Vector and Matrix algebra. More...

Classes
class	Matrix
	Matrix<D, N>: a D x D matrix of numbers of type N. More...
class	MultiDimensionalVector
	A `D` -dimensionally nested std::vector of objects of type `T`. More...
class	MultiDimensionalVector< T, 1 >
	Specialization of NestedVector<T, D> for `D` = 1. More...
struct	NumAxes
	Determine number of rotation axes in D-dimensional space. More...
struct	NumAxes< 0 >
	Specialization for zero-dimensional space (no rotation possible) More...
struct	NumAxes< 1 >
	Specialization for one-dimensional space (no rotation possible) More...
class	RotationAxes
	How to generate a Rotation matrix from a Rotation component. More...
class	RotationAxes< 3 >
	Rotation axes in three dimensions, manually specified. More...
class	RotationAxes< 4 >
	Rotation axes in four dimensions, manually specified. More...
class	RotationBase
	Interface Rotation<D, N> implements. More...
class	Rotation
	Rotation in D-dimensional space defined by angles about the main axes. More...
class	Vector
	Vector<D, N>: a D-dimensional vector of numbers of type N. More...
Functions
template<unsigned D, typename N >
Matrix< D, N >	operator* (const Matrix< D, N > &A, const Matrix< D, N > &B)
	Matrix multiplication.
template<unsigned D, typename N >
Vector< D, N >	operator* (const Matrix< D, N > &M, const Vector< D, N > &V)
	Apply the Matrix on a vector.
template<unsigned D, typename N >
std::ostream &	operator<< (std::ostream &, const Matrix< D, N > &)
	Matrix output operator.
template<typename T , unsigned D>
std::ostream &	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	find (MultiDimensionalVector< T, D-1 > const &find_me, MultiDimensionalVector< T, D > &v)
	Find an element in a MultiDimensionalVector.
template<typename T1 , typename T2 , unsigned D, typename Function >
Function	for_each (MultiDimensionalVector< T1, D > &v1, MultiDimensionalVector< T2, D > &v2, Function f)
	Loop over two MultiDimensionalVector s simultaneously, applying a function on both elements.
template<typename T1 , typename T2 , unsigned D, typename Function >
Function	for_each (const MultiDimensionalVector< T1, D > &v1, const MultiDimensionalVector< T2, D > &v2, Function f)
	Loop over two MultiDimensionalVector s simultaneously, applying a const function on both elements.
template<typename T1 , typename T2 , typename T3 , unsigned D, typename Function >
Function	for_each (MultiDimensionalVector< T1, D > &v1, MultiDimensionalVector< T2, D > &v2, MultiDimensionalVector< T3, D > &v3, Function f)
	Loop over three MultiDimensionalVector s simultaneously, applying a function on all elements.
template<typename T1 , typename T2 , typename T3 , unsigned D, typename Function >
Function	for_each (const MultiDimensionalVector< T1, D > &v1, const MultiDimensionalVector< T2, D > &v2, const MultiDimensionalVector< T3, D > &v3, Function f)
	Loop over three MultiDimensionalVector s simultaneously, applying a const function on all elements.
template<typename T >
std::ostream &	operator<< (std::ostream &s, MultiDimensionalVector< T, 1 > const &v)
	Print a MultiDimensionalVector<T, 1> on a std::ostream.
template<typename T1 , typename T2 , typename Function >
Function	for_each (MultiDimensionalVector< T1, 1 > &v1, MultiDimensionalVector< T2, 1 > &v2, Function f)
	Loop over two MultiDimensionalVector s simultaneously, applying a function on both elements.
template<typename T1 , typename T2 , typename Function >
Function	for_each (const MultiDimensionalVector< T1, 1 > &v1, const MultiDimensionalVector< T2, 1 > &v2, Function f)
	Loop over two MultiDimensionalVector s simultaneously, applying a const function on both elements.
template<typename T1 , typename T2 , typename T3 , typename Function >
Function	for_each (MultiDimensionalVector< T1, 1 > &v1, MultiDimensionalVector< T2, 1 > &v2, MultiDimensionalVector< T3, 1 > &v3, Function f)
	Loop over three MultiDimensionalVector s simultaneously, applying a function on all elements.
template<typename T1 , typename T2 , typename T3 , typename Function >
Function	for_each (const MultiDimensionalVector< T1, 1 > &v1, const MultiDimensionalVector< T2, 1 > &v2, const MultiDimensionalVector< T3, 1 > &v3, Function f)
	Loop over three MultiDimensionalVector s simultaneously, applying a const function on all elements.
std::ostream &	operator<< (std::ostream &o, const RotationBase &)
	RotationBase output operator.
template<unsigned D, typename N >
Rotation< D, N >	operator+ (const Rotation< D, N > &A, const Rotation< D, N > &B)
	Returns the sum of two Rotation s.
template<unsigned D, typename N >
std::ostream &	operator<< (std::ostream &o, const Rotation< D, N > &v)
	Rotation output operator.
template<unsigned D, typename N >
std::istringstream &	operator>> (std::istringstream &in, Rotation< D, N > &v)
	Rotation input operator.
template<typename N >
Rotation< 3, N >	makeRotation (N const &r0, N const &r1, N const &r2)
	Generator function for a 3-dimensional Rotation.
template<typename N >
Rotation< 4, N >	makeRotation (N const &r0, N const &r1, N const &r2, N const &r3, N const &r4, N const &r5)
	Generator function for a 4-dimensional Rotation.
template<unsigned D, typename N >
Vector< D, N >	operator- (const Vector< D, N > &v)
	Unary minus.
template<unsigned D, typename N >
Vector< D, N >	operator+ (const Vector< D, N > &x, const Vector< D, N > &y)
	Plus.
template<unsigned D, typename N >
Vector< D, N >	operator- (const Vector< D, N > &x, const Vector< D, N > &y)
	Binary minus.
template<unsigned D, typename N >
Vector< D, N >	operator* (const Vector< D, N > &x, const N &s)
template<unsigned D, typename N >
Vector< D, N >	operator* (const N &s, const Vector< D, N > &x)
template<unsigned D, typename N >
N	operator* (const Vector< D, N > &x, const Vector< D, N > &y)
	scalar multiplication between two Vectors (dot product)
template<unsigned D, typename N >
Vector< D, N >	operator/ (const Vector< D, N > &x, const N &s)
template<unsigned D, typename N >
Vector< D, N >	operator/ (const Vector< D, N > &x, const Vector< D, N > &y)
	divide every component of one vector by same component of another
template<unsigned D, typename N >
Vector< D, N >	scale (const Vector< D, N > &x, const Vector< D, N > &y)
	multiply every component of one vector with same component of another
template<unsigned D, typename N >
bool	operator== (const Vector< D, N > &one, const Vector< D, N > &other)
	Comparison operator: Test for equality.
template<unsigned D, typename N >
bool	operator!= (const Vector< D, N > &one, const Vector< D, N > &other)
	Comparison operator: Test for inequality.
template<unsigned D, typename N >
bool	operator< (const Vector< D, N > &one, const Vector< D, N > &other)
	Ordering needed to use Vector as key for a std::map.
template<unsigned D, typename N >
N	sqnorm (const Vector< D, N > &x)
template<unsigned D, typename N >
std::ostream &	operator<< (std::ostream &s, const Vector< D, N > &v)
	Vector output operator.
template<unsigned D, typename N >
std::istringstream &	operator>> (std::istringstream &in, Vector< D, N > &v)
	Vector input operator.
template<typename N >
Vector< 3, N >	vcross (Vector< 3, N > a, Vector< 3, N > b)
	Cross product of two 3-Vectors.
template<typename N >
Vector< 4, N >	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 >	vnormalize (const Vector< D, N > &x)
	Normalizes a 3-Vector out-of-place.
template<typename N >
Vector< 2, N >	makeVector (N const &x0, N const &x1)
	Generator function for a 2-dimensional Vector.
template<typename N >
Vector< 3, N >	makeVector (N const &x0, N const &x1, N const &x2)
	Generator function for a 3-dimensional Vector.
template<typename N >
Vector< 4, N >	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 >	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 >	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 >	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 >	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 >	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 >	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.

Detailed Description

Vector and Matrix algebra.

Function Documentation

template<typename T1 , typename T2 , typename T3 , unsigned D, typename Function >

Function VecMath::for_each	(	MultiDimensionalVector< T1, D > &	v1,
		MultiDimensionalVector< T2, D > &	v2,
		MultiDimensionalVector< T3, D > &	v3,
		Function	f
	)

Loop over three MultiDimensionalVector s simultaneously, applying a function on all elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
v3	The MultiDimensionalVector containing the third arguments going into `f`.
f	The function that is applied on every element of `v1`, `v2` `v2` and `v3`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
T3	Type of the elements in the third MultiDimensionalVector; type of the third argument to `f`.
D	Dimensionality (nesting depth) of both MultiDimensionalVector s.
Function	A ternary function object or function taking a `T1`, `const` `T1&` or `T1&` as first argument, a `T2`, `const` `T2&` or `T2&` as second argument, and a `T2`, `const` `T2&` or `T3&` as third argument.

References for_each(), max_element(), std::min(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<typename T1 , typename T2 , typename T3 , unsigned D, typename Function >

Function VecMath::for_each	(	const MultiDimensionalVector< T1, D > &	v1,
		const MultiDimensionalVector< T2, D > &	v2,
		const MultiDimensionalVector< T3, D > &	v3,
		Function	f
	)

Loop over three MultiDimensionalVector s simultaneously, applying a const function on all elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
v3	The MultiDimensionalVector containing the third arguments going into `f`.
f	The function that is applied on every element of `v1`, `v2` `v2` and `v3`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
T3	Type of the elements in the third MultiDimensionalVector; type of the third argument to `f`.
D	Dimensionality (nesting depth) of both MultiDimensionalVector s.
Function	A ternary function object or function taking a `T1`, `const` `T1&` or `T1&` as first argument, a `T2`, `const` `T2&` or `T2&` as second argument, and a `T2`, `const` `T2&` or `T3&` as third argument.

References for_each(), max_element(), std::min(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<typename T1 , typename T2 , typename Function >

Function VecMath::for_each	(	MultiDimensionalVector< T1, 1 > &	v1,
		MultiDimensionalVector< T2, 1 > &	v2,
		Function	f
	)

Loop over two MultiDimensionalVector s simultaneously, applying a function on both elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
f	The function that is applied on every element of `v1` and `v2`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
Function	A binary function object or function taking a `T1`, `const` `T1&` or `T1&` as first argument, and a `T2`, `const` `T2&` or `T2&` as second argument.

References max_element(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<typename T1 , typename T2 , unsigned D, typename Function >

Function VecMath::for_each	(	MultiDimensionalVector< T1, D > &	v1,
		MultiDimensionalVector< T2, D > &	v2,
		Function	f
	)

Loop over two MultiDimensionalVector s simultaneously, applying a function on both elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
f	The function that is applied on every element of `v1` and `v2`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
D	Dimensionality (nesting depth) of both MultiDimensionalVector s.
Function	A binary function object or function taking a `T1`, `const` `T1&` or `T1&` as first argument, and a `T2`, `const` `T2&` or `T2&` as second argument.

References max_element(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

Referenced by for_each(), VertexHolder< N, P, NUM >::for_each_vertex_transformed(), and VertexHolder< N, P, NUM >::for_each_vertex_transformed_projected().

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template<typename T1 , typename T2 , typename Function >

Function VecMath::for_each	(	const MultiDimensionalVector< T1, 1 > &	v1,
		const MultiDimensionalVector< T2, 1 > &	v2,
		Function	f
	)

Loop over two MultiDimensionalVector s simultaneously, applying a const function on both elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
f	The function that is applied on every element of `v1` and `v2`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
Function	A binary function object or function taking a `T1` or `const` `T1&` as first argument, and a `T2` or `const` `T2&` as second argument.

References max_element(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<typename T1 , typename T2 , typename T3 , typename Function >

Function VecMath::for_each	(	MultiDimensionalVector< T1, 1 > &	v1,
		MultiDimensionalVector< T2, 1 > &	v2,
		MultiDimensionalVector< T3, 1 > &	v3,
		Function	f
	)

Loop over three MultiDimensionalVector s simultaneously, applying a function on all elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
v3	The MultiDimensionalVector containing the third arguments going into `f`.
f	The function that is applied on every element of `v1`, `v2` `v2` and `v3`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
T3	Type of the elements in the third MultiDimensionalVector; type of the third argument to `f`.
Function	A ternary function object or function taking a `T1`, `const` `T1&` or `T1&` as first argument, a `T2`, `const` `T2&` or `T2&` as second argument, and a `T2`, `const` `T2&` or `T3&` as third argument.

References max_element(), std::min(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<typename T1 , typename T2 , unsigned D, typename Function >

Function VecMath::for_each	(	const MultiDimensionalVector< T1, D > &	v1,
		const MultiDimensionalVector< T2, D > &	v2,
		Function	f
	)

Loop over two MultiDimensionalVector s simultaneously, applying a const function on both elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
f	The function that is applied on every element of `v1` and `v2`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
D	Dimensionality (nesting depth) of both MultiDimensionalVector s.
Function	A binary function object or function taking a `T1` or `const` `T1&` as first argument, and a `T2` or `const` `T2&` as second argument.

References for_each(), max_element(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<typename T1 , typename T2 , typename T3 , typename Function >

Function VecMath::for_each	(	const MultiDimensionalVector< T1, 1 > &	v1,
		const MultiDimensionalVector< T2, 1 > &	v2,
		const MultiDimensionalVector< T3, 1 > &	v3,
		Function	f
	)

Loop over three MultiDimensionalVector s simultaneously, applying a const function on all elements.

Parameters:

v1	The MultiDimensionalVector containing the first arguments going into `f`.
v2	The MultiDimensionalVector containing the second arguments going into `f`.
v3	The MultiDimensionalVector containing the third arguments going into `f`.
f	The function that is applied on every element of `v1`, `v2` `v2` and `v3`.

Template Parameters:

T1	Type of the elements in the first MultiDimensionalVector; type of the first argument to `f`.
T2	Type of the elements in the second MultiDimensionalVector; type of the second argument to `f`.
T3	Type of the elements in the third MultiDimensionalVector; type of the third argument to `f`.
Function	A ternary function object or function taking a `T1`, `const` `T1&` or `T1&` as first argument, a `T2`, `const` `T2&` or `T2&` as second argument, and a `T2`, `const` `T2&` or `T3&` as third argument.

References max_element(), std::min(), min(), and VecMath::MultiDimensionalVector< T, D >::size().

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template<unsigned D, typename N >

Vector< D, N > VecMath::operator*	(	const Vector< D, N > &	x,
		const N &	s
	)

Parameters:

x	Vector
s	scalar type

Returns:: x*s

template<unsigned D, typename N >

Vector< D, N > VecMath::operator*	(	const N &	s,
		const Vector< D, N > &	x
	)

Parameters:

x	Vector
s	scalar type

Returns:: x*s

template<unsigned D, typename N >

N VecMath::operator*	(	const Vector< D, N > &	x,
		const Vector< D, N > &	y
	)

scalar multiplication between two Vectors (dot product)

Parameters:

x	First factor
y	Second factor

Returns:: dot product < x, y >

template<unsigned D, typename N >

Vector< D, N > VecMath::operator+	(	const Vector< D, N > &	x,
		const Vector< D, N > &	y
	)

Plus.

Parameters:

x	first operand
y	second operand

Returns:: x+y

template<unsigned D, typename N >

Rotation< D, N > VecMath::operator+	(	const Rotation< D, N > &	A,
		const Rotation< D, N > &	B
	)

Returns the sum of two Rotation s.

Parameters:

A	first operand
B	second operand

Returns:: A+B

template<unsigned D, typename N >

Vector< D, N > VecMath::operator- ( const Vector< D, N > & v )

Unary minus.

Returns:: -v

template<unsigned D, typename N >

Vector< D, N > VecMath::operator-	(	const Vector< D, N > &	x,
		const Vector< D, N > &	y
	)

Binary minus.

Parameters:

x	first operand
y	second operand

Returns:: x-y

template<unsigned D, typename N >

Vector< D, N > VecMath::operator/	(	const Vector< D, N > &	x,
		const N &	s
	)

Parameters:

x	Dividend
s	Scalar divisor

Returns:: *this/s

template<unsigned D, typename N >

Vector< D, N > VecMath::operator/	(	const Vector< D, N > &	x,
		const Vector< D, N > &	y
	)

divide every component of one vector by same component of another

Parameters:

X	Dividend
y	Divisor

Returns:: scaled vector

template<unsigned D, typename N >

bool VecMath::operator<	(	const Vector< D, N > &	one,
		const Vector< D, N > &	other
	)

Ordering needed to use Vector as key for a std::map.

Returns:: whether absolute value of this is less than the other Vector's

References sqnorm().

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template<unsigned D, typename N >

Vector< D, N > VecMath::scale	(	const Vector< D, N > &	x,
		const Vector< D, N > &	y
	)

multiply every component of one vector with same component of another

Parameters:

X	Dividend
y	Divisor

Returns:: scaled vector

template<unsigned D, typename N >

N VecMath::sqnorm ( const Vector< D, N > & x )

Returns:: the squared norm of the vector,

Referenced by xyz2RGBColorManager::findClosestPoints(), Util::glVertex(), VecMath::Rotation< D, N >::operator bool(), operator<(), FunctionValueGrid< N, P, NUM >::setBoundaries(), FunctionValueGrid< N, P, NUM >::setGridSize(), and vnormalize().

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Classes

Functions

Detailed Description

Function Documentation