Interval defines the concept of a mathematical interval and provides operations on it including arithmetic operations, construction, and IO. More...

#include <IntervalArithmetic.h>

Public Member Functions
	Interval ()
	Constructor.

	Interval (const T &min, const T &max)
	Constructor. More...

	Interval (const Interval< T > &i)
	Copy constructor. More...

	Interval (Interval< T > &&i)
	Move constructor. More...

Interval< T > &	operator= (const Interval< T > &i)
	Assignment operator. More...

Interval< T > &	operator= (Interval< T > &&i)
	Move assignment operator. More...

bool	overlapsWith (const Interval< T > &i) const

bool	contains (const T &val) const

bool	containsZero () const

bool	isApprox (const Interval< T > &i, const T &epsilon) const

bool	operator== (const Interval< T > &i) const

bool	operator!= (const Interval< T > &i) const

Interval< T > &	addThickness (const T &thickness)
	Widens the current interval by thickness on both sides. More...

Interval< T > &	extendToInclude (const T &x)
	Widens the current interval on one end to include x. More...

Interval< T > &	extendToInclude (const Interval< T > &i)
	Widens the current interval on both ends to include i. More...

Interval< T >	inverse () const

Interval< T >	operator/ (const Interval< T > &i) const

Interval< T > &	operator/= (const Interval< T > &i)

Interval< T >	square () const

T	getMin () const

T	getMax () const

Interval< T >	lowerHalf () const

Interval< T >	upperHalf () const


Interval< T >	operator+ (const Interval< T > &i) const

Interval< T >	operator+ (const T &v) const

Interval< T > &	operator+= (const Interval< T > &i)

Interval< T > &	operator+= (const T &v)

Interval< T >	operator- () const

Interval< T >	operator- (const Interval< T > &i) const

Interval< T >	operator- (const T &v) const

Interval< T > &	operator-= (const Interval< T > &i)

Interval< T > &	operator-= (const T &v)

Interval< T >	operator* (const Interval< T > &i) const

Interval< T >	operator* (const T &v) const

Interval< T > &	*operator=** (const Interval< T > &i)

Interval< T > &	*operator=** (const T &v)

Static Public Member Functions
static Interval< T >	minToMax (const T &a1, const T &a2)
	Generate an interval from min to max based on the inputs. More...

static Interval< T >	minToMax (const T &a1, const T &a2, const T &a3)
	Generate an interval from min to max based on the inputs. More...

static Interval< T >	minToMax (const T &a1, const T &a2, const T &a3, const T &a4)
	Generate an interval from min to max based on the inputs. More...

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

template<class P >
void	IntervalArithmetic_addadd (const Interval< P > &a, const Interval< P > &b, Interval< P > *res)
	Calculate the sum of three intervals res + a + b. More...

template<class P >
void	IntervalArithmetic_sub (const Interval< P > &a, const Interval< P > &b, Interval< P > *res)
	Calculate the difference of two intervals. More...

template<class P >
void	IntervalArithmetic_addsub (const Interval< P > &a, const Interval< P > &b, Interval< P > *res)
	Add the difference of two intervals to an existing value. More...

template<class P >
void	IntervalArithmetic_mul (const Interval< P > &a, const Interval< P > &b, Interval< P > *res)
	Calculate the product of two intervals. More...

template<class P >
void	IntervalArithmetic_addmul (const Interval< P > &a, const Interval< P > &b, Interval< P > *res)
	Add the product of two intervals to an existing value. More...

template<class P >
void	IntervalArithmetic_submul (const Interval< P > &a, const Interval< P > &b, Interval< P > *res)
	Subtract the product of two intervals from an existing value. More...

Detailed Description

template<class T>
class SurgSim::Math::Interval< T >

Interval defines the concept of a mathematical interval and provides operations on it including arithmetic operations, construction, and IO.

Template Parameters

T	underlying data type over which the interval is defined.

See also: IntervalND<T, N> and IntervalND<T, 3>

Constructor & Destructor Documentation

§ Interval() [1/3]

template<class T >

SurgSim::Math::Interval< T >::Interval	(	const T &	min,
		const T &	max
	)

Constructor.

Parameters

min	Lower bound of the constructed interval
max	Upper bound of the constructed interval

Exceptions

if	max is less than min

§ Interval() [2/3]

template<class T >

SurgSim::Math::Interval< T >::Interval ( const Interval< T > & i )

Copy constructor.

Parameters

i	Interval to be copied

§ Interval() [3/3]

template<class T >

SurgSim::Math::Interval< T >::Interval ( Interval< T > && i )

Move constructor.

Parameters

i	Interval to be copied

Member Function Documentation

§ addThickness()

template<class T >

Interval< T > & SurgSim::Math::Interval< T >::addThickness ( const T & thickness )

Widens the current interval by thickness on both sides.

Parameters

thickness the amount to widen the current interval on both sides

Returns: the current interval after modification

§ contains()

template<class T >

bool SurgSim::Math::Interval< T >::contains ( const T & val ) const

Parameters

val	the value to test for inclusion in the interval

Returns: true if the current interval contains val

§ containsZero()

template<class T >

bool SurgSim::Math::Interval< T >::containsZero ( ) const

Returns: true if the current interval contains 0

§ extendToInclude() [1/2]

template<class T >

Interval< T > & SurgSim::Math::Interval< T >::extendToInclude ( const T & x )

Widens the current interval on one end to include x.

Parameters

x	the value to be included in the interval

Returns: the current interval extended to include x

§ extendToInclude() [2/2]

template<class T >

Interval< T > & SurgSim::Math::Interval< T >::extendToInclude ( const Interval< T > & i )

Widens the current interval on both ends to include i.

Parameters

i	the interval to be wholly contained in the current interval

Returns: the current interval extended to include the entirety of i

§ getMax()

template<class T >

T SurgSim::Math::Interval< T >::getMax ( ) const

Returns: the upper limit of the interval

§ getMin()

template<class T >

T SurgSim::Math::Interval< T >::getMin ( ) const

Returns: the lower limit of the interval

§ inverse()

template<class T >

Interval< T > SurgSim::Math::Interval< T >::inverse ( ) const

Returns: the inverse of the current interval

Exceptions

if	the interval includes 0

§ isApprox()

template<class T >

bool SurgSim::Math::Interval< T >::isApprox	(	const Interval< T > &	i,
		const T &	epsilon
	)		const

Parameters

i	the interval to be tested
epsilon	the nearness parameter

Returns: true if the current interval is within epsilon of the input interval

§ lowerHalf()

template<class T >

Interval< T > SurgSim::Math::Interval< T >::lowerHalf ( ) const

Returns: the interval from the lower limit to the midpoint

§ minToMax() [1/3]

template<class T >

Interval< T > SurgSim::Math::Interval< T >::minToMax	(	const T &	a1,
		const T &	a2
	)

static

Generate an interval from min to max based on the inputs.

Parameters

a1	first input value
a2	second input value

Returns: an interval spanning the minimum input to the maximum input.

§ minToMax() [2/3]

template<class T >

Interval< T > SurgSim::Math::Interval< T >::minToMax	(	const T &	a1,
		const T &	a2,
		const T &	a3
	)

static

Generate an interval from min to max based on the inputs.

Parameters

a1	first input value
a2	second input value
a3	third input value

Returns: an interval spanning the minimum input to the maximum input.

§ minToMax() [3/3]

template<class T >

Interval< T > SurgSim::Math::Interval< T >::minToMax	(	const T &	a1,
		const T &	a2,
		const T &	a3,
		const T &	a4
	)

static

Generate an interval from min to max based on the inputs.

Parameters

a1	first input value
a2	second input value
a3	third input value
a4	fourth input value

Returns: an interval spanning the minimum input to the maximum input.

§ operator!=()

template<class T >

bool SurgSim::Math::Interval< T >::operator!= ( const Interval< T > & i ) const

Parameters

i	the interval to be tested

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

§ operator+()

template<class T >

Interval< T > SurgSim::Math::Interval< T >::operator+ ( const Interval< T > & i ) const

Standard arithmetic operators extended to intervals

§ operator/()

template<class T >

Interval< T > SurgSim::Math::Interval< T >::operator/ ( const Interval< T > & i ) const

Parameters

i	the interval to be divided by

Returns: the current interval multiplied by the inverse of i

Exceptions

if	i includes 0

§ operator/=()

template<class T >

Interval< T > & SurgSim::Math::Interval< T >::operator/= ( const Interval< T > & i )

Parameters

i	the interval to be divided by

Returns: the current interval multiplied by the inverse of i

Exceptions

if	i includes 0

Note: the current interval is modified by this operation

§ operator=() [1/2]

template<class T >

Interval< T > & SurgSim::Math::Interval< T >::operator= ( const Interval< T > & i )

Assignment operator.

Parameters

i	Interval to be copied

§ operator=() [2/2]

template<class T >

Interval< T > & SurgSim::Math::Interval< T >::operator= ( Interval< T > && i )

Move assignment operator.

Parameters

i	Interval to be moved

§ operator==()

template<class T >

bool SurgSim::Math::Interval< T >::operator== ( const Interval< T > & i ) const

Parameters

i	the interval to be tested

Returns: true if the current interval is identical to the input interval

§ overlapsWith()

template<class T >

bool SurgSim::Math::Interval< T >::overlapsWith ( const Interval< T > & i ) const

Parameters

i	the interval the current interval will be tested against

Returns: true if the input interval overlaps the current interval

§ square()

template<class T >

Interval< T > SurgSim::Math::Interval< T >::square ( ) const

Returns: the square of the current interval

Note: if the original interval contains 0, then the result will have the minimum identically set to 0

§ upperHalf()

template<class T >

Interval< T > SurgSim::Math::Interval< T >::upperHalf ( ) const

Returns: the interval from the midpoint to the upper limit

Friends And Related Function Documentation

§ IntervalArithmetic_add

template<class T>

template<class P >

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

friend

Calculate the sum of two intervals.

Template Parameters

P	underlying type of the interval

Parameters

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

§ IntervalArithmetic_addadd

template<class T>

template<class P >

void IntervalArithmetic_addadd	(	const Interval< P > &	a,
		const Interval< P > &	b,
		Interval< P > *	res
	)

friend

Calculate the sum of three intervals res + a + b.

Template Parameters

P	underlying type of the interval

Parameters

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

§ IntervalArithmetic_addmul

template<class T>

template<class P >

void IntervalArithmetic_addmul	(	const Interval< P > &	a,
		const Interval< P > &	b,
		Interval< P > *	res
	)

friend

Add the product of two intervals to an existing value.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval
b	the second interval
res	[in/out] the result of res + (a * b)

§ IntervalArithmetic_addsub

template<class T>

template<class P >

void IntervalArithmetic_addsub	(	const Interval< P > &	a,
		const Interval< P > &	b,
		Interval< P > *	res
	)

friend

Add the difference of two intervals to an existing value.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval
b	the second interval
res	[in/out] the result of res + (a - b)

§ IntervalArithmetic_mul

template<class T>

template<class P >

void IntervalArithmetic_mul	(	const Interval< P > &	a,
		const Interval< P > &	b,
		Interval< P > *	res
	)

friend

Calculate the product of two intervals.

Template Parameters

P	underlying type of the interval

Parameters

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

§ IntervalArithmetic_sub

template<class T>

template<class P >

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

friend

Calculate the difference of two intervals.

Template Parameters

P	underlying type of the interval

Parameters

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

§ IntervalArithmetic_submul

template<class T>

template<class P >

void IntervalArithmetic_submul	(	const Interval< P > &	a,
		const Interval< P > &	b,
		Interval< P > *	res
	)

friend

Subtract the product of two intervals from an existing value.

Template Parameters

P	underlying type of the interval

Parameters

a	the first interval
b	the second interval
res	[in/out] the result of res - (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

Static Public Member Functions

Friends

Detailed Description

template<class T> class SurgSim::Math::Interval< T >

Constructor & Destructor Documentation

§ Interval() [1/3]

§ Interval() [2/3]

§ Interval() [3/3]

Member Function Documentation

§ addThickness()

§ contains()

§ containsZero()

§ extendToInclude() [1/2]

§ extendToInclude() [2/2]

§ getMax()

§ getMin()

§ inverse()

§ isApprox()

§ lowerHalf()

§ minToMax() [1/3]

§ minToMax() [2/3]

§ minToMax() [3/3]

§ operator!=()

§ operator+()

§ operator/()

§ operator/=()

§ operator=() [1/2]

§ operator=() [2/2]

§ operator==()

§ overlapsWith()

§ square()

§ upperHalf()

Friends And Related Function Documentation

§ IntervalArithmetic_add

§ IntervalArithmetic_addadd

§ IntervalArithmetic_addmul

§ IntervalArithmetic_addsub

§ IntervalArithmetic_mul

§ IntervalArithmetic_sub

§ IntervalArithmetic_submul

template<class T>
class SurgSim::Math::Interval< T >