💿🐜 Antkeeper source code
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969 lines
22 KiB
969 lines
22 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_MATH_QUATERNION_HPP
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#define ANTKEEPER_MATH_QUATERNION_HPP
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#include "math/constants.hpp"
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#include "math/matrix.hpp"
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#include "math/vector.hpp"
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#include <cmath>
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#include <istream>
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#include <ostream>
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namespace math {
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/**
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* Quaternion composed of a real scalar part and imaginary vector part.
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*
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* @tparam T Scalar type.
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*/
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template <class T>
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struct quaternion
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{
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/// Scalar type.
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typedef T scalar_type;
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/// Vector type.
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typedef vector<T, 3> vector_type;
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/// Rotation matrix type.
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typedef matrix<T, 3, 3> matrix_type;
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/// Quaternion real part.
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scalar_type r;
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/// Quaternion imaginary part.
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vector_type i;
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/// Returns a reference to the quaternion real part.
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/// @{
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constexpr inline scalar_type& w() noexcept
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{
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return r;
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}
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constexpr inline const scalar_type& w() const noexcept
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{
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return r;
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}
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/// @}
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/// Returns a reference to the first element of the quaternion imaginary part.
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/// @{
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constexpr inline scalar_type& x() noexcept
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{
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return i.x();
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}
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constexpr inline const scalar_type& x() const noexcept
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{
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return i.x();
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}
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/// @}
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/// Returns a reference to the second element of the quaternion imaginary part.
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/// @{
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constexpr inline scalar_type& y() noexcept
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{
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return i.y();
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}
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constexpr inline const scalar_type& y() const noexcept
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{
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return i.y();
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}
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/// @}
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/// Returns a reference to the third element of the quaternion imaginary part.
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/// @{
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constexpr inline scalar_type& z() noexcept
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{
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return i.z();
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}
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constexpr inline const scalar_type& z() const noexcept
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{
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return i.z();
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}
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/// @}
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/**
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* Returns a quaternion representing a rotation about the x-axis.
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*
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* @param angle Angle of rotation, in radians.
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*
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* @return Quaternion representing an x-axis rotation.
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*/
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static quaternion rotate_x(scalar_type angle)
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{
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return {std::cos(angle * T(0.5)), std::sin(angle * T(0.5)), T(0), T(0)};
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}
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/**
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* Returns a quaternion representing a rotation about the y-axis.
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*
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* @param angle Angle of rotation, in radians.
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*
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* @return Quaternion representing an y-axis rotation.
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*/
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static quaternion rotate_y(scalar_type angle)
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{
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return {std::cos(angle * T(0.5)), T(0), std::sin(angle * T(0.5)), T(0)};
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}
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/**
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* Returns a quaternion representing a rotation about the z-axis.
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*
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* @param angle Angle of rotation, in radians.
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* @return Quaternion representing an z-axis rotation.
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*/
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static quaternion rotate_z(scalar_type angle)
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{
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return {std::cos(angle * T(0.5)), T(0), T(0), std::sin(angle * T(0.5))};
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}
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/**
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* Type-casts the quaternion scalars using `static_cast`.
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*
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* @tparam U Target scalar type.
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*
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* @return Type-casted quaternion.
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*/
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template <class U>
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constexpr inline explicit operator quaternion<U>() const noexcept
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{
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return {static_cast<U>(r), vector<U, 3>(i)};
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}
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/**
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* Constructs a matrix representing the rotation described the quaternion.
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*
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* @return Rotation matrix.
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*/
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constexpr explicit operator matrix_type() const noexcept
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{
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const T xx = x() * x();
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const T xy = x() * y();
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const T xz = x() * z();
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const T xw = x() * w();
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const T yy = y() * y();
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const T yz = y() * z();
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const T yw = y() * w();
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const T zz = z() * z();
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const T zw = z() * w();
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return
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{
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T(1) - (yy + zz) * T(2), (xy + zw) * T(2), (xz - yw) * T(2),
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(xy - zw) * T(2), T(1) - (xx + zz) * T(2), (yz + xw) * T(2),
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(xz + yw) * T(2), (yz - xw) * T(2), T(1) - (xx + yy) * T(2)
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};
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}
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/**
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* Casts the quaternion to a 4-element vector, with the real part as the first element and the imaginary part as the following three elements.
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*
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* @return Vector containing the real and imaginary parts of the quaternion.
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*/
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constexpr inline explicit operator vector<T, 4>() const noexcept
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{
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return {r, i[0], i[1], i[2]};
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}
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/// Returns a zero quaternion, where every scalar is equal to zero.
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static constexpr quaternion zero() noexcept
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{
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return {};
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}
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/// Returns a rotation identity quaternion.
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static constexpr quaternion identity() noexcept
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{
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return {T{1}, vector_type::zero()};
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}
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};
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/**
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* Adds two quaternions.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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*
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* @return Sum of the two quaternions.
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*/
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template <class T>
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constexpr quaternion<T> add(const quaternion<T>& a, const quaternion<T>& b) noexcept;
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/**
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* Adds a quaternion and a scalar.
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*
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* @param a First value.
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* @param b Second second value.
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*
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* @return Sum of the quaternion and scalar.
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*/
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template <class T>
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constexpr quaternion<T> add(const quaternion<T>& a, T b) noexcept;
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/**
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* Calculates the conjugate of a quaternion.
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*
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* @param q Quaternion from which the conjugate will be calculated.
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*
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* @return Conjugate of the quaternion.
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*/
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template <class T>
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constexpr quaternion<T> conjugate(const quaternion<T>& q) noexcept;
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/**
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* Calculates the dot product of two quaternions.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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*
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* @return Dot product of the two quaternions.
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*/
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template <class T>
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constexpr T dot(const quaternion<T>& a, const quaternion<T>& b) noexcept;
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/**
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* Divides a quaternion by another quaternion.
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*
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* @param a First value.
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* @param b Second value.
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*
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* @return Result of the division.
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*/
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template <class T>
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constexpr quaternion<T> div(const quaternion<T>& a, const quaternion<T>& b) noexcept;
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/**
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* Divides a quaternion by a scalar.
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*
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* @param a Quaternion.
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* @param b Scalar.
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*
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* @return Result of the division.
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*/
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template <class T>
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constexpr quaternion<T> div(const quaternion<T>& a, T b) noexcept;
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/**
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* Divides a scalar by a quaternion.
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*
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* @param a Scalar.
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* @param b Quaternion.
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*
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* @return Result of the division.
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*/
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template <class T>
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constexpr quaternion<T> div(T a, const quaternion<T>& b) noexcept;
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/**
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* Calculates the inverse length of a quaternion.
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*
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* @param q Quaternion to calculate the inverse length of.
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*
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* @return Inverse length of the quaternion.
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*/
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template <class T>
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T inv_length(const quaternion<T>& q);
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/**
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* Calculates the length of a quaternion.
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*
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* @param q Quaternion to calculate the length of.
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*
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* @return Length of the quaternion.
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*/
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template <class T>
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T length(const quaternion<T>& q);
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/**
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* Performs linear interpolation between two quaternions.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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* @param t Interpolation factor.
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*
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* @return Interpolated quaternion.
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*/
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template <class T>
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constexpr quaternion<T> lerp(const quaternion<T>& a, const quaternion<T>& b, T t) noexcept;
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/**
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* Creates a unit quaternion rotation using forward and up vectors.
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*
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* @param forward Unit forward vector.
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* @param up Unit up vector.
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*
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* @return Unit rotation quaternion.
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*/
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template <class T>
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quaternion<T> look_rotation(const vector<T, 3>& forward, vector<T, 3> up);
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/**
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* Multiplies two quaternions.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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*
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* @return Product of the two quaternions.
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*/
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template <class T>
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constexpr quaternion<T> mul(const quaternion<T>& a, const quaternion<T>& b) noexcept;
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/**
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* Multiplies a quaternion by a scalar.
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*
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* @param a First value.
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* @param b Second value.
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*
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* @return Product of the quaternion and scalar.
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*/
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template <class T>
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constexpr quaternion<T> mul(const quaternion<T>& a, T b) noexcept;
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/**
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* Calculates the product of a quaternion and a vector.
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*
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* @param a First value.
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* @param b second value.
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*
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* @return Product of the quaternion and vector.
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*/
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/// @{
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template <class T>
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constexpr vector<T, 3> mul(const quaternion<T>& a, const vector<T, 3>& b) noexcept;
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template <class T>
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constexpr vector<T, 3> mul(const vector<T, 3>& a, const quaternion<T>& b) noexcept;
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/// @}
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/**
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* Negates a quaternion.
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*
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* @param q Quaternion to negate.
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*
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* @return Negated quaternion.
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*/
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template <class T>
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constexpr quaternion<T> negate(const quaternion<T>& q) noexcept;
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/**
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* Performs normalized linear interpolation between two quaternions.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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* @param t Interpolation factor.
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*
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* @return Interpolated quaternion.
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*/
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template <class T>
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quaternion<T> nlerp(const quaternion<T>& a, const quaternion<T>& b, T t);
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/**
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* Normalizes a quaternion.
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*
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* @param q Quaternion to normalize.
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*
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* @return Normalized quaternion.
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*/
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template <class T>
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quaternion<T> normalize(const quaternion<T>& q);
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/**
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* Creates a rotation from an angle and axis.
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*
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* @param angle Angle of rotation (in radians).
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* @param axis Axis of rotation
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*
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* @return Quaternion representing the rotation.
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*/
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template <class T>
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quaternion<T> angle_axis(T angle, const vector<T, 3>& axis);
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/**
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* Calculates the minimum rotation between two normalized direction vectors.
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*
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* @param source Normalized source direction.
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* @param destination Normalized destination direction.
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*
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* @return Quaternion representing the minimum rotation between the source and destination vectors.
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*/
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template <class T>
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quaternion<T> rotation(const vector<T, 3>& source, const vector<T, 3>& destination);
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/**
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* Performs spherical linear interpolation between two quaternions.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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* @param t Interpolation factor.
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*
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* @return Interpolated quaternion.
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*/
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template <class T>
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quaternion<T> slerp(const quaternion<T>& a, const quaternion<T>& b, T t, T error = T{1e-6});
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/**
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* Calculates the square length of a quaternion. The square length can be calculated faster than the length because a call to `std::sqrt` is saved.
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*
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* @param q Quaternion to calculate the square length of.
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*
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* @return Square length of the quaternion.
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*/
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template <class T>
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constexpr T sqr_length(const quaternion<T>& q) noexcept;
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/**
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* Subtracts a quaternion from another quaternion.
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*
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* @param a First quaternion.
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* @param b Second quaternion.
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*
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* @return Difference between the quaternions.
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*/
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template <class T>
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constexpr quaternion<T> sub(const quaternion<T>& a, const quaternion<T>& b) noexcept;
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/**
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* Subtracts a quaternion and a scalar.
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*
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* @param a First value.
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* @param b Second second.
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*
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* @return Difference between the quaternion and scalar.
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*/
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/// @{
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template <class T>
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constexpr quaternion<T> sub(const quaternion<T>& a, T b) noexcept;
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template <class T>
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constexpr quaternion<T> sub(T a, const quaternion<T>& b) noexcept;
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/// @}
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/**
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* Decomposes a quaternion into swing and twist rotation components.
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*
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* @param[in] q Quaternion to decompose.
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* @param[in] a Axis of twist rotation.
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* @param[out] swing Swing rotation component.
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* @param[out] twist Twist rotation component.
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* @param[in] error Threshold at which a number is considered zero.
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*
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* @see https://www.euclideanspace.com/maths/geometry/rotations/for/decomposition/
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*/
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template <class T>
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void swing_twist(const quaternion<T>& q, const vector<T, 3>& a, quaternion<T>& qs, quaternion<T>& qt, T error = T{1e-6});
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/**
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* Converts a 3x3 rotation matrix to a quaternion.
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*
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* @param m Rotation matrix.
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*
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* @return Unit quaternion representing the rotation described by @p m.
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*/
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template <class T>
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quaternion<T> quaternion_cast(const matrix<T, 3, 3>& m);
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template <class T>
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constexpr inline quaternion<T> add(const quaternion<T>& a, const quaternion<T>& b) noexcept
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{
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return {a.r + b.r, a.i + b.i};
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}
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template <class T>
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constexpr inline quaternion<T> add(const quaternion<T>& a, T b) noexcept
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{
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return {a.r + b, a.i + b};
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}
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template <class T>
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constexpr inline quaternion<T> conjugate(const quaternion<T>& q) noexcept
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{
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return {q.r, -q.i};
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}
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template <class T>
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constexpr inline T dot(const quaternion<T>& a, const quaternion<T>& b) noexcept
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{
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return a.r * b.r + dot(a.i, b.i);
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}
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template <class T>
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constexpr inline quaternion<T> div(const quaternion<T>& a, const quaternion<T>& b) noexcept
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{
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return {a.r / b.r, a.i / b.i};
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}
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template <class T>
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constexpr inline quaternion<T> div(const quaternion<T>& a, T b) noexcept
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{
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return {a.r / b, a.i / b};
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}
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template <class T>
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constexpr inline quaternion<T> div(T a, const quaternion<T>& b) noexcept
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{
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return {a / b.r, a / b.i};
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}
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template <class T>
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inline T inv_length(const quaternion<T>& q)
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{
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return T{1} / length(q);
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}
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template <class T>
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inline T length(const quaternion<T>& q)
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{
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return std::sqrt(sqr_length(q));
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}
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template <class T>
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constexpr inline quaternion<T> lerp(const quaternion<T>& a, const quaternion<T>& b, T t) noexcept
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{
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return
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{
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(b.r - a.r) * t + a.r,
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(b.i - a.i) * t + a.i
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};
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}
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template <class T>
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quaternion<T> look_rotation(const vector<T, 3>& forward, vector<T, 3> up)
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{
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vector<T, 3> right = normalize(cross(forward, up));
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up = cross(right, forward);
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matrix<T, 3, 3> m =
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{
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right,
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up,
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-forward
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};
|
|
|
|
// Convert to quaternion
|
|
return normalize(quaternion_cast(m));
|
|
}
|
|
|
|
template <class T>
|
|
constexpr quaternion<T> mul(const quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return
|
|
{
|
|
-a.x() * b.x() - a.y() * b.y() - a.z() * b.z() + a.w() * b.w(),
|
|
a.x() * b.w() + a.y() * b.z() - a.z() * b.y() + a.w() * b.x(),
|
|
-a.x() * b.z() + a.y() * b.w() + a.z() * b.x() + a.w() * b.y(),
|
|
a.x() * b.y() - a.y() * b.x() + a.z() * b.w() + a.w() * b.z()
|
|
};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline quaternion<T> mul(const quaternion<T>& a, T b) noexcept
|
|
{
|
|
return {a.r * b, a.i * b};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr vector<T, 3> mul(const quaternion<T>& a, const vector<T, 3>& b) noexcept
|
|
{
|
|
return a.i * dot(a.i, b) * T(2) + b * (a.r * a.r - sqr_length(a.i)) + cross(a.i, b) * a.r * T(2);
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline vector<T, 3> mul(const vector<T, 3>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return mul(conjugate(b), a);
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline quaternion<T> negate(const quaternion<T>& q) noexcept
|
|
{
|
|
return {-q.r, -q.i};
|
|
}
|
|
|
|
template <class T>
|
|
quaternion<T> nlerp(const quaternion<T>& a, const quaternion<T>& b, T t)
|
|
{
|
|
return normalize(add(mul(a, T(1) - t), mul(b, t * std::copysign(T(1), dot(a, b)))));
|
|
}
|
|
|
|
template <class T>
|
|
inline quaternion<T> normalize(const quaternion<T>& q)
|
|
{
|
|
return mul(q, inv_length(q));
|
|
}
|
|
|
|
template <class T>
|
|
quaternion<T> angle_axis(T angle, const vector<T, 3>& axis)
|
|
{
|
|
angle *= T{0.5};
|
|
return {std::cos(angle), axis * std::sin(angle)};
|
|
}
|
|
|
|
template <class T>
|
|
quaternion<T> rotation(const vector<T, 3>& source, const vector<T, 3>& destination)
|
|
{
|
|
quaternion<T> q = {dot(source, destination), cross(source, destination)};
|
|
q.w() += length(q);
|
|
return normalize(q);
|
|
}
|
|
|
|
template <class T>
|
|
quaternion<T> slerp(const quaternion<T>& a, const quaternion<T>& b, T t, T error)
|
|
{
|
|
T cos_theta = dot(a, b);
|
|
|
|
if (cos_theta > T(1) - error)
|
|
return normalize(lerp(a, b, t));
|
|
|
|
cos_theta = std::max<T>(T(-1), std::min<T>(T(1), cos_theta));
|
|
const T theta = std::acos(cos_theta) * t;
|
|
|
|
quaternion<T> c = normalize(sub(b, mul(a, cos_theta)));
|
|
|
|
return add(mul(a, std::cos(theta)), mul(c, std::sin(theta)));
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline T sqr_length(const quaternion<T>& q) noexcept
|
|
{
|
|
return q.r * q.r + sqr_length(q.i);
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline quaternion<T> sub(const quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return {a.r - b.r, a.i - b.i};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline quaternion<T> sub(const quaternion<T>& a, T b) noexcept
|
|
{
|
|
return {a.r - b, a.i - b};
|
|
}
|
|
|
|
template <class T>
|
|
constexpr inline quaternion<T> sub(T a, const quaternion<T>& b) noexcept
|
|
{
|
|
return {a - b.r, a - b.i};
|
|
}
|
|
|
|
template <class T>
|
|
void swing_twist(const quaternion<T>& q, const vector<T, 3>& a, quaternion<T>& qs, quaternion<T>& qt, T error)
|
|
{
|
|
if (sqr_length(q.i) > error)
|
|
{
|
|
qt = normalize(quaternion<T>{q.w(), a * dot(a, q.i)});
|
|
qs = mul(q, conjugate(qt));
|
|
}
|
|
else
|
|
{
|
|
qt = angle_axis(pi<T>, a);
|
|
|
|
const vector<T, 3> qa = mul(q, a);
|
|
const vector<T, 3> sa = cross(a, qa);
|
|
if (sqr_length(sa) > error)
|
|
qs = angle_axis(std::acos(dot(a, qa)), sa);
|
|
else
|
|
qs = quaternion<T>::identity();
|
|
}
|
|
}
|
|
|
|
template <class T>
|
|
quaternion<T> quaternion_cast(const matrix<T, 3, 3>& m)
|
|
{
|
|
const T t = trace(m);
|
|
|
|
if (t > T(0))
|
|
{
|
|
T s = T(0.5) / std::sqrt(t + T(1));
|
|
return
|
|
{
|
|
T(0.25) / s,
|
|
(m[1][2] - m[2][1]) * s,
|
|
(m[2][0] - m[0][2]) * s,
|
|
(m[0][1] - m[1][0]) * s
|
|
};
|
|
}
|
|
else
|
|
{
|
|
if (m[0][0] > m[1][1] && m[0][0] > m[2][2])
|
|
{
|
|
T s = T(2) * std::sqrt(T(1) + m[0][0] - m[1][1] - m[2][2]);
|
|
|
|
return
|
|
{
|
|
(m[1][2] - m[2][1]) / s,
|
|
T(0.25) * s,
|
|
(m[1][0] + m[0][1]) / s,
|
|
(m[2][0] + m[0][2]) / s
|
|
};
|
|
}
|
|
else if (m[1][1] > m[2][2])
|
|
{
|
|
T s = T(2) * std::sqrt(T(1) + m[1][1] - m[0][0] - m[2][2]);
|
|
return
|
|
{
|
|
(m[2][0] - m[0][2]) / s,
|
|
(m[1][0] + m[0][1]) / s,
|
|
T(0.25) * s,
|
|
(m[2][1] + m[1][2]) / s
|
|
};
|
|
}
|
|
else
|
|
{
|
|
T s = T(2) * std::sqrt(T(1) + m[2][2] - m[0][0] - m[1][1]);
|
|
return
|
|
{
|
|
(m[0][1] - m[1][0]) / s,
|
|
(m[2][0] + m[0][2]) / s,
|
|
(m[2][1] + m[1][2]) / s,
|
|
T(0.25) * s
|
|
};
|
|
}
|
|
}
|
|
}
|
|
|
|
namespace operators {
|
|
|
|
/// @copydoc add(const quaternion<T>&, const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator+(const quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return add(a, b);
|
|
}
|
|
|
|
/// @copydoc add(const quaternion<T>&, T)
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator+(const quaternion<T>& a, T b) noexcept
|
|
{
|
|
return add(a, b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator+(T a, const quaternion<T>& b) noexcept
|
|
{
|
|
return add(b, a);
|
|
}
|
|
/// @}
|
|
|
|
/// @copydoc div(const quaternion<T>&, const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator/(const quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return div(a, b);
|
|
}
|
|
|
|
/// @copydoc div(const quaternion<T>&, T)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator/(const quaternion<T>& a, T b) noexcept
|
|
{
|
|
return div(a, b);
|
|
}
|
|
|
|
/// @copydoc div(T, const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator/(T a, const quaternion<T>& b) noexcept
|
|
{
|
|
return div(a, b);
|
|
}
|
|
|
|
/// @copydoc mul(const quaternion<T>&, const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator*(const quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
|
|
/// @copydoc mul(const quaternion<T>&, T)
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator*(const quaternion<T>& a, T b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator*(T a, const quaternion<T>& b) noexcept
|
|
{
|
|
return mul(b, a);
|
|
}
|
|
/// @}
|
|
|
|
/// @copydoc mul(const quaternion<T>&, const vector<T, 3>&)
|
|
template <class T>
|
|
constexpr inline vector<T, 3> operator*(const quaternion<T>& a, const vector<T, 3>& b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
|
|
/// @copydoc mul(const vector<T, 3>&, const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline vector<T, 3> operator*(const vector<T, 3>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return mul(a, b);
|
|
}
|
|
|
|
/// @copydoc sub(const quaternion<T>&, const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator-(const quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return sub(a, b);
|
|
}
|
|
|
|
/// @copydoc sub(const quaternion<T>&, T)
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator-(const quaternion<T>& a, T b) noexcept
|
|
{
|
|
return sub(a, b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator-(T a, const quaternion<T>& b) noexcept
|
|
{
|
|
return sub(a, b);
|
|
}
|
|
/// @}
|
|
|
|
/// @copydoc negate(const quaternion<T>&)
|
|
template <class T>
|
|
constexpr inline quaternion<T> operator-(const quaternion<T>& q) noexcept
|
|
{
|
|
return negate(q);
|
|
}
|
|
|
|
/**
|
|
* Adds two values and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator+=(quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return (a = a + b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator+=(quaternion<T>& a, T b) noexcept
|
|
{
|
|
return (a = a + b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Subtracts the first value by the second value and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator-=(quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return (a = a - b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator-=(quaternion<T>& a, T b) noexcept
|
|
{
|
|
return (a = a - b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Multiplies two values and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator*=(quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return (a = a * b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator*=(quaternion<T>& a, T b) noexcept
|
|
{
|
|
return (a = a * b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Divides the first value by the second value and stores the result in the first value.
|
|
*
|
|
* @param a First value.
|
|
* @param b Second value.
|
|
*
|
|
* @return Reference to the first value.
|
|
*/
|
|
/// @{
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator/=(quaternion<T>& a, const quaternion<T>& b) noexcept
|
|
{
|
|
return (a = a / b);
|
|
}
|
|
template <class T>
|
|
constexpr inline quaternion<T>& operator/=(quaternion<T>& a, T b) noexcept
|
|
{
|
|
return (a = a / b);
|
|
}
|
|
/// @}
|
|
|
|
/**
|
|
* Writes the real and imaginary parts of a quaternion to an output stream, with each number delimeted by a space.
|
|
*
|
|
* @param os Output stream.
|
|
* @param q Quaternion.
|
|
*
|
|
* @return Output stream.
|
|
*/
|
|
template <class T>
|
|
std::ostream& operator<<(std::ostream& os, const math::quaternion<T>& q)
|
|
{
|
|
os << q.r << ' ' << q.i;
|
|
return os;
|
|
}
|
|
|
|
/**
|
|
* Reads the real and imaginary parts of a quaternion from an input stream, with each number delimeted by a space.
|
|
*
|
|
* @param is Input stream.
|
|
* @param q Quaternion.
|
|
*
|
|
* @return Input stream.
|
|
*/
|
|
template <class T>
|
|
std::istream& operator>>(std::istream& is, const math::quaternion<T>& q)
|
|
{
|
|
is >> q.r;
|
|
is >> q.i;
|
|
return is;
|
|
}
|
|
|
|
} // namespace operators
|
|
|
|
} // namespace math
|
|
|
|
using namespace math::operators;
|
|
|
|
#endif // ANTKEEPER_MATH_QUATERNION_HPP
|