mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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382 lines
14 KiB
C++
382 lines
14 KiB
C++
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/*=============================================================================
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Copyright (c) 2011-2016 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_QUATERNION_ARITHMETIC_OPERATORS_HPP
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#define SPROUT_MATH_QUATERNION_ARITHMETIC_OPERATORS_HPP
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#include <sprout/config.hpp>
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#include <sprout/math/quaternion/quaternion.hpp>
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namespace sprout {
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namespace math {
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//
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// operator+
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator+(T const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs + rhs.R_component_1(),
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rhs.R_component_2(),
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rhs.R_component_3(),
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rhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator+(sprout::math::quaternion<T> const& lhs, T const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() + rhs,
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lhs.R_component_2(),
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lhs.R_component_3(),
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lhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator+(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.real() + rhs.R_component_1(),
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lhs.imag() + rhs.R_component_2(),
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rhs.R_component_3(),
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rhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator+(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() + rhs.real(),
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lhs.R_component_2() + rhs.imag(),
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lhs.R_component_3(),
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lhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator+(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() + rhs.R_component_1(),
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lhs.R_component_2() + rhs.R_component_2(),
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lhs.R_component_3() + rhs.R_component_3(),
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lhs.R_component_4() + rhs.R_component_4()
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);
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}
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//
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// operator-
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator-(T const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs - rhs.R_component_1(),
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rhs.R_component_2(),
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rhs.R_component_3(),
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rhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator-(sprout::math::quaternion<T> const& lhs, T const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() - rhs,
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lhs.R_component_2(),
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lhs.R_component_3(),
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lhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator-(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.real() - rhs.R_component_1(),
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lhs.imag() - rhs.R_component_2(),
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rhs.R_component_3(),
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rhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator-(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() - rhs.real(),
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lhs.R_component_2() - rhs.imag(),
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lhs.R_component_3(),
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lhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator-(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() - rhs.R_component_1(),
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lhs.R_component_2() - rhs.R_component_2(),
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lhs.R_component_3() - rhs.R_component_3(),
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lhs.R_component_4() - rhs.R_component_4()
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);
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}
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//
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// operator*
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator*(T const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs * rhs.R_component_1(),
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lhs * rhs.R_component_2(),
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lhs * rhs.R_component_3(),
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lhs * rhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator*(sprout::math::quaternion<T> const& lhs, T const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() * rhs,
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lhs.R_component_2() * rhs,
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lhs.R_component_3() * rhs,
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lhs.R_component_4() * rhs
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);
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}
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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mul_qc_impl(T const& a, T const& b, T const& c, T const& d, T const& ar, T const& br) {
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return sprout::math::quaternion<T>(
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+a * ar - b * br,
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+a * br + b * ar,
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+c * ar + d * br,
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-c * br + d * ar
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);
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}
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} // namespace detail
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator*(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::detail::mul_qc_impl(
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lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
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rhs.real(), rhs.imag()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator*(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
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return sprout::math::detail::mul_qc_impl(
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rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4(),
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lhs.real(), lhs.imag()
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);
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}
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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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) {
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return sprout::math::quaternion<T>(
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+a * ar - b * br - c * cr - d * dr,
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+a * br + b * ar + c * dr - d * cr,
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+a * cr - b * dr + c * ar + d * br,
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+a * dr + b * cr - c * br + d * ar
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);
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}
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} // namespace detail
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator*(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::detail::mul_qq_impl(
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lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
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rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()
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);
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}
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//
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// operator/
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator/(T const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::quaternion<T>(
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lhs / rhs.R_component_1(),
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lhs / rhs.R_component_2(),
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lhs / rhs.R_component_3(),
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lhs / rhs.R_component_4()
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator/(sprout::math::quaternion<T> const& lhs, T const& rhs) {
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return sprout::math::quaternion<T>(
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lhs.R_component_1() / rhs,
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lhs.R_component_2() / rhs,
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lhs.R_component_3() / rhs,
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lhs.R_component_4() / rhs
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);
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}
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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div_qq_impl_4(sprout::array<T, 4> const& tt) {
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return sprout::math::quaternion<T>(
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tt[0], tt[1], tt[2], tt[3]
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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div_qq_impl_3(sprout::array<T, 4> const& tr, T const& mixam, sprout::array<T, 4> const& tt) {
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return sprout::math::detail::div_qq_impl_3(
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sprout::math::detail::mul(tt, mixam / sprout::math::detail::sum(tr))
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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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) {
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return sprout::math::detail::div_qq_impl_3(
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sprout::math::detail::mul(tr, tr), mixam,
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sprout::array<T, 4>{{
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+a * tr[0] + b * tr[1] + c * tr[2] + d * tr[3],
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-a * tr[1] + b * tr[0] - c * tr[3] + d * tr[2],
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-a * tr[2] + b * tr[3] + c * tr[0] - d * tr[1],
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-a * tr[3] - b * tr[2] + c * tr[1] + d * tr[0]
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}}
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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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) {
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return sprout::math::detail::div_qq_impl_2(
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a, b, c, d, sprout::math::detail::mul(tr, mixam), mixam
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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div_qq_impl(T const& a, T const& b, T const& c, T const& d, sprout::array<T, 4> const& tr) {
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return sprout::math::detail::div_qq_impl_1(
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a, b, c, d, tr,
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static_cast<T>(1) / sprout::math::detail::abs_max(tr)
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);
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}
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} // namespace detail
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator/(sprout::complex<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::detail::div_qq_impl(
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lhs.real(), lhs.imag(), static_cast<T>(0), static_cast<T>(0),
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sprout::array<T, 4>{{rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()}}
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator/(sprout::math::quaternion<T> const& lhs, sprout::complex<T> const& rhs) {
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return sprout::math::detail::div_qq_impl(
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lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
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sprout::array<T, 4>{{rhs.real(), rhs.imag(), static_cast<T>(0), static_cast<T>(0)}}
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);
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator/(sprout::math::quaternion<T> const& lhs, sprout::math::quaternion<T> const& rhs) {
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return sprout::math::detail::div_qq_impl(
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lhs.R_component_1(), lhs.R_component_2(), lhs.R_component_3(), lhs.R_component_4(),
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sprout::array<T, 4>{{rhs.R_component_1(), rhs.R_component_2(), rhs.R_component_3(), rhs.R_component_4()}}
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);
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}
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//
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// operator+
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// operator-
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator+(sprout::math::quaternion<T> const& q) {
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return q;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::math::quaternion<T>
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operator-(sprout::math::quaternion<T> const& q) {
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return sprout::math::quaternion<T>(-q.R_component_1(), -q.R_component_2(), -q.R_component_3(), -q.R_component_4());
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}
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//
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// operator==
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// operator!=
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//
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template<typename T>
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inline SPROUT_CONSTEXPR bool
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operator==(T const& lhs, sprout::math::quaternion<T> const& rhs) {
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return rhs.R_component_1() == lhs
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&& rhs.R_component_2() == static_cast<T>(0)
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&& rhs.R_component_3() == static_cast<T>(0)
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&& rhs.R_component_4() == static_cast<T>(0)
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR bool
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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
|
||
|
|
|
||
|
|
} // namespace math
|
||
|
|
} // namespace sprout
|
||
|
|
|
||
|
|
#endif // #ifndef SPROUT_MATH_QUATERNION_ARITHMETIC_OPERATORS_HPP
|