Vector2 Class Reference

Detailed Description

Note: We assume that the coordinates XX and YY are adjacent in memory, which allows us to define an automatic conversion to a C-array. This is not guaranteed by the C-standard, but it usually works though...

Public Member Functions
	Vector2 ()
	by default, coordinates are not initialized
	Vector2 (const real x, const real y)
	construct from values
	Vector2 (const real x, const real y, const real)
	construct from values
	Vector2 (const real v[])
	construct from address
	Vector2 (const real v[], const int &d)
	construct from array of size d
	~Vector2 ()
	destructor (is not-virtual: do not derive from this class)
	operator real * ()
	implicit conversion to a modifiable real[] array
	operator const real * () const
	implicit conversion to a const real[] array
real *	addr ()
	conversion to a 'real array'
real &	operator[] (const unsigned ii)
	modifiable access to individual coordinates
void	get (const real b[])
	replace coordinates by the ones provided
void	get (const real v[], const int &d)
	copy coordinates from array of size d
void	put (real b[]) const
	copy coordinates to given array
void	addTo (real b[]) const
	add to given array
void	addFrom (real b[])
	change coordinates by adding given array
void	subTo (real b[]) const
	subtract to given array
void	subFrom (real b[])
	change coordinates by subtracting given array
void	set (const real x, const real y)
	change coordinates
void	set (const real x, const real y, const real)
	change coordinates
void	oppose ()
	change signs of all coordinates
real	normSqr () const
	the square of the standard norm
real	norm () const
	the standard norm = sqrt(x^2+y^2)
real	normXY () const
	the 2D norm = sqrt(x^2+y^2)
real	distanceSqr (Vector2 const &a) const
	square of the distance to other point == (a-this).normSqr()
real	distance (Vector2 const &a) const
	distance to other point == (a-this).norm()
real	minimum () const
	returns min(x, y, z)
real	maximum () const
	returns max(x, y, z)
real	norm_inf () const
	the infinite norm = max(|x|, |y|, |z|)
void	normalize (const real n=1.0)
	normalize to norm=n
const Vector2	normalized (const real n=1.0) const
	returns the colinear vector of norm=n
const Vector2	orthogonal () const
	returns a perpendicular vector, of comparable but unspecified norm
const Vector2	orthogonal (const real n) const
	returns a perpendicular vector, of norm n
void	getEulerAngles (real &angle) const
	get the Euler angles
void	setFromEulerAngles (const real angle)
	set from Euler angles
const Vector2	e_mul (const real b[]) const
	returns the element-by-element product
const Vector2	e_div (const real b[]) const
	returns the element-by-element division
void	operator+= (Vector2 const &b)
	addition of another vector b
void	operator-= (Vector2 const &b)
	subtraction of another vector b
void	operator*= (const real b)
	multiplication by a scalar
void	operator/= (const real b)
	division by a scalar
std::string	str () const
	conversion to a string
void	print (FILE *out=stdout) const
	print to a file
void	pprint (FILE *out=stdout) const
	print to a file, surrounded by parenthesis
void	println (FILE *out=stdout) const
	print, followed by a new line
void	addRand (real s)
	add a random component in [-s, s] to each coordinate
const Vector2	randPerp (real n) const
	a vector of norm n, orthogonal to *this, chosen randomly and uniformly

Static Public Member Functions
static unsigned	dimensionality ()
	dimensionality
static Vector2	make (const real b[])
	create new Vector with coordinates from the given array
static const Vector2	randBox ()
	random Vector with coordinates set randomly and independently in [-1,+1]
static const Vector2	randBox (real n)
	set all coordinates randomly and independently in [-n,+n]
static const Vector2	randUnit ()
	random Vector of norm = 1; sampling is uniform
static const Vector2	randUnit (real n)
	return a random vector of norm = n; sampling is uniform
static const Vector2	randBall ()
	return a random vector of norm <= 1; sampling is uniform
static const Vector2	randBall (real n)
	return a random vector of norm <= n; sampling is uniform
static const Vector2	randGauss (real n)
	return a random vector with Normally distributed coordinates ~ N(0,n)

Public Attributes
real	XX
	coordinates are public
real	YY

Friends
const Vector2	operator+ (Vector2 const &a, Vector2 const &b)
	addition of two vectors
const Vector2	operator- (Vector2 const &a, Vector2 const &b)
	subtraction of two vectors
const Vector2	operator+ (Vector2 const &b)
	unary + operator does nothing
const Vector2	operator- (Vector2 const &b)
	opposition of a vector
real	vecProd (Vector2 const &a, Vector2 const &b)
	the cross product of two vectors is a Z-Vector More...
const Vector2	vecProd (Vector2 const &a, const real b)
	cross product of a vector with a Z-Vector
const Vector2	vecProd (const real a, Vector2 const &b)
	cross product of a Z-vector with a Vector
real	operator* (Vector2 const &a, Vector2 const &b)
	scalar product of two vectors
const Vector2	operator* (Vector2 const &a, const real s)
	multiplication by scalar s
const Vector2	operator* (const real s, Vector2 const &a)
	mutiplication by scalar s
const Vector2	operator/ (Vector2 const &a, const real s)
	division by scalar s
bool	operator== (Vector2 const &a, Vector2 const &b)
	equality test
bool	operator!= (Vector2 const &a, Vector2 const &b)
	non-equality test

Friends And Related Function Documentation

real vecProd ( Vector2 const &  a, Vector2 const &  b  )

friend

In dimension 2, we define a cross-product operator which returns a real, which in this case represents a Vector aligned with the Z axis. We also define the cross-product with a scalar, also corresponding to a Vector aligned with Z. This is a fair contraction of the 3D vector product.