Vector and Matrix algebra

Classes
class	VecMath::Matrix< D, N >
	Matrix<D, N>: a D x D matrix of numbers of type N. More...
class	VecMath::MultiDimensionalVector< T, D >
	A D -dimensionally nested std::vector of objects of type T. More...
struct	VecMath::NumAxes< D >
	Determine number of rotation axes in D-dimensional space. More...
class	VecMath::RotationAxes< D >
	How to generate a Rotation matrix from a Rotation component. More...
class	VecMath::Rotation< D, N >
	Rotation in D-dimensional space defined by angles about the main axes. More...
class	VecMath::Vector< D, N >
	Vector<D, N>: a D-dimensional vector of numbers of type N. More...
Functions
template<unsigned D, typename N >
Matrix< D, N >	VecMath::operator* (const Matrix< D, N > &A, const Matrix< D, N > &B)
	Matrix multiplication.
template<unsigned D, typename N >
Vector< D, N >	VecMath::operator* (const Matrix< D, N > &M, const Vector< D, N > &V)
	Apply the Matrix on a vector.
template<unsigned D, typename N >
std::ostream &	VecMath::operator<< (std::ostream &, const Matrix< D, N > &)
	Matrix output operator.
template<typename T , unsigned D>
std::ostream &	VecMath::operator<< (std::ostream &s, MultiDimensionalVector< T, D > const &v)
	Print a MultiDimensionalVector<T, D> on a std::ostream.
template<typename T , unsigned D>
MultiDimensionalVector< T, D > ::iterator	VecMath::find (MultiDimensionalVector< T, D-1 > const &find_me, MultiDimensionalVector< T, D > &v)
	Find an element in a MultiDimensionalVector.
template<typename T >
std::ostream &	VecMath::operator<< (std::ostream &s, MultiDimensionalVector< T, 1 > const &v)
	Print a MultiDimensionalVector<T, 1> on a std::ostream.
std::ostream &	VecMath::operator<< (std::ostream &o, const RotationBase &)
	RotationBase output operator.
template<unsigned D, typename N >
std::ostream &	VecMath::operator<< (std::ostream &o, const Rotation< D, N > &v)
	Rotation output operator.
template<unsigned D, typename N >
std::istringstream &	VecMath::operator>> (std::istringstream &in, Rotation< D, N > &v)
	Rotation input operator.
template<unsigned D, typename N >
std::ostream &	VecMath::operator<< (std::ostream &s, const Vector< D, N > &v)
	Vector output operator.
template<unsigned D, typename N >
std::istringstream &	VecMath::operator>> (std::istringstream &in, Vector< D, N > &v)
	Vector input operator.
template<typename N >
Vector< 3, N >	VecMath::vcross (Vector< 3, N > a, Vector< 3, N > b)
	Cross product of two 3-Vectors.
template<typename N >
Vector< 4, N >	VecMath::vcross (Vector< 4, N > a, Vector< 4, N > b, Vector< 4, N > c)
	Cross product of three 4-Vectors.
template<unsigned D, typename N >
Vector< D, N >	VecMath::vnormalize (const Vector< D, N > &x)
	Normalizes a 3-Vector out-of-place.
template<typename N >
Vector< 2, N >	VecMath::makeVector (N const &x0, N const &x1)
	Generator function for a 2-dimensional Vector.
template<typename N >
Vector< 3, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2)
	Generator function for a 3-dimensional Vector.
template<typename N >
Vector< 4, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3)
	Generator function for a 4-dimensional Vector.
template<typename N >
Vector< 5, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3, N const &x4)
	Generator function for a 5-dimensional Vector.
template<typename N >
Vector< 6, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3, N const &x4, N const &x5)
	Generator function for a 6-dimensional Vector.
template<typename N >
Vector< 7, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3, N const &x4, N const &x5, N const &x6)
	Generator function for a 7-dimensional Vector.
template<typename N >
Vector< 8, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3, N const &x4, N const &x5, N const &x6, N const &x7)
	Generator function for a 8-dimensional Vector.
template<typename N >
Vector< 9, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3, N const &x4, N const &x5, N const &x6, N const &x7, N const &x8)
	Generator function for a 9-dimensional Vector.
template<typename N >
Vector< 10, N >	VecMath::makeVector (N const &x0, N const &x1, N const &x2, N const &x3, N const &x4, N const &x5, N const &x6, N const &x7, N const &x8, N const &x9)
	Generator function for a 10-dimensional Vector.

---

Function Documentation

template<typename T , unsigned D>

MultiDimensionalVector< T, D >::iterator VecMath::find	(	MultiDimensionalVector< T, D-1 > const &	find_me,
		MultiDimensionalVector< T, D > &	v
	)

Find an element in a MultiDimensionalVector.

Parameters:

find_me	The element to find in the vector v
v	The vector to search for element find_me

Returns:

The MultiDimensionalVector<T,D>::iterator pointing to the element or v.end() if it is not in v

References VecMath::MultiDimensionalVector< T, D >::begin(), and VecMath::MultiDimensionalVector< T, D >::end().

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template<typename N >

Vector< 10, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3,
		N const &	x4,
		N const &	x5,
		N const &	x6,
		N const &	x7,
		N const &	x8,
		N const &	x9
	)

Generator function for a 10-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.
x4	fifth element of the Vector.
x5	sixth element of the Vector.
x6	seventh element of the Vector.
x7	eighth element of the Vector.
x8	ninth element of the Vector.
x9	tenth element of the Vector.

template<typename N >

Vector< 3, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2
	)

Generator function for a 3-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.

template<typename N >

Vector< 4, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3
	)

Generator function for a 4-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.

template<typename N >

Vector< 5, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3,
		N const &	x4
	)

Generator function for a 5-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.
x4	fifth element of the Vector.

template<typename N >

Vector< 6, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3,
		N const &	x4,
		N const &	x5
	)

Generator function for a 6-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.
x4	fifth element of the Vector.
x5	sixth element of the Vector.

template<typename N >

Vector< 7, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3,
		N const &	x4,
		N const &	x5,
		N const &	x6
	)

Generator function for a 7-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.
x4	fifth element of the Vector.
x5	sixth element of the Vector.
x6	seventh element of the Vector.

template<typename N >

Vector< 8, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3,
		N const &	x4,
		N const &	x5,
		N const &	x6,
		N const &	x7
	)

Generator function for a 8-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.
x4	fifth element of the Vector.
x5	sixth element of the Vector.
x6	seventh element of the Vector.
x7	eighth element of the Vector.

template<typename N >

Vector< 9, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1,
		N const &	x2,
		N const &	x3,
		N const &	x4,
		N const &	x5,
		N const &	x6,
		N const &	x7,
		N const &	x8
	)

Generator function for a 9-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.
x2	third element of the Vector.
x3	fourth element of the Vector.
x4	fifth element of the Vector.
x5	sixth element of the Vector.
x6	seventh element of the Vector.
x7	eighth element of the Vector.
x8	ninth element of the Vector.

template<typename N >

Vector< 2, N > VecMath::makeVector	(	N const &	x0,
		N const &	x1
	)

Generator function for a 2-dimensional Vector.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

x0	first element of the Vector.
x1	second element of the Vector.

template<unsigned D, typename N >

Matrix< D, N > VecMath::operator*	(	const Matrix< D, N > &	A,
		const Matrix< D, N > &	B
	)

Matrix multiplication.

Template Parameters:

D	dimension of the matrix
N	numerical type of the matrix elements

Parameters:

A	Matrix that is multiplied upon
B	Matrix to multiply with

Returns:

A * B

template<unsigned D, typename N >

Vector< D, N > VecMath::operator*	(	const Matrix< D, N > &	M,
		const Vector< D, N > &	V
	)

Apply the Matrix on a vector.

Template Parameters:

D	dimension of the matrix
N	numerical type of the matrix elements

Parameters:

V	Vector to multiply with (project)
M	Matrix to print

Returns:

M * V

template<unsigned D, typename N >

std::ostream & VecMath::operator<<	(	std::ostream &	o,
		const Vector< D, N > &	v
	)

Vector output operator.

Template Parameters:

D	dimension of the vector
N	numerical type of the vector elements

Parameters:

o	ostream to push into
v	Vector to print

Returns:

o; a new ostream to push Vectors and stuff into

References std::setprecision().

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template<unsigned D, typename N >

std::ostream & VecMath::operator<<	(	std::ostream &	o,
		const Rotation< D, N > &	v
	)

Rotation output operator.

Parameters:

o	ostream to push into
v	Rotation to print

Returns:

a new ostream to push Rotations and stuff into

template<typename T , unsigned D>

std::ostream & VecMath::operator<<	(	std::ostream &	s,
		MultiDimensionalVector< T, D > const &	v
	)

Print a MultiDimensionalVector<T, D> on a std::ostream.

Parameters:

s	The ostream to which v is sent
v	The vector to print

Returns:

s

References copy().

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std::ostream & VecMath::operator<<	(	std::ostream &	o,
		const RotationBase &	r
	)

RotationBase output operator.

This operator is not intended to be used in a production environment. It is defined so it can be overridden using late binding by a Rotation. In fact, it simply prints the typeid of the class.

Parameters:

o	ostream to push into
r	the RotationBase to print

Returns:

a new ostream to push Rotations and stuff into

template<typename T >

std::ostream & VecMath::operator<<	(	std::ostream &	s,
		MultiDimensionalVector< T, 1 > const &	v
	)

Print a MultiDimensionalVector<T, 1> on a std::ostream.

Parameters:

s	The ostream to which v is sent
v	The vector to print

Returns:

s

References copy().

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template<unsigned D, typename N >

std::ostream & VecMath::operator<<	(	std::ostream &	o,
		const Matrix< D, N > &	M
	)

Matrix output operator.

Template Parameters:

D	dimension of the matrix
N	numerical type of the matrix elements

Parameters:

o	ostream to push into
M	Matrix to print

Returns:

a new ostream to push Matrices and stuff into

References std::endl(), std::setprecision(), and std::setw().

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template<unsigned D, typename N >

std::istringstream & VecMath::operator>>	(	std::istringstream &	in,
		Vector< D, N > &	v
	)

Vector input operator.

Template Parameters:

D	dimension of the vector
N	numerical type of the vector elements

Parameters:

in	istringstream to read from
v	Vector to read

Returns:

in - a new istringstream to read stuff from

References VecMath::Vector< D, N >::dimension().

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template<unsigned D, typename N >

std::istringstream & VecMath::operator>>	(	std::istringstream &	in,
		Rotation< D, N > &	v
	)

Rotation input operator.

Parameters:

in	istringstream to read from
v	Rotation to read

Returns:

a new istringstream to read stuff from

References VecMath::Rotation< D, N >::r().

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template<typename N >

Vector< 3, N > VecMath::vcross	(	Vector< 3, N >	a,
		Vector< 3, N >	b
	)

Cross product of two 3-Vectors.

Specialization of the function template for D = 3.

Template Parameters:

N	numerical type of the vector elements

Parameters:

a	first operand of cross product
b	second operand of cross product

Returns:

a x b

Referenced by RealFunction::normal().

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template<typename N >

Vector< 4, N > VecMath::vcross	(	Vector< 4, N >	a,
		Vector< 4, N >	b,
		Vector< 4, N >	c
	)

Cross product of three 4-Vectors.

Specialization of the function template for D = 4.

Template Parameters:

N	numerical type of the vector elements.

Parameters:

a	first operand of cross product.
b	second operand of cross product.
c	third operand of cross product.

Returns:

a x b x c

template<unsigned D, typename N >

Vector< D, N > VecMath::vnormalize

(

const Vector< D, N > &

x

)

Normalizes a 3-Vector out-of-place.

Template Parameters:

D	dimension of the vector
N	numerical type of the vector elements

Parameters:

x	Vector to be normalized

Returns:

its normalized value

References norm(), sqnorm(), and sqrt().

Referenced by RealFunction::normal().

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