER_DATA_GENERATOR(double)
|
|
|
|
|
|
private:
|
|
|
|
};
|
|
|
|
|
|
template<>
|
|
class quaternion<long double>
|
|
{
|
|
public:
|
|
|
|
typedef long double value_type;
|
|
|
|
BOOST_QUATERNION_CONSTRUCTOR_GENERATOR(long double)
|
|
|
|
// UNtemplated copy constructor
|
|
// (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
|
|
// (a), (a,b), (a,b,c), (a,b,c,d)
|
|
// (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b),(c,d))
|
|
template<typename T, typename charT, class traits>
|
|
::std::basic_istream<charT,traits> & operator >> ( ::std::basic_istream<charT,traits> & is,
|
|
quaternion<T> & q)
|
|
{
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
#else
|
|
const ::std::ctype<charT> & ct = ::std::use_facet< ::std::ctype<charT> >(is.getloc());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
T a = T();
|
|
T b = T();
|
|
T c = T();
|
|
T d = T();
|
|
|
|
::std::complex<T> u = ::std::complex<T>();
|
|
::std::complex<T> v = ::std::complex<T>();
|
|
|
|
charT ch = charT();
|
|
char cc;
|
|
|
|
is >> ch; // get the first lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d)), ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,))
|
|
{
|
|
is >> ch; // get the second lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "((", possible: ((a)), ((a),c), ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,))
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> u; // we extract the first and second components
|
|
a = u.real();
|
|
b = u.imag();
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the next lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: ((a)) or ((a,b))
|
|
{
|
|
q = quaternion<T>(a,b);
|
|
}
|
|
else if (cc == ',') // read "((a)," or "((a,b),", possible: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)), ((a,b,),(c,d,))
|
|
{
|
|
is >> v; // we extract the third and fourth components
|
|
c = v.real();
|
|
d = v.imag();
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the last lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: ((a),c), ((a),(c)), ((a),(c,d)), ((a,b),c), ((a,b),(c)) or ((a,b,),(c,d,))
|
|
{
|
|
q = quaternion<T>(a,b,c,d);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "(a", possible: (a), (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d))
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> a; // we extract the first component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the third lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (a)
|
|
{
|
|
q = quaternion<T>(a);
|
|
}
|
|
else if (cc == ',') // read "(a,", possible: (a,b), (a,b,c), (a,b,c,d), (a,(c)), (a,(c,d))
|
|
{
|
|
is >> ch; // get the fourth lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == '(') // read "(a,(", possible: (a,(c)), (a,(c,d))
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> v; // we extract the third and fourth component
|
|
|
|
c = v.real();
|
|
d = v.imag();
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the ninth lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (a,(c)) or (a,(c,d))
|
|
{
|
|
q = quaternion<T>(a,b,c,d);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // read "(a,b", possible: (a,b), (a,b,c), (a,b,c,d)
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> b; // we extract the second component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the fifth lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (a,b)
|
|
{
|
|
q = quaternion<T>(a,b);
|
|
}
|
|
else if (cc == ',') // read "(a,b,", possible: (a,b,c), (a,b,c,d)
|
|
{
|
|
is >> c; // we extract the third component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the seventh lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (a,b,c)
|
|
{
|
|
q = quaternion<T>(a,b,c);
|
|
}
|
|
else if (cc == ',') // read "(a,b,c,", possible: (a,b,c,d)
|
|
{
|
|
is >> d; // we extract the fourth component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
is >> ch; // get the ninth lexeme
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
cc = ch;
|
|
#else
|
|
cc = ct.narrow(ch, char());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
|
|
if (cc == ')') // format: (a,b,c,d)
|
|
{
|
|
q = quaternion<T>(a,b,c,d);
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // error
|
|
{
|
|
is.setstate(::std::ios_base::failbit);
|
|
}
|
|
}
|
|
}
|
|
else // format: a
|
|
{
|
|
is.putback(ch);
|
|
|
|
is >> a; // we extract the first component
|
|
|
|
if (!is.good()) goto finish;
|
|
|
|
q = quaternion<T>(a);
|
|
}
|
|
|
|
finish:
|
|
return(is);
|
|
}
|
|
|
|
|
|
template<typename T, typename charT, class traits>
|
|
::std::basic_ostream<charT,traits> & operator << ( ::std::basic_ostream<charT,traits> & os,
|
|
quaternion<T> const & q)
|
|
{
|
|
::std::basic_ostringstream<charT,traits> s;
|
|
|
|
s.flags(os.flags());
|
|
#ifdef BOOST_NO_STD_LOCALE
|
|
#else
|
|
s.imbue(os.getloc());
|
|
#endif /* BOOST_NO_STD_LOCALE */
|
|
s.precision(os.precision());
|
|
|
|
s << '(' << q.R_component_1() << ','
|
|
<< q.R_component_2() << ','
|
|
<< q.R_component_3() << ','
|
|
<< q.R_component_4() << ')';
|
|
|
|
return os << s.str();
|
|
}
|
|
|
|
|
|
// values
|
|
|
|
template<typename T>
|
|
inline T real(quaternion<T> const & q)
|
|
{
|
|
return(q.real());
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> unreal(quaternion<T> const & q)
|
|
{
|
|
return(q.unreal());
|
|
}
|
|
|
|
|
|
#define BOOST_QUATERNION_VALARRAY_LOADER \
|
|
using ::std::valarray; \
|
|
\
|
|
valarray<T> temp(4); \
|
|
\
|
|
temp[0] = q.R_component_1(); \
|
|
temp[1] = q.R_component_2(); \
|
|
temp[2] = q.R_component_3(); \
|
|
temp[3] = q.R_component_4();
|
|
|
|
|
|
template<typename T>
|
|
inline T sup(quaternion<T> const & q)
|
|
{
|
|
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
|
using ::std::abs;
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
BOOST_QUATERNION_VALARRAY_LOADER
|
|
|
|
return((abs(temp).max)());
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline T l1(quaternion<T> const & q)
|
|
{
|
|
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
|
using ::std::abs;
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
BOOST_QUATERNION_VALARRAY_LOADER
|
|
|
|
return(abs(temp).sum());
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline T abs(quaternion<T> const & q)
|
|
{
|
|
#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP
|
|
using ::std::abs;
|
|
#endif /* BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP */
|
|
|
|
using ::std::sqrt;
|
|
|
|
BOOST_QUATERNION_VALARRAY_LOADER
|
|
|
|
T maxim = (abs(temp).max)(); // overflow protection
|
|
|
|
if (maxim == static_cast<T>(0))
|
|
{
|
|
return(maxim);
|
|
}
|
|
else
|
|
{
|
|
T mixam = static_cast<T>(1)/maxim; // prefer multiplications over divisions
|
|
|
|
temp *= mixam;
|
|
|
|
temp *= temp;
|
|
|
|
return(maxim*sqrt(temp.sum()));
|
|
}
|
|
|
|
//return(sqrt(norm(q)));
|
|
}
|
|
|
|
|
|
#undef BOOST_QUATERNION_VALARRAY_LOADER
|
|
|
|
|
|
// Note: This is the Cayley norm, not the Euclidian norm...
|
|
|
|
template<typename T>
|
|
inline T norm(quaternion<T>const & q)
|
|
{
|
|
return(real(q*conj(q)));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> conj(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 quaternion<T> spherical( T const & rho,
|
|
T const & theta,
|
|
T const & phi1,
|
|
T const & phi2)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
//T a = cos(theta)*cos(phi1)*cos(phi2);
|
|
//T b = sin(theta)*cos(phi1)*cos(phi2);
|
|
//T c = sin(phi1)*cos(phi2);
|
|
//T d = sin(phi2);
|
|
|
|
T courrant = static_cast<T>(1);
|
|
|
|
T d = sin(phi2);
|
|
|
|
courrant *= cos(phi2);
|
|
|
|
T c = sin(phi1)*courrant;
|
|
|
|
courrant *= cos(phi1);
|
|
|
|
T b = sin(theta)*courrant;
|
|
T a = cos(theta)*courrant;
|
|
|
|
return(rho*quaternion<T>(a,b,c,d));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> semipolar( T const & rho,
|
|
T const & alpha,
|
|
T const & theta1,
|
|
T const & theta2)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
T a = cos(alpha)*cos(theta1);
|
|
T b = cos(alpha)*sin(theta1);
|
|
T c = sin(alpha)*cos(theta2);
|
|
T d = sin(alpha)*sin(theta2);
|
|
|
|
return(rho*quaternion<T>(a,b,c,d));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> multipolar( T const & rho1,
|
|
T const & theta1,
|
|
T const & rho2,
|
|
T const & theta2)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
T a = rho1*cos(theta1);
|
|
T b = rho1*sin(theta1);
|
|
T c = rho2*cos(theta2);
|
|
T d = rho2*sin(theta2);
|
|
|
|
return(quaternion<T>(a,b,c,d));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> cylindrospherical( T const & t,
|
|
T const & radius,
|
|
T const & longitude,
|
|
T const & latitude)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
|
|
|
|
T b = radius*cos(longitude)*cos(latitude);
|
|
T c = radius*sin(longitude)*cos(latitude);
|
|
T d = radius*sin(latitude);
|
|
|
|
return(quaternion<T>(t,b,c,d));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> cylindrical(T const & r,
|
|
T const & angle,
|
|
T const & h1,
|
|
T const & h2)
|
|
{
|
|
using ::std::cos;
|
|
using ::std::sin;
|
|
|
|
T a = r*cos(angle);
|
|
T b = r*sin(angle);
|
|
|
|
return(quaternion<T>(a,b,h1,h2));
|
|
}
|
|
|
|
|
|
// transcendentals
|
|
// (please see the documentation)
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> exp(quaternion<T> const & q)
|
|
{
|
|
using ::std::exp;
|
|
using ::std::cos;
|
|
|
|
using ::boost::math::sinc_pi;
|
|
|
|
T u = exp(real(q));
|
|
|
|
T z = abs(unreal(q));
|
|
|
|
T w = sinc_pi(z);
|
|
|
|
return(u*quaternion<T>(cos(z),
|
|
w*q.R_component_2(), w*q.R_component_3(),
|
|
w*q.R_component_4()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> cos(quaternion<T> const & q)
|
|
{
|
|
using ::std::sin;
|
|
using ::std::cos;
|
|
using ::std::cosh;
|
|
|
|
using ::boost::math::sinhc_pi;
|
|
|
|
T z = abs(unreal(q));
|
|
|
|
T w = -sin(q.real())*sinhc_pi(z);
|
|
|
|
return(quaternion<T>(cos(q.real())*cosh(z),
|
|
w*q.R_component_2(), w*q.R_component_3(),
|
|
w*q.R_component_4()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> sin(quaternion<T> const & q)
|
|
{
|
|
using ::std::sin;
|
|
using ::std::cos;
|
|
using ::std::cosh;
|
|
|
|
using ::boost::math::sinhc_pi;
|
|
|
|
T z = abs(unreal(q));
|
|
|
|
T w = +cos(q.real())*sinhc_pi(z);
|
|
|
|
return(quaternion<T>(sin(q.real())*cosh(z),
|
|
w*q.R_component_2(), w*q.R_component_3(),
|
|
w*q.R_component_4()));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> tan(quaternion<T> const & q)
|
|
{
|
|
return(sin(q)/cos(q));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> cosh(quaternion<T> const & q)
|
|
{
|
|
return((exp(+q)+exp(-q))/static_cast<T>(2));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> sinh(quaternion<T> const & q)
|
|
{
|
|
return((exp(+q)-exp(-q))/static_cast<T>(2));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
inline quaternion<T> tanh(quaternion<T> const & q)
|
|
{
|
|
return(sinh(q)/cosh(q));
|
|
}
|
|
|
|
|
|
template<typename T>
|
|
quaternion<T> pow(quaternion<T> const & q,
|
|
int n)
|
|
{
|
|
if (n > 1)
|
|
{
|
|
int m = n>>1;
|
|
|
|
quaternion<T> result = pow(q, m);
|
|
|
|
result *= result;
|
|
|
|
if (n != (m<<1))
|
|
{
|
|
result *= q; // n odd
|
|
}
|
|
|
|
return(result);
|
|
}
|
|
else if (n == 1)
|
|
{
|
|
return(q);
|
|
}
|
|
else if (n == 0)
|
|
{
|
|
return(quaternion<T>(static_cast<T>(1)));
|
|
}
|
|
else /* n < 0 */
|
|
{
|
|
return(pow(quaternion<T>(static_cast<T>(1))/q,-n));
|
|
}
|
|
}
|
|
|
|
|
|
// helper templates for converting copy constructors (definition)
|
|
|
|
namespace detail
|
|
{
|
|
|
|
template< typename T,
|
|
typename U
|
|
>
|
|
quaternion<T> quaternion_type_converter(quaternion<U> const & rhs)
|
|
{
|
|
return(quaternion<T>( static_cast<T>(rhs.R_component_1()),
|
|
static_cast<T>(rhs.R_component_2()),
|
|
static_cast<T>(rhs.R_component_3()),
|
|
static_cast<T>(rhs.R_component_4())));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* BOOST_QUATERNION_HPP */
|