IntervalND<T,3> defines the concept of a group of mathematical intervals specialized to 3 intervals and provides operations on them including arithmetic operations, construction, and IO. More...

#include <IntervalArithmetic.h>

Public Member Functions
	IntervalND ()
	Constructor.

	IntervalND (const std::array< Interval< T >, 3 > &x)
	Constructor. More...

	IntervalND (const Interval< T > &x, const Interval< T > &y, const Interval< T > &z)
	Constructor. More...

	IntervalND (const IntervalND< T, 3 > &i)
	Copy constructor. More...

	IntervalND (IntervalND< T, 3 > &&i)
	Move constructor. More...

	IntervalND (const std::array< T, 3 > &a, const std::array< T, 3 > &b)
	Constructor. More...

IntervalND< T, 3 > &	operator= (const IntervalND< T, 3 > &i)
	Assignment operator. More...

IntervalND< T, 3 > &	operator= (IntervalND< T, 3 > &&i)
	Move assignment operator. More...

bool	overlapsWith (const IntervalND< T, 3 > &interval) const

bool	isApprox (const IntervalND< T, 3 > &interval, const T &epsilon) const

bool	operator== (const IntervalND< T, 3 > &i) const

bool	operator!= (const IntervalND< T, 3 > &i) const

IntervalND< T, 3 > &	addThickness (const T &thickness)
	Widens every interval in the current interval group by thickness on both sides. More...

IntervalND< T, 3 >	inverse () const

IntervalND< T, 3 >	operator/ (const IntervalND< T, 3 > &i) const

IntervalND< T, 3 > &	operator/= (const IntervalND< T, 3 > &i)

Interval< T >	dotProduct (const IntervalND< T, 3 > &i) const

IntervalND< T, 3 >	crossProduct (const IntervalND< T, 3 > &i) const

Interval< T >	magnitudeSquared () const

Interval< T >	magnitude () const

const Interval< T > &	getAxis (size_t i) const


IntervalND< T, 3 >	operator+ (const IntervalND< T, 3 > &i) const

IntervalND< T, 3 > &	operator+= (const IntervalND< T, 3 > &i)

IntervalND< T, 3 >	operator- (const IntervalND< T, 3 > &i) const

IntervalND< T, 3 > &	operator-= (const IntervalND< T, 3 > &i)

IntervalND< T, 3 >	operator* (const IntervalND< T, 3 > &i) const

IntervalND< T, 3 > &	*operator=** (const IntervalND< T, 3 > &i)

Friends
template<class P >
void	IntervalArithmetic_add (const IntervalND< P, 3 > &a, const IntervalND< P, 3 > &b, IntervalND< P, 3 > *res)
	Calculate the sum of two interval groups. More...

template<class P >
void	IntervalArithmetic_sub (const IntervalND< P, 3 > &a, const IntervalND< P, 3 > &b, IntervalND< P, 3 > *res)
	Calculate the difference of two interval groups. More...

template<class P >
void	IntervalArithmetic_crossProduct (const IntervalND< P, 3 > &a, const IntervalND< P, 3 > &b, IntervalND< P, 3 > *res)
	Calculate the cross product of two interval groups. More...

template<class P >
void	IntervalArithmetic_dotProduct (const IntervalND< P, 3 > &a, const IntervalND< P, 3 > &b, Interval< P > *res)
	Calculate the dot product of two interval groups. More...

Detailed Description

template<class T>
class SurgSim::Math::IntervalND< T, 3 >

IntervalND<T,3> defines the concept of a group of mathematical intervals specialized to 3 intervals and provides operations on them including arithmetic operations, construction, and IO.

Template Parameters

T	underlying data type over which the interval is defined.

See also: Interval<T> and IntervalND<T, N>

Constructor & Destructor Documentation

§ IntervalND() [1/5]

template<class T >

SurgSim::Math::IntervalND< T, 3 >::IntervalND ( const std::array< Interval< T >, 3 > & x )

explicit

Constructor.

Parameters

x	array of 3 intervals to be copied into the group

§ IntervalND() [2/5]

template<class T >

SurgSim::Math::IntervalND< T, 3 >::IntervalND	(	const Interval< T > &	x,
		const Interval< T > &	y,
		const Interval< T > &	z
	)

Constructor.

Parameters

x	first interval to be added to the 3 group
y	second interval to be added to the 3 group
z	third interval to be added to the 3 group

§ IntervalND() [3/5]

template<class T >

SurgSim::Math::IntervalND< T, 3 >::IntervalND ( const IntervalND< T, 3 > & i )

Copy constructor.

Parameters

i	interval 3 group to copied

§ IntervalND() [4/5]

template<class T >

SurgSim::Math::IntervalND< T, 3 >::IntervalND ( IntervalND< T, 3 > && i )

Move constructor.

Parameters

i	Interval to be copied

§ IntervalND() [5/5]

template<class T >

SurgSim::Math::IntervalND< T, 3 >::IntervalND	(	const std::array< T, 3 > &	a,
		const std::array< T, 3 > &	b
	)

Constructor.

Parameters

a	array of 3 values to be used as the respective minimums for the interval entries.
b	array of 3 values to be used as the respective maximums for the interval entries.

Member Function Documentation

§ addThickness()

template<class T >

IntervalND< T, 3 > & SurgSim::Math::IntervalND< T, 3 >::addThickness ( const T & thickness )

Widens every interval in the current interval group by thickness on both sides.

Parameters

thickness the amount to widen on both sides

Returns: the current interval group after modification

§ crossProduct()

template<class T >

IntervalND< T, 3 > SurgSim::Math::IntervalND< T, 3 >::crossProduct ( const IntervalND< T, 3 > & i ) const

Parameters

i	the input interval group

Returns: the interval cross product of the current 3 group and interval

§ dotProduct()

template<class T >

Interval< T > SurgSim::Math::IntervalND< T, 3 >::dotProduct ( const IntervalND< T, 3 > & i ) const

Parameters

i	the input interval group

Returns: the interval dot product of the current 3 group and interval

§ getAxis()

template<class T >

const Interval< T > & SurgSim::Math::IntervalND< T, 3 >::getAxis ( size_t i ) const

Parameters

i	the selector for the interval to be returned

Returns: the ith interval in the current 3 group

§ inverse()

template<class T >

IntervalND< T, 3 > SurgSim::Math::IntervalND< T, 3 >::inverse ( ) const

Returns: the inverse of each interval in the 3 interval group

Exceptions

if	any interval includes 0

§ isApprox()

template<class T >

bool SurgSim::Math::IntervalND< T, 3 >::isApprox	(	const IntervalND< T, 3 > &	interval,
		const T &	epsilon
	)		const

Parameters

interval	the interval group to be tested
epsilon	the nearness parameter

Returns: true if each interval in the input group is approximately equal to its correspondent element in interval.

§ magnitude()

template<class T >

Interval< T > SurgSim::Math::IntervalND< T, 3 >::magnitude ( ) const

Returns: the interval magnitude for the current 3 group

§ magnitudeSquared()

template<class T >

Interval< T > SurgSim::Math::IntervalND< T, 3 >::magnitudeSquared ( ) const

Returns: the square of the interval magnitude for the current 3 group

§ operator!=()

template<class T >

bool SurgSim::Math::IntervalND< T, 3 >::operator!= ( const IntervalND< T, 3 > & i ) const

Parameters

i	the interval group to be tested

Returns: true if the current interval 3 group is not identical to the input 3 group i

§ operator+()

template<class T >

IntervalND< T, 3 > SurgSim::Math::IntervalND< T, 3 >::operator+ ( const IntervalND< T, 3 > & i ) const

Standard arithmetic operators extended to 3 interval groups

§ operator/()

template<class T >

IntervalND< T, 3 > SurgSim::Math::IntervalND< T, 3 >::operator/ ( const IntervalND< T, 3 > & i ) const

Parameters

i	the interval to be divided by

Returns: the product of each interval in the 3 group multiplied by the inverse of its correspondent in i

Exceptions

if	any component of interval includes 0

§ operator/=()

template<class T >

IntervalND< T, 3 > & SurgSim::Math::IntervalND< T, 3 >::operator/= ( const IntervalND< T, 3 > & i )

Parameters

i	the interval to be divided by

Returns: the product of each interval in the 3 group multiplied by the inverse of its correspondent in i

Note: the current interval is modified by this operation

§ operator=() [1/2]

template<class T >

IntervalND< T, 3 > & SurgSim::Math::IntervalND< T, 3 >::operator= ( const IntervalND< T, 3 > & i )

Assignment operator.

Parameters

i	Interval 3 group to be copied

§ operator=() [2/2]

template<class T >

IntervalND< T, 3 > & SurgSim::Math::IntervalND< T, 3 >::operator= ( IntervalND< T, 3 > && i )

Move assignment operator.

Parameters

i	Interval to be moved

§ operator==()

template<class T >

bool SurgSim::Math::IntervalND< T, 3 >::operator== ( const IntervalND< T, 3 > & i ) const

Parameters

i	the interval group to be tested

Returns: true if the current interval 3 group is identical to the input 3 group i

§ overlapsWith()

template<class T >

bool SurgSim::Math::IntervalND< T, 3 >::overlapsWith ( const IntervalND< T, 3 > & interval ) const

Parameters

interval the interval group the current group will be tested against

Returns: true if the input 3 group interval overlaps the current 3 group

Friends And Related Function Documentation

§ IntervalArithmetic_add

template<class T >

template<class P >

void IntervalArithmetic_add	(	const IntervalND< P, 3 > &	a,
		const IntervalND< P, 3 > &	b,
		IntervalND< P, 3 > *	res
	)

friend

Calculate the sum of two interval groups.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval group
b	the second interval group
res	[out] the result of a + b

§ IntervalArithmetic_crossProduct

template<class T >

template<class P >

void IntervalArithmetic_crossProduct	(	const IntervalND< P, 3 > &	a,
		const IntervalND< P, 3 > &	b,
		IntervalND< P, 3 > *	res
	)

friend

Calculate the cross product of two interval groups.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval group
b	the second interval group
res	[out] the cross product of a and b

§ IntervalArithmetic_dotProduct

template<class T >

template<class P >

void IntervalArithmetic_dotProduct	(	const IntervalND< P, 3 > &	a,
		const IntervalND< P, 3 > &	b,
		Interval< P > *	res
	)

friend

Calculate the dot product of two interval groups.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval group
b	the second interval group
res	[out] the dot product of a and b

§ IntervalArithmetic_sub

template<class T >

template<class P >

void IntervalArithmetic_sub	(	const IntervalND< P, 3 > &	a,
		const IntervalND< P, 3 > &	b,
		IntervalND< P, 3 > *	res
	)

friend

Calculate the difference of two interval groups.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval group
b	the second interval group
res	[out] the result of a - b

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

SurgSim/Math/IntervalArithmetic.h
SurgSim/Math/IntervalArithmetic-inl.h

Public Member Functions

Friends

Detailed Description

template<class T> class SurgSim::Math::IntervalND< T, 3 >

Constructor & Destructor Documentation

§ IntervalND() [1/5]

§ IntervalND() [2/5]

§ IntervalND() [3/5]

§ IntervalND() [4/5]

§ IntervalND() [5/5]

Member Function Documentation

§ addThickness()

§ crossProduct()

§ dotProduct()

§ getAxis()

§ inverse()

§ isApprox()

§ magnitude()

§ magnitudeSquared()

§ operator!=()

§ operator+()

§ operator/()

§ operator/=()

§ operator=() [1/2]

§ operator=() [2/2]

§ operator==()

§ overlapsWith()

Friends And Related Function Documentation

§ IntervalArithmetic_add

§ IntervalArithmetic_crossProduct

§ IntervalArithmetic_dotProduct

§ IntervalArithmetic_sub

template<class T>
class SurgSim::Math::IntervalND< T, 3 >