Vector types and operations. More...

Classes
struct	Crux::Vector< T, 2 >
	2-dimensional vector. More...
struct	Crux::Vector< T, 3 >
	3-dimensional vector. More...
struct	Crux::Vector< T, 4 >
	4-dimensional vector. More...
struct	Crux::Vector< T, N >
	General N-dimensional fixed-size vector container. More...

Typedefs
using	Crux::ivec3 = Vector<int, 3>
	2D integer vector
using	Crux::ivec4 = Vector<int, 4>
	3D integer vector
using	Crux::uvec2 = Vector<unsigned, 2>
	4D integer vector
using	Crux::uvec3 = Vector<unsigned, 3>
	2D unsigned vector
using	Crux::uvec4 = Vector<unsigned, 4>
	3D unsigned vector
using	Crux::vec2 = Vector<float, 2>
	4D unsigned vector
using	Crux::vec3 = Vector<float, 3>
	2D float vector
using	Crux::vec4 = Vector<float, 4>
	3D float vector
using	Crux::dvec2 = Vector<double, 2>
	4D float vector
using	Crux::dvec3 = Vector<double, 3>
	2D double vector
using	Crux::dvec4 = Vector<double, 4>
	3D double vector

Functions
template<typename T, size_t N>
constexpr Vector< T, N >	Crux::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 >	Crux::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 >	Crux::operator* (const Vector< T, N > &a, const T &scalar)
	Scalar multiplication (vector * scalar).
template<typename T, size_t N>
constexpr Vector< T, N >	Crux::operator* (const T &scalar, const Vector< T, N > &a)
	Scalar multiplication (scalar * vector).
template<typename T, size_t N>
constexpr Vector< T, N >	Crux::operator/ (const Vector< T, N > &a, const T &scalar)
	Scalar division of a vector.
template<typename T, size_t N>
constexpr Vector< T, N > &	Crux::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 > &	Crux::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 > &	Crux::operator*= (Vector< T, N > &a, const T &scalar)
	Compound scalar multiplication assignment (vector *= scalar).
template<typename T, size_t N>
constexpr Vector< T, N > &	Crux::operator/= (Vector< T, N > &a, const T &scalar)
	Compound scalar division assignment (vector /= scalar).
template<typename T, size_t N>
constexpr T	Crux::Dot (const Vector< T, N > &a, const Vector< T, N > &b)
	Dot product of two vectors.
template<typename T>
constexpr Vector< T, 3 >	Crux::Cross (const Vector< T, 3 > &a, const Vector< T, 3 > &b)
	Cross product for 3D vectors.
template<typename T, size_t N>
constexpr T	Crux::LengthSq (const Vector< T, N > &a)
	Squared length (magnitude) of a vector.
template<typename T, size_t N>
T	Crux::Length (const Vector< T, N > &a)
	Length (magnitude) of a vector.
template<typename T, size_t N>
Vector< T, N >	Crux::Normalize (const Vector< T, N > &a)
	Normalizes a vector to unit length.
template<typename T, size_t N>
constexpr Vector< T, N >	Crux::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 >	Crux::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 >	Crux::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 >	Crux::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 >	Crux::Abs (const Vector< T, N > &a)
	Element-wise absolute value of a vector.
template<typename T, size_t N>
constexpr bool	Crux::operator== (const Vector< T, N > &a, const Vector< T, N > &b)
	Approximate equality comparison with tolerance.
template<typename T, size_t N>
constexpr bool	Crux::operator!= (const Vector< T, N > &a, const Vector< T, N > &b)
	Inequality comparison.
template<typename T, size_t N>
T	Crux::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 >	Crux::Lerp (const Vector< T, N > &a, const Vector< T, N > &b, T t)
	Linear interpolation between two vectors.

Detailed Description

Vector types and operations.

Contains all functionality related to vector math and operations on vector types.

Typedef Documentation

◆ dvec2

using Crux::dvec2 = Vector<double, 2>

4D float vector

◆ dvec3

using Crux::dvec3 = Vector<double, 3>

2D double vector

◆ dvec4

using Crux::dvec4 = Vector<double, 4>

3D double vector

◆ ivec3

using Crux::ivec3 = Vector<int, 3>

2D integer vector

◆ ivec4

using Crux::ivec4 = Vector<int, 4>

3D integer vector

◆ uvec2

using Crux::uvec2 = Vector<unsigned, 2>

4D integer vector

◆ uvec3

using Crux::uvec3 = Vector<unsigned, 3>

2D unsigned vector

◆ uvec4

using Crux::uvec4 = Vector<unsigned, 4>

3D unsigned vector

◆ vec2

using Crux::vec2 = Vector<float, 2>

4D unsigned vector

◆ vec3

using Crux::vec3 = Vector<float, 3>

2D float vector

◆ vec4

using Crux::vec4 = Vector<float, 4>

3D float vector

Function Documentation

◆ Abs()

template<typename T, size_t N>

Vector< T, N > Crux::Abs ( const Vector< T, N > & a )

constexpr

Element-wise absolute value of a vector.

Returns a new vector where each component is the absolute value of the corresponding component of the input vector.

Parameters

a	Input vector.

Returns: A new vector containing the absolute values of each component.

◆ AngleBetween()

template<typename T, size_t N>

T Crux::AngleBetween	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

inline

Angle between two vectors in radians.

Computes the angle between two vectors using the dot product formula.

Parameters

a	First vector.
b	Second vector.

Returns: Angle in radians, clamped to the range [-Pi, Pi].

◆ Cross()

template<typename T>

Vector< T, 3 > Crux::Cross	(	const Vector< T, 3 > &	a,
		const Vector< T, 3 > &	b )

constexpr

Cross product for 3D vectors.

Computes the cross product of two 3D vectors, resulting in a vector orthogonal to both.

Parameters

a	First vector.
b	Second vector.

Returns: Cross product vector.

◆ Dot()

template<typename T, size_t N>

T Crux::Dot	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Dot product of two vectors.

Computes the dot product (scalar product) of two vectors, which is the sum of the products of their corresponding components.

Parameters

a	First vector.
b	Second vector.

Returns: Sum of component-wise products.

◆ Length()

template<typename T, size_t N>

T Crux::Length ( const Vector< T, N > & a )

inline

Length (magnitude) of a vector.

Parameters

a	Input vector.

Returns: Length of the vector.

◆ LengthSq()

template<typename T, size_t N>

T Crux::LengthSq ( const Vector< T, N > & a )

constexpr

Squared length (magnitude) of a vector.

Computes the squared length without taking the square root, which is more efficient.

Parameters

a	Input vector.

Returns: Squared length of the vector.

◆ Lerp()

template<typename T, size_t N>

Vector< T, N > Crux::Lerp	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b,
		T	t )

constexpr

Linear interpolation between two vectors.

Performs linear interpolation between two vectors based on a factor t.

Parameters

a	First vector.
b	Second vector.
t	Interpolation factor (0.0 to 1.0).

◆ MaxComponent()

template<typename T, size_t N>

Vector< T, N > Crux::MaxComponent	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Element-wise maximum of two vectors.

Returns a vector where each component is the maximum of the corresponding components of the input vectors.

Parameters

a	First vector.
b	Second vector.

Returns: Vector containing the maximum components.

◆ MinComponent()

template<typename T, size_t N>

Vector< T, N > Crux::MinComponent	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Element-wise minimum of two vectors.

Returns a vector where each component is the minimum of the corresponding components of a and b.

Parameters

a	First vector.
b	Second vector.

Returns: A vector containing the minimum components.

◆ Normalize()

template<typename T, size_t N>

Vector< T, N > Crux::Normalize ( const Vector< T, N > & a )

inline

Normalizes a vector to unit length.

Normalization scales the vector to have a length of 1, preserving its direction.

Note: If the vector's length is below Epsilon<T>, returns the original vector.

Parameters

a	Input vector to normalize.

Returns: Normalized vector.

◆ operator!=()

template<typename T, size_t N>

bool Crux::operator!=	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Inequality comparison.

Returns: True if any component differs by more than Epsilon<T>.

◆ operator*() [1/2]

template<typename T, size_t N>

Vector< T, N > Crux::operator*	(	const T &	scalar,
		const Vector< T, N > &	a )

constexpr

Scalar multiplication (scalar * vector).

Multiplies each component of the vector by the scalar value.

Parameters

scalar	Scalar value to multiply by.
a	Input vector.

Returns: A new vector containing the scaled components.

◆ operator*() [2/2]

template<typename T, size_t N>

Vector< T, N > Crux::operator*	(	const Vector< T, N > &	a,
		const T &	scalar )

constexpr

Scalar multiplication (vector * scalar).

Multiplies each component of the vector by the scalar value.

Parameters

a	Input vector.
scalar	Scalar value to multiply by.

Returns: A new vector containing the scaled components.

◆ operator*=()

template<typename T, size_t N>

Vector< T, N > & Crux::operator*=	(	Vector< T, N > &	a,
		const T &	scalar )

constexpr

Compound scalar multiplication assignment (vector *= scalar).

Multiplies each component of the vector by the scalar.

Parameters

a	Vector to be multiplied.
scalar	Scalar value to multiply by.

Returns: Reference to the modified vector.

◆ operator+()

template<typename T, size_t N>

Vector< T, N > Crux::operator+	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Component-wise addition of two vectors.

Adds corresponding components of two vectors of the same size.

Parameters

a	First vector.
b	Second vector.

Returns: A new vector containing the sum of the components.

◆ operator+=()

template<typename T, size_t N>

Vector< T, N > & Crux::operator+=	(	Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Compound addition assignment (vector += vector).

Adds each component of vector b to the corresponding component of vector a.

Parameters

a	Vector to be modified.
b	Vector to add to a.

Returns: Reference to the modified vector a.

◆ operator-()

template<typename T, size_t N>

Vector< T, N > Crux::operator-	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Component-wise subtraction of two vectors.

Subtracts corresponding components of vector b from vector a.

Parameters

a	First vector.
b	Second vector.

Returns: A new vector containing the difference of the components.

◆ operator-=()

template<typename T, size_t N>

Vector< T, N > & Crux::operator-=	(	Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Compound subtraction assignment (vector -= vector).

Subtracts each component of vector b from the corresponding component of vector a.

Parameters

a	Vector to be modified.
b	Vector to subtract from a.

Returns: Reference to the modified vector a.

◆ operator/()

template<typename T, size_t N>

Vector< T, N > Crux::operator/	(	const Vector< T, N > &	a,
		const T &	scalar )

constexpr

Scalar division of a vector.

Divides each component of the vector by the scalar value.

Parameters

a	Input vector.
scalar	Scalar value to divide by.

Returns: A new vector containing the divided components.

◆ operator/=()

template<typename T, size_t N>

Vector< T, N > & Crux::operator/=	(	Vector< T, N > &	a,
		const T &	scalar )

constexpr

Compound scalar division assignment (vector /= scalar).

Divides each component of the vector by the scalar.

Parameters

a	Vector to be divided.
scalar	Scalar value to divide by.

Returns: Reference to the modified vector.

◆ operator==()

template<typename T, size_t N>

bool Crux::operator==	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Approximate equality comparison with tolerance.

Returns: True if all components differ by less than Epsilon<T>.

◆ Project()

template<typename T, size_t N>

Vector< T, N > Crux::Project	(	const Vector< T, N > &	a,
		const Vector< T, N > &	b )

constexpr

Projects vector a onto vector b.

Projects vector a onto vector b, returning the component of a that lies in the direction of b.

Parameters

a	Input vector to project.
b	Vector onto which a is projected.

Returns: Projected vector.

◆ Reflect()

template<typename T, size_t N>

Vector< T, N > Crux::Reflect	(	const Vector< T, N > &	a,
		const Vector< T, N > &	normal )

constexpr

Reflects vector a around the given normal.

Reflects vector a across the plane defined by the normal vector.

Parameters

a	Input vector to reflect.
normal	Normal vector defining the reflection plane.

Returns: Reflected vector.

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ dvec2

◆ dvec3

◆ dvec4

◆ ivec3

◆ ivec4

◆ uvec2

◆ uvec3

◆ uvec4

◆ vec2

◆ vec3

◆ vec4

Function Documentation

◆ Abs()

◆ AngleBetween()

◆ Cross()

◆ Dot()

◆ Length()

◆ LengthSq()

◆ Lerp()

◆ MaxComponent()

◆ MinComponent()

◆ Normalize()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ Project()

◆ Reflect()