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Sprout/sprout/math/quaternion.hpp
bolero-MURAKAMI 7af7bbee05 add quaternion using decl
2016-01-25 12:20:54 +09:00

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/*=============================================================================
Copyright (c) 2011-2015 Bolero MURAKAMI
https://github.com/bolero-MURAKAMI/Sprout
Distributed under the sprout Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.sprout.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_MATH_QUATERNION_HPP
#define SPROUT_MATH_QUATERNION_HPP
#include <iosfwd>
#include <sstream>
#include <locale>
#include <sprout/config.hpp>
#include <sprout/math/abs.hpp>
#include <sprout/math/cos.hpp>
#include <sprout/math/sin.hpp>
#include <sprout/math/cosh.hpp>
#include <sprout/math/exp.hpp>
#include <sprout/math/abs.hpp>
//#include <sprout/math/sinc.hpp>
//#include <sprout/math/sinhc.hpp>
#include <sprout/complex/complex.hpp>
#include <sprout/range/algorithm/max_element.hpp>
#include <sprout/range/numeric/accumulate.hpp>
namespace sprout {
namespace math {
namespace detail {
template<typename T>
class abs_less {
public:
SPROUT_CONSTEXPR T
operator()(T const& lhs, T const& rhs) const {
return sprout::math::abs(lhs) < sprout::math::abs(rhs);
}
};
template<typename T>
class abs_plus {
public:
SPROUT_CONSTEXPR T
operator()(T const& lhs, T const& rhs) const {
return sprout::math::abs(lhs) + sprout::math::abs(rhs);
}
};
template<typename T, std::size_t N>
SPROUT_CONSTEXPR T
abs_max(sprout::array<T, N> const& c) {
return sprout::math::abs(*sprout::range::max_element(c, sprout::math::detail::abs_less<T>()));
}
template<typename T, std::size_t N>
SPROUT_CONSTEXPR T
sum(sprout::array<T, N> const& c) {
return sprout::range::accumulate(c, static_cast<T>(0));
}
template<typename T, std::size_t N>
SPROUT_CONSTEXPR T
abs_sum(sprout::array<T, N> const& c) {
return sprout::range::accumulate(c, static_cast<T>(0), sprout::math::detail::abs_plus<T>());
}
template<typename T>
SPROUT_CONSTEXPR sprout::array<T, 2>
mul(sprout::array<T, 2> const& l, T const& r) {
return sprout::array<T, 2>{{
l[0] * r,
l[1] * r,
}};
}
template<typename T>
SPROUT_CONSTEXPR sprout::array<T, 2>
mul(sprout::array<T, 2> const& l, sprout::array<T, 2> const& r) {
return sprout::array<T, 2>{{
l[0] * r[0],
l[1] * r[1],
}};
}
template<typename T>
SPROUT_CONSTEXPR sprout::array<T, 4>
mul(sprout::array<T, 4> const& l, T const& r) {
return sprout::array<T, 4>{{
l[0] * r,
l[1] * r,
l[2] * r,
l[3] * r
}};
}
template<typename T>
SPROUT_CONSTEXPR sprout::array<T, 4>
mul(sprout::array<T, 4> const& l, sprout::array<T, 4> const& r) {
return sprout::array<T, 4>{{
l[0] * r[0],
l[1] * r[1],
l[2] * r[2],
l[3] * r[3]
}};
}
} // namespace detail
#define SPROUT_QUATERNION_ACCESSOR_GENERATOR(type) \
SPROUT_CONSTEXPR type real() const { \
return (a); \
} \
SPROUT_CONSTEXPR quaternion<type> unreal() const { \
return (quaternion<type>(static_cast<type>(0), b, c, d)); \
} \
SPROUT_CONSTEXPR type R_component_1() const { \
return (a); \
} \
SPROUT_CONSTEXPR type R_component_2() const { \
return (b); \
} \
SPROUT_CONSTEXPR type R_component_3() const { \
return (c); \
} \
SPROUT_CONSTEXPR type R_component_4() const { \
return (d); \
} \
SPROUT_CONSTEXPR sprout::complex<type> C_component_1() const { \
return sprout::complex<type>(a, b); \
} \
SPROUT_CONSTEXPR sprout::complex<type> C_component_2() const { \
return sprout::complex<type>(c, d); \
}
#define SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(type) \
template<typename X> \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(quaternion<X> const& a_affecter) { \
a = static_cast<type>(a_affecter.R_component_1()); \
b = static_cast<type>(a_affecter.R_component_2()); \
c = static_cast<type>(a_affecter.R_component_3()); \
d = static_cast<type>(a_affecter.R_component_4()); \
return *this; \
} \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(quaternion<type> const& a_affecter) { \
a = a_affecter.a; \
b = a_affecter.b; \
c = a_affecter.c; \
d = a_affecter.d; \
return *this; \
} \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(type const& a_affecter) { \
a = a_affecter; \
b = c = d = static_cast<type>(0); \
return *this; \
} \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator=(sprout::complex<type> const& a_affecter) { \
a = a_affecter.real(); \
b = a_affecter.imag(); \
c = d = static_cast<type>(0); \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(type) \
type a; \
type b; \
type c; \
type d;
//
// quaternion
//
template<typename T>
class quaternion {
public:
typedef T value_type;
protected:
SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(T)
public:
explicit SPROUT_CONSTEXPR quaternion(
T const& requested_a = T(),
T const& requested_b = T(),
T const& requested_c = T(),
T const& requested_d = T()
)
: a(requested_a)
, b(requested_b)
, c(requested_c)
, d(requested_d)
{}
explicit SPROUT_CONSTEXPR quaternion(
sprout::complex<T> const& z0,
sprout::complex<T> const& z1 = sprout::complex<T>()
)
: a(z0.real())
, b(z0.imag())
, c(z1.real())
, d(z1.imag())
{}
template<typename X>
explicit SPROUT_CONSTEXPR quaternion(quaternion<X> const& a_recopier)
: a(static_cast<T>(a_recopier.R_component_1()))
, b(static_cast<T>(a_recopier.R_component_2()))
, c(static_cast<T>(a_recopier.R_component_3()))
, d(static_cast<T>(a_recopier.R_component_4()))
{}
SPROUT_QUATERNION_ACCESSOR_GENERATOR(T)
SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(T)
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(T const& rhs) {
T at = a + rhs;
a = at;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(sprout::complex<T> const& rhs) {
T at = a + rhs.real();
T bt = b + rhs.imag();
a = at;
b = bt;
return *this;
}
template<typename X>
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator+=(quaternion<X> const& rhs) {
T at = a + static_cast<T>(rhs.R_component_1());
T bt = b + static_cast<T>(rhs.R_component_2());
T ct = c + static_cast<T>(rhs.R_component_3());
T dt = d + static_cast<T>(rhs.R_component_4());
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(T const& rhs) {
T at = a - rhs;
a = at;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(sprout::complex<T> const& rhs) {
T at = a - rhs.real();
T bt = b - rhs.imag();
a = at;
b = bt;
return *this;
}
template<typename X>
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator-=(quaternion<X> const& rhs) {
T at = a - static_cast<T>(rhs.R_component_1());
T bt = b - static_cast<T>(rhs.R_component_2());
T ct = c - static_cast<T>(rhs.R_component_3());
T dt = d - static_cast<T>(rhs.R_component_4());
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(T const& rhs) {
T at = a * rhs;
T bt = b * rhs;
T ct = c * rhs;
T dt = d * rhs;
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(sprout::complex<T> const& rhs) {
T ar = rhs.real();
T br = rhs.imag();
T at = +a * ar - b * br;
T bt = +a * br + b * ar;
T ct = +c * ar + d * br;
T dt = -c * br + d * ar;
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
template<typename X>
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator*=(quaternion<X> const& rhs) {
T ar = static_cast<T>(rhs.R_component_1());
T br = static_cast<T>(rhs.R_component_2());
T cr = static_cast<T>(rhs.R_component_3());
T dr = static_cast<T>(rhs.R_component_4());
T at = +a * ar - b * br - c * cr - d * dr;
T bt = +a * br + b * ar + c * dr - d * cr;
T ct = +a * cr - b * dr + c * ar + d * br;
T dt = +a * dr + b * cr - c * br + d * ar;
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(T const& rhs) {
T at = a / rhs;
T bt = b / rhs;
T ct = c / rhs;
T dt = d / rhs;
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(sprout::complex<T> const& rhs) {
T ar = rhs.real();
T br = rhs.imag();
T denominator = ar * ar + br * br;
T at =(+a * ar + b * br) / denominator;
T bt =(-a * br + b * ar) / denominator;
T ct =(+c * ar - d * br) / denominator;
T dt =(+c * br + d * ar) / denominator;
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
template<typename X>
SPROUT_CXX14_CONSTEXPR quaternion<T>& operator/=(quaternion<X> const& rhs) {
T ar = static_cast<T>(rhs.R_component_1());
T br = static_cast<T>(rhs.R_component_2());
T cr = static_cast<T>(rhs.R_component_3());
T dr = static_cast<T>(rhs.R_component_4());
T denominator = ar * ar + br * br + cr * cr + dr * dr;
T at =(+a * ar + b * br + c * cr + d * dr) / denominator;
T bt =(-a * br + b * ar - c * dr + d * cr) / denominator;
T ct =(-a * cr + b * dr + c * ar - d * br) / denominator;
T dt =(-a * dr - b * cr + c * br + d * ar) / denominator;
a = at;
b = bt;
c = ct;
d = dt;
return *this;
}
};
template<>
class quaternion<float>;
template<>
class quaternion<double>;
template<>
class quaternion<long double>;
#define SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(type) \
explicit SPROUT_CONSTEXPR quaternion( \
type const& requested_a = static_cast<type>(0), \
type const& requested_b = static_cast<type>(0), \
type const& requested_c = static_cast<type>(0), \
type const& requested_d = static_cast<type>(0) \
) \
: a(requested_a) \
, b(requested_b) \
, c(requested_c) \
, d(requested_d) \
{} \
explicit SPROUT_CONSTEXPR quaternion( \
sprout::complex<type> const& z0, \
sprout::complex<type> const& z1 = sprout::complex<type>() \
) \
: a(z0.real()) \
, b(z0.imag()) \
, c(z1.real()) \
, d(z1.imag()) \
{}
#define SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(type const& rhs) { \
a += rhs; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(sprout::complex<type> const& rhs) { \
a += rhs.real(); \
b += rhs.imag(); \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3(type) \
template<typename X> \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator+=(quaternion<X> const& rhs) { \
a += static_cast<type>(rhs.R_component_1()); \
b += static_cast<type>(rhs.R_component_2()); \
c += static_cast<type>(rhs.R_component_3()); \
d += static_cast<type>(rhs.R_component_4()); \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(type const& rhs) { \
a -= rhs; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(sprout::complex<type> const& rhs) { \
a -= rhs.real(); \
b -= rhs.imag(); \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3(type) \
template<typename X> \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator-=(quaternion<X> const& rhs) { \
a -= static_cast<type>(rhs.R_component_1()); \
b -= static_cast<type>(rhs.R_component_2()); \
c -= static_cast<type>(rhs.R_component_3()); \
d -= static_cast<type>(rhs.R_component_4()); \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(type const& rhs) { \
a *= rhs; \
b *= rhs; \
c *= rhs; \
d *= rhs; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(sprout::complex<type> const& rhs) { \
type ar = rhs.real(); \
type br = rhs.imag(); \
type at = +a * ar - b * br; \
type bt = +a * br + b * ar; \
type ct = +c * ar + d * br; \
type dt = -c * br + d * ar; \
a = at; \
b = bt; \
c = ct; \
d = dt; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3(type) \
template<typename X> \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator*=(quaternion<X> const& rhs) { \
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; \
}
#define SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(type const& rhs) { \
a /= rhs; \
b /= rhs; \
c /= rhs; \
d /= rhs; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(sprout::complex<type> const& rhs) { \
sprout::array<type, 2> tr{{ \
rhs.real(), \
rhs.imag() \
}}; \
type mixam = static_cast<type>(1) / sprout::math::detail::abs_max(tr); \
tr = sprout::math::detail::mul(tr, mixam); \
sprout::array<type, 4> tt{{ \
+a * tr[0] + b * tr[1], \
-a * tr[1] + b * tr[0], \
+c * tr[0] - d * tr[1], \
+c * tr[1] + d * tr[0] \
}}; \
tr = sprout::math::detail::mul(tr, tr); \
tt = sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr)); \
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3(type) \
template<typename X> \
SPROUT_CXX14_CONSTEXPR quaternion<type>& operator/=(quaternion<X> const& rhs) { \
sprout::array<type, 4> tr{{ \
static_cast<type>(rhs.R_component_1()), \
static_cast<type>(rhs.R_component_2()), \
static_cast<type>(rhs.R_component_3()), \
static_cast<type>(rhs.R_component_4()) \
}}; \
type mixam = static_cast<type>(1) / sprout::math::detail::abs_max(tr); \
tr = sprout::math::detail::mul(tr, mixam); \
sprout::array<type, 4> tt{{ \
+a * tr[0] + b * tr[1] + c * tr[2] + d * tr[3], \
-a * tr[1] + b * tr[0] - c * tr[3] + d * tr[2], \
-a * tr[2] + b * tr[3] + c * tr[0] - d * tr[1], \
-a * tr[3] - b * tr[2] + c * tr[1] + d * tr[0] \
}}; \
tr = sprout::math::detail::mul(tr, tr); \
tt = sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr)); \
a = tt[0]; \
b = tt[1]; \
c = tt[2]; \
d = tt[3]; \
return *this; \
}
#define SPROUT_QUATERNION_MEMBER_ADD_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1(type) \
SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2(type) \
SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3(type)
#define SPROUT_QUATERNION_MEMBER_SUB_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1(type) \
SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2(type) \
SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3(type)
#define SPROUT_QUATERNION_MEMBER_MUL_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1(type) \
SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2(type) \
SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3(type)
#define SPROUT_QUATERNION_MEMBER_DIV_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1(type) \
SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2(type) \
SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3(type)
#define SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_ADD_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_SUB_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_MUL_GENERATOR(type) \
SPROUT_QUATERNION_MEMBER_DIV_GENERATOR(type)
template<>
class quaternion<float> {
public:
typedef float value_type;
protected:
SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(float)
public:
SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(float)
explicit SPROUT_CONSTEXPR quaternion(quaternion<double> const& a_recopier);
explicit SPROUT_CONSTEXPR quaternion(quaternion<long double> const& a_recopier);
SPROUT_QUATERNION_ACCESSOR_GENERATOR(float)
SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(float)
SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(float)
};
template<>
class quaternion<double> {
public:
typedef double value_type;
protected:
SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(double)
public:
SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(double)
explicit SPROUT_CONSTEXPR quaternion(quaternion<float> const& a_recopier);
explicit SPROUT_CONSTEXPR quaternion(quaternion<long double> const& a_recopier);
SPROUT_QUATERNION_ACCESSOR_GENERATOR(double)
SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(double)
SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(double)
};
template<>
class quaternion<long double> {
public:
typedef double value_type;
protected:
SPROUT_QUATERNION_MEMBER_DATA_GENERATOR(long double)
public:
SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR(long double)
explicit SPROUT_CONSTEXPR quaternion(quaternion<float> const& a_recopier);
explicit SPROUT_CONSTEXPR quaternion(quaternion<double> const& a_recopier);
SPROUT_QUATERNION_ACCESSOR_GENERATOR(long double)
SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR(long double)
SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR(long double)
};
SPROUT_CONSTEXPR sprout::math::quaternion<float>::quaternion(sprout::math::quaternion<double> const& a_recopier)
: a(static_cast<float>(a_recopier.R_component_1()))
, b(static_cast<float>(a_recopier.R_component_2()))
, c(static_cast<float>(a_recopier.R_component_3()))
, d(static_cast<float>(a_recopier.R_component_4()))
{}
SPROUT_CONSTEXPR sprout::math::quaternion<float>::quaternion(sprout::math::quaternion<long double> const& a_recopier)
: a(static_cast<float>(a_recopier.R_component_1()))
, b(static_cast<float>(a_recopier.R_component_2()))
, c(static_cast<float>(a_recopier.R_component_3()))
, d(static_cast<float>(a_recopier.R_component_4()))
{}
SPROUT_CONSTEXPR sprout::math::quaternion<double>::quaternion(sprout::math::quaternion<float> const& a_recopier)
: a(static_cast<double>(a_recopier.R_component_1()))
, b(static_cast<double>(a_recopier.R_component_2()))
, c(static_cast<double>(a_recopier.R_component_3()))
, d(static_cast<double>(a_recopier.R_component_4()))
{}
SPROUT_CONSTEXPR sprout::math::quaternion<double>::quaternion(sprout::math::quaternion<long double> const& a_recopier)
: a(static_cast<double>(a_recopier.R_component_1()))
, b(static_cast<double>(a_recopier.R_component_2()))
, c(static_cast<double>(a_recopier.R_component_3()))
, d(static_cast<double>(a_recopier.R_component_4()))
{}
SPROUT_CONSTEXPR sprout::math::quaternion<long double>::quaternion(sprout::math::quaternion<float> const& a_recopier)
: a(static_cast<long double>(a_recopier.R_component_1()))
, b(static_cast<long double>(a_recopier.R_component_2()))
, c(static_cast<long double>(a_recopier.R_component_3()))
, d(static_cast<long double>(a_recopier.R_component_4()))
{}
SPROUT_CONSTEXPR sprout::math::quaternion<long double>::quaternion(sprout::math::quaternion<double> const& a_recopier)
: a(static_cast<long double>(a_recopier.R_component_1()))
, b(static_cast<long double>(a_recopier.R_component_2()))
, c(static_cast<long double>(a_recopier.R_component_3()))
, d(static_cast<long double>(a_recopier.R_component_4()))
{}
#undef SPROUT_QUATERNION_MEMBER_ALGEBRAIC_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_ADD_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_SUB_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_MUL_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_DIV_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_1
#undef SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_2
#undef SPROUT_QUATERNION_MEMBER_ADD_GENERATOR_3
#undef SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_1
#undef SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_2
#undef SPROUT_QUATERNION_MEMBER_SUB_GENERATOR_3
#undef SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_1
#undef SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_2
#undef SPROUT_QUATERNION_MEMBER_MUL_GENERATOR_3
#undef SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_1
#undef SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_2
#undef SPROUT_QUATERNION_MEMBER_DIV_GENERATOR_3
#undef SPROUT_QUATERNION_CONSTRUCTOR_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_ASSIGNMENT_GENERATOR
#undef SPROUT_QUATERNION_MEMBER_DATA_GENERATOR
#undef SPROUT_QUATERNION_ACCESSOR_GENERATOR
//
// operator+
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs + rhs.R_component_1(),
rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() + rhs,
lhs.R_component_2(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.real() + rhs.R_component_1(),
lhs.imag() + rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() + rhs.real(),
lhs.R_component_2() + rhs.imag(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() + rhs.R_component_1(),
lhs.R_component_2() + rhs.R_component_2(),
lhs.R_component_3() + rhs.R_component_3(),
lhs.R_component_4() + rhs.R_component_4()
);
}
//
// operator-
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs - rhs.R_component_1(),
rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() - rhs,
lhs.R_component_2(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.real() - rhs.R_component_1(),
lhs.imag() - rhs.R_component_2(),
rhs.R_component_3(),
rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() - rhs.real(),
lhs.R_component_2() - rhs.imag(),
lhs.R_component_3(),
lhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() - rhs.R_component_1(),
lhs.R_component_2() - rhs.R_component_2(),
lhs.R_component_3() - rhs.R_component_3(),
lhs.R_component_4() - rhs.R_component_4()
);
}
//
// operator*
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs * rhs.R_component_1(),
lhs * rhs.R_component_2(),
lhs * rhs.R_component_3(),
lhs * rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() * rhs,
lhs.R_component_2() * rhs,
lhs.R_component_3() * rhs,
lhs.R_component_4() * rhs
);
}
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
mul_qc_impl(T const& a, T const& b, T const& c, T const& d, T const& ar, T const& br) {
return sprout::math::quaternion<T>(
+a * ar - b * br,
+a * br + b * ar,
+c * ar + d * br,
-c * br + d * ar
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::mul_qc_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
rhs.real(), rhs.imag()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::detail::mul_qc_impl(
rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4(),
lhs.real(), lhs.imag()
);
}
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
mul_qq_impl(T const& a, T const& b, T const& c, T const& d, T const& ar, T const& br, T const& cr, T const& dr) {
return sprout::math::quaternion<T>(
+a * ar - b * br - c * cr - d * dr,
+a * br + b * ar + c * dr - d * cr,
+a * cr - b * dr + c * ar + d * br,
+a * dr + b * cr - c * br + d * ar
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator*(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::mul_qq_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()
);
}
//
// operator/
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(T const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::quaternion<T>(
lhs / rhs.R_component_1(),
lhs / rhs.R_component_2(),
lhs / rhs.R_component_3(),
lhs / rhs.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::math::quaternion<T> const& lhs, T const& rhs) {
return sprout::math::quaternion<T>(
lhs.R_component_1() / rhs,
lhs.R_component_2() / rhs,
lhs.R_component_3() / rhs,
lhs.R_component_4() / rhs
);
}
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_4(sprout::array<T, 4> const& tt) {
return sprout::math::quaternion<T>(
tt[0], tt[1], tt[2], tt[3]
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_3(sprout::array<T, 4> const& tr, T const& mixam, sprout::array<T, 4> const& tt) {
return sprout::math::detail::div_qq_impl_3(
sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr))
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_2(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr, T const& mixam) {
return sprout::math::detail::div_qq_impl_3(
sprout::math::detail::mul(tr, tr), mixam,
sprout::array<T, 4>{{
+a * tr[0] + b * tr[1] + c * tr[2] + d * tr[3],
-a * tr[1] + b * tr[0] - c * tr[3] + d * tr[2],
-a * tr[2] + b * tr[3] + c * tr[0] - d * tr[1],
-a * tr[3] - b * tr[2] + c * tr[1] + d * tr[0]
}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl_1(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr, T const& mixam) {
return sprout::math::detail::div_qq_impl_2(
a, b, c, d, sprout::math::detail::mul(tr, mixam), mixam
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
div_qq_impl(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr) {
return sprout::math::detail::div_qq_impl_1(
a, b, c, d, tr,
static_cast<T>(1) / sprout::math::detail::abs_max(tr)
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::div_qq_impl(
lhs.real(), lhs.imag(), static_cast<T>(0), static_cast<T>(0),
sprout::array<T, 4>{{rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
return sprout::math::detail::div_qq_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
sprout::array<T, 4>{{rhs.real(), rhs.imag(), static_cast<T>(0), static_cast<T>(0)}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator/(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
return sprout::math::detail::div_qq_impl(
lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
sprout::array<T, 4>{{rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()}}
);
}
//
// operator+
// operator-
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator+(sprout::math::quaternion<T> const& q) {
return q;
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
operator-(sprout::math::quaternion<T> const& q) {
return sprout::math::quaternion<T>(-q.R_component_1(), -q.R_component_2(), -q.R_component_3(), -q.R_component_4());
}
//
// operator==
// operator!=
//
template<typename T>
inline SPROUT_CONSTEXPR bool
operator==(T const& lhs, sprout::math::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 SPROUT_CONSTEXPR bool
operator==(sprout::math::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 SPROUT_CONSTEXPR bool
operator==(sprout::complex<T> const& lhs, sprout::math::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 SPROUT_CONSTEXPR bool
operator==(sprout::math::quaternion<T> const& lhs, sprout::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 SPROUT_CONSTEXPR bool
operator==(sprout::math::quaternion<T> const& lhs, sprout::math::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 SPROUT_QUATERNION_NOT_EQUAL_GENERATOR \
{ \
return !(lhs == rhs); \
}
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(T const& lhs, sprout::math::quaternion<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::math::quaternion<T> const& lhs, T const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
template<typename T>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs)
SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
#undef SPROUT_QUATERNION_NOT_EQUAL_GENERATOR
//
// operator<<
// operator>>
//
template<typename T, typename Elem, typename Traits>
inline SPROUT_NON_CONSTEXPR std::basic_ostream<Elem, Traits>&
operator<<( std::basic_ostream<Elem, Traits>& lhs, sprout::math::quaternion<T> const& rhs) {
std::basic_ostringstream<Elem, Traits> s;
s.flags(lhs.flags());
s.imbue(lhs.getloc());
s.precision(lhs.precision());
s
<< '('
<< rhs.R_component_1() << ','
<< rhs.R_component_2() << ','
<< rhs.R_component_3() << ','
<< rhs.R_component_4()
<< ')'
;
return lhs << s.str();
}
template<typename T, typename Elem, typename Traits>
inline SPROUT_NON_CONSTEXPR std::basic_istream<Elem, Traits>&
operator>>(std::basic_istream<Elem, Traits>& lhs, sprout::math::quaternion<T>& rhs) {
std::ctype<Elem> const& ct = std::use_facet<std::ctype<Elem> >(lhs.getloc());
T a = T();
T b = T();
T c = T();
T d = T();
sprout::complex<T> u = sprout::complex<T>();
sprout::complex<T> v = sprout::complex<T>();
Elem ch = Elem();
char cc;
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == '(') {
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == '(') {
lhs.putback(ch);
lhs >> u;
a = u.real();
b = u.imag();
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a, b);
} else if (cc == ',') {
lhs >> v;
c = v.real();
d = v.imag();
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a, b, c, d);
} else {
lhs.setstate(std::ios_base::failbit);
}
} else {
lhs.setstate(std::ios_base::failbit);
}
} else {
lhs.putback(ch);
lhs >> a;
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a);
} else if (cc == ',') {
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == '(') {
lhs.putback(ch);
lhs >> v;
c = v.real();
d = v.imag();
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a, b, c, d);
} else {
lhs.setstate(std::ios_base::failbit);
}
} else {
lhs.putback(ch);
lhs >> b;
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a, b);
} else if (cc == ',') {
lhs >> c;
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a, b, c);
} else if (cc == ',') {
lhs >> d;
if (!lhs.good()) {
goto finish;
}
lhs >> ch;
if (!lhs.good()) {
goto finish;
}
cc = ct.narrow(ch, char());
if (cc == ')') {
rhs = sprout::math::quaternion<T>(a, b, c, d);
} else {
lhs.setstate(std::ios_base::failbit);
}
} else {
lhs.setstate(std::ios_base::failbit);
}
} else {
lhs.setstate(std::ios_base::failbit);
}
}
} else {
lhs.setstate(std::ios_base::failbit);
}
}
} else {
lhs.putback(ch);
lhs >> a;
if (!lhs.good()) {
goto finish;
}
rhs = sprout::math::quaternion<T>(a);
}
finish:
return lhs;
}
//
// real
// unreal
//
template<typename T>
inline SPROUT_CONSTEXPR T
real(sprout::math::quaternion<T> const& q) {
return q.real();
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
unreal(sprout::math::quaternion<T> const& q) {
return q.unreal();
}
//
// sup
// l1
//
template<typename T>
inline SPROUT_CONSTEXPR T
sup(sprout::math::quaternion<T> const& q) {
return sprout::math::detail::abs_max(
sprout::array<T, 4>{{
q.R_component_1(),
q.R_component_2(),
q.R_component_3(),
q.R_component_4()
}}
);
}
template<typename T>
inline SPROUT_CONSTEXPR T
l1(sprout::math::quaternion<T> const& q) {
return sprout::math::detail::abs_sum(
sprout::array<T, 4>{{
q.R_component_1(),
q.R_component_2(),
q.R_component_3(),
q.R_component_4()
}}
);
}
//
// abs
//
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR T
abs_q_impl_3(sprout::array<T, 4> const& temp, T const& maxim) {
return maxim * sprout::math::sqrt(sprout::math::detail::sum(sprout::math::detail::mul(temp, temp)));
}
template<typename T>
inline SPROUT_CONSTEXPR T
abs_q_impl_2(sprout::array<T, 4> const& temp, T const& maxim) {
return sprout::math::detail::abs_q_impl_3(
sprout::math::detail::mul(temp, maxim), maxim
);
}
template<typename T>
inline SPROUT_CONSTEXPR T
abs_q_impl_1(sprout::array<T, 4> const& temp, T const& maxim) {
return maxim == static_cast<T>(0) ? sprout::math::quaternion<T>(maxim)
: sprout::math::detail::abs_q_impl_2(
temp, static_cast<T>(1) / maxim
)
;
}
template<typename T>
inline SPROUT_CONSTEXPR T
abs_q_impl(sprout::array<T, 4> const& temp) {
return sprout::math::detail::abs_q_impl_1(
temp, sprout::math::detail::abs_max(temp)
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR T
abs(sprout::math::quaternion<T> const& q) {
return sprout::math::detail::abs_q_impl(
sprout::array<T, 4>{{
q.R_component_1(),
q.R_component_2(),
q.R_component_3(),
q.R_component_4()
}}
);
}
#undef SPROUT_QUATERNION_ARRAY_LOADER
//
// conj
// norm
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
conj(sprout::math::quaternion<T> const& q) {
return sprout::math::quaternion<T>(
+q.R_component_1(),
-q.R_component_2(),
-q.R_component_3(),
-q.R_component_4()
);
}
template<typename T>
inline SPROUT_CONSTEXPR T
norm(sprout::math::quaternion<T> const& q) {
return sprout::math::real(q * sprout::math::conj(q));
}
//
// spherical
// semipolar
// multipolar
// cylindrospherical
// cylindrical
//
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
spherical_impl(T const& rho, T const& theta, T const& phi1, T const& phi2, T const& p1, T const& p2) {
return rho * sprout::math::quaternion<T>(
sprout::math::cos(theta) * (p2 * p1),
sprout::math::sin(theta) * (p2 * p1),
sprout::math::sin(phi1) * p2,
sprout::math::sin(phi2)
);
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
spherical(T const& rho, T const& theta, T const& phi1, T const& phi2) {
return sprout::math::detail::spherical_impl(
rho, theta, phi1, phi2,
sprout::math::cos(phi1), sprout::math::cos(phi2)
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
semipolar(T const& rho, T const& alpha, T const& theta1, T const& theta2) {
return rho * sprout::math::quaternion<T>(
sprout::math::cos(alpha) * sprout::math::cos(theta1),
sprout::math::cos(alpha) * sprout::math::sin(theta1),
sprout::math::sin(alpha) * sprout::math::cos(theta2),
sprout::math::sin(alpha) * sprout::math::sin(theta2)
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
multipolar(T const& rho1, T const& theta1, T const& rho2, T const& theta2) {
return sprout::math::quaternion<T>(
rho1 * sprout::math::cos(theta1),
rho1 * sprout::math::sin(theta1),
rho2 * sprout::math::cos(theta2),
rho2 * sprout::math::sin(theta2)
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
cylindrospherical(T const& t, T const& radius, T const& longitude, T const& latitude) {
return sprout::math::quaternion<T>(
t,
radius * sprout::math::cos(longitude) * sprout::math::cos(latitude),
radius * sprout::math::sin(longitude) * sprout::math::cos(latitude),
radius * sprout::math::sin(latitude)
);
}
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
cylindrical(T const& r, T const& angle, T const& h1, T const& h2) {
return sprout::math::quaternion<T>(
r * sprout::math::cos(angle),
r * sprout::math::sin(angle),
h1,
h2
);
}
//
// exp
//
// !!!
// namespace detail {
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// exp_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
// return sprout::math::exp(sprout::math::real(q)) * sprout::math::quaternion<T>(
// sprout::math::cos(z),
// w * q.R_component_2(),
// w * q.R_component_3(),
// w * q.R_component_4()
// );
// }
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// exp_impl(sprout::math::quaternion<T> const& q, T const& z) {
// return sprout::math::detail::exp_impl_1(
// q, z,
// sprout::math::sinc_pi(z)
// );
// }
// } // namespace detail
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// exp(sprout::math::quaternion<T> const& q) {
// return sprout::math::detail::exp_impl(
// q,
// sprout::math::abs(sprout::math::unreal(q))
// );
// }
//
// cos
// sin
// tan
//
// !!!
// namespace detail {
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// cos_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
// return sprout::math::quaternion<T>(
// sprout::math::cos(q.real()) * sprout::math::cosh(z),
// w * q.R_component_2(),
// w * q.R_component_3(),
// w * q.R_component_4()
// );
// }
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// cos_impl(sprout::math::quaternion<T> const& q, T const& z) {
// return sprout::math::detail::cos_impl_1(
// q, z,
// -sprout::math::sin(q.real()) * sprout::math::sinhc_pi(z)
// );
// }
// } // namespace detail
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// cos(sprout::math::quaternion<T> const& q) {
// return sprout::math::detail::cos_impl(
// q,
// sprout::math::abs(sprout::math::unreal(q))
// );
// }
// namespace detail {
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// sin_impl_1(sprout::math::quaternion<T> const& q, T const& z, T const& w) {
// return sprout::math::quaternion<T>(
// sprout::math::sin(q.real()) * sprout::math::cosh(z),
// w * q.R_component_2(),
// w * q.R_component_3(),
// w * q.R_component_4()
// );
// }
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// sin_impl(sprout::math::quaternion<T> const& q, T const& z) {
// return sprout::math::detail::sin_impl_1(
// q, z,
// +sprout::math::cos(q.real()) * sprout::math::sinhc_pi(z)
// );
// }
// } // namespace detail
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// sin(sprout::math::quaternion<T> const& q) {
// return sprout::math::detail::sin_impl(
// q,
// sprout::math::abs(sprout::math::unreal(q))
// );
// }
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// tan(sprout::math::quaternion<T> const& q) {
// return sprout::math::sin(q) / sprout::math::cos(q);
// }
//
// cosh
// sinh
// tanh
//
// !!!
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// cosh(sprout::math::quaternion<T> const& q) {
// return (sprout::math::exp(+q) + sprout::math::exp(-q)) / static_cast<T>(2);
// }
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// sinh(sprout::math::quaternion<T> const& q) {
// return (sprout::math::exp(+q) - sprout::math::exp(-q)) / static_cast<T>(2);
// }
// template<typename T>
// inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
// tanh(sprout::math::quaternion<T> const& q) {
// return sprout::math::sinh(q) / sprout::math::cosh(q);
// }
//
// pow
//
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
pow_q_impl(sprout::math::quaternion<T> const& q, int n, int m, sprout::math::quaternion<T> const& result) {
return n != m << 1 ? result * result * q
: result * result
;
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
pow(sprout::math::quaternion<T> const& q, int n) {
return n > 1 ? sprout::math::detail::pow_q_impl(
q, n, n >> 1, sprout::math::pow(q, n >> 1)
)
: n == 1 ? q
: n == 0 ? sprout::math::quaternion<T>(static_cast<T>(1))
: sprout::math::pow(sprout::math::quaternion<T>(static_cast<T>(1)) / q, -n)
;
}
} // namespace math
using sprout::math::quaternion;
using sprout::math::real;
using sprout::math::unreal;
using sprout::math::sup;
using sprout::math::l1;
using sprout::math::abs;
using sprout::math::conj;
using sprout::math::norm;
using sprout::math::spherical;
using sprout::math::semipolar;
using sprout::math::multipolar;
using sprout::math::cylindrospherical;
using sprout::math::cylindrical;
// using sprout::math::exp;
// using sprout::math::cos;
// using sprout::math::sin;
// using sprout::math::tan;
// using sprout::math::cosh;
// using sprout::math::sinh;
// using sprout::math::tanh;
using sprout::math::pow;
} // namespace sprout
#endif // #ifndef SPROUT_MATH_QUATERNION_HPP
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