Classes
class	eagine::math::unit_spherical_coordinate< T, V >
	Class representing unit spherical coordinate. More...

class	eagine::math::bezier_curves< Type, Parameter, Order >
	A sequence of Bezier curves, possibly connected at end points. More...

class	eagine::math::cubic_bezier_loop< Type, Parameter >
	A closed smooth cubic Bezier spline passing through all input points. More...

struct	eagine::math::bezier_t< Type, Parameter, N >
	Helper class for bezier curve segment calculations. More...

struct	eagine::math::matrix< T, C, R, RM, V >
	Basic RxC matrix implementation template. More...

struct	eagine::math::is_row_major< matrix< T, C, R, RM, V > >
	Class testing if a matrix type is row-major. More...

struct	eagine::math::reordered_matrix< matrix< T, C, R, RM, V > >
	Implementation of reordered_matrix_t. More...

struct	eagine::math::is_matrix_constructor< X >
	Indicates if the specified type `X` is a matrix constructor. More...

struct	eagine::math::constructed_matrix< X >
	Gets the constructed matrix type for a matrix constructor type. More...

class	eagine::math::convertible_matrix_constructor< MC >
	Helper class used in matrix constructor implementation. More...

class	eagine::math::identity< matrix< T, R, C, RM, V > >
	Identity matrix constructor. More...

class	eagine::math::looking_at_y_up< matrix< T, 4, 4, RM, V > >
	Implements constructor of look-at matrix used for camera transformations. More...

class	eagine::math::orbiting_y_up< matrix< T, 4, 4, RM, V > >
	Implements constructor of orbiting matrix used for camera transformations. More...

class	eagine::math::ortho< matrix< T, 4, 4, RM, V > >
	Implements constructor of orthographic projection matrix. More...

class	eagine::math::perspective< matrix< T, 4, 4, RM, V > >
	Implements constructor of perspective projection matrix. More...

class	eagine::math::reflection_I< matrix< T, 4, 4, RM, V >, I >
	Implements constructor of reflection transformation matrix. More...

class	eagine::math::rotation_I< matrix< T, 4, 4, RM, V >, I >
	Implements constructor of rotation transformation matrix. More...

class	eagine::math::scale< matrix< T, 4, 4, RM, V > >
	Implements constructor of scale transformation matrix. More...

class	eagine::math::uniform_scale< matrix< T, 4, 4, RM, V > >
	Implements constructor of uniform scale transformation matrix. More...

class	eagine::math::translation< matrix< T, 4, 4, RM, V > >
	Implements constructor of translation transformation matrix. More...

class	eagine::math::basic_line< T, N, V >
	Basic template for lines in N-dimensional space. More...

class	eagine::math::basic_triangle< T, N, V >
	Basic template for triangles in N-dimensional space. More...

class	eagine::math::basic_sphere< T, N, V >
	Basic template for spheres in N-dimensional space. More...

struct	eagine::math::scalar< T, N, V >
	Basic scalar implementation template. More...

class	eagine::math::sign< T >
	Class representing a positive or negative numeric sign. More...

struct	eagine::math::tmat< T, C, R, RM, V >
	Generic template for RxC dimensional matrices. More...

struct	eagine::math::tvec< T, N, V >
	Generic template for N-dimensional vectors. More...

struct	eagine::math::vector< T, N, V >
	Basic N-dimensional vector implementation template. More...

Typedefs
template<typename X >
using	eagine::math::reordered_matrix_t = typename reordered_matrix< X >::type
	Trait returns a reordered (switch row/column-major) type for a matrix type.

template<typename X >
using	eagine::math::constructed_matrix_t = typename constructed_matrix< X >::type
	Trait returning the matrix type constructed by constructor type X.

template<typename T , bool V>
using	eagine::math::matrix_looking_at_y_up = convertible_matrix_constructor< looking_at_y_up< matrix< T, 4, 4, true, V > >>
	Alias for constructor of look-at matrix used for camera transformations.

template<typename T , bool V>
using	eagine::math::matrix_orbiting_y_up = convertible_matrix_constructor< orbiting_y_up< matrix< T, 4, 4, true, V > >>
	Alias for constructor of orbiting matrix used for camera transformations.

template<typename T , bool V>
using	eagine::math::matrix_ortho = convertible_matrix_constructor< ortho< matrix< T, 4, 4, true, V > >>
	Alias for constructor of orthographic projection matrix.

template<typename T , bool V>
using	eagine::math::matrix_perspective = convertible_matrix_constructor< perspective< matrix< T, 4, 4, true, V > >>
	Alias for constructor of perspective projection matrix.

template<typename M >
using	eagine::math::reflection_x = reflection_I< M, 0 >
	Alias for implementation of constructor of reflection along x-axis matrix.

template<typename M >
using	eagine::math::reflection_y = reflection_I< M, 1 >
	Alias for implementation of constructor of reflection along y-axis matrix.

template<typename M >
using	eagine::math::reflection_z = reflection_I< M, 2 >
	Alias for implementation of constructor of reflection along z-axis matrix.

template<typename T , bool V>
using	eagine::math::matrix_reflection_x = convertible_matrix_constructor< reflection_x< matrix< T, 4, 4, true, V > >>
	Alias for constructor of reflection along x-axis transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_reflection_y = convertible_matrix_constructor< reflection_y< matrix< T, 4, 4, true, V > >>
	Alias for constructor of reflection along y-axis transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_reflection_z = convertible_matrix_constructor< reflection_z< matrix< T, 4, 4, true, V > >>
	Alias for constructor of reflection along z-axis transformation matrix. More...

template<typename M >
using	eagine::math::rotation_x = rotation_I< M, 0 >
	Alias for implementation of constructor of rotation along x-axis matrix.

template<typename M >
using	eagine::math::rotation_y = rotation_I< M, 1 >
	Alias for implementation of constructor of rotation along y-axis matrix.

template<typename M >
using	eagine::math::rotation_z = rotation_I< M, 2 >
	Alias for implementation of constructor of rotation along z-axis matrix.

template<typename T , bool V>
using	eagine::math::matrix_rotation_x = convertible_matrix_constructor< rotation_x< matrix< T, 4, 4, true, V > >>
	Alias for constructor of rotation along x-axis transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_rotation_y = convertible_matrix_constructor< rotation_y< matrix< T, 4, 4, true, V > >>
	Alias for constructor of rotation along y-axis transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_rotation_z = convertible_matrix_constructor< rotation_z< matrix< T, 4, 4, true, V > >>
	Alias for constructor of rotation along z-axis transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_scale = convertible_matrix_constructor< scale< matrix< T, 4, 4, true, V > >>
	Alias for constructor of scale transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_uniform_scale = convertible_matrix_constructor< uniform_scale< matrix< T, 4, 4, true, V > >>
	Alias for constructor of uniform scale transformation matrix. More...

template<typename T , bool V>
using	eagine::math::matrix_translation = convertible_matrix_constructor< translation< matrix< T, 4, 4, true, V > >>
	Alias for constructor of uniform translation transformation matrix. More...

template<typename T , bool V>
using	eagine::math::line = basic_line< T, 3, V >
	Alias for lines in 3D space.

template<typename T , bool V>
using	eagine::math::triangle = basic_triangle< T, 3, V >
	Alias for triangles in 3D space.

template<typename T , bool V>
using	eagine::math::sphere = basic_sphere< T, 3, V >
	Alias for spheres in 3D space.

Functions
template<typename T , bool V>
auto	eagine::math::to_cartesian (unit_spherical_coordinate< T, V > c) noexcept -> vector< T, 3, V >
	Converts unit spherical coordinate to cartesian vector.

template<typename T , bool V>
auto	eagine::math::to_unit_spherical (vector< T, 3, V > v) noexcept -> unit_spherical_coordinate< T, V >
	Converts cartesian vector to unit spherical coordinate.

template<typename T >
static constexpr auto	eagine::math::is_positive_power_of_2 (T value) noexcept -> std::enable_if_t< std::is_integral_v< T >, bool >
	Indicates if `value` is a positive integral power of two.

template<typename T >
static constexpr auto	eagine::math::greatest_common_divisor (T l, T r) noexcept -> std::enable_if_t< std::is_integral_v< T >, T >
	Returns the greates common divisor of arguments `l` and `r`.

template<typename T >
static constexpr auto	eagine::math::signum (T x) noexcept
	Returns 1 if `x` is non-negative, returns -1 otherwise.

template<typename T >
static constexpr auto	eagine::math::minimum (T a, T b) noexcept
	Returns the minimum value of `a` and `b`.

template<typename T , typename... P>
static constexpr auto	eagine::math::minimum (T a, T b, T c, P... d) noexcept
	Returns the minimum value from multiple arguments.

template<typename T >
static constexpr auto	eagine::math::maximum (T a, T b) noexcept
	Returns the maximum value of `a` and `b`.

template<typename T , typename... P>
static constexpr auto	eagine::math::maximum (T a, T b, T c, P... d) noexcept
	Returns the maximum value from multiple arguments.

template<typename T >
static constexpr auto	eagine::math::ratio (T a, T b) noexcept -> optionally_valid< T >
	Returns `a` divided by `b` if `b` is not zero.

template<typename T >
static constexpr auto	eagine::math::reciprocal (T x) noexcept -> optionally_valid< T >
	Returns the reciprocal of `x` if `x` is not zero.

template<typename T , typename Min , typename Max >
static constexpr auto	eagine::math::clamp (T x, Min min, Max max) noexcept
	Clamps `x` to be between `min` and `max`.

template<typename T , typename S , typename E >
static constexpr auto	eagine::math::ramp (T x, S start, E end) noexcept
	Normalizes `x` to (0, 1), where `start` = 0 and `end` = 1.

template<typename T , typename A >
static constexpr auto	eagine::math::blend (T v1, T v2, A alpha) noexcept
	Blends `v1` and `v2`, using `alpha` as the blending factor.

template<typename T >
static constexpr auto	eagine::math::inverse_logistic (T x) noexcept
	Calculates the inverse logistic (log(x) - log(1 - x)) of `x`.

template<typename T >
static constexpr auto	eagine::math::logistic (T x) noexcept
	Calculates the logistic (1 / (1 + exp(-x))) of `x`.

template<typename T , typename C >
static constexpr auto	eagine::math::sigmoid01 (T x, C c) noexcept
	Calculates the sigmoid of `x`. The value `c` controls steepness. More...

template<typename T >
static constexpr auto	eagine::math::sigmoid01 (T x) noexcept
	Calculates the default sigmoid of `x`. More...

template<typename T >
static auto	eagine::math::sine_sigmoid01 (T x)
	Calculates goniometric sigmoid (cos in interval (0, 1)) of `x`. More...

template<typename T >
static constexpr auto	eagine::math::sine_wave01 (T x) noexcept
	Calculates sine of `x`, mapped to interval (0, 1). More...

template<typename T >
static constexpr auto	eagine::math::cosine_wave01 (T x) noexcept
	Calculates cosine of `x`, mapped to interval (0, 1). More...

template<typename T , typename U = T>
static constexpr auto	eagine::math::saw (T x, U u=T(1)) noexcept
	Calculates floating-point modulo of `x` in intervals of `u`.

template<typename T >
static constexpr auto	eagine::math::factorial (T n) noexcept -> std::enable_if_t< std::is_integral_v< T >, T >
	Calculates factorial of `n`.

template<typename T >
static constexpr auto	eagine::math::binomial (T n, T k) noexcept -> std::enable_if_t< std::is_integral_v< T >, T >
	Calculates binomial coefficient of `n` over `k`.

template<typename T , typename C >
static auto	eagine::math::interpolate_linear (const T &a, const T &b, C coef)
	Linear interpolation between `a` and `b`. More...

template<typename T , typename C >
static auto	eagine::math::lerp (const T &a, const T &b, C coef)
	Same as interpolate_linear. More...

template<typename T , typename C >
static auto	eagine::math::smooth_lerp (const T &a, const T &b, C coef)
	Linear interpolation with `coef` transformed by sine_sigmoid01. More...

template<typename T , typename C >
static auto	eagine::math::smooth_oscillate (const T &a, C coef)
	Smooth interpolation between negative `a` and `a`. More...

template<typename T , bool V>
static constexpr auto	eagine::math::line_sphere_intersection (const line< T, V > &ray, const sphere< T, V > &sph) noexcept -> std::pair< optionally_valid< vector< T, 3, V >>, optionally_valid< vector< T, 3, V >>>
	Finds line-sphere intersection points. More...

template<typename T , bool V>
static constexpr auto	eagine::math::nearest_line_sphere_intersection (const line< T, V > &ray, const sphere< T, V > &sph) noexcept -> optionally_valid< vector< T, 3, V >>
	Finds nearest line-sphere intersection point. More...

template<typename T , bool V>
static auto	eagine::math::line_triangle_intersection (const line< T, V > &ray, const triangle< T, V > &tri) noexcept -> optionally_valid< vector< T, 3, V >>
	Finds line-triangle intersection point.

template<typename T , int N, bool V>
static auto	eagine::math::operator<< (std::ostream &o, const vector< T, N, V > &v) -> std::ostream &
	Operator for writing vector into output stream.

template<typename T , int C, int R, bool V>
static auto	eagine::math::operator<< (std::ostream &o, const matrix< T, C, R, true, V > &m) -> std::ostream &
	Operator for writing row-major matrix into output stream.

template<typename T , int C, int R, bool V>
static auto	eagine::math::operator<< (std::ostream &o, const matrix< T, C, R, false, V > &m) -> std::ostream &
	Operator for writing column-major matrix into output stream.

template<typename T , int N, bool V>
static auto	eagine::math::operator<< (std::ostream &o, const basic_line< T, N, V > &l) -> std::ostream &
	Operator for writing line into output stream.

template<typename T , int N, bool V>
static auto	eagine::math::operator<< (std::ostream &o, const basic_triangle< T, N, V > &t) -> std::ostream &
	Operator for writing triangle into output stream.

template<typename T , bool V>
static auto	eagine::math::operator<< (std::ostream &o, const sphere< T, V > &s) -> std::ostream &
	Operator for writing sphere into output stream.

template<typename T , int C, int R, bool RM, bool V>
static constexpr auto	eagine::math::rows (const matrix< T, C, R, RM, V > &) noexcept
	Returns then number of matrix rows.

template<typename T , int C, int R, bool RM, bool V>
static constexpr auto	eagine::math::columns (const matrix< T, C, R, RM, V > &) noexcept
	Returns then number of matrix columns.

template<typename T , int C, int R, bool RM, bool V>
static constexpr auto	eagine::math::row_major (const matrix< T, C, R, RM, V > &) noexcept
	Indicates if a matrix is row-major.

template<typename T , int N, bool RM, bool V>
static constexpr auto	eagine::math::dimension (const matrix< T, N, N, RM, V > &) noexcept
	Returns the dimension of a square matrix.

template<int CI, int RI, typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_cm (const matrix< T, C, R, false, V > &m) noexcept -> std::enable_if_t<(CI< C &&RI< R), T >
	Returns the matrix element at [CI, RI]. Column-major implementation.

template<int CI, int RI, typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_cm (const matrix< T, C, R, true, V > &m) noexcept -> std::enable_if_t<(CI< C &&RI< R), T >
	Returns the matrix element at [CI, RI]. Row-major implementation.

template<typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_cm (const matrix< T, C, R, false, V > &m, int ci, int ri) noexcept -> T
	Returns the matrix element at [ci, ri]. Column-major implementation.

template<typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_cm (const matrix< T, C, R, true, V > &m, int ci, int ri) noexcept -> T
	Returns the matrix element at [ci, ri]. Row-major implementation.

template<int RI, int CI, typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_rm (const matrix< T, C, R, false, V > &m) noexcept -> std::enable_if_t<(CI< C &&RI< R), T >
	Returns the matrix element at [RI, CI]. Column-major implementation.

template<int RI, int CI, typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_rm (const matrix< T, C, R, true, V > &m) noexcept -> std::enable_if_t<(CI< C &&RI< R), T >
	Returns the matrix element at [RI, CI]. Row-major implementation.

template<typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_rm (const matrix< T, C, R, false, V > &m, int ri, int ci) noexcept -> T
	Returns the matrix element at [ri, ci]. Column-major implementation.

template<typename T , int C, int R, bool V>
static constexpr auto	eagine::math::get_rm (const matrix< T, C, R, true, V > &m, int ri, int ci) noexcept -> T
	Returns the matrix element at [ri, ci]. Row-major implementation.

template<int CI, int RI, typename T , int C, int R, bool V>
static auto	eagine::math::set_cm (matrix< T, C, R, false, V > &m, T v) noexcept -> std::enable_if_t<(CI< C &&RI< R)>
	Sets the matrix element at [CI, RI]. Column-major implementation.

template<int CI, int RI, typename T , int C, int R, bool V>
static auto	eagine::math::set_cm (matrix< T, C, R, true, V > &m, T v) noexcept -> std::enable_if_t<(CI< C &&RI< R)>
	Sets the matrix element at [CI, RI]. Row-major implementation.

template<typename T , int C, int R, bool V>
static void	eagine::math::set_cm (matrix< T, C, R, false, V > &m, int ci, int ri, T v) noexcept
	Sets the matrix element at [ci, ri]. Column-major implementation.

template<typename T , int C, int R, bool V>
static void	eagine::math::set_cm (matrix< T, C, R, true, V > &m, int ci, int ri, T v) noexcept
	Sets the matrix element at [ci, ri]. Row-major implementation.

template<int RI, int CI, typename T , int C, int R, bool V>
static auto	eagine::math::set_rm (matrix< T, C, R, false, V > &m, T v) noexcept -> std::enable_if_t<(CI< C &&RI< R)>
	Sets the matrix element at [RI, CI]. Column-major implementation.

template<int RI, int CI, typename T , int C, int R, bool V>
static auto	eagine::math::set_rm (matrix< T, C, R, true, V > &m, T v) noexcept -> std::enable_if_t<(CI< C &&RI< R)>
	Sets the matrix element at [RI, CI]. Row-major implementation.

template<typename T , int C, int R, bool V>
static void	eagine::math::set_rm (matrix< T, C, R, false, V > &m, int ri, int ci, T v) noexcept
	Sets the matrix element at [ri, ci]. Column-major implementation.

template<typename T , int C, int R, bool V>
static void	eagine::math::set_rm (matrix< T, C, R, true, V > &m, int ri, int ci, T v) noexcept
	Sets the matrix element at [ri, ci]. Row-major implementation.

template<typename T , int C, int R, bool RM, bool V>
static auto	eagine::math::transpose (const matrix< T, C, R, RM, V > &m) noexcept -> matrix< T, R, C, RM, V >
	Transposes a matrix.

template<typename T , int C, int R, bool RM, bool V>
static auto	eagine::math::reorder (const matrix< T, C, R, RM, V > &m) noexcept -> matrix< T, C, R, !RM, V >
	Returns a matrix reordered (switches row/column major).

template<typename T , int C, int R, bool V>
static constexpr auto	eagine::math::make_row_major (matrix< T, C, R, true, V > m) noexcept -> matrix< T, C, R, true, V >
	Returns a matrix ordered as row-major.

template<typename T , int C, int R, bool V>
static auto	eagine::math::make_row_major (const matrix< T, C, R, false, V > &m) noexcept -> matrix< T, C, R, true, V >
	Returns a matrix ordered as row-major.

template<typename T , int C, int R, bool V>
static constexpr auto	eagine::math::make_column_major (matrix< T, C, R, false, V > m) noexcept -> matrix< T, C, R, false, V >
	Returns a matrix ordered as column-major.

template<typename T , int C, int R, bool V>
static auto	eagine::math::make_column_major (const matrix< T, C, R, true, V > &m) noexcept -> matrix< T, C, R, false, V >
	Returns a matrix ordered as column-major.

template<int I, typename T , int C, int R, bool RM, bool V>
static constexpr auto	eagine::math::major_vector (const matrix< T, C, R, RM, V > &m) noexcept -> std::enable_if_t<(I<(RM ? R :C)), vector< T,(RM ? C :R), V >>
	Returns the I-th major vector of a matrix.

template<int I, typename T , int C, int R, bool RM, bool V>
static auto	eagine::math::minor_vector (const matrix< T, C, R, RM, V > &m) noexcept -> std::enable_if_t<(I<(RM ? C :R)), vector< T,(RM ? R :C), V >>
	Returns the I-th minor vector of a matrix.

template<int I, typename T , int C, int R, bool V>
static constexpr auto	eagine::math::row (const matrix< T, C, R, true, V > &m) noexcept -> vector< T, C, V >
	Returns the I-th row vector of a matrix. Row-major implementation.

template<int I, typename T , int C, int R, bool V>
static auto	eagine::math::row (const matrix< T, C, R, false, V > &m) noexcept -> vector< T, C, V >
	Returns the I-th row vector of a matrix. Column-major implementation.

template<typename T , int R, int C, bool RM, bool V>
static auto	eagine::math::row (const matrix< T, C, R, RM, V > &m, int i) noexcept -> vector< T, C, V >
	Returns the i-th row vector of a matrix.

template<int I, typename T , int C, int R, bool V>
static constexpr auto	eagine::math::column (const matrix< T, C, R, false, V > &m) noexcept -> vector< T, R, V >
	Returns the I-th column vector of a matrix. Column-major implementation.

template<int I, typename T , int C, int R, bool V>
static auto	eagine::math::column (const matrix< T, C, R, true, V > &m) noexcept -> vector< T, R, V >
	Returns the I-th column vector of a matrix. Row-major implementation.

template<typename T , int R, int C, bool RM, bool V>
static auto	eagine::math::column (const matrix< T, C, R, RM, V > &m, int i) noexcept -> vector< T, R, V >
	Returns the i-th column vector of a matrix.

template<typename T , int M, int N, int K, bool RM1, bool RM2, bool V>
static auto	eagine::math::multiply (const matrix< T, K, M, RM1, V > &m1, const matrix< T, N, K, RM2, V > &m2) noexcept -> matrix< T, N, M, RM1, V >
	Matrix multiplication function.

template<typename T , int C, int R, bool RM, bool V>
static auto	eagine::math::multiply (const matrix< T, C, R, RM, V > &m, const vector< T, C, V > &v) noexcept -> vector< T, R, V >
	Matrix-vector multiplication function.

template<typename MC1 , typename MC2 , typename = std::enable_if_t< is_matrix_constructor<MC1>::value && is_matrix_constructor<MC2>::value && are_multiplicable<constructed_matrix_t<MC1>, constructed_matrix_t<MC2>>::value>>
static auto	eagine::math::operator* (const MC1 &mc1, const MC2 &mc2) noexcept
	Multiplication operator for matrix constructors. More...

template<bool RM, typename MC >
static constexpr auto	eagine::math::construct_matrix (const MC &c) noexcept -> std::enable_if_t< is_matrix_constructor_v< MC > &&is_row_major_v< constructed_matrix_t< MC >>==RM, constructed_matrix_t< MC >>
	Uses the specified matrix constructor `c` to construct a matrix.

template<typename MC1 , typename MC2 , typename = std::enable_if_t< is_matrix_constructor_v<MC1> && is_matrix_constructor_v<MC2> && are_multiplicable<constructed_matrix_t<MC1>, constructed_matrix_t<MC2>>::value>>
static auto	eagine::math::multiply (const MC1 &mc1, const MC2 &mc2) noexcept
	Multiplies the results of two matrix constructors. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_elimination (matrix< T, Ca, R, true, V > &a, matrix< T, Cb, R, true, V > &b) noexcept -> bool
	Implements gaussian elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_elimination (matrix< T, Ca, R, false, V > &a, matrix< T, Cb, R, true, V > &b) noexcept -> bool
	Implements gaussian elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_elimination (matrix< T, Ca, R, true, V > &a, matrix< T, Cb, R, false, V > &b) noexcept -> bool
	Implements gaussian elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_elimination (matrix< T, Ca, R, false, V > &a, matrix< T, Cb, R, false, V > &b) noexcept -> bool
	Implements gaussian elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_jordan_elimination (matrix< T, Ca, R, true, V > &a, matrix< T, Cb, R, true, V > &b) noexcept -> bool
	Implements gauss-jordan elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_jordan_elimination (matrix< T, Ca, R, false, V > &a, matrix< T, Cb, R, true, V > &b) noexcept -> bool
	Implements gauss-jordan elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_jordan_elimination (matrix< T, Ca, R, true, V > &a, matrix< T, Cb, R, false, V > &b) noexcept -> bool
	Implements gauss-jordan elimination on matrices `a` and `b`. More...

template<typename T , int Ca, int Cb, int R, bool V>
static auto	eagine::math::gauss_jordan_elimination (matrix< T, Ca, R, false, V > &a, matrix< T, Cb, R, false, V > &b) noexcept -> bool
	Implements gauss-jordan elimination on matrices `a` and `b`. More...

template<typename T , int N, bool RM, bool V>
static auto	eagine::math::inverse_matrix (matrix< T, N, N, RM, V > m) noexcept -> optionally_valid< matrix< T, N, N, RM, V >>
	Returns the inverse matrix to the matrix passed as argument.

template<typename Ctr , typename = std::enable_if_t<is_matrix_constructor_v<Ctr>>>
static auto	eagine::math::inverse_matrix (const Ctr &ctr) noexcept
	Returns the inverse matrix to the matrix constructed by the argument.

template<typename T , int N, bool V>
static constexpr auto	eagine::math::dimension (const vector< T, N, V > &) noexcept
	Returns the dimension of a vector.

template<typename T , int N, bool V>
static auto	eagine::math::is_zero (const vector< T, N, V > &v) noexcept -> bool
	Tests if a vector has zero lenght.

template<typename T , int N, bool V>
static constexpr auto	eagine::math::dot (const vector< T, N, V > &a, const vector< T, N, V > &b) noexcept
	Vector dot product.

template<typename T , bool V>
static auto	eagine::math::perpendicular (const vector< T, 2, V > &a) noexcept
	Returns a vector perpendicular to argument.

template<typename T , bool V>
static auto	eagine::math::cross (const vector< T, 3, V > &a, const vector< T, 3, V > &b) noexcept
	3D vector cross product.

template<typename T , int N, bool V>
static constexpr auto	eagine::math::magnitude (const vector< T, N, V > &a) noexcept
	Returns the magnitude of a vector. Same as length.

template<typename T , int N, bool V>
static constexpr auto	eagine::math::length (const vector< T, N, V > &a) noexcept
	Returns the length of a vector.

template<typename T , int N, bool V>
static auto	eagine::math::normalized (const vector< T, N, V > &a) noexcept
	Returns normalized argument.

template<typename T , int N, bool V>
static constexpr auto	eagine::math::distance (const vector< T, N, V > &a, const vector< T, N, V > &b) noexcept
	Returns the distance between two vectors.

Variables
template<typename X >
const auto	eagine::math::is_row_major_v
	Trait indicating if a matrix type is row-major.

template<typename X >
constexpr auto	eagine::math::is_matrix_constructor_v
	Trait indicating if a type X is a matrix constructor. More...

static constexpr const auto	eagine::math::pi
	The pi constant. More...

static const auto	eagine::math::phi
	The phi constant. More...

Detailed Description

Typedef Documentation

◆ matrix_reflection_x

template<typename T , bool V>

using eagine::math::matrix_reflection_x = typedef convertible_matrix_constructor<reflection_x<matrix<T, 4, 4, true, V> >>

Alias for constructor of reflection along x-axis transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_rotation_z; matrix_reflection_y; matrix_reflection_z; matrix_scale; matrix_uniform_scale

◆ matrix_reflection_y

template<typename T , bool V>

using eagine::math::matrix_reflection_y = typedef convertible_matrix_constructor<reflection_y<matrix<T, 4, 4, true, V> >>

Alias for constructor of reflection along y-axis transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_rotation_z; matrix_reflection_x; matrix_reflection_z; matrix_scale; matrix_uniform_scale

◆ matrix_reflection_z

template<typename T , bool V>

using eagine::math::matrix_reflection_z = typedef convertible_matrix_constructor<reflection_z<matrix<T, 4, 4, true, V> >>

Alias for constructor of reflection along z-axis transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_rotation_z; matrix_reflection_x; matrix_reflection_y; matrix_scale; matrix_uniform_scale

◆ matrix_rotation_x

template<typename T , bool V>

using eagine::math::matrix_rotation_x = typedef convertible_matrix_constructor<rotation_x<matrix<T, 4, 4, true, V> >>

Alias for constructor of rotation along x-axis transformation matrix.

See also: matrix_translation; matrix_rotation_y; matrix_rotation_z; matrix_scale; matrix_uniform_scale

Examples: application/000_stencil_shadow/resources.cpp, application/021_cel_shading/resources.cpp, application/023_sketch/resources.cpp, application/025_recursive_cube/resources.cpp, application/026_halo/resources.cpp, oglplus/012_glfw3_glew_cube.cpp, and oglplus/020_glfw3_glew_recursive_cube.cpp.

◆ matrix_rotation_y

template<typename T , bool V>

using eagine::math::matrix_rotation_y = typedef convertible_matrix_constructor<rotation_y<matrix<T, 4, 4, true, V> >>

Alias for constructor of rotation along y-axis transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_z; matrix_reflection_x; matrix_reflection_y; matrix_reflection_z; matrix_scale; matrix_uniform_scale

Examples: application/021_cel_shading/resources.cpp, application/025_recursive_cube/resources.cpp, oglplus/012_glfw3_glew_cube.cpp, and oglplus/020_glfw3_glew_recursive_cube.cpp.

◆ matrix_rotation_z

template<typename T , bool V>

using eagine::math::matrix_rotation_z = typedef convertible_matrix_constructor<rotation_z<matrix<T, 4, 4, true, V> >>

Alias for constructor of rotation along z-axis transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_reflection_x; matrix_reflection_y; matrix_reflection_z; matrix_scale; matrix_uniform_scale

Examples: application/021_cel_shading/resources.cpp, application/025_recursive_cube/resources.cpp, oglplus/012_glfw3_glew_cube.cpp, and oglplus/020_glfw3_glew_recursive_cube.cpp.

◆ matrix_scale

template<typename T , bool V>

using eagine::math::matrix_scale = typedef convertible_matrix_constructor<scale<matrix<T, 4, 4, true, V> >>

Alias for constructor of scale transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_rotation_z; matrix_uniform_scale

◆ matrix_translation

template<typename T , bool V>

using eagine::math::matrix_translation = typedef convertible_matrix_constructor<translation<matrix<T, 4, 4, true, V> >>

Alias for constructor of uniform translation transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_rotation_z; matrix_reflection_x; matrix_reflection_y; matrix_reflection_z; matrix_scale; matrix_uniform_scale

Examples: application/025_recursive_cube/main.cpp, oglplus/012_glfw3_glew_cube.cpp, and oglplus/020_glfw3_glew_recursive_cube.cpp.

◆ matrix_uniform_scale

template<typename T , bool V>

using eagine::math::matrix_uniform_scale = typedef convertible_matrix_constructor<uniform_scale<matrix<T, 4, 4, true, V> >>

Alias for constructor of uniform scale transformation matrix.

See also: matrix_translation; matrix_rotation_x; matrix_rotation_y; matrix_rotation_z; matrix_reflection_x; matrix_reflection_y; matrix_reflection_z; matrix_scale

Function Documentation

◆ cosine_wave01()

template<typename T >

static constexpr auto eagine::math::cosine_wave01 ( T x )

staticconstexprnoexcept

Calculates cosine of x, mapped to interval (0, 1).

Precondition: 0 <= x <= 1

◆ gauss_elimination() [1/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_elimination	(	matrix< T, Ca, R, false, V > &	a,
		matrix< T, Cb, R, false, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gaussian elimination on matrices a and b.

See also: gauss_jordan_elimination

◆ gauss_elimination() [2/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_elimination	(	matrix< T, Ca, R, false, V > &	a,
		matrix< T, Cb, R, true, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gaussian elimination on matrices a and b.

See also: gauss_jordan_elimination

◆ gauss_elimination() [3/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_elimination	(	matrix< T, Ca, R, true, V > &	a,
		matrix< T, Cb, R, false, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gaussian elimination on matrices a and b.

See also: gauss_jordan_elimination

◆ gauss_elimination() [4/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_elimination	(	matrix< T, Ca, R, true, V > &	a,
		matrix< T, Cb, R, true, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gaussian elimination on matrices a and b.

See also: gauss_jordan_elimination

Referenced by eagine::math::gauss_elimination(), and eagine::math::gauss_jordan_elimination().

◆ gauss_jordan_elimination() [1/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_jordan_elimination	(	matrix< T, Ca, R, false, V > &	a,
		matrix< T, Cb, R, false, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gauss-jordan elimination on matrices a and b.

See also: gauss_elimination; inverse_matrix

◆ gauss_jordan_elimination() [2/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_jordan_elimination	(	matrix< T, Ca, R, false, V > &	a,
		matrix< T, Cb, R, true, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gauss-jordan elimination on matrices a and b.

See also: gauss_elimination; inverse_matrix

◆ gauss_jordan_elimination() [3/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_jordan_elimination	(	matrix< T, Ca, R, true, V > &	a,
		matrix< T, Cb, R, false, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gauss-jordan elimination on matrices a and b.

See also: gauss_elimination; inverse_matrix

◆ gauss_jordan_elimination() [4/4]

template<typename T , int Ca, int Cb, int R, bool V>

static auto eagine::math::gauss_jordan_elimination	(	matrix< T, Ca, R, true, V > &	a,
		matrix< T, Cb, R, true, V > &	b
	)		-> bool

inlinestaticnoexcept

Implements gauss-jordan elimination on matrices a and b.

See also: gauss_elimination; inverse_matrix

Referenced by eagine::math::gauss_jordan_elimination(), and eagine::math::inverse_matrix().

◆ interpolate_linear()

template<typename T , typename C >

static auto eagine::math::interpolate_linear	(	const T &	a,
		const T &	b,
		C	coef
	)

inlinestatic

Linear interpolation between a and b.

See also: lerp

Referenced by eagine::math::lerp().

◆ lerp()

template<typename T , typename C >

static auto eagine::math::lerp	(	const T &	a,
		const T &	b,
		C	coef
	)

inlinestatic

Same as interpolate_linear.

See also: interpolate_linear

Referenced by eagine::math::smooth_lerp().

◆ line_sphere_intersection()

template<typename T , bool V>

static constexpr auto eagine::math::line_sphere_intersection	(	const line< T, V > &	ray,
		const sphere< T, V > &	sph
	)		-> std:: pair<optionally_valid<vector<T, 3, V>>, optionally_valid<vector<T, 3, V>>>

staticconstexprnoexcept

Finds line-sphere intersection points.

See also: nearest_line_sphere_intersection

◆ multiply()

template<typename MC1 , typename MC2 , typename = std::enable_if_t< is_matrix_constructor_v<MC1> && is_matrix_constructor_v<MC2> && are_multiplicable<constructed_matrix_t<MC1>, constructed_matrix_t<MC2>>::value>>

static auto eagine::math::multiply	(	const MC1 &	mc1,
		const MC2 &	mc2
	)

inlinestaticnoexcept

Multiplies the results of two matrix constructors.

This is typically more efficient than constructing the two matrices and multiplying them.

◆ nearest_line_sphere_intersection()

template<typename T , bool V>

static constexpr auto eagine::math::nearest_line_sphere_intersection	(	const line< T, V > &	ray,
		const sphere< T, V > &	sph
	)		-> optionally_valid<vector<T, 3, V>>

staticconstexprnoexcept

Finds nearest line-sphere intersection point.

See also: line_sphere_intersection

◆ operator*()

template<typename MC1 , typename MC2 , typename = std::enable_if_t< is_matrix_constructor<MC1>::value && is_matrix_constructor<MC2>::value && are_multiplicable<constructed_matrix_t<MC1>, constructed_matrix_t<MC2>>::value>>

static auto eagine::math::operator*	(	const MC1 &	mc1,
		const MC2 &	mc2
	)

inlinestaticnoexcept

Multiplication operator for matrix constructors.

Doing multiplication on matrix constructors is typically more efficient than doing multiplication on the constructed matrices, because it can save row/column reordering operations.

◆ sigmoid01() [1/2]

template<typename T >

static constexpr auto eagine::math::sigmoid01 ( T x )

staticconstexprnoexcept

Calculates the default sigmoid of x.

Precondition: 0 <= x <= 1

◆ sigmoid01() [2/2]

template<typename T , typename C >

static constexpr auto eagine::math::sigmoid01	(	T	x,
		C	c
	)

staticconstexprnoexcept

Calculates the sigmoid of x. The value c controls steepness.

Precondition: 0 <= x <= 1

Referenced by eagine::animated_value< T, F, S >::get(), and eagine::math::sigmoid01().

◆ sine_sigmoid01()

template<typename T >

static auto eagine::math::sine_sigmoid01 ( T x )

inlinestatic

Calculates goniometric sigmoid (cos in interval (0, 1)) of x.

Precondition: 0 <= x <= 1

Referenced by eagine::math::smooth_lerp().

◆ sine_wave01()

template<typename T >

static constexpr auto eagine::math::sine_wave01 ( T x )

staticconstexprnoexcept

Calculates sine of x, mapped to interval (0, 1).

Precondition: 0 <= x <= 1

◆ smooth_lerp()

template<typename T , typename C >

static auto eagine::math::smooth_lerp	(	const T &	a,
		const T &	b,
		C	coef
	)

inlinestatic

Linear interpolation with coef transformed by sine_sigmoid01.

See also: interpolate_linear; sine_sigmoid01

Examples: application/019_scaled_cubes/resources.cpp.

Referenced by eagine::oglp::orbiting_camera::orbit(), and eagine::math::smooth_oscillate().

◆ smooth_oscillate()

template<typename T , typename C >

static auto eagine::math::smooth_oscillate	(	const T &	a,
		C	coef
	)

inlinestatic

Smooth interpolation between negative a and a.

See also: smooth_lerp

Variable Documentation

◆ is_matrix_constructor_v

template<typename X >

constexpr auto eagine::math::is_matrix_constructor_v

constexpr

Trait indicating if a type X is a matrix constructor.

Matrix constructor types define a nullary call operator that can construct a matrix instantiation.

◆ phi

eagine::math::phi

static

The phi constant.

See also: pi

◆ pi

eagine::math::pi

staticconstexpr

The pi constant.

See also: phi

Referenced by eagine::math::cosine_wave01(), eagine::right_angles_(), eagine::math::sine_sigmoid01(), eagine::math::sine_wave01(), and eagine::turns_().

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ matrix_reflection_x

◆ matrix_reflection_y

◆ matrix_reflection_z

◆ matrix_rotation_x

◆ matrix_rotation_y

◆ matrix_rotation_z

◆ matrix_scale

◆ matrix_translation

◆ matrix_uniform_scale

Function Documentation

◆ cosine_wave01()

◆ gauss_elimination() [1/4]

◆ gauss_elimination() [2/4]

◆ gauss_elimination() [3/4]

◆ gauss_elimination() [4/4]

◆ gauss_jordan_elimination() [1/4]

◆ gauss_jordan_elimination() [2/4]

◆ gauss_jordan_elimination() [3/4]

◆ gauss_jordan_elimination() [4/4]

◆ interpolate_linear()

◆ lerp()

◆ line_sphere_intersection()

◆ multiply()

◆ nearest_line_sphere_intersection()

◆ operator*()

◆ sigmoid01() [1/2]

◆ sigmoid01() [2/2]

◆ sine_sigmoid01()

◆ sine_wave01()

◆ smooth_lerp()

◆ smooth_oscillate()

Variable Documentation

◆ is_matrix_constructor_v

◆ phi

◆ pi