Vectors represent a direction and Magnitude. More...

#include <Vector.h>

Public Member Functions
	Vector ()
	Construct a unit vector of a given type and size.

	Vector (std::initializer_list< T > ilst)
	Construct a Vector with initial values.

T	At (size_t index) const
	Return the element At index i.

void	Set (size_t index, T value)
	Set a new value for the vector.

T	Magnitude () const
	Compute the length of the vector.

void	SetEpsilon (T eps)
	Set equivalence tolerance.

bool	IsZero () const
	Determine whether this is a zero vector.

Vector	UnitVector () const
	Obtain the unit vector for this vector.

bool	IsUnitVector () const
	Determine if this is a unit vector.

T	Angle (const Vector< T, N > &other) const
	Compute the Angle between two vectors.

bool	IsParallel (const Vector< T, N > &other) const
	Determine whether two vectors are parallel.

bool	IsOrthogonal (const Vector< T, N > &other) const
	Determine if two vectors are orthogonal or perpendicular to each other.

Vector	ProjectParallel (const Vector< T, N > &basis) const
	Project this vector onto some basis vector.

Vector	ProjectOrthogonal (const Vector< T, N > &basis)
	Project this vector perpendicularly onto some basis vector.

Vector	Cross (const Vector< T, N > &other) const
	Compute the cross product of two vectors.

Vector	operator+ (const Vector< T, N > &other) const
	Vector addition.

Vector	operator- (const Vector< T, N > &other) const
	Vector subtraction.

Vector	operator* (const T k) const
	Scalar multiplication.

Vector	operator/ (const T k) const
	Scalar division.

T	operator* (const Vector< T, N > &other) const
	Compute the Dot product between two vectors.

bool	operator== (const Vector< T, N > &other) const
	Vector equivalence.

bool	operator!= (const Vector< T, N > &other) const
	Vector non-equivalence.

const T &	operator[] (size_t i) const
	Array indexing into vector.

Friends
std::ostream &	operator<< (std::ostream &outs, const Vector< T, N > &vec)
	Write a vector a stream in the form "<i, j, ...>".

Detailed Description

template<typename T, size_t N>
class scmp::geom::Vector< T, N >

Vectors represent a direction and Magnitude.

Vector provides a standard interface for dimensionless fixed-size vectors. Once instantiated, they cannot be modified.

Note that while the class is templated, it's intended to be used with floating-point types.

Vectors can be indexed like arrays, and they contain an epsilon value that defines a tolerance for equality.

Constructor & Destructor Documentation

◆ Vector() [1/2]

template<typename T , size_t N>

scmp::geom::Vector< T, N >::Vector ( )

inline

Construct a unit vector of a given type and size.

◆ Vector() [2/2]

template<typename T , size_t N>

scmp::geom::Vector< T, N >::Vector ( std::initializer_list< T > ilst )

inline

Construct a Vector with initial values.

If given an initializer_list, the vector is created with those values. There must be exactly N elements in the list.

Parameters

ilst	An intializer list with N elements of type T.

Member Function Documentation

◆ Angle()

template<typename T , size_t N>

T scmp::geom::Vector< T, N >::Angle ( const Vector< T, N > & other ) const

inline

Compute the Angle between two vectors.

Parameters

other Another vector.

Returns: The Angle in radians between the two vectors.

◆ At()

template<typename T , size_t N>

T scmp::geom::Vector< T, N >::At ( size_t index ) const

inline

Return the element At index i.

Exceptions

std::out_of_range if the index is out of bounds.

Parameters

index The index of the item to retrieve.

Returns: The value At the index.

◆ Cross()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::Cross ( const Vector< T, N > & other ) const

inline

Compute the cross product of two vectors.

This is only defined over three-dimensional vectors.

Exceptions

std::out_of_range if this is not a three-dimensional vector.

Parameters

other Another 3D vector.

Returns: The Cross product vector.

◆ IsOrthogonal()

template<typename T , size_t N>

bool scmp::geom::Vector< T, N >::IsOrthogonal ( const Vector< T, N > & other ) const

inline

Determine if two vectors are orthogonal or perpendicular to each other.

Parameters

other Another vector

Returns: True if the two vectors are orthogonal.

◆ IsParallel()

template<typename T , size_t N>

bool scmp::geom::Vector< T, N >::IsParallel ( const Vector< T, N > & other ) const

inline

Determine whether two vectors are parallel.

Parameters

other Another vector

Returns: True if the Angle between the vectors is zero.

◆ IsUnitVector()

template<typename T , size_t N>

bool scmp::geom::Vector< T, N >::IsUnitVector ( ) const

inline

Determine if this is a unit vector.

Returns: true if the vector is a unit vector.

◆ IsZero()

template<typename T , size_t N>

bool scmp::geom::Vector< T, N >::IsZero ( ) const

inline

Determine whether this is a zero vector.

Returns: true if the vector is zero.

◆ Magnitude()

template<typename T , size_t N>

T scmp::geom::Vector< T, N >::Magnitude ( ) const

inline

Compute the length of the vector.

Returns: The length of the vector.

◆ operator!=()

template<typename T , size_t N>

bool scmp::geom::Vector< T, N >::operator!= ( const Vector< T, N > & other ) const

inline

Vector non-equivalence.

Parameters

other The other vector.

Returns: Return true if any of the components of both vectors are not within the tolerance value.

◆ operator*() [1/2]

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::operator* ( const T k ) const

inline

Scalar multiplication.

Parameters

k	The scaling value.

Returns: A new vector that is this vector scaled by k.

◆ operator*() [2/2]

template<typename T , size_t N>

T scmp::geom::Vector< T, N >::operator* ( const Vector< T, N > & other ) const

inline

Compute the Dot product between two vectors.

Parameters

other The other vector.

Returns: A scalar value that is the Dot product of the two vectors.

◆ operator+()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::operator+ ( const Vector< T, N > & other ) const

inline

Vector addition.

Parameters

other The vector to be added.

Returns: A new vector that is the result of adding this and the other vector.

◆ operator-()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::operator- ( const Vector< T, N > & other ) const

inline

Vector subtraction.

Parameters

other The vector to be subtracted from this vector.

Returns: A new vector that is the result of subtracting the other vector from this one.

◆ operator/()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::operator/ ( const T k ) const

inline

Scalar division.

Parameters

k	The scaling value

Returns: A new vector that is this vector scaled by 1/k.

◆ operator==()

template<typename T , size_t N>

bool scmp::geom::Vector< T, N >::operator== ( const Vector< T, N > & other ) const

inline

Vector equivalence.

Parameters

other The other vector.

Returns: Return true if all the components of both vectors are within the tolerance value.

◆ operator[]()

template<typename T , size_t N>

const T & scmp::geom::Vector< T, N >::operator[] ( size_t i ) const

inline

Array indexing into vector.

Note that the values of the vector cannot be modified. Instead, something like the following must be done:

Vector3D a {1.0, 2.0, 3.0};

Vector3D b {a[0], a[1]*2.0, a[2]};

scmp::geom::Vector

Vectors represent a direction and Magnitude.

Definition Vector.h:57

scmp::geom::MakeQuaternion

Quaternionf MakeQuaternion(Vector3F axis, float angle)

Convenience Quaternion construction function.

Parameters

i	The component index.

Returns: The value of the vector component At i.

◆ ProjectOrthogonal()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::ProjectOrthogonal ( const Vector< T, N > & basis )

inline

Project this vector perpendicularly onto some basis vector.

This is also called the rejection of the vector.

Parameters

basis The basis vector to be projected onto.

Returns: A vector that is the orthogonal projection of this onto the basis vector.

◆ ProjectParallel()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::ProjectParallel ( const Vector< T, N > & basis ) const

inline

Project this vector onto some basis vector.

Parameters

basis The basis vector to be projected onto.

Returns: A vector that is the projection of this onto the basis vector.

◆ Set()

template<typename T , size_t N>

void scmp::geom::Vector< T, N >::Set	(	size_t	index,
		T	value
	)

inline

Set a new value for the vector.

This is used to modify the vector in place.

Exceptions

std::out_of_range if the index is out of bounds.

Parameters

index	The index to insert the value At.
value

◆ SetEpsilon()

template<typename T , size_t N>

void scmp::geom::Vector< T, N >::SetEpsilon ( T eps )

inline

Set equivalence tolerance.

Set the tolerance for equality checks. At a minimum, this accounts for systemic errors in floating math arithmetic.

Parameters

eps	is the maximum difference between this vector and another.

◆ UnitVector()

template<typename T , size_t N>

Vector scmp::geom::Vector< T, N >::UnitVector ( ) const

inline

Obtain the unit vector for this vector.

Returns: The unit vector

Friends And Related Symbol Documentation

◆ operator<<

template<typename T , size_t N>

std::ostream & operator<<	(	std::ostream &	outs,
		const Vector< T, N > &	vec
	)

friend

Write a vector a stream in the form "<i, j, ...>".

Parameters

outs	An output stream.
vec	The vector to be formatted.

Returns: The output stream.

The documentation for this class was generated from the following file:

include/scmp/geom/Vector.h

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Vector() [1/2]

◆ Vector() [2/2]

Member Function Documentation

◆ Angle()

◆ At()

◆ Cross()

◆ IsOrthogonal()

◆ IsParallel()

◆ IsUnitVector()

◆ IsZero()

◆ Magnitude()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator+()

◆ operator-()

◆ operator/()

◆ operator==()

◆ operator[]()

◆ ProjectOrthogonal()

◆ ProjectParallel()

◆ Set()

◆ SetEpsilon()

◆ UnitVector()

Friends And Related Symbol Documentation

◆ operator<<