The interval template represents a closed interval of two numbers, i.e. More...

#include <interval.h>

Public Member Functions
interval operations
	interval ()
	construct empty interval
	interval (bool)
	Construct interval over all valid values of the value type, where the parameter is only a dummy to distinguish this constructor from the standard constructor.
	interval (const interval< T > &I)
	copy constructor
	interval (const T &lb, const T &ub)
	Contruct interval from bounds, sort bounds if necessary. To construct empty interval call the standard constructor.
bool	empty () const
	check if interval is empty
void	clear ()
	set to empty interval
bool	contains (const T &v) const
	check if given value is contained in interval
T	center () const
	return the center value, which is only valid if the interval is not empty
T	size () const
	return the size of the interval
interval< T > &	intersect (const interval< T > &I)
	set interval to intersection with given interval and return reference to this interval
interval< T >	intersection (const interval< T > &I) const
	return intersection interval
interval< T > &	extend (const T &v)
	extend interval such that it includes the given value
interval< T > &	extend (const T vs[], size_t n)
	extend interval such that it includes the n given values
interval< T > &	extend (const std::vector< T > &vs)
	extend interval such that it includes the given values
interval< T > &	extension (const T &v)
	return extension of interval so that it includes the given value
interval< T > &	extend (const interval< T > &I)
	extend interval such that it includes the given interval
interval< T > &	extension (const interval< T > &J)
	return extension of interval so that it includes the given interval
scalar operators
interval< T > &	operator*= (const T &s)
	scale the interval
interval< T >	operator* (const T &s) const
	return scaled interval
interval< T > &	operator/= (const T &s)
	divide the interval
interval< T >	operator/ (const T &s) const
	return divided interval
interval< T > &	operator+= (const T &s)
	right shift interval by adding scalar to both bounds
interval< T >	operator+ (const T &s) const
	return right shifted interval
interval< T > &	operator-= (const T &s)
	left shift interval by subtracting scalar from both bounds
interval< T >	operator- (const T &s) const
	return left shifted interval
interval operators
interval< T > &	operator*= (const interval< T > &I)
	compute the interval of all values of all products of values from the two intervals
interval< T >	operator* (const interval< T > &J) const
	return the interval of all values of products of values from the two intervals
interval< T > &	operator/= (const interval< T > &I)
	Compute the interval of all values of all quotients of values from the two intervals.
interval< T >	operator/ (const interval< T > &J) const
	return the interval of all values of quotients of values from the two intervals. See also comments on the /= operator().
interval< T >	operator- () const
	unary minus operator reflects interval at zero value
interval< T > &	operator+= (const interval< T > &I)
	compute interval of all sums of values from the two intervals
interval< T >	operator+ (const interval< T > &J) const
	return interval of all sums of values from the two intervals
interval< T > &	operator-= (const interval< T > &I)
	compute interval of all differences of values from the two intervals
interval< T >	operator- (const interval< T > &J) const
	return interval of all differences of values from the two intervals
comparison operators
bool	operator== (const interval< T > &I) const
	check for equality of two intervals
bool	operator!= (const interval< T > &I) const
	check for inequality of two intervals
bool	operator< (const interval< T > &I) const
	only returns true if both intervals are not empty and the operator holds for all values in both intervals
bool	operator> (const interval< T > &I) const
	only returns true if both intervals are not empty and the operator holds for all values in both intervals

Public Attributes
T	lower_bound
T	upper_bound

Detailed Description

template<typename T>
class cgv::math::interval< T >

The interval template represents a closed interval of two numbers, i.e.

[a,b]. All arithmetic operators are overloaded for the interval template. This allows to compute bounds for an arbitrary expression. For example if the variable x is from the interval [-1,1] then the expression x*x is from the interval [0,1], which can be computed via \codebegin interval<int> x(-1,1); interval<int> e = x*x; std::cout << e << std::endl; \codeend Furthermore, the interval template supports further interval based operations like intersection and extension of an interval.

Definition at line 26 of file interval.h.

Constructor & Destructor Documentation

◆ interval() [1/4]

template<typename T>

cgv::math::interval< T >::interval ( )

inline

construct empty interval

Definition at line 37 of file interval.h.

Referenced by extend(), extend(), extend(), extend(), extension(), extension(), intersect(), intersection(), interval(), operator!=(), operator*(), operator*(), operator*=(), operator*=(), operator+(), operator+(), operator+=(), operator+=(), operator-(), operator-(), operator-(), operator-=(), operator-=(), operator/(), operator/(), operator/=(), operator/=(), operator<(), operator==(), and operator>().

◆ interval() [2/4]

template<typename T>

cgv::math::interval< T >::interval ( bool )

inline

Construct interval over all valid values of the value type, where the parameter is only a dummy to distinguish this constructor from the standard constructor.

This constructor relies on cgv::type::traits::min and cgv::type::traits::max. Thus if you want to build intervals over non standard types, you need to ensure that these two traits are instantiated for your type when using this constructor.

Definition at line 43 of file interval.h.

◆ interval() [3/4]

template<typename T>

cgv::math::interval< T >::interval ( const interval< T > & I )

inline

copy constructor

Definition at line 45 of file interval.h.

References interval().

◆ interval() [4/4]

template<typename T>

cgv::math::interval< T >::interval	(	const T &	lb,
		const T &	ub )

inline

Contruct interval from bounds, sort bounds if necessary. To construct empty interval call the standard constructor.

Definition at line 47 of file interval.h.

Member Function Documentation

◆ center()

template<typename T>

T cgv::math::interval< T >::center ( ) const

inline

return the center value, which is only valid if the interval is not empty

Definition at line 55 of file interval.h.

◆ clear()

template<typename T>

void cgv::math::interval< T >::clear ( )

inline

set to empty interval

Definition at line 51 of file interval.h.

◆ contains()

template<typename T>

bool cgv::math::interval< T >::contains ( const T & v ) const

inline

check if given value is contained in interval

Definition at line 53 of file interval.h.

Referenced by operator/=().

◆ empty()

template<typename T>

bool cgv::math::interval< T >::empty ( ) const

inline

check if interval is empty

Definition at line 49 of file interval.h.

Referenced by extend(), extend(), operator*=(), operator+=(), operator-(), operator/=(), operator<(), operator==(), operator>(), and size().

◆ extend() [1/4]

template<typename T>

interval< T > & cgv::math::interval< T >::extend ( const interval< T > & I )

inline

extend interval such that it includes the given interval

Definition at line 92 of file interval.h.

References empty(), extend(), and interval().

◆ extend() [2/4]

template<typename T>

interval< T > & cgv::math::interval< T >::extend ( const std::vector< T > & vs )

inline

extend interval such that it includes the given values

Definition at line 84 of file interval.h.

References extend(), and interval().

◆ extend() [3/4]

template<typename T>

interval< T > & cgv::math::interval< T >::extend ( const T & v )

inline

extend interval such that it includes the given value

Definition at line 67 of file interval.h.

References empty(), and interval().

Referenced by extend(), extend(), extend(), extension(), extension(), operator*=(), operator+=(), and operator/=().

◆ extend() [4/4]

template<typename T>

interval< T > & cgv::math::interval< T >::extend	(	const T	vs[],
		size_t	n )

inline

extend interval such that it includes the n given values

Definition at line 78 of file interval.h.

References extend(), and interval().

◆ extension() [1/2]

template<typename T>

interval< T > & cgv::math::interval< T >::extension ( const interval< T > & J )

inline

return extension of interval so that it includes the given interval

Definition at line 100 of file interval.h.

References extend(), and interval().

◆ extension() [2/2]

template<typename T>

interval< T > & cgv::math::interval< T >::extension ( const T & v )

inline

return extension of interval so that it includes the given value

Definition at line 90 of file interval.h.

References extend(), and interval().

◆ intersect()

template<typename T>

interval< T > & cgv::math::interval< T >::intersect ( const interval< T > & I )

inline

set interval to intersection with given interval and return reference to this interval

Definition at line 59 of file interval.h.

References interval().

Referenced by intersection().

◆ intersection()

template<typename T>

interval< T > cgv::math::interval< T >::intersection ( const interval< T > & I ) const

inline

return intersection interval

Definition at line 65 of file interval.h.

References intersect(), and interval().

◆ operator!=()

template<typename T>

bool cgv::math::interval< T >::operator!= ( const interval< T > & I ) const

inline

check for inequality of two intervals

Definition at line 181 of file interval.h.

References interval().

◆ operator*() [1/2]

template<typename T>

interval< T > cgv::math::interval< T >::operator* ( const interval< T > & J ) const

inline

return the interval of all values of products of values from the two intervals

Definition at line 134 of file interval.h.

References interval().

◆ operator*() [2/2]

template<typename T>

interval< T > cgv::math::interval< T >::operator* ( const T & s ) const

inline

return scaled interval

Definition at line 107 of file interval.h.

References interval().

◆ operator*=() [1/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator*= ( const interval< T > & I )

inline

compute the interval of all values of all products of values from the two intervals

Definition at line 125 of file interval.h.

References empty(), extend(), and interval().

◆ operator*=() [2/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator*= ( const T & s )

inline

scale the interval

Definition at line 105 of file interval.h.

References interval().

◆ operator+() [1/2]

template<typename T>

interval< T > cgv::math::interval< T >::operator+ ( const interval< T > & J ) const

inline

return interval of all sums of values from the two intervals

Definition at line 166 of file interval.h.

References interval().

◆ operator+() [2/2]

template<typename T>

interval< T > cgv::math::interval< T >::operator+ ( const T & s ) const

inline

return right shifted interval

Definition at line 115 of file interval.h.

References interval().

◆ operator+=() [1/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator+= ( const interval< T > & I )

inline

compute interval of all sums of values from the two intervals

Definition at line 156 of file interval.h.

References empty(), extend(), and interval().

◆ operator+=() [2/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator+= ( const T & s )

inline

right shift interval by adding scalar to both bounds

Definition at line 113 of file interval.h.

References interval().

◆ operator-() [1/3]

template<typename T>

interval< T > cgv::math::interval< T >::operator- ( ) const

inline

unary minus operator reflects interval at zero value

Definition at line 154 of file interval.h.

References empty(), and interval().

◆ operator-() [2/3]

template<typename T>

interval< T > cgv::math::interval< T >::operator- ( const interval< T > & J ) const

inline

return interval of all differences of values from the two intervals

Definition at line 170 of file interval.h.

References interval().

◆ operator-() [3/3]

template<typename T>

interval< T > cgv::math::interval< T >::operator- ( const T & s ) const

inline

return left shifted interval

Definition at line 119 of file interval.h.

References interval().

◆ operator-=() [1/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator-= ( const interval< T > & I )

inline

compute interval of all differences of values from the two intervals

Definition at line 168 of file interval.h.

References interval().

◆ operator-=() [2/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator-= ( const T & s )

inline

left shift interval by subtracting scalar from both bounds

Definition at line 117 of file interval.h.

References interval().

◆ operator/() [1/2]

template<typename T>

interval< T > cgv::math::interval< T >::operator/ ( const interval< T > & J ) const

inline

return the interval of all values of quotients of values from the two intervals. See also comments on the /= operator().

Definition at line 152 of file interval.h.

References interval().

◆ operator/() [2/2]

template<typename T>

interval< T > cgv::math::interval< T >::operator/ ( const T & s ) const

inline

return divided interval

Definition at line 111 of file interval.h.

References interval().

◆ operator/=() [1/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator/= ( const interval< T > & I )

inline

Compute the interval of all values of all quotients of values from the two intervals.

Notice that if zero is contained in the second interval, the result is the complete interval of all valid values and the same precondition holds as for the constructor with the bool dummy parameter interval(bool).

Definition at line 139 of file interval.h.

References contains(), empty(), extend(), and interval().

◆ operator/=() [2/2]

template<typename T>

interval< T > & cgv::math::interval< T >::operator/= ( const T & s )

inline

divide the interval

Definition at line 109 of file interval.h.

References interval().

◆ operator<()

template<typename T>

bool cgv::math::interval< T >::operator< ( const interval< T > & I ) const

inline

only returns true if both intervals are not empty and the operator holds for all values in both intervals

Definition at line 185 of file interval.h.

References empty(), and interval().

◆ operator==()

template<typename T>

bool cgv::math::interval< T >::operator== ( const interval< T > & I ) const

inline

check for equality of two intervals

Definition at line 176 of file interval.h.

References empty(), and interval().

◆ operator>()

template<typename T>

bool cgv::math::interval< T >::operator> ( const interval< T > & I ) const

inline

only returns true if both intervals are not empty and the operator holds for all values in both intervals

Definition at line 189 of file interval.h.

References empty(), and interval().

◆ size()

template<typename T>

T cgv::math::interval< T >::size ( ) const

inline

return the size of the interval

Definition at line 57 of file interval.h.

References empty().

Member Data Documentation

◆ lower_bound

template<typename T>

T cgv::math::interval< T >::lower_bound

Definition at line 30 of file interval.h.

◆ upper_bound

template<typename T>

T cgv::math::interval< T >::upper_bound

Definition at line 32 of file interval.h.

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

cgv/math/interval.h

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ interval() [1/4]

◆ interval() [2/4]

◆ interval() [3/4]

◆ interval() [4/4]

Member Function Documentation

◆ center()

◆ clear()

◆ contains()

◆ empty()

◆ extend() [1/4]

◆ extend() [2/4]

◆ extend() [3/4]

◆ extend() [4/4]

◆ extension() [1/2]

◆ extension() [2/2]

◆ intersect()

◆ intersection()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator<()

◆ operator==()

◆ operator>()

◆ size()

Member Data Documentation

◆ lower_bound

◆ upper_bound