Namespaces
	Detail

Functions
bool	abs (bool x)

unsigned char	abs (char x)

unsigned short	abs (short x)

unsigned char	abs (signed char x)

unsigned char	abs (unsigned char x)

unsigned int	abs (unsigned int x)

unsigned long long	abs (unsigned long long x)

unsigned long	abs (unsigned long x)

unsigned short	abs (unsigned short x)

template<typename T1 , typename T2 >
bool	AlmostEquals (T1 x1, T2 x2)

template<typename TReturn , typename TInput >
TReturn	CastWithRangeCheck (TInput x)

template<TReturn , typename TInput >
	Ceil (TInput x)

template<typename TInput1 , typename TInput2 >
bool	ExactlyEquals (const TInput1 &x1, const TInput2 &x2)

template<typename T >
T	FloatAddULP (T x, typename Detail::FloatIEEE< T >::IntType ulps)

template<typename T >
bool	FloatAlmostEqual (T x1, T x2, typename Detail::FloatIEEE< T >::IntType maxUlps=4, typename Detail::FloatIEEE< T >::FloatType maxAbsoluteDifference=0.1 *itk::NumericTraits< T >::epsilon())

template<typename T >
Detail::FloatIEEE< T >::IntType	FloatDifferenceULP (T x1, T x2)

template<TReturn , typename TInput >
	Floor (TInput x)

template<typename T1 , typename T2 >
bool	NotAlmostEquals (T1 x1, T2 x2)

template<typename TInput1 , typename TInput2 >
bool	NotExactlyEquals (const TInput1 &x1, const TInput2 &x2)

template<typename TReturn , typename TInput >
TReturn	Round (TInput x)

template<TReturn , typename TInput >
	RoundHalfIntegerToEven (TInput x)

template<TReturn , typename TInput >
	RoundHalfIntegerUp (TInput x)

template<typename TReturnType = uintmax_t>
constexpr TReturnType	UnsignedPower (const uintmax_t base, const uintmax_t exponent) noexcept

template<typename TReturnType = uintmax_t>
constexpr TReturnType	UnsignedProduct (const uintmax_t a, const uintmax_t b) noexcept


ITKCommon_EXPORT bool	IsPrime (unsigned short n)

ITKCommon_EXPORT bool	IsPrime (unsigned int n)

ITKCommon_EXPORT bool	IsPrime (unsigned long n)

ITKCommon_EXPORT bool	IsPrime (unsigned long long n)


ITKCommon_EXPORT unsigned short	GreatestPrimeFactor (unsigned short n)

ITKCommon_EXPORT unsigned int	GreatestPrimeFactor (unsigned int n)

ITKCommon_EXPORT unsigned long	GreatestPrimeFactor (unsigned long n)

ITKCommon_EXPORT unsigned long long	GreatestPrimeFactor (unsigned long long n)

Variables
static constexpr double	deg_per_rad = vnl_math::deg_per_rad

static constexpr double	e = vnl_math::e

static constexpr double	eps = vnl_math::eps

static constexpr double	euler = vnl_math::euler

static constexpr float	float_eps = vnl_math::float_eps

static constexpr float	float_sqrteps = vnl_math::float_sqrteps

static constexpr double	ln10 = vnl_math::ln10

static constexpr double	ln2 = vnl_math::ln2

static constexpr double	log10e = vnl_math::log10e

static constexpr double	log2e = vnl_math::log2e

static constexpr double	one_over_pi = vnl_math::one_over_pi

static constexpr double	one_over_sqrt2pi = vnl_math::one_over_sqrt2pi

static constexpr double	pi = vnl_math::pi

static constexpr double	pi_over_180 = vnl_math::pi_over_180

static constexpr double	pi_over_2 = vnl_math::pi_over_2

static constexpr double	pi_over_4 = vnl_math::pi_over_4

static constexpr double	sqrt1_2 = vnl_math::sqrt1_2

static constexpr double	sqrt1_3 = vnl_math::sqrt1_3

static constexpr double	sqrt2 = vnl_math::sqrt2

static constexpr double	sqrt2pi = vnl_math::sqrt2pi

static constexpr double	sqrteps = vnl_math::sqrteps

static constexpr double	two_over_pi = vnl_math::two_over_pi

static constexpr double	two_over_sqrtpi = vnl_math::two_over_sqrtpi

static constexpr double	twopi = vnl_math::twopi

Function Documentation

◆ abs() [1/9]

bool itk::Math::abs ( bool x )

inline

Examples: Examples/RegistrationITKv4/ImageRegistration11.cxx, Examples/RegistrationITKv4/ImageRegistration14.cxx, Examples/RegistrationITKv4/ImageRegistration15.cxx, SphinxExamples/src/Core/Common/DistanceBetweenPoints/Code.cxx, and SphinxExamples/src/Filtering/MathematicalMorphology/GenerateStructureElementsWithAccurateArea/Code.cxx.

Definition at line 843 of file itkMath.h.

Referenced by itk::ScanlineFilterCommon< TInputImage, TOutputImage >::CheckNeighbors(), itk::SimplexMeshAdaptTopologyFilter< TInputMesh, TOutputMesh >::SimplexCellVisitor::ComputeArea(), itk::Function::AdaptiveEqualizationHistogram< TInputPixel, TOutputPixel >::CumulativeFunction(), itk::BSplineKernelFunction< VSplineOrder, TRealValueType >::Evaluate(), itk::Function::Max3(), itk::Functor::Abs< TInput, TOutput >::operator()(), itk::Functor::SimilarVectorsFunctor< TInputImage::ValueType >::operator()(), itk::Functor::SimilarPixelsFunctor< TInputImage::ValueType >::operator()(), itk::Functor::InverseDeconvolutionFunctor< TInput1, TInput2, TOutput >::operator()(), itk::HessianToObjectnessMeasureImageFilter< TInputImage, TOutputImage >::AbsLessCompare::operator()(), itk::Functor::WienerDeconvolutionFunctor< TPixel >::operator()(), itk::detail::sortEigenValuesByMagnitude(), and itk::SimplexMeshAdaptTopologyFilter< TInputMesh, TOutputMesh >::SimplexCellVisitor::Visit().

◆ abs() [2/9]

unsigned char itk::Math::abs ( char x )

inline

Definition at line 858 of file itkMath.h.

◆ abs() [3/9]

unsigned short itk::Math::abs ( short x )

inline

Definition at line 863 of file itkMath.h.

◆ abs() [4/9]

unsigned char itk::Math::abs ( signed char x )

inline

Definition at line 853 of file itkMath.h.

◆ abs() [5/9]

unsigned char itk::Math::abs ( unsigned char x )

inline

Definition at line 848 of file itkMath.h.

◆ abs() [6/9]

unsigned int itk::Math::abs ( unsigned int x )

inline

Definition at line 873 of file itkMath.h.

◆ abs() [7/9]

unsigned long long itk::Math::abs ( unsigned long long x )

inline

Definition at line 884 of file itkMath.h.

Referenced by FloatAlmostEqual().

◆ abs() [8/9]

unsigned long itk::Math::abs ( unsigned long x )

inline

Definition at line 878 of file itkMath.h.

◆ abs() [9/9]

unsigned short itk::Math::abs ( unsigned short x )

inline

Definition at line 868 of file itkMath.h.

◆ AlmostEquals()

template<typename T1 , typename T2 >

bool itk::Math::AlmostEquals	(	T1	x1,
		T2	x2
	)

inline

Provide consistent equality checks between values of potentially different scalar or complex types.

template< typename T1, typename T2 > AlmostEquals( T1 x1, T2 x2 )

template< typename T1, typename T2 > NotAlmostEquals( T1 x1, T2 x2 )

This function compares two scalar or complex values of potentially different types. For maximum extensibility the function is implemented through a series of templated structs which direct the AlmostEquals() call to the correct function by evaluating the parameter's types.

Overall algorithm: If both values are complex... separate values into real and imaginary components and compare them separately

If one of the values is complex.. see if the imaginary part of the complex value is approximately 0 ... compare real part of complex value with scalar value

If both values are scalars...

To compare two floating point types... use FloatAlmostEqual.

To compare a floating point and an integer type... Use static_cast<FloatingPointType>(integerValue) and call FloatAlmostEqual

To compare signed and unsigned integers... Check for negative value or overflow, then cast and use ==

To compare two signed or two unsigned integers ... Use ==

To compare anything else ... Use ==

Parameters

x1	first scalar value to compare
x2	second scalar value to compare

Definition at line 688 of file itkMath.h.

Referenced by itk::AnchorErodeDilateLine< TInputPix, TCompare >::Compare(), NotAlmostEquals(), and itk::DivideImageFilter< TInputImage1, TInputImage2, TOutputImage >::VerifyPreconditions().

◆ CastWithRangeCheck()

template<typename TReturn , typename TInput >

TReturn itk::Math::CastWithRangeCheck ( TInput x )

inline

Definition at line 214 of file itkMath.h.

References itkConceptMacro.

◆ Ceil()

template<TReturn , typename TInput >

itk::Math::Ceil ( TInput x )

Round towards plus infinity.

The behavior of overflow is undefined due to numerous implementations.

Warning: argument absolute value must be less than INT_MAX/2 for vnl_math_ceil to be guaranteed to work.; We also assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

◆ ExactlyEquals()

template<typename TInput1 , typename TInput2 >

bool itk::Math::ExactlyEquals	(	const TInput1 &	x1,
		const TInput2 &	x2
	)

inline

Return the result of an exact comparison between two scalar values of potentially different types.

template <typename TInput1, typename TInput2> inline bool ExactlyEquals( const TInput & x1, const TInput & x2 )

template <typename TInput1, typename TInput2> inline bool NotExactlyEquals( const TInput & x1, const TInput & x2 )

These functions complement the EqualsComparison functions and determine if two scalar values are exactly equal using the compilers casting rules when comparing two different types. While this is also easily accomplished by using the equality operators, use of this function demonstrates the intent of an exact equality check and thus improves readability and clarity of code. In addition, this function suppresses float-equal warnings produced when using Clang.

Parameters

x1	first floating point value to compare
x2	second floating point value to compare

Definition at line 726 of file itkMath.h.

Referenced by itk::BSplineKernelFunction< VSplineOrder, TRealValueType >::Evaluate(), itk::BSplineDerivativeKernelFunction< VSplineOrder, TRealValueType >::Evaluate(), NotExactlyEquals(), itk::Functor::Equal< TInput1, TInput2, TOutput >::operator()(), itk::Functor::ExpNegative< TInputImage::PixelType, TOutputImage::PixelType >::operator==(), itk::Functor::IntensityWindowingTransform< TInputImage::PixelType, TOutputImage::PixelType >::operator==(), itk::Functor::VectorMagnitudeLinearTransform< TInputImage::PixelType, TOutputImage::PixelType >::operator==(), itk::Functor::WeightedAdd2< typename TInputImage1::PixelType, typename TInputImage2::PixelType, typename TOutputImage::PixelType >::operator==(), itk::Functor::IntensityLinearTransform< TInputImage::PixelType, TOutputImage::PixelType >::operator==(), itk::Functor::Sigmoid< TInputImage::PixelType, TOutputImage::PixelType >::operator==(), itk::Functor::LabelOverlayFunctor< FeatureImagePixelType, LabelMapPixelType, OutputImagePixelType >::operator==(), itk::Functor::BinaryThreshold< TInputImage::PixelType, TOutputImage::PixelType >::operator==(), itk::KLMDynamicBorderArray< TBorder >::operator>(), itk::LaplacianSegmentationLevelSetFunction< TImageType, TFeatureImageType >::SetAdvectionWeight(), itk::SigmoidImageFilter< TInputImage, TOutputImage >::SetAlpha(), itk::SigmoidImageFilter< TInputImage, TOutputImage >::SetBeta(), itk::FastMarchingImageFilter< TLevelSet, TSpeedImage >::SetBinaryMask(), itk::SigmoidImageFilter< TInputImage, TOutputImage >::SetOutputMaximum(), itk::SigmoidImageFilter< TInputImage, TOutputImage >::SetOutputMinimum(), and itk::ShapeUniqueLabelMapFilter< TImage >::TemplatedGenerateData().

◆ FloatAddULP()

template<typename T >

T itk::Math::FloatAddULP	(	T	x,
		typename Detail::FloatIEEE< T >::IntType	ulps
	)

inline

Add the given ULPs (units in the last place) to a float.

If the given ULPs can are negative, they are subtracted.

See also: FloatAlmostEqual; FloatDifferenceULP

Definition at line 271 of file itkMath.h.

References itk::Math::Detail::FloatIEEE< T >::asFloat, and itk::Math::Detail::FloatIEEE< T >::asInt.

◆ FloatAlmostEqual()

template<typename T >

bool itk::Math::FloatAlmostEqual	(	T	x1,
		T	x2,
		typename Detail::FloatIEEE< T >::IntType	maxUlps = `4`,
		typename Detail::FloatIEEE< T >::FloatType	maxAbsoluteDifference = `0.1 * itk::NumericTraits<T>::epsilon()`
	)

inline

Compare two floats and return if they are effectively equal.

Determining when floats are almost equal is difficult because of their IEEE bit representation. This function uses the integer representation of the float to determine if they are almost equal.

The implementation is based off the explanation in the white papers:

This function is not a cure-all, and reading those articles is important to understand its appropriate use in the context of ULPs, zeros, subnormals, infinities, and NANs. For example, it is preferable to use this function on two floats directly instead of subtracting them and comparing them to zero.

The tolerance is specified in ULPs (units in the last place), i.e. how many floats there are in between the numbers. Therefore, the tolerance depends on the magnitude of the values that are being compared. A second tolerance is a maximum difference allowed, which is important when comparing numbers close to zero.

A NAN compares as not equal to a number, but two NAN's may compare as equal to each other.

Parameters

x1	first floating value to compare
x2	second floating value to compare
maxUlps	maximum units in the last place to be considered equal
maxAbsoluteDifference	maximum absolute difference to be considered equal

Definition at line 310 of file itkMath.h.

References abs(), and FloatDifferenceULP().

◆ FloatDifferenceULP()

template<typename T >

Detail::FloatIEEE<T>::IntType itk::Math::FloatDifferenceULP	(	T	x1,
		T	x2
	)

inline

Return the signed distance in ULPs (units in the last place) between two floats.

This is the signed distance, i.e., if x1 > x2, then the result is positive.

See also: FloatAlmostEqual; FloatAddULP

Definition at line 255 of file itkMath.h.

References itk::Math::Detail::FloatIEEE< T >::AsULP().

Referenced by FloatAlmostEqual().

◆ Floor()

template<TReturn , typename TInput >

itk::Math::Floor ( TInput x )

Round towards minus infinity.

The behavior of overflow is undefined due to numerous implementations.

Warning: argument absolute value must be less than NumbericTraits<TReturn>::max()/2 for vnl_math_floor to be guaranteed to work.; We also assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

◆ GreatestPrimeFactor() [1/4]

ITKCommon_EXPORT unsigned int itk::Math::GreatestPrimeFactor ( unsigned int n )

Return the greatest factor of the decomposition in prime numbers.

◆ GreatestPrimeFactor() [2/4]

ITKCommon_EXPORT unsigned long long itk::Math::GreatestPrimeFactor ( unsigned long long n )

Return the greatest factor of the decomposition in prime numbers.

◆ GreatestPrimeFactor() [3/4]

ITKCommon_EXPORT unsigned long itk::Math::GreatestPrimeFactor ( unsigned long n )

Return the greatest factor of the decomposition in prime numbers.

◆ GreatestPrimeFactor() [4/4]

ITKCommon_EXPORT unsigned short itk::Math::GreatestPrimeFactor ( unsigned short n )

Return the greatest factor of the decomposition in prime numbers.

◆ IsPrime() [1/4]

ITKCommon_EXPORT bool itk::Math::IsPrime ( unsigned int n )

Return whether the number is a prime number or not.

Note: Negative numbers cannot be prime.

◆ IsPrime() [2/4]

ITKCommon_EXPORT bool itk::Math::IsPrime ( unsigned long long n )

Return whether the number is a prime number or not.

Note: Negative numbers cannot be prime.

◆ IsPrime() [3/4]

ITKCommon_EXPORT bool itk::Math::IsPrime ( unsigned long n )

Return whether the number is a prime number or not.

Note: Negative numbers cannot be prime.

◆ IsPrime() [4/4]

ITKCommon_EXPORT bool itk::Math::IsPrime ( unsigned short n )

Return whether the number is a prime number or not.

Note: Negative numbers cannot be prime.

◆ NotAlmostEquals()

template<typename T1 , typename T2 >

bool itk::Math::NotAlmostEquals	(	T1	x1,
		T2	x2
	)

inline

Examples: Examples/Statistics/KdTree.cxx.

Definition at line 696 of file itkMath.h.

References AlmostEquals().

Referenced by itk::Functor::Div< TInput1, TInput2, TOutput >::operator()().

◆ NotExactlyEquals()

template<typename TInput1 , typename TInput2 >

bool itk::Math::NotExactlyEquals	(	const TInput1 &	x1,
		const TInput2 &	x2
	)

inline

Definition at line 736 of file itkMath.h.

References ExactlyEquals().

◆ Round()

template<typename TReturn , typename TInput >

TReturn itk::Math::Round ( TInput x )

inline

Round towards nearest integer (This is a synonym for RoundHalfIntegerUp)

Template Parameters

TReturn	must be an integer type
TInput	must be float or double

See also: RoundHalfIntegerUp<TReturn, TInput>()

Definition at line 179 of file itkMath.h.

◆ RoundHalfIntegerToEven()

template<TReturn , typename TInput >

itk::Math::RoundHalfIntegerToEven ( TInput x )

Round towards nearest integer.

Template Parameters

TReturn	must be an integer type
TInput	must be float or double halfway cases are rounded towards the nearest even integer, e.g. RoundHalfIntegerToEven( 1.5) == 2 RoundHalfIntegerToEven(-1.5) == -2 RoundHalfIntegerToEven( 2.5) == 2 RoundHalfIntegerToEven( 3.5) == 4

The behavior of overflow is undefined due to numerous implementations.

Warning: We assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

◆ RoundHalfIntegerUp()

template<TReturn , typename TInput >

itk::Math::RoundHalfIntegerUp ( TInput x )

Round towards nearest integer.

Template Parameters

TReturn	must be an integer type
TInput	must be float or double halfway cases are rounded upward, e.g. RoundHalfIntegerUp( 1.5) == 2 RoundHalfIntegerUp(-1.5) == -1 RoundHalfIntegerUp( 2.5) == 3

The behavior of overflow is undefined due to numerous implementations.

Warning: The argument absolute value must be less than NumbericTraits<TReturn>::max()/2 for RoundHalfIntegerUp to be guaranteed to work.; We also assume that the rounding mode is not changed from the default one (or at least that it is always restored to the default one).

◆ UnsignedPower()

template<typename TReturnType = uintmax_t>

constexpr TReturnType itk::Math::UnsignedPower	(	const uintmax_t	base,
		const uintmax_t	exponent
	)

constexprnoexcept

Calculates base ^ exponent. Numeric overflow triggers a compilation error in "constexpr context" and a debug assert failure at run-time. Otherwise equivalent to C++11 static_cast<uintmax_t>(std::pow(base, exponent))

Note: UnsignedPower(0, 0) is not supported, as zero to the power of zero has no agreed-upon value: https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero

Definition at line 796 of file itkMath.h.

Referenced by itk::ConnectedImageNeighborhoodShape< VImageDimension >::CalculateNumberOfConnectedNeighbors().

◆ UnsignedProduct()

template<typename TReturnType = uintmax_t>

constexpr TReturnType itk::Math::UnsignedProduct	(	const uintmax_t	a,
		const uintmax_t	b
	)

constexprnoexcept

Returns a * b. Numeric overflow triggers a compilation error in "constexpr context" and a debug assert failure at run-time.

Definition at line 774 of file itkMath.h.

Referenced by itk::ConnectedImageNeighborhoodShape< VImageDimension >::CalculateBinomialCoefficient(), and itk::ConnectedImageNeighborhoodShape< VImageDimension >::CalculateNumberOfHypercubesOnBoundaryOfCube().

Variable Documentation

◆ deg_per_rad

constexpr double itk::Math::deg_per_rad = vnl_math::deg_per_rad

staticconstexpr

\[ \frac{180}{\pi} \]

Definition at line 80 of file itkMath.h.

◆ e

constexpr double itk::Math::e = vnl_math::e

staticconstexpr

\[e\]

The base of the natural logarithm or Euler's number

Examples: Examples/Filtering/CompositeFilterExample.cxx, Examples/IO/DicomImageReadChangeHeaderWrite.cxx, Examples/IO/DicomImageReadWrite.cxx, Examples/IO/IOPlugin.cxx, Examples/IO/XML/itkParticleSwarmOptimizerDOMReader.cxx, Examples/IO/XML/itkParticleSwarmOptimizerSAXReader.cxx, Examples/IO/XML/itkParticleSwarmOptimizerSAXWriter.cxx, Examples/RegistrationITKv4/DeformableRegistration1.cxx, Examples/RegistrationITKv4/DeformableRegistration10.cxx, Examples/RegistrationITKv4/DeformableRegistration11.cxx, Examples/RegistrationITKv4/DeformableRegistration12.cxx, Examples/RegistrationITKv4/DeformableRegistration4.cxx, Examples/RegistrationITKv4/DeformableRegistration6.cxx, Examples/RegistrationITKv4/DeformableRegistration7.cxx, Examples/RegistrationITKv4/DeformableRegistration8.cxx, Examples/RegistrationITKv4/DeformableRegistration9.cxx, Examples/RegistrationITKv4/ImageRegistration11.cxx, Examples/RegistrationITKv4/ImageRegistration14.cxx, Examples/RegistrationITKv4/ImageRegistration15.cxx, Examples/RegistrationITKv4/ImageRegistration18.cxx, Examples/RegistrationITKv4/ImageRegistration19.cxx, Examples/RegistrationITKv4/IterativeClosestPoint1.cxx, Examples/RegistrationITKv4/IterativeClosestPoint2.cxx, Examples/RegistrationITKv4/IterativeClosestPoint3.cxx, Examples/RegistrationITKv4/MultiStageImageRegistration1.cxx, Examples/RegistrationITKv4/MultiStageImageRegistration2.cxx, Examples/Segmentation/GeodesicActiveContourShapePriorLevelSetImageFilter.cxx, Examples/Segmentation/WatershedSegmentation1.cxx, Examples/Statistics/ScalarImageMarkovRandomField1.cxx, SphinxExamples/src/Core/QuadEdgeMesh/CutMesh/Code.cxx, SphinxExamples/src/Core/QuadEdgeMesh/ExtractVertexOnMeshBoundaries/Code.cxx, SphinxExamples/src/Core/QuadEdgeMesh/GetListOfFacesAroundAGivenVertex/Code.cxx, SphinxExamples/src/Core/QuadEdgeMesh/PrintVertexNeighbors/Code.cxx, SphinxExamples/src/Filtering/BinaryMathematicalMorphology/ErodeABinaryImage/Code.cxx, SphinxExamples/src/Filtering/ImageFeature/DetectEdgesWithCannyEdgeDetectionFilter/Code.cxx, SphinxExamples/src/Filtering/ImageFeature/LaplacianRecursiveGaussianImageFilter/Code.cxx, SphinxExamples/src/Filtering/ImageFilterBase/CastAnImageToAnotherType/Code.cxx, SphinxExamples/src/Filtering/ImageGrid/Create3DVolume/Code.cxx, SphinxExamples/src/Filtering/MathematicalMorphology/ErodeAGrayscaleImage/Code.cxx, SphinxExamples/src/Filtering/Thresholding/ThresholdAnImageUsingBinary/Code.cxx, SphinxExamples/src/Filtering/Thresholding/ThresholdAnImageUsingOtsu/Code.cxx, SphinxExamples/src/ImageCompareCommand.cxx, SphinxExamples/src/IO/ImageBase/ReadUnknownImageType/Code.cxx, and SphinxExamples/src/Registration/Metricsv4/RegisterTwoPointSets/Code.cxx.

Definition at line 56 of file itkMath.h.

Referenced by itk::TotalProgressReporter::CheckAbortGenerateData(), itk::ProgressReporter::CheckAbortGenerateData(), itk::DiscretePrincipalCurvaturesQuadEdgeMeshFilter< TInputMesh, TOutputMesh >::ComputeMeanAndGaussianCurvatures(), itk::Concept::AdditiveOperators< T1, T2, T3 >::Constraints::const_constraints(), itk::Concept::MultiplyOperator< T1, T2, T3 >::Constraints::const_constraints(), itk::Concept::DivisionOperators< T1, T2, T3 >::Constraints::const_constraints(), itk::Concept::BitwiseOperators< T1, T2, T3 >::Constraints::const_constraints(), itk::Concept::BracketOperator< T1, T2, T3 >::Constraints::const_constraints(), itk::Functor::DivideOrZeroOut< typename TInputImage1::PixelType, typename TInputImage2::PixelType, typename TOutputImage::PixelType >::DivideOrZeroOut(), itk::Versor< TParametersValueType >::Epsilon(), itk::DiscreteMeanCurvatureQuadEdgeMeshFilter< TInputMesh, TOutputMesh >::EstimateCurvature(), itk::QuadEdgeMeshEulerOperatorSplitEdgeFunction< TMesh, TQEType >::Evaluate(), itk::MatrixOrthogonalityTolerance< double >::GetTolerance(), itk::MatrixOrthogonalityTolerance< float >::GetTolerance(), itk::ConstNeighborhoodIterator< TSparseImageType >::IsAtEnd(), itk::Functor::Sigmoid< TInputImage::PixelType, TOutputImage::PixelType >::operator()(), itk::operator<<(), itk::PDEDeformableRegistrationFunction< TFixedImage, TMovingImage, TDisplacementField >::SetEnergy(), itk::GPUPDEDeformableRegistrationFunction< TFixedImage, TMovingImage, TDisplacementField >::SetEnergy(), itk::LevelSetFunction< TImageType >::SetEpsilonMagnitude(), itk::PDEDeformableRegistrationFunction< TFixedImage, TMovingImage, TDisplacementField >::SetGradientStep(), itk::GPUPDEDeformableRegistrationFunction< TFixedImage, TMovingImage, TDisplacementField >::SetGradientStep(), itk::PDEDeformableRegistrationFunction< TFixedImage, TMovingImage, TDisplacementField >::SetNormalizeGradient(), itk::GPUPDEDeformableRegistrationFunction< TFixedImage, TMovingImage, TDisplacementField >::SetNormalizeGradient(), and TestPointsContainer().

◆ eps

constexpr double itk::Math::eps = vnl_math::eps

staticconstexpr

Examples: Examples/DataRepresentation/Mesh/Mesh3.cxx, SphinxExamples/src/Core/Common/DistanceBetweenPoints/Code.cxx, and SphinxExamples/src/Core/Mesh/AccessDataInCells/Code.cxx.

Definition at line 97 of file itkMath.h.

Referenced by itk::MultiphaseFiniteDifferenceImageFilter< TInputImage, TFeatureImage, TOutputImage, TFunction, unsigned int >::MultiphaseFiniteDifferenceImageFilter().

◆ euler

constexpr double itk::Math::euler = vnl_math::euler

staticconstexpr

euler constant

Definition at line 94 of file itkMath.h.

◆ float_eps

constexpr float itk::Math::float_eps = vnl_math::float_eps

staticconstexpr

Definition at line 100 of file itkMath.h.

◆ float_sqrteps

constexpr float itk::Math::float_sqrteps = vnl_math::float_sqrteps

staticconstexpr

Definition at line 101 of file itkMath.h.

◆ ln10

constexpr double itk::Math::ln10 = vnl_math::ln10

staticconstexpr

\[ \log_e 10 \]

Definition at line 64 of file itkMath.h.

◆ ln2

constexpr double itk::Math::ln2 = vnl_math::ln2

staticconstexpr

\[ \log_e 2 \]

Definition at line 62 of file itkMath.h.

◆ log10e

constexpr double itk::Math::log10e = vnl_math::log10e

staticconstexpr

\[ \log_{10} e \]

Definition at line 60 of file itkMath.h.

◆ log2e

constexpr double itk::Math::log2e = vnl_math::log2e

staticconstexpr

\[ \log_2 e \]

Definition at line 58 of file itkMath.h.

◆ one_over_pi

constexpr double itk::Math::one_over_pi = vnl_math::one_over_pi

staticconstexpr

\[ \frac{1}{\pi} \]

Definition at line 76 of file itkMath.h.

◆ one_over_sqrt2pi

constexpr double itk::Math::one_over_sqrt2pi = vnl_math::one_over_sqrt2pi

staticconstexpr

\[ \frac{1}{\sqrt{2\pi}} \]

Definition at line 86 of file itkMath.h.

◆ pi

constexpr double itk::Math::pi = vnl_math::pi

staticconstexpr

\[ \pi \]

Examples: Examples/DataRepresentation/Mesh/PointSetWithVectors.cxx, Examples/DataRepresentation/Mesh/RGBPointSet.cxx, Examples/Filtering/SpatialObjectToImage1.cxx, Examples/Filtering/SpatialObjectToImage2.cxx, Examples/Filtering/SpatialObjectToImage3.cxx, Examples/RegistrationITKv4/ChangeInformationImageFilter.cxx, Examples/RegistrationITKv4/ImageRegistration13.cxx, Examples/RegistrationITKv4/ImageRegistration14.cxx, Examples/RegistrationITKv4/ImageRegistration5.cxx, Examples/RegistrationITKv4/ImageRegistration6.cxx, Examples/RegistrationITKv4/ImageRegistration7.cxx, Examples/RegistrationITKv4/ImageRegistration9.cxx, Examples/Segmentation/HoughTransform2DCirclesImageFilter.cxx, SphinxExamples/src/Core/Common/ApplyCustomOperationToEachPixelInImage/Code.cxx, SphinxExamples/src/Core/Common/PiConstant/Code.cxx, SphinxExamples/src/Filtering/ImageGradient/ImplementationOfSnakes/Code.cxx, SphinxExamples/src/Filtering/ImageGrid/ChangeImageOriginSpacingOrDirection/Code.cxx, SphinxExamples/src/Filtering/MathematicalMorphology/GenerateStructureElementsWithAccurateArea/Code.cxx, SphinxExamples/src/Numerics/Optimizers/ExhaustiveOptimizer/Code.cxx, and SphinxExamples/src/Registration/Metricsv4/RegisterTwoPointSets/Code.cxx.

Definition at line 66 of file itkMath.h.

Referenced by itk::DiscretePrincipalCurvaturesQuadEdgeMeshFilter< TInputMesh, TOutputMesh >::ComputeMeanAndGaussianCurvatures(), itk::DelaunayConformingQuadEdgeMeshFilter< TInputMesh, TOutputMesh >::Dyer07Criterion(), itk::DiscreteGaussianCurvatureQuadEdgeMeshFilter< TInputMesh, TOutputMesh >::EstimateCurvature(), itk::GaborKernelFunction< TRealValueType >::Evaluate(), itk::Statistics::MersenneTwisterRandomVariateGenerator::GetNormalVariate(), itk::PhasedArray3DSpecialCoordinatesImage< TPixel >::PhasedArray3DSpecialCoordinatesImage(), and itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Sinc().

◆ pi_over_180

constexpr double itk::Math::pi_over_180 = vnl_math::pi_over_180

staticconstexpr

\[ \frac{\pi}{180} \]

Definition at line 74 of file itkMath.h.

◆ pi_over_2

constexpr double itk::Math::pi_over_2 = vnl_math::pi_over_2

staticconstexpr

\[ \frac{\pi}{2} \]

Definition at line 70 of file itkMath.h.

Referenced by itk::PhasedArray3DSpecialCoordinatesImage< TPixel >::TransformPhysicalPointToContinuousIndex(), and itk::PhasedArray3DSpecialCoordinatesImage< TPixel >::TransformPhysicalPointToIndex().

◆ pi_over_4

constexpr double itk::Math::pi_over_4 = vnl_math::pi_over_4

staticconstexpr

\[ \frac{\pi}{4} \]

Definition at line 72 of file itkMath.h.

◆ sqrt1_2

constexpr double itk::Math::sqrt1_2 = vnl_math::sqrt1_2

staticconstexpr

\[ \sqrt{ \frac{1}{2}} \]

Definition at line 90 of file itkMath.h.

◆ sqrt1_3

constexpr double itk::Math::sqrt1_3 = vnl_math::sqrt1_3

staticconstexpr

\[ \sqrt{ \frac{1}{3}} \]

Definition at line 92 of file itkMath.h.

◆ sqrt2

constexpr double itk::Math::sqrt2 = vnl_math::sqrt2

staticconstexpr

\[ \sqrt{2} \]

Definition at line 88 of file itkMath.h.

◆ sqrt2pi

constexpr double itk::Math::sqrt2pi = vnl_math::sqrt2pi

staticconstexpr

\[ \sqrt{2\pi} \]

Definition at line 82 of file itkMath.h.

◆ sqrteps

constexpr double itk::Math::sqrteps = vnl_math::sqrteps

staticconstexpr

Definition at line 98 of file itkMath.h.

◆ two_over_pi

constexpr double itk::Math::two_over_pi = vnl_math::two_over_pi

staticconstexpr

\[ \frac{2}{\pi} \]

Definition at line 78 of file itkMath.h.

◆ two_over_sqrtpi

constexpr double itk::Math::two_over_sqrtpi = vnl_math::two_over_sqrtpi

staticconstexpr

\[ \frac{2}{\sqrt{\pi}} \]

Definition at line 84 of file itkMath.h.

◆ twopi

constexpr double itk::Math::twopi = vnl_math::twopi

staticconstexpr

\[ 2\pi \]

Examples: Examples/Segmentation/HoughTransform2DCirclesImageFilter.cxx.

Definition at line 68 of file itkMath.h.

Namespaces

Functions

Variables

Function Documentation

◆ abs() [1/9]

◆ abs() [2/9]

◆ abs() [3/9]

◆ abs() [4/9]

◆ abs() [5/9]

◆ abs() [6/9]

◆ abs() [7/9]

◆ abs() [8/9]

◆ abs() [9/9]

◆ AlmostEquals()

◆ CastWithRangeCheck()

◆ Ceil()

◆ ExactlyEquals()

◆ FloatAddULP()

◆ FloatAlmostEqual()

◆ FloatDifferenceULP()

◆ Floor()

◆ GreatestPrimeFactor() [1/4]

◆ GreatestPrimeFactor() [2/4]

◆ GreatestPrimeFactor() [3/4]

◆ GreatestPrimeFactor() [4/4]

◆ IsPrime() [1/4]

◆ IsPrime() [2/4]

◆ IsPrime() [3/4]

◆ IsPrime() [4/4]

◆ NotAlmostEquals()

◆ NotExactlyEquals()

◆ Round()

◆ RoundHalfIntegerToEven()

◆ RoundHalfIntegerUp()

◆ UnsignedPower()

◆ UnsignedProduct()

Variable Documentation

◆ deg_per_rad

◆ e

◆ eps

◆ euler

◆ float_eps

◆ float_sqrteps

◆ ln10

◆ ln2

◆ log10e

◆ log2e

◆ one_over_pi

◆ one_over_sqrt2pi

◆ pi

◆ pi_over_180

◆ pi_over_2

◆ pi_over_4

◆ sqrt1_2

◆ sqrt1_3

◆ sqrt2

◆ sqrt2pi

◆ sqrteps

◆ two_over_pi

◆ two_over_sqrtpi

◆ twopi