Basic class for vectors. More...

#include <Vector.h>

Inheritance diagram for Vector:

Public Member Functions
	Vector (size_t size=1)
	Vector constructor. More...

	Vector (const Vector &vec)
	Vector copy constructor. More...

	Vector (const Matrix &mat)
	Vector from Matrix constructor. More...

virtual	~Vector ()
	Vector destructor. More...

Vector &	operator= (const Vector &vec)
	Vector assignment operator. More...

double &	operator() (size_t ix)
	Vector element access. More...

const double &	operator() (size_t ix) const
	Vector element access (`const` version). More...

Vector	operator- () const
	Unary minus. More...

Vector &	operator+= (const Vector &vec)
	Vector addition-assignment operator. More...

Vector &	operator-= (const Vector &vec)
	Vector subtraction-assignment operator. More...

Vector &	operator*= (double s)
	Vector-scalar multiplication-assignment operator. More...

Vector &	operator/= (double s)
	Vector-scalar multiplication-assignment operator. More...

double	dot (const Vector &vec) const
	Vector dot product. More...

Vector	cross (const Vector &vec) const
	Vector cross product. More...

double	norm () const
	Vector norm. More...

double	squaredNorm () const
	SquaredVector norm. More...

Public Member Functions inherited from Matrix
	Matrix (size_t size=1)
	Square Matrix constructor. More...

	Matrix (size_t rows, size_t cols)
	General Matrix constructor. More...

	Matrix (const Matrix &mat)
	Matrix copy constructor. More...

virtual	~Matrix ()
	Matrix destructor. More...

Matrix &	operator= (const Matrix &mat)
	Matrix assignment operator. More...

double &	operator() (size_t row, size_t col)
	Matrix element access. More...

const double &	operator() (size_t row, size_t col) const
	Matrix element access (`const` version). More...

size_t	numRows () const
	Number of rows in a Matrix. More...

size_t	numCols () const
	Number of columns in a Matrix. More...

size_t	numElements () const
	Number of elements in a Matrix. More...

Matrix	operator- () const
	Unary minus. More...

Matrix &	operator+= (const Matrix &mat)
	Matrix addition-assignment operator. More...

Matrix &	operator-= (const Matrix &mat)
	Matrix subtraction-assignment operator. More...

Matrix &	operator*= (double s)
	Matrix-scalar multiplication-assignment operator. More...

Matrix &	operator/= (double s)
	Matrix-scalar multiplication-assignment operator. More...

Matrix	transpose () const
	Matrix transpose. More...

Related Functions
(Note that these are not member functions.)
Vector	operator+ (const Vector &lhs, const Vector &rhs)
	Vector addition operator. More...

Vector	operator- (const Vector &lhs, const Vector &rhs)
	Vector subtraction operator. More...

Vector	operator* (double s, const Vector &vec)
	scalar-Vector multiplication operator. More...

Vector	operator* (const Vector &vec, double s)
	scalar-Vector multiplication operator. More...

Vector	operator/ (const Vector &vec, double s)
	Vector-scalar division operator. More...

Related Functions inherited from Matrix
Matrix	operator+ (const Matrix &lhs, const Matrix &rhs)
	Matrix addition operator. More...

Matrix	operator- (const Matrix &lhs, const Matrix &rhs)
	Matrix subtraction operator. More...

Matrix	operator* (double s, const Matrix &mat)
	scalar-Matrix multiplication operator. More...

Matrix	operator* (const Matrix &mat, double s)
	Matrix-scalar multiplication operator. More...

Matrix	operator/ (const Matrix &mat, double s)
	Matrix-scalar division operator. More...

std::ostream &	operator<< (std::ostream &outputStream, const Matrix &mat)
	Stream insertion operator. More...

std::istream &	operator>> (std::istream &inputStream, Matrix &mat)
	Stream extraction operator. More...

Additional Inherited Members
Static Public Member Functions inherited from Matrix
static Matrix	identity (size_t rows, size_t cols)
	Factory method for Identity Matrices. More...

static Matrix	zero (size_t rows, size_t cols)
	Factory method for Zero Matrices. More...

Protected Attributes inherited from Matrix
size_t	rows_
	Number of rows in the Matrix. More...

size_t	cols_
	Number of columns in the Matrix. More...

std::vector< double >	data_
	Storage for Matrix data elements. More...

Detailed Description

Basic class for vectors.

A Vector is a Matrix with exactly one column, and in many cases can be dealt with as such. However, having a separate Vector class means that we can implement Vector-specific behaviour like dot and cross products. Since all Vectors are Matrices, Vector is a subclass of Matrix.

Many Matrix operations (such as + and *) are overloaded in cases when a Vector is gauranteed to be the result. Thus Matrix*Vector is overloaded (it is always a Vector), but Vector*Matrix is not - we can just use Matrix*Matrix for that. Most of these just call the Matrix equivalents, so this provides some convenience at the cost of a layer of redirecton.

Note that a Vector as a mathematical object, is quite distinct from a std:vector, which is essentially an array.

Constructor & Destructor Documentation

◆ Vector() [1/3]

Vector::Vector ( size_t size = 1 )

Vector constructor.

This constructor creates a Vector of the specified size. If no size is provided, it creates a 1-Vector, and so also provides a default constructor.

Parameters

size	The size of the resulting Vector.

◆ Vector() [2/3]

Vector::Vector ( const Vector & vec )

Vector copy constructor.

This constructor creates a new Vector which is a copy of an existing one. The new Vector has independent storage etc.

Parameters

vec	The Vector to copy.

◆ Vector() [3/3]

Vector::Vector ( const Matrix & mat )

Vector from Matrix constructor.

This constructor creates a new Vector which is a copy of an existing Matrix. The Matrix must have exactly one column. This form allows us to turn a Matrix into a Vector when needed.

Parameters

mat	The Matrix to copy.

◆ ~Vector()

Vector::~Vector ( )

virtual

Vector destructor.

As with Matrices, there's not a lot to do here. The destructor is virtual in case we want to make subclasses of Vector (like Point or Normal)

Member Function Documentation

◆ cross()

Vector Vector::cross ( const Vector & vec ) const

Vector cross product.

This computes the cross product of two vectors, u.cross(v). The Vectors must both be 3-vectors.

Parameters

vec	The Vector to take the cross product with.

Returns: The cross product of this and vec.

◆ dot()

double Vector::dot ( const Vector & vec ) const

Vector dot product.

This computes the dot product of two vectors, u.dot(v). The two Vectors must have the same size.

Parameters

vec	The Vector to take the dot product with.

Returns: The dot product of vec and this

◆ norm()

double Vector::norm ( ) const

Vector norm.

This computes the norm or length of a Vector. Technically, this is the L2- or Euclidean norm. Other norms exist, but this is the one that is concerns us most of the time.

Returns: The norm (length) of of this.

◆ operator()() [1/2]

double & Vector::operator() ( size_t ix )

Vector element access.

This method provides access to the elements of a Vector using the syntax v(i). This notation is equivalent to v.operator()(i). Since a reference is returned, this can be used for assignment, eg: v(1)=3.1415; The value of ix must less than the size of the Vector.

Parameters

ix	The element of the Vector to access.

Returns: A reference to the requested element of the Vector.

◆ operator()() [2/2]

const double & Vector::operator() ( size_t ix ) const

Vector element access (const version).

This method provides access to the elements of a Vector using the syntax v(i). Since a const reference is returned, this cannot be used for assignment, but it can be applied to const Vector. The value of ix must less than the size of the Vector.

Parameters

ix	The element of the Vector to access.

Returns: A const reference to the requested element of the Vector.

◆ operator*=()

Vector & Vector::operator*= ( double s )

Vector-scalar multiplication-assignment operator.

This scales a Vector in place.

Parameters

s	The scalar multiplier to apply to `this`.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator+=()

Vector & Vector::operator+= ( const Vector & vec )

Vector addition-assignment operator.

This adds a Vector to an existing one in place. The two Vectors must have the same size.

Parameters

vec	The Vector to add to `this`.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator-()

Vector Vector::operator- ( ) const

Unary minus.

This provides the ability to negate a Vector. -v is equivalent to v.operator-()

Returns: A negated version of the Vector.

◆ operator-=()

Vector & Vector::operator-= ( const Vector & vec )

Vector subtraction-assignment operator.

This subtracts a Vector from an existing one in place. The two Vectors must have the same size.

Parameters

vec	The Vector to subtract from `this`.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator/=()

Vector & Vector::operator/= ( double s )

Vector-scalar multiplication-assignment operator.

This divides a Vector in place.

Parameters

s	The scalar multiplier to divide `this` by.

Returns: A reference to the updated this, to allow chaining of assignment.

◆ operator=()

Vector & Vector::operator= ( const Vector & vec )

Vector assignment operator.

This allows expressions like u = v; where u and v are Vectors. It also allows chained assignment, like u = v = w;

Parameters

vec	The Vector on the right hand side of the assignment.

Returns: a reference to this, to allow chaining of assignment.

◆ squaredNorm()

double Vector::squaredNorm ( ) const

SquaredVector norm.

This computes the squared norm or length of a Vector. Technically, this is the squared L2- or Euclidean norm. Other norms exist, but this is the one that is concerns us most of the time.

Computing the squared norm (rather than the norm itself) is often sufficient for a task (eg: to see which of two Vectors is shorter), and avoids a sqrt operation.

Returns: The norm (length) of of this.

Friends And Related Function Documentation

◆ operator*() [1/2]

Vector operator*	(	const Vector &	vec,
		double	s
	)

This creates the product of a Vector and a scalar.

Parameters

vec	The Vector to be scaled.
s	The scalar value to multiply the Matrix by.

Returns: The Vector formed by vec*s.

◆ operator*() [2/2]

Vector operator*	(	double	s,
		const Vector &	vec
	)

This creates the product of a scalar and a Vector.

Parameters

s	The scalar value to multiply the Matrix by.
vec	The Vector to be scaled.

Returns: The Vector formed by s*vec.

◆ operator+()

Vector operator+	(	const Vector &	lhs,
		const Vector &	rhs
	)

This performs addition of two Vectors. The two Vectors must have the same size

Parameters

lhs	The Vector on the left hand side of the +.
rhs	The Vector on the right hand side of the +.

Returns: The Vector formed by lhs + rhs.

◆ operator-()

Vector operator-	(	const Vector &	lhs,
		const Vector &	rhs
	)

This performs subtraction of two Vectors. The two Vectors must have the same size

Parameters

lhs	The Vector on the left hand side of the -.
rhs	The Vector on the right hand side of the -.

Returns: Vector formed by lhs - rhs.

◆ operator/()

Vector operator/	(	const Vector &	vec,
		double	s
	)

This creates the result of a Vector divided by a scalar. Division by a scalar, s, is essentially the same as multiplcation (or scaling) by 1/s. Division by numbers close to 0 will result in NaN and Inf values and wildly unstable results as normal.

Parameters

vec	The Vector to be scaled.
s	The scalar value to divide the Matrix by.

Returns: The Vector formed by vec/s.

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

Public Member Functions

Related Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Vector() [1/3]

◆ Vector() [2/3]

◆ Vector() [3/3]

◆ ~Vector()

Member Function Documentation

◆ cross()

◆ dot()

◆ norm()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/=()

◆ operator=()

◆ squaredNorm()

Friends And Related Function Documentation

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator+()

◆ operator-()

◆ operator/()