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