Namespaces
namespace	Detail
namespace	Entropy
namespace	Hash

Classes
struct	Matrix
	Generic fixed-size matrix container. More...
class	Random
	Static wrapper around RandomEngine for convenience. More...
class	RandomEngine
	High-performance 64-bit state, 32-bit output PRNG based on PCG32. More...
struct	Vector
	General N-dimensional fixed-size vector container. More...
struct	Vector< T, 2 >
	2-dimensional vector. More...
struct	Vector< T, 3 >
	3-dimensional vector. More...
struct	Vector< T, 4 >
	4-dimensional vector. More...

Typedefs
using	mat2 = Matrix<float, 2, 2>
	2x2 single-precision floating-point matrix.
using	mat3 = Matrix<float, 3, 3>
	3x3 single-precision floating-point matrix.
using	mat4 = Matrix<float, 4, 4>
	4x4 single-precision floating-point matrix.
using	dmat2 = Matrix<double, 2, 2>
	2x2 double-precision floating-point matrix.
using	dmat3 = Matrix<double, 3, 3>
	3x3 double-precision floating-point matrix.
using	dmat4 = Matrix<double, 4, 4>
	4x4 double-precision floating-point matrix.
using	imat2 = Matrix<int, 2, 2>
	2x2 integer matrix.
using	imat3 = Matrix<int, 3, 3>
	3x3 integer matrix.
using	imat4 = Matrix<int, 4, 4>
	4x4 integer matrix.
using	ivec2 = Vector<int, 2>
using	ivec3 = Vector<int, 3>
	2D integer vector
using	ivec4 = Vector<int, 4>
	3D integer vector
using	uvec2 = Vector<unsigned, 2>
	4D integer vector
using	uvec3 = Vector<unsigned, 3>
	2D unsigned vector
using	uvec4 = Vector<unsigned, 4>
	3D unsigned vector
using	vec2 = Vector<float, 2>
	4D unsigned vector
using	vec3 = Vector<float, 3>
	2D float vector
using	vec4 = Vector<float, 4>
	3D float vector
using	dvec2 = Vector<double, 2>
	4D float vector
using	dvec3 = Vector<double, 3>
	2D double vector
using	dvec4 = Vector<double, 4>
	3D double vector

Functions
template<typename T>
constexpr T	Lerp (T a, T b, float t)
	Linear interpolation between a and b by factor t.
template<typename T>
constexpr T	Min (T a, T b)
	Return the minimum of two values.
template<typename T>
constexpr T	Max (T a, T b)
	Return the maximum of two values.
template<typename T>
constexpr T	Clamp (T value, T min, T max)
	Clamp a value between a minimum and maximum.
template<typename T>
constexpr T	Saturate (T value)
	Clamp a value to the [0,1] range.
template<typename T>
constexpr T	Sign (T value)
	Signum function: returns -1, 0, or +1.
template<typename T>
constexpr T	Abs (T value)
	Absolute value.
template<typename T>
constexpr T	Floor (T value)
	Floor function for floating-point values.
template<typename T>
constexpr T	Ceil (T value)
	Ceiling function for floating-point values.
template<typename T>
constexpr T	Fract (T value)
	Fractional part of a value.
template<typename T>
constexpr T	Square (T value)
	Square of a value.
template<typename T>
constexpr T	Cube (T value)
	Cube of a value.
constexpr float	Smoothstep (float edge0, float edge1, float x)
	Smoothstep interpolation between edge0 and edge1.
constexpr float	CTInverseSqrt (float x)
	Fast compile-time inverse square root (single Newton step).
constexpr float	CTSqrt (const float x)
	Fast compile-time square root using bit manipulation.
float	InverseSqrt (const float x)
	Inverse square root using hardware rsqrt.
float	Sqrt (const float x)
	Standard square root using hardware sqrt.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	operator+ (const Matrix< T, Rows, Cols > &a, const Matrix< T, Rows, Cols > &b)
	Adds two matrices element-wise.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	operator- (const Matrix< T, Rows, Cols > &a, const Matrix< T, Rows, Cols > &b)
	Subtracts two matrices element-wise.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	operator* (const Matrix< T, Rows, Cols > &a, const T &scalar)
	Multiplies each matrix element by a scalar.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	operator* (const T &scalar, const Matrix< T, Rows, Cols > &a)
	Multiplies each matrix element by a scalar.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	operator/ (const Matrix< T, Rows, Cols > &a, const T &scalar)
	Divides each matrix element by a scalar.
template<typename T, size_t RowsA, size_t ColsA, size_t ColsB>
constexpr Matrix< T, RowsA, ColsB >	operator* (const Matrix< T, RowsA, ColsA > &a, const Matrix< T, ColsA, ColsB > &b)
	Performs matrix multiplication (dot product).
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	Zero ()
	Generates a zero matrix of size Rows x Cols.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Cols, Rows >	Transpose (const Matrix< T, Rows, Cols > &a)
	Transposes the given matrix (rows become columns).
template<typename T>
constexpr Matrix< T, 4, 4 >	RotateX (T angle)
	Creates a 4x4 rotation matrix around the X axis.
template<typename T>
constexpr Matrix< T, 4, 4 >	RotateY (T angle)
	Creates a 4x4 rotation matrix around the Y axis.
template<typename T>
constexpr Matrix< T, 4, 4 >	RotateZ (T angle)
	Creates a 4x4 rotation matrix around the Z axis.
template<typename T>
constexpr Matrix< T, 2, 2 >	Scale (T tx, T ty)
	Constructs a 2D scaling matrix.
template<typename T>
constexpr Matrix< T, 4, 4 >	Scale (T sx, T sy, T sz)
	Constructs a 4x4 3D non-uniform scaling matrix.
template<typename T>
constexpr Matrix< T, 4, 4 >	Scale (const Vector< T, 3 > &s)
	Constructs a 4x4 3D non-uniform scaling matrix from a vector.
template<typename T, size_t N>
constexpr Matrix< T, N, N >	Scale (T s)
	Constructs a uniform scaling matrix of size N x N.
template<typename T>
constexpr Matrix< T, 3, 3 >	Translate (T tx, T ty)
	Constructs a 3x3 2D translation matrix.
constexpr Matrix< float, 4, 4 >	Translate (float tx, float ty, float tz)
	Constructs a 4x4 3D translation matrix.
template<typename T>
constexpr Matrix< T, 4, 4 >	Translate (const Matrix< T, 4, 4 > &m, const Vector< T, 3 > &v)
	Applies a 3D translation to a 4x4 matrix using a vector.
template<typename T, size_t N>
constexpr Matrix< T, N, N >	Identity ()
	Generates an identity matrix of size NxN.
template<typename T, size_t N>
constexpr T	Trace (const Matrix< T, N, N > &a)
	Computes the trace (sum of diagonal elements) of a square matrix.
template<typename T, size_t Rows, size_t Cols>
constexpr T	Norm (const Matrix< T, Rows, Cols > &a)
	Computes the Frobenius norm of the matrix.
template<typename T, size_t Rows, size_t Cols>
constexpr Matrix< T, Rows, Cols >	Normalize (const Matrix< T, Rows, Cols > &a)
	Normalizes the matrix by dividing each element by the Frobenius norm.
template<typename T>
constexpr T	Determinant (const Matrix< T, 2, 2 > &a)
	Computes the determinant of a 2x2 matrix.
template<typename T>
constexpr T	Determinant (const Matrix< T, 3, 3 > &a)
	Computes the determinant of a 3x3 matrix.
template<typename T>
constexpr T	Determinant (const Matrix< T, 4, 4 > &a)
	Computes the determinant of a 4x4 matrix.
template<typename T>
constexpr Matrix< T, 2, 2 >	Inverse (const Matrix< T, 2, 2 > &a)
	Computes the inverse of a 2x2 matrix.
template<typename T>
constexpr Matrix< T, 3, 3 >	Inverse (const Matrix< T, 3, 3 > &a)
	Computes the inverse of a 3x3 matrix.
template<typename T>
constexpr Matrix< T, 4, 4 >	Inverse (const Matrix< T, 4, 4 > &a)
	Computes the inverse of a 4x4 matrix.
template<typename T>
constexpr Matrix< T, 3, 3 >	ToMat3 (const Matrix< T, 4, 4 > &m)
	Converts a 4x4 Matrix into a 3x3 Matrix.
template<typename T>
constexpr Matrix< T, 4, 4 >	LookAt (const Vector< T, 3 > &position, const Vector< T, 3 > &target, const Vector< T, 3 > &up)
	Creates a look-at view matrix using position, target, and up vectors.
constexpr float	Radians (float degrees)
	Convert degrees to radians.
constexpr Vector< float, 3 >	Radians (Vector< float, 3 > vector)
	Convert a Vector3s components from degrees to radians.
constexpr float	Degrees (float radians)
	Convert radians to degrees.
constexpr Vector< float, 3 >	Degrees (Vector< float, 3 > vector)
	Convert a Vector3s components from radians to degrees.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
float	Sin (float radians)
	Computes the sine of an angle in radians using a fast polynomial approximation.
template<Detail::PrecisionMode Mode = Detail::PrecisionMode::Standard>
float	Cos (float radians)
	Computes the cosine of an angle in radians using a fast polynomial approximation.
template<typename T, size_t N>
constexpr Vector< T, N >	operator+ (const Vector< T, N > &a, const Vector< T, N > &b)
	Component-wise addition of two vectors.
template<typename T, size_t N>
constexpr Vector< T, N >	operator- (const Vector< T, N > &a, const Vector< T, N > &b)
	Component-wise subtraction of two vectors.
template<typename T, size_t N>
constexpr Vector< T, N >	operator* (const Vector< T, N > &a, const T &scalar)
	Scalar multiplication (vector * scalar).
template<typename T, size_t N>
constexpr Vector< T, N >	operator* (const T &scalar, const Vector< T, N > &a)
	Scalar multiplication (scalar * vector).
template<typename T, size_t N>
constexpr Vector< T, N >	operator/ (const Vector< T, N > &a, const T &scalar)
	Scalar division of a vector.
template<typename T, size_t N>
constexpr Vector< T, N > &	operator+= (Vector< T, N > &a, const Vector< T, N > &b)
	Compound addition assignment (vector += vector).
template<typename T, size_t N>
constexpr Vector< T, N > &	operator-= (Vector< T, N > &a, const Vector< T, N > &b)
	Compound subtraction assignment (vector -= vector).
template<typename T, size_t N>
constexpr Vector< T, N > &	operator*= (Vector< T, N > &a, const T &scalar)
	Compound scalar multiplication assignment (vector *= scalar).
template<typename T, size_t N>
constexpr Vector< T, N > &	operator/= (Vector< T, N > &a, const T &scalar)
	Compound scalar division assignment (vector /= scalar).
template<typename T, size_t N>
constexpr T	Dot (const Vector< T, N > &a, const Vector< T, N > &b)
	Dot product of two vectors.
template<typename T>
constexpr Vector< T, 3 >	Cross (const Vector< T, 3 > &a, const Vector< T, 3 > &b)
	Cross product for 3D vectors.
template<typename T, size_t N>
constexpr T	LengthSq (const Vector< T, N > &a)
	Squared length (magnitude) of a vector.
template<typename T, size_t N>
T	Length (const Vector< T, N > &a)
	Length (magnitude) of a vector.
template<typename T, size_t N>
Vector< T, N >	Normalize (const Vector< T, N > &a)
	Normalizes a vector to unit length.
template<typename T, size_t N>
constexpr Vector< T, N >	Project (const Vector< T, N > &a, const Vector< T, N > &b)
	Projects vector a onto vector b.
template<typename T, size_t N>
constexpr Vector< T, N >	Reflect (const Vector< T, N > &a, const Vector< T, N > &normal)
	Reflects vector a around the given normal.
template<typename T, size_t N>
constexpr Vector< T, N >	MinComponent (const Vector< T, N > &a, const Vector< T, N > &b)
	Element-wise minimum of two vectors.
template<typename T, size_t N>
constexpr Vector< T, N >	MaxComponent (const Vector< T, N > &a, const Vector< T, N > &b)
	Element-wise maximum of two vectors.
template<typename T, size_t N>
constexpr Vector< T, N >	Abs (const Vector< T, N > &a)
	Element-wise absolute value of a vector.
template<typename T, size_t N>
constexpr bool	operator== (const Vector< T, N > &a, const Vector< T, N > &b)
	Approximate equality comparison with tolerance.
template<typename T, size_t N>
constexpr bool	operator!= (const Vector< T, N > &a, const Vector< T, N > &b)
	Inequality comparison.
template<typename T, size_t N>
T	AngleBetween (const Vector< T, N > &a, const Vector< T, N > &b)
	Angle between two vectors in radians.
template<typename T, size_t N>
constexpr Vector< T, N >	Lerp (const Vector< T, N > &a, const Vector< T, N > &b, T t)
	Linear interpolation between two vectors.
template<typename T>
constexpr bool	operator== (const Vector< T, 2 > &lhs, const Vector< T, 2 > &rhs)
	Equality comparison for 2D vectors.
template<typename T>
constexpr bool	operator!= (const Vector< T, 2 > &lhs, const Vector< T, 2 > &rhs)
	Inequality comparison for 2D vectors.
template<typename T>
constexpr bool	operator== (const Vector< T, 3 > &lhs, const Vector< T, 3 > &rhs)
	Equality comparison for 3D vectors.
template<typename T>
constexpr bool	operator!= (const Vector< T, 3 > &lhs, const Vector< T, 3 > &rhs)
	Inequality comparison for 3D vectors.
template<typename T>
constexpr bool	operator== (const Vector< T, 4 > &lhs, const Vector< T, 4 > &rhs)
	Equality comparison for 4D vectors.
template<typename T>
constexpr bool	operator!= (const Vector< T, 4 > &lhs, const Vector< T, 4 > &rhs)
	Inequality comparison for 4D vectors.

Variables
template<typename T>
constexpr T	Pi = static_cast<T>(3.14159265358979323846)
	The value of pi.
template<typename T>
constexpr T	TwoPi = static_cast<T>(6.28318530717958647692)
	The value of 2pi (two pi).
template<typename T>
constexpr T	HalfPi = static_cast<T>(1.57079632679489661923)
	The value of pi/2 (half pi).
template<typename T>
constexpr T	QuarterPi = static_cast<T>(0.78539816339744830961)
	The value of pi/4 (quarter pi).
template<typename T>
constexpr T	InvPi = static_cast<T>(0.31830988618379067153)
	1/pi (inverse pi).
template<typename T>
constexpr T	InvTwoPi = static_cast<T>(0.15915494309189533576)
	1/(2pi) (inverse two pi).
template<typename T>
constexpr T	DegToRad = Pi<T> / static_cast<T>(180)
	Degrees-to-radians conversion factor (pi/180).
template<typename T>
constexpr T	RadToDeg = static_cast<T>(180) / Pi<T>
	Radians-to-degrees conversion factor (180/pi).
template<typename T>
constexpr T	Sqrt2 = static_cast<T>(1.41421356237309504880)
	sqrt2 (square root of two).
template<typename T>
constexpr T	InvSqrt2 = static_cast<T>(0.70710678118654752440)
	1/sqrt2 (inverse square root of two).
template<typename T>
constexpr T	Sqrt3 = static_cast<T>(1.73205080756887729352)
	sqrt3 (square root of three).
template<typename T>
constexpr T	InvSqrt3 = static_cast<T>(0.57735026918962576450)
	1/sqrt3 (inverse square root of three).
template<typename T>
constexpr T	E = static_cast<T>(2.71828182845904523536)
	Euler's number (e).
template<typename T>
constexpr T	InvE = static_cast<T>(0.36787944117144232159)
	1/e (inverse of Euler's number).
template<typename T>
constexpr T	Ln2 = static_cast<T>(0.69314718055994530942)
	Natural logarithm of 2 (ln(2)).
template<typename T>
constexpr T	Ln10 = static_cast<T>(2.30258509299404568402)
	Natural logarithm of 10 (ln(10)).
template<typename T>
constexpr T	Log2E = static_cast<T>(1.44269504088896340736)
	Base-2 logarithm of e (log2(e)).
template<typename T>
constexpr T	Log10E = static_cast<T>(0.43429448190325182765)
	Base-10 logarithm of e (log10(e)).
template<typename T>
constexpr T	Phi = static_cast<T>(1.61803398874989484820)
	The golden ratio.
template<typename T>
constexpr T	Epsilon = static_cast<T>(1e-7)
	Small epsilon for floating-point comparisons.

Typedef Documentation

◆ ivec2

using Crux::ivec2 = Vector<int, 2>

Function Documentation

◆ operator!=() [1/3]

template<typename T>

bool Crux::operator!=	(	const Vector< T, 2 > &	lhs,
		const Vector< T, 2 > &	rhs )

constexpr

Inequality comparison for 2D vectors.

◆ operator!=() [2/3]

template<typename T>

bool Crux::operator!=	(	const Vector< T, 3 > &	lhs,
		const Vector< T, 3 > &	rhs )

constexpr

Inequality comparison for 3D vectors.

◆ operator!=() [3/3]

template<typename T>

bool Crux::operator!=	(	const Vector< T, 4 > &	lhs,
		const Vector< T, 4 > &	rhs )

constexpr

Inequality comparison for 4D vectors.

◆ operator==() [1/3]

template<typename T>

bool Crux::operator==	(	const Vector< T, 2 > &	lhs,
		const Vector< T, 2 > &	rhs )

constexpr

Equality comparison for 2D vectors.

◆ operator==() [2/3]

template<typename T>

bool Crux::operator==	(	const Vector< T, 3 > &	lhs,
		const Vector< T, 3 > &	rhs )

constexpr

Equality comparison for 3D vectors.

◆ operator==() [3/3]

template<typename T>

bool Crux::operator==	(	const Vector< T, 4 > &	lhs,
		const Vector< T, 4 > &	rhs )

constexpr

Equality comparison for 4D vectors.

Variable Documentation

◆ DegToRad

template<typename T>

T Crux::DegToRad = Pi<T> / static_cast<T>(180)

inlineconstexpr

Degrees-to-radians conversion factor (pi/180).

◆ E

template<typename T>

T Crux::E = static_cast<T>(2.71828182845904523536)

inlineconstexpr

Euler's number (e).

◆ Epsilon

template<typename T>

T Crux::Epsilon = static_cast<T>(1e-7)

inlineconstexpr

Small epsilon for floating-point comparisons.

◆ HalfPi

template<typename T>

T Crux::HalfPi = static_cast<T>(1.57079632679489661923)

inlineconstexpr

The value of pi/2 (half pi).

◆ InvE

template<typename T>

T Crux::InvE = static_cast<T>(0.36787944117144232159)

inlineconstexpr

1/e (inverse of Euler's number).

◆ InvPi

template<typename T>

T Crux::InvPi = static_cast<T>(0.31830988618379067153)

inlineconstexpr

1/pi (inverse pi).

◆ InvSqrt2

template<typename T>

T Crux::InvSqrt2 = static_cast<T>(0.70710678118654752440)

inlineconstexpr

1/sqrt2 (inverse square root of two).

◆ InvSqrt3

template<typename T>

T Crux::InvSqrt3 = static_cast<T>(0.57735026918962576450)

inlineconstexpr

1/sqrt3 (inverse square root of three).

◆ InvTwoPi

template<typename T>

T Crux::InvTwoPi = static_cast<T>(0.15915494309189533576)

inlineconstexpr

1/(2pi) (inverse two pi).

◆ Ln10

template<typename T>

T Crux::Ln10 = static_cast<T>(2.30258509299404568402)

inlineconstexpr

Natural logarithm of 10 (ln(10)).

◆ Ln2

template<typename T>

T Crux::Ln2 = static_cast<T>(0.69314718055994530942)

inlineconstexpr

Natural logarithm of 2 (ln(2)).

◆ Log10E

template<typename T>

T Crux::Log10E = static_cast<T>(0.43429448190325182765)

inlineconstexpr

Base-10 logarithm of e (log10(e)).

◆ Log2E

template<typename T>

T Crux::Log2E = static_cast<T>(1.44269504088896340736)

inlineconstexpr

Base-2 logarithm of e (log2(e)).

◆ Phi

template<typename T>

T Crux::Phi = static_cast<T>(1.61803398874989484820)

inlineconstexpr

The golden ratio.

◆ Pi

template<typename T>

T Crux::Pi = static_cast<T>(3.14159265358979323846)

inlineconstexpr

The value of pi.

◆ QuarterPi

template<typename T>

T Crux::QuarterPi = static_cast<T>(0.78539816339744830961)

inlineconstexpr

The value of pi/4 (quarter pi).

◆ RadToDeg

template<typename T>

T Crux::RadToDeg = static_cast<T>(180) / Pi<T>

inlineconstexpr

Radians-to-degrees conversion factor (180/pi).

◆ Sqrt2

template<typename T>

T Crux::Sqrt2 = static_cast<T>(1.41421356237309504880)

inlineconstexpr

sqrt2 (square root of two).

◆ Sqrt3

template<typename T>

T Crux::Sqrt3 = static_cast<T>(1.73205080756887729352)

inlineconstexpr

sqrt3 (square root of three).

◆ TwoPi

template<typename T>

T Crux::TwoPi = static_cast<T>(6.28318530717958647692)

inlineconstexpr

The value of 2pi (two pi).

Namespaces

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ ivec2

Function Documentation

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

Variable Documentation

◆ DegToRad

◆ E

◆ Epsilon

◆ HalfPi

◆ InvE

◆ InvPi

◆ InvSqrt2

◆ InvSqrt3

◆ InvTwoPi

◆ Ln10

◆ Ln2

◆ Log10E

◆ Log2E

◆ Phi

◆ Pi

◆ QuarterPi

◆ RadToDeg

◆ Sqrt2

◆ Sqrt3

◆ TwoPi