Common Mathematical Functions

Functions
template<typename T >
T	BALL::Maths::abs (const T &t)
template<typename T >
T	BALL::Maths::frac (const T &t)
template<typename T >
T	BALL::Maths::max (const T &a, const T &b)
template<typename T >
T	BALL::Maths::max (const T &a, const T &b, const T &ct)
template<typename T >
T	BALL::Maths::min (const T &a, const T &b)
template<typename T >
T	BALL::Maths::min (const T &a, const T &b, const T &ct)
template<typename T >
T	BALL::Maths::round (const T &t)
template<typename T >
T	BALL::Maths::sgn (const T &t)
template<typename T >
bool	BALL::Maths::isFinite (const T &t)
template<typename T >
bool	BALL::Maths::isNan (const T &t)
template<typename T >
bool	BALL::Maths::isInfinite (const T &t)
template<typename T >
bool	BALL::Maths::isZero (const T &t)
template<typename T >
bool	BALL::Maths::isNotZero (const T &t)
template<typename T1 , typename T2 >
bool	BALL::Maths::isEqual (const T1 &a, const T2 &b)
template<typename T1 , typename T2 >
bool	BALL::Maths::isNotEqual (const T1 &a, const T2 &b)
template<typename T1 , typename T2 >
bool	BALL::Maths::isLess (const T1 &a, const T2 &b)
template<typename T1 , typename T2 >
bool	BALL::Maths::isLessOrEqual (const T1 &a, const T2 &b)
template<typename T1 , typename T2 >
bool	BALL::Maths::isGreaterOrEqual (const T1 &a, const T2 &b)
template<typename T1 , typename T2 >
bool	BALL::Maths::isGreater (const T1 &a, const T2 &b)
template<typename T >
long	BALL::Maths::floor (const T &t)
template<typename T >
long	BALL::Maths::ceiling (const T &t)
template<typename T1 , typename T2 >
Index	BALL::Maths::compare (const T1 &a, const T2 &b)
template<typename T >
bool	BALL::Maths::isNear (const T &a, const T &b, const T &max_diff)
double	BALL::Maths::rint (double x)
	round to integral value in floating-point format

---

Detailed Description

Namespace: BALL::Maths

---

Function Documentation

template<typename T >

T BALL::Maths::abs

(

const T &

t

)

[inline]

Return the absolute value of a number.

Parameters:

t

the number

Returns:

T the absolute value

References BALL_ABS.

Referenced by BALL::GetAngle(), BALL::TSimpleBox3< T >::getDepth(), BALL::GetDistance(), BALL::TSimpleBox3< T >::getHeight(), BALL::GetIntersection(), BALL::TSimpleBox3< T >::getSurface(), BALL::TSimpleBox3< T >::getVolume(), BALL::TSimpleBox3< T >::getWidth(), BALL::Maths::isEqual(), BALL::Maths::isNear(), BALL::Maths::isNotEqual(), BALL::Maths::isNotZero(), and BALL::Maths::isZero().

template<typename T >

long BALL::Maths::ceiling

(

const T &

t

)

[inline]

Return the ceiling of a number.

Parameters:

t

the number

Returns:

T the ceiling

References BALL::Maths::isEqual(), and BALL::Maths::isLess().

template<typename T1 , typename T2 >

Index BALL::Maths::compare	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Compare two numbers to each other.

Parameters:

	a	the first number
	b	the second number

Returns:

Index -1 a < b; 0 a = b; 1 a > b

References BALL::Maths::isEqual(), and BALL::Maths::isLess().

template<typename T >

long BALL::Maths::floor

(

const T &

t

)

[inline]

Return the floor of a number.

Parameters:

t

the number

Returns:

T the floor

References BALL::Maths::isEqual(), and BALL::Maths::isGreater().

Referenced by BALL::HashGrid3< Item >::calculateMinSpacing(), BALL::HashGrid3< Item >::getBox(), BALL::TRegularData1D< ValueType >::getClosestIndex(), BALL::TRegularData1D< ValueType >::getClosestValue(), BALL::TFFT3D< ComplexTraits >::getInterpolatedValue(), BALL::TFFT2D< ComplexTraits >::getInterpolatedValue(), BALL::TFFT1D< ComplexTraits >::getInterpolatedValue(), BALL::TRegularData1D< ValueType >::getLowerIndex(), and BALL::TRegularData1D< ValueType >::operator()().

template<typename T >

T BALL::Maths::frac

(

const T &

t

)

[inline]

Return the fraction of a number.

Parameters:

t

the number

Returns:

T the fraction

template<typename T1 , typename T2 >

bool BALL::Maths::isEqual	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Test whether a number is equal to another.

Parameters:

	a	the first number
	b	the second number

Returns:

bool, true if the absolute distance of a and b is below Constants::EPSILON

References BALL::Maths::abs(), and BALL::Constants::EPSILON.

Referenced by BALL::Maths::ceiling(), BALL::Maths::compare(), BALL::Maths::floor(), BALL::TQuaternion< T >::fromAxisAngle(), BALL::TQuaternion< T >::getAngle(), BALL::TQuaternion< T >::getAxis(), BALL::GetIntersection(), BALL::TSphere3< float >::has(), BALL::TSimpleBox3< T >::has(), BALL::TLine3< T >::has(), BALL::TCircle3< float >::has(), BALL::TMatrix4x4< T >::isEqual(), BALL::TQuaternion< T >::normalize(), BALL::TVector4< T >::operator==(), BALL::TVector2< T >::operator==(), BALL::TSphere3< float >::operator==(), BALL::TCircle3< float >::operator==(), BALL::TAngle< T >::operator==(), and BALL::TQuaternion< T >::toAxisAngle().

template<typename T >

bool BALL::Maths::isFinite

(

const T &

t

)

[inline]

Test whether a number is finite.

Parameters:

t

the number

Returns:

bool, true if t is finite

Referenced by BALL::Maths::isInfinite().

template<typename T1 , typename T2 >

bool BALL::Maths::isGreater	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Test whether a number is greater compared to another.

Parameters:

	a	the first number
	b	the second number

Returns:

bool, true if a is greater than b

References BALL::Constants::EPSILON.

Referenced by BALL::Maths::floor(), BALL::GetIntersection(), BALL::TAngle< T >::normalize(), and BALL::TAngle< T >::operator>().

template<typename T1 , typename T2 >

bool BALL::Maths::isGreaterOrEqual	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Test whether a number is greater or equal compared to another.

Parameters:

	a	the first number
	b	the second number

Returns:

bool, true if a is greater or equal than b

References BALL::Constants::EPSILON.

Referenced by BALL::GetIntersection(), and BALL::TAngle< T >::operator>=().

template<typename T >

bool BALL::Maths::isInfinite

(

const T &

t

)

[inline]

Test whether a number is infinite.

Parameters:

t

the number

Returns:

bool, true if t equals inf or -inf

References BALL::Maths::isFinite(), and BALL::Maths::isNan().

template<typename T1 , typename T2 >

bool BALL::Maths::isLess	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Test whether a number is less compared to another.

Parameters:

	a	the first number
	b	the second number

Returns:

bool, true if a is smaller than b

References BALL::Constants::EPSILON.

Referenced by BALL::Maths::ceiling(), BALL::Maths::compare(), BALL::TVector3< float >::getAngle_(), BALL::GetIntersection(), BALL::TSimpleBox3< T >::has(), BALL::TPlane3< T >::hessify(), BALL::TSimpleBox3< T >::isIntersecting(), BALL::TAngle< T >::normalize(), BALL::TAngle< T >::operator<(), BALL::SolveQuadraticEquation(), and BALL::SolveSystem().

template<typename T1 , typename T2 >

bool BALL::Maths::isLessOrEqual	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Test whether a number is less or equal compared to another.

Parameters:

	a	the first number
	b	the second number

Returns:

bool, true if a is less or equal b

References BALL::Constants::EPSILON.

Referenced by BALL::TSphere3< float >::has(), BALL::TCircle3< float >::has(), and BALL::TAngle< T >::operator<=().

template<typename T >

bool BALL::Maths::isNan

(

const T &

t

)

[inline]

Test whether a value is not a number.

Parameters:

t

the number

Returns:

bool, true if t equals nan

Referenced by BALL::Maths::isInfinite(), and BALL::SolveSystem().

template<typename T >

bool BALL::Maths::isNear	(	const T &	a,
		const T &	b,
		const T &	max_diff
	)			[inline]

Test whether two numbers are close to each other.

Parameters:

	a	the first number
	b	the second number
	max_diff	the maximum allowed difference between the two numbers

Returns:

bool, true if the absolute distance between a and b is below max_diff

References BALL::Maths::abs().

template<typename T1 , typename T2 >

bool BALL::Maths::isNotEqual	(	const T1 &	a,
		const T2 &	b
	)			[inline]

Test whether a number is not equal to another.

Parameters:

	a	the first number
	b	the second number

Returns:

bool, true if the absolute distance of a and b is at least Constants::EPSILON

References BALL::Maths::abs(), and BALL::Constants::EPSILON.

Referenced by BALL::GetIntersection(), BALL::TVector4< T >::operator!=(), BALL::TVector2< T >::operator!=(), BALL::TSphere3< float >::operator!=(), BALL::TCircle3< float >::operator!=(), and BALL::TAngle< T >::operator!=().

template<typename T >

bool BALL::Maths::isNotZero

(

const T &

t

)

[inline]

Test whether a number is not zero.

Parameters:

t

the number

Returns:

bool, true, if the absolute value of t is at least Constants::EPSILON

References BALL::Maths::abs(), and BALL::Constants::EPSILON.

Referenced by BALL::TVector3< float >::getAngle_(), BALL::GetDistance(), and BALL::TLine3< T >::has().

template<typename T >

bool BALL::Maths::isZero

(

const T &

t

)

[inline]

Test whether a number is zero.

Parameters:

t

the number

Returns:

bool, true if the absolute value of t is below Constants::EPSILON

References BALL::Maths::abs(), and BALL::Constants::EPSILON.

Referenced by BALL::GetAngle(), BALL::GetDistance(), BALL::GetIntersection(), BALL::TPlane3< T >::has(), BALL::TCircle3< float >::has(), BALL::isComplanar(), BALL::TSphere3< float >::isEmpty(), BALL::isIntersecting(), BALL::isOrthogonal(), BALL::TVector4< T >::isOrthogonalTo(), BALL::TVector3< T >::isZero(), BALL::TVector2< T >::isZero(), BALL::TVector4< T >::normalize(), BALL::TVector3< T >::normalize(), BALL::TVector2< T >::normalize(), BALL::TVector4< T >::operator/(), BALL::TVector4< T >::operator/=(), BALL::SolveQuadraticEquation(), BALL::SolveSystem(), BALL::SolveSystem2(), and BALL::TPlane3< T >::TPlane3().

template<typename T >

T BALL::Maths::max	(	const T &	a,
		const T &	b,
		const T &	ct
	)			[inline]

Return the greatest of three numbers.

Parameters:

	a	the first number
	b	the second number
	ct	the third number

Returns:

T the greatest number

References BALL_MAX3.

template<typename T >

T BALL::Maths::max	(	const T &	a,
		const T &	b
	)			[inline]

Return the greater of two numbers.

Parameters:

	a	the first number
	b	the second number

Returns:

T the greatest number

References BALL_MAX.

Referenced by BALL::TFFT3D< ComplexTraits >::getInterpolatedValue(), BALL::TFFT2D< ComplexTraits >::getInterpolatedValue(), BALL::TFFT1D< ComplexTraits >::getInterpolatedValue(), BALL::PeakList< Peak< float > >::getMaxIntensity(), BALL::PeakList< Peak< float > >::getMinIntensity(), BALL::AssignBondOrderProcessor::getTotalCharge(), BALL::AssignBondOrderProcessor::getTotalPenalty(), BALL::TMatrix4x4< T >::invert(), BALL::TSimpleBox3< T >::join(), BALL::TFFT3D< ComplexTraits >::operator==(), BALL::TFFT2D< ComplexTraits >::operator==(), and BALL::TFFT1D< ComplexTraits >::operator==().

template<typename T >

T BALL::Maths::min	(	const T &	a,
		const T &	b,
		const T &	ct
	)			[inline]

Return the smallest of three numbers.

Parameters:

	a	the first number
	b	the second number
	ct	the third number

Returns:

T the smallest number

References BALL_MIN3.

template<typename T >

T BALL::Maths::min	(	const T &	a,
		const T &	b
	)			[inline]

Return the smallest of two numbers.

Parameters:

	a	the first number
	b	the second number

Returns:

T the smallest number

References BALL_MIN.

Referenced by BALL::TFFT3D< ComplexTraits >::getInterpolatedValue(), BALL::TFFT2D< ComplexTraits >::getInterpolatedValue(), BALL::TFFT1D< ComplexTraits >::getInterpolatedValue(), BALL::PeakList< Peak< float > >::getMinIntensity(), BALL::TSimpleBox3< T >::join(), BALL::TFFT3D< ComplexTraits >::operator==(), BALL::TFFT2D< ComplexTraits >::operator==(), and BALL::TFFT1D< ComplexTraits >::operator==().

double BALL::Maths::rint

(

double

x

)

[inline]

round to integral value in floating-point format

Referenced by BALL::TFFT3D< ComplexTraits >::operator[](), BALL::TFFT2D< ComplexTraits >::operator[](), BALL::TFFT1D< ComplexTraits >::operator[](), BALL::TFFT3D< ComplexTraits >::phase(), BALL::TFFT2D< ComplexTraits >::phase(), BALL::TFFT1D< ComplexTraits >::phase(), BALL::TFFT3D< ComplexTraits >::translate(), BALL::TFFT2D< ComplexTraits >::translate(), and BALL::TFFT1D< ComplexTraits >::translate().

template<typename T >

T BALL::Maths::round

(

const T &

t

)

[inline]

Round a number and return the result.

Parameters:

t

the number

Returns:

T the result

template<typename T >

T BALL::Maths::sgn

(

const T &

t

)

[inline]

Return the sign of a number.

Parameters:

t

the number

Returns:

Index -1 t < 0; 0 t = 0; 1 t > 0

References BALL_SGN.