firefly::utilities::vector Namespace Reference

Functions
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	angle_between (firefly::vector< T, Length > const &v1, firefly::vector< U, Length > const &v2, double delta=1e-6)
	Calculates the angle between two vectors in radians.
template<vector_type T, vector_type U, std::size_t Length>
bool	are_anti_parallel (firefly::vector< T, Length > const &v1, firefly::vector< U, Length > const &v2)
	Checks if two vectors are anti-parallel.
template<vector_type T, vector_type U, std::size_t Length>
bool	are_parallel (firefly::vector< T, Length > const &v1, firefly::vector< U, Length > const &v2)
	Checks if two vectors are parallel.
template<vector_type T, vector_type U, std::size_t Length>
bool	are_orthogonal (firefly::vector< T, Length > const &v1, firefly::vector< U, Length > const &v2, double delta=1e-6)
	Checks if two- vectors are orthogonal.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	area_parallelogram (firefly::vector< T, Length > const &v1, firefly::vector< U, Length > const &v2)
	Computes the area of the parallelogram formed by two vectors.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	area_triangle (firefly::vector< T, Length > const &v1, firefly::vector< U, Length > const &v2)
	Computes the area of the triangle formed by two vectors.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	projection (firefly::vector< T, Length > const &source_vector, firefly::vector< U, Length > const &target_vector)
	Projects a source vector onto a target vector.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	rejection (firefly::vector< T, Length > const &source_vector, firefly::vector< U, Length > const &target_vector)
	Rejects a source vector from a target vector.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	distance (firefly::vector< T, Length > const &vector_a, firefly::vector< U, Length > const &vector_b)
	Computes the Euclidean distance between two vectors.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	reflection (firefly::vector< T, Length > const &source_vector, firefly::vector< U, Length > const &target_vector)
	Reflects a source vector across a target vector.
template<vector_type T>
constexpr auto	rotate_2d (firefly::vector< T, 2 > const &vector, double angle_rad)
	Rotates a 2D vector by a given angle (in radians).
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	scalar_projection (firefly::vector< T, Length > const &source_vector, firefly::vector< U, Length > const &target_vector)
	Computes the scalar projection of a source vector onto a target vector.
template<vector_type T, vector_type U, std::size_t Length>
constexpr auto	lerp (firefly::vector< T, Length > const &vector_a, firefly::vector< U, Length > const &vector_b, double t)
	Performs linear interpolation (Lerp) between two vectors.

Function Documentation

angle_between()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::angle_between ( firefly::vector< T, Length > const &  v1, firefly::vector< U, Length > const &  v2, double  delta = 1e-6  )

constexpr

Calculates the angle between two vectors in radians.

This function computes the angle between two vectors, v1 and v2, of the same length. It uses the dot product and the norms of the vectors to determine the cosine of the angle.

Template Parameters

T	Type of the first vector. Must be an arithmetic type.
U	Type of the second vector. Must be an arithmetic type.
Length	Length of both vectors.

Parameters

v1	First vector of type firefly::vector<T, Length>.
v2	Second vector of type firefly::vector<U, Length>.
delta	A small tolerance value for numerical stability (default is 1e-6).

Exceptions

std::logic_error

when norm is zero. This usually happens when zero vector is passed

Returns

The angle between the two vectors in radians. The result is clamped between -1.0 and 1.0.

Note

Only arithmetic types are allowed for T and U.

are_anti_parallel()

template<vector_type T, vector_type U, std::size_t Length>

bool firefly::utilities::vector::are_anti_parallel	(	firefly::vector< T, Length > const &	v1,
		firefly::vector< U, Length > const &	v2
	)

Checks if two vectors are anti-parallel.

Two vectors are considered anti-parallel if they are in opposite direction.

Template Parameters

T	Type of the first vector.
U	Type of the second vector.
Length	Length of both vectors.

Parameters

v1	First vector of type firefly::vector<T, Length>.
v2	Second vector of type firefly::vector<U, Length>.

Exceptions

std::logic_error

when norm is zero. This usually happens when zero vector is passed

Returns

true if the vectors are anti-parallel, false otherwise.

Note

Only arithmetic types are allowed for T and U.

are_orthogonal()

template<vector_type T, vector_type U, std::size_t Length>

bool firefly::utilities::vector::are_orthogonal	(	firefly::vector< T, Length > const &	v1,
		firefly::vector< U, Length > const &	v2,
		double	delta = 1e-6
	)

Checks if two- vectors are orthogonal.

Two vectors are considered orthogonal if the angle between them is close to 90 degrees (or π/2 radians).

Template Parameters

T	Type of the first vector.
U	Type of the second vector.
Length	Length of both vectors.

Parameters

v1	First vector of type firefly::vector<T, Length>.
v2	Second vector of type firefly::vector<U, Length>.
delta	A small tolerance value for numerical stability (default is 1e-6).

Exceptions

std::logic_error

when norm is zero. This usually happens when zero vector is passed

Returns

true if the vectors are orthogonal, false otherwise.

Note

Only arithmetic types are allowed for T and U.

are_parallel()

template<vector_type T, vector_type U, std::size_t Length>

bool firefly::utilities::vector::are_parallel	(	firefly::vector< T, Length > const &	v1,
		firefly::vector< U, Length > const &	v2
	)

Checks if two vectors are parallel.

Two vectors are considered parallel if they are same or opposite directions.

Template Parameters

T	Type of the first vector.
U	Type of the second vector.
Length	Length of both vectors.

Parameters

v1	First vector of type firefly::vector<T, Length>.
v2	Second vector of type firefly::vector<U, Length>.

Exceptions

std::logic_error

when norm is zero. This usually happens when zero vector is passed

Returns

true if the vectors are parallel, false otherwise.

Note

Only arithmetic types are allowed for T and U.

area_parallelogram()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::area_parallelogram ( firefly::vector< T, Length > const &  v1, firefly::vector< U, Length > const &  v2  )

constexpr

Computes the area of the parallelogram formed by two vectors.

Template Parameters

T	The type of the elements in the first vector.
U	The type of the elements in the second vector.
Length	The number of dimensions of the vectors.

Parameters

v1	The first vector.
v2	The second vector.

Returns

The area of the parallelogram formed by v1 and v2.

Note

Only arithmetic types are allowed for T and U.

area_triangle()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::area_triangle ( firefly::vector< T, Length > const &  v1, firefly::vector< U, Length > const &  v2  )

constexpr

Computes the area of the triangle formed by two vectors.

Template Parameters

T	The type of the elements in the first vector.
U	The type of the elements in the second vector.
Length	The number of dimensions of the vectors.

Parameters

v1	The first vector.
v2	The second vector.

Returns

The area of the triangle formed by v1 and v2.

Note

Only arithmetic types are allowed for T and U.

distance()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::distance ( firefly::vector< T, Length > const &  vector_a, firefly::vector< U, Length > const &  vector_b  )

constexpr

Computes the Euclidean distance between two vectors.

Template Parameters

T	The type of the elements in the first vector.
U	The type of the elements in the second vector.
Length	The number of dimensions of the vectors.

Parameters

vector_a	The first vector.
vector_b	The second vector.

Returns

The distance between vector_a and vector_b.

lerp()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::lerp ( firefly::vector< T, Length > const &  vector_a, firefly::vector< U, Length > const &  vector_b, double  t  )

constexpr

Performs linear interpolation (Lerp) between two vectors.

Template Parameters

T	The type of the elements in the first vector.
U	The type of the elements in the second vector.
Length	The number of dimensions of the vectors.

Parameters

vector_a	The first vector.
vector_b	The second vector.
t	The interpolation parameter, typically in the range [0, 1].

Returns

The interpolated vector between vector_a and vector_b.

projection()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::projection ( firefly::vector< T, Length > const &  source_vector, firefly::vector< U, Length > const &  target_vector  )

constexpr

Projects a source vector onto a target vector.

Template Parameters

T	The type of the elements in the source vector.
U	The type of the elements in the target vector.
Length	The number of dimensions of the vectors.

Parameters

source_vector	The vector being projected.
target_vector	The vector onto which the source_vector is projected.

Returns

The projection of source_vector onto target_vector.

reflection()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::reflection ( firefly::vector< T, Length > const &  source_vector, firefly::vector< U, Length > const &  target_vector  )

constexpr

Reflects a source vector across a target vector.

Template Parameters

T	The type of the elements in the source vector.
U	The type of the elements in the target vector.
Length	The number of dimensions of the vectors.

Parameters

source_vector	The vector being reflected.
target_vector	The vector across which the source_vector is reflected.

Returns

The reflected vector of source_vector across target_vector.

rejection()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::rejection ( firefly::vector< T, Length > const &  source_vector, firefly::vector< U, Length > const &  target_vector  )

constexpr

Rejects a source vector from a target vector.

Template Parameters

T	The type of the elements in the source vector.
U	The type of the elements in the target vector.
Length	The number of dimensions of the vectors.

Parameters

source_vector	The vector being rejected.
target_vector	The vector from which the source_vector is rejected.

Returns

The component of source_vector orthogonal to target_vector.

rotate_2d()

template<vector_type T>

constexpr auto firefly::utilities::vector::rotate_2d ( firefly::vector< T, 2 > const &  vector, double  angle_rad  )

constexpr

Rotates a 2D vector by a given angle (in radians).

Template Parameters

T	The type of the elements in the vector.

Parameters

vector	The 2D vector to rotate.
angle_rad	The angle in radians to rotate the vector.

Returns

The rotated vector.

scalar_projection()

template<vector_type T, vector_type U, std::size_t Length>

constexpr auto firefly::utilities::vector::scalar_projection ( firefly::vector< T, Length > const &  source_vector, firefly::vector< U, Length > const &  target_vector  )

constexpr

Computes the scalar projection of a source vector onto a target vector.

Template Parameters

T	The type of the elements in the source vector.
U	The type of the elements in the target vector.
Length	The number of dimensions of the vectors.

Parameters

source_vector	The vector being projected.
target_vector	The vector onto which the source_vector is projected.

Returns

The scalar projection of source_vector onto target_vector.