quaternion.hpp File Reference

Quaternion operations and related mathematical functions. More...

#include "mat.hpp"
#include "quaternion.inl"

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Classes
class	mal_math::qua< T >
	Represents a quaternion with primitive type T. More...

Namespaces
namespace	mal_math
	Contains mathematical utility functions and classes.

Typedefs
using	mal_math::quat = qua<float>
using	mal_math::dquat = qua<double>

Functions
template<size_t size, Primitive T>
constexpr std::istream &	mal_math::operator>> (std::istream &is, vec< size, T > &vec)
	Reads a vector of given size from an input stream.
template<size_t size, Primitive T>
constexpr std::ostream &	mal_math::operator<< (std::ostream &os, vec< size, T > &vec)
	Writes a vector of given size to an output stream.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator* (U const value, qua< T > const &vector) noexcept
	Scalar-quaternion multiplication.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator/ (U const value, qua< T > const &vector) noexcept
	Scalar-quaternion division.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator* (qua< T > const &vector, U const value) noexcept
	Quaternion-scalar multiplication.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator/ (qua< T > const &vector, U const value) noexcept
	Quaternion-scalar division.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator+ (qua< T > const &left, qua< U > const &right) noexcept
	Quaternion addition.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator- (qua< T > const &left, qua< U > const &right) noexcept
	Quaternion subtraction.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator* (qua< T > const &left, qua< U > const &right) noexcept
	Quaternion multiplication.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::operator/ (qua< T > const &left, qua< U > const &right) noexcept
	Quaternion division.
template<Primitive T, Primitive U>
constexpr T	mal_math::dot (qua< T > const &left, qua< U > const &right) noexcept
	Computes the dot product of two quaternions.
template<Primitive T>
constexpr T	mal_math::angle (qua< T > const &quaternion) noexcept
	Computes the angle (or magnitude) of a quaternion.
template<Primitive T>
constexpr T	mal_math::pitch (qua< T > const &quaternion) noexcept
	Computes the pitch from a quaternion.
template<Primitive T>
constexpr T	mal_math::yaw (qua< T > const &quaternion) noexcept
	Computes the yaw from a quaternion.
template<Primitive T>
constexpr T	mal_math::roll (qua< T > const &quaternion) noexcept
	Computes the roll from a quaternion.
template<Primitive T>
constexpr vec< 3, T >	mal_math::QuaternionToEuler (qua< T > const &quaternion) noexcept
	Converts a quaternion to Euler angles.
template<Primitive T>
constexpr qua< T >	mal_math::QuaternionFromEuler (vec< 3, T > const &angles) noexcept
	Creates a quaternion from Euler angles given in a vector.
template<Primitive T> requires (std::is_floating_point_v<T>)
constexpr qua< T >	mal_math::QuaternionFromEuler (T roll, T pitch, T yaw) noexcept
	Creates a quaternion from individual Euler angles.
template<AnyMat U> requires (U::size.x == 3 && U::size.y == 3 && std::is_floating_point_v<typename U::type>)
constexpr qua< typename U::type >	mal_math::QuaternionFromRotationMatrix (U const &mat) noexcept
	Creates a quaternion from a 3x3 rotation matrix.
template<Primitive T>
constexpr qua< T >	mal_math::operator* (qua< T > const &q, qua< T > const &p) noexcept
	Quaternion-Quaternion multiplication.
template<Primitive T>
constexpr vec< 3, T >	mal_math::operator* (qua< T > const &q, vec< 3, T > const &v) noexcept
	Quaternion-Vector multiplication.
template<Primitive T>
constexpr vec< 3, T >	mal_math::operator* (vec< 3, T > const &v, qua< T > const &q) noexcept
	Vector-Quaternion multiplication.
template<Primitive T>
constexpr qua< T >	mal_math::conjugate (qua< T > const &q) noexcept
	Computes the conjugate of a quaternion.
template<Primitive T>
constexpr qua< T >	mal_math::inverse (qua< T > const &q) noexcept
	Computes the inverse of a quaternion.
template<Primitive T, Primitive U>
constexpr vec< 3, T >	mal_math::cross (qua< T > const &left, vec< 3, U > const &right) noexcept
	Cross product between quaternion and vector.
template<Primitive T, Primitive U>
constexpr vec< 3, T >	mal_math::cross (vec< 3, U > const &left, qua< T > const &right) noexcept
	Cross product between vector and quaternion.
template<Primitive T, Primitive U>
constexpr qua< T >	mal_math::cross (qua< T > const &left, qua< U > const &right) noexcept
	Computes the cross product of two quaternions.
template<Primitive T>
constexpr mat< 4, 4, T >	mal_math::rotate (mat< 4, 4, T > const &matrix, qua< T > const &q) noexcept
	Rotates a 4x4 matrix using a quaternion.
template<Primitive T>
constexpr T	mal_math::length (qua< T > const &q) noexcept
	Computes the length (or magnitude) of a quaternion.
template<Primitive T>
constexpr qua< T >	mal_math::normalize (qua< T > const &q) noexcept
	Normalizes a quaternion.

Detailed Description

Quaternion operations and related mathematical functions.

This header file provides the definition and utility functions for quaternions. Quaternions are mathematical objects used to represent rotations in 3D space without the gimbal lock issues that can be encountered with Euler angles. The file includes functions to convert between quaternions and various other forms of representing orientation and rotation, such as Euler angles and rotation matrices.

Definition in file quaternion.hpp.