ITK  5.0.0
Insight Segmentation and Registration Toolkit
Namespaces | Functions | Variables
itk::Math Namespace Reference

Namespaces

 Detail
 

Functions

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)
 
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

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
x1first scalar value to compare
x2second scalar value to compare

Definition at line 669 of file itkMath.h.

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

template<typename TReturn , typename TInput >
TReturn itk::Math::CastWithRangeCheck ( TInput  x)
inline

Definition at line 207 of file itkMath.h.

References itkConceptMacro.

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).
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 potetially 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
x1first floating point value to compare
x2second floating point value to compare

Definition at line 707 of file itkMath.h.

Referenced by itk::BSplineKernelFunction< VSplineOrder, TRealValueType >::Evaluate(), itk::BSplineDerivativeKernelFunction< VSplineOrder, TRealValueType >::Evaluate(), NotExactlyEquals(), itk::Point< double, Self::ImageDimension >::operator!=(), itk::Functor::Equal< TInput1, TInput2, TOutput >::operator()(), itk::Point< double, Self::ImageDimension >::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().

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 264 of file itkMath.h.

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

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
x1first floating value to compare
x2second floating values to compare
maxUlpsmaximum units in the last place to be considered equal
maxAbsoluteDifferencemaximum absolute difference to be considered equal

Definition at line 303 of file itkMath.h.

References itk::Math::Detail::FloatIEEE< T >::AsULP(), and 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 248 of file itkMath.h.

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

Referenced by FloatAlmostEqual().

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

Return the greatest factor of the decomposition in prime numbers.

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

Return the greatest factor of the decomposition in prime numbers.

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

Return the greatest factor of the decomposition in prime numbers.

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

Return the greatest factor of the decomposition in prime numbers.

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.
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.
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.
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.
template<typename T1 , typename T2 >
bool itk::Math::NotAlmostEquals ( T1  x1,
T2  x2 
)
inline
Examples:
Examples/Statistics/KdTree.cxx.

Definition at line 677 of file itkMath.h.

References AlmostEquals().

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

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

Definition at line 718 of file itkMath.h.

References ExactlyEquals().

Referenced by itk::Functor::VectorMagnitudeLinearTransform< TInputImage::PixelType, TOutputImage::PixelType >::operator!=(), itk::Functor::WeightedAdd2< typename TInputImage1::PixelType, typename TInputImage2::PixelType, typename TOutputImage::PixelType >::operator!=(), itk::Functor::ExpNegative< TInputImage::PixelType, TOutputImage::PixelType >::operator!=(), itk::Functor::IntensityWindowingTransform< TInputImage::PixelType, TOutputImage::PixelType >::operator!=(), itk::Functor::IntensityLinearTransform< TInputImage::PixelType, TOutputImage::PixelType >::operator!=(), itk::Functor::Sigmoid< TInputImage::PixelType, TOutputImage::PixelType >::operator!=(), itk::Functor::BinaryThreshold< TInputImage::PixelType, TOutputImage::PixelType >::operator!=(), itk::Functor::LabelOverlayFunctor< FeatureImagePixelType, LabelMapPixelType, OutputImagePixelType >::operator!=(), itk::Functor::NotEqual< TInput1, TInput2, TOutput >::operator()(), itk::VariableSizeMatrix< T >::operator==(), itk::Matrix< double, Self::ImageDimension, Self::ImageDimension >::operator==(), itk::NarrowBandLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType, Image< TOutputPixelType, TInputImage::ImageDimension > >::SetAdvectionScaling(), itk::SegmentationLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType >::SetAdvectionScaling(), itk::GaussianInterpolateImageFunction< TInputImage, TCoordRep >::SetAlpha(), itk::NotImageFilter< TInputImage, TOutputImage >::SetBackgroundValue(), itk::ConstantPadImageFilter< TInputImage, TOutputImage >::SetConstant(), itk::DivideOrZeroOutImageFilter< TInputImage1, TInputImage2, TOutputImage >::SetConstant(), itk::NarrowBandLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType, Image< TOutputPixelType, TInputImage::ImageDimension > >::SetCurvatureScaling(), itk::SegmentationLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType >::SetCurvatureScaling(), itk::GeodesicActiveContourLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType >::SetDerivativeSigma(), itk::SegmentationLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType >::SetFeatureScaling(), itk::NotImageFilter< TInputImage, TOutputImage >::SetForegroundValue(), itk::CannyEdgeDetectionImageFilter< ImageType, ImageType >::SetMaximumError(), itk::MaskNegatedImageFilter< TInputImage, TMaskImage, TOutputImage >::SetOutsideValue(), itk::MaskImageFilter< TInputImage, TMaskImage, TOutputImage >::SetOutsideValue(), itk::NarrowBandLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType, Image< TOutputPixelType, TInputImage::ImageDimension > >::SetPropagationScaling(), itk::SegmentationLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType >::SetPropagationScaling(), itk::ShapePriorSegmentationLevelSetImageFilter< TInputImage, TFeatureImage, TOutputPixelType >::SetShapePriorScaling(), itk::DivideOrZeroOutImageFilter< TInputImage1, TInputImage2, TOutputImage >::SetThreshold(), itk::CannyEdgeDetectionImageFilter< ImageType, ImageType >::SetVariance(), TestCellDataContainer(), and TestPointDataContainer().

template<typename TReturn , typename TInput >
TReturn itk::Math::Round ( TInput  x)
inline

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

Template Parameters
TReturnmust be an integer type
TInputmust be float or double
See Also
RoundHalfIntegerUp<TReturn, TInput>()

Definition at line 176 of file itkMath.h.

template<TReturn , typename TInput >
itk::Math::RoundHalfIntegerToEven ( TInput  x)

Round towards nearest integer.

Template Parameters
TReturnmust be an integer type
TInputmust 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).
template<TReturn , typename TInput >
itk::Math::RoundHalfIntegerUp ( TInput  x)

Round towards nearest integer.

Template Parameters
TReturnmust be an integer type
TInputmust 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).

Variable Documentation

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

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

Definition at line 77 of file itkMath.h.

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

\[e\]

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/RegistrationITKv3/DeformableRegistration1.cxx, Examples/RegistrationITKv3/DeformableRegistration10.cxx, Examples/RegistrationITKv3/DeformableRegistration11.cxx, Examples/RegistrationITKv3/DeformableRegistration12.cxx, Examples/RegistrationITKv3/DeformableRegistration7.cxx, Examples/RegistrationITKv3/DeformableRegistration8.cxx, Examples/RegistrationITKv3/DeformableRegistration9.cxx, Examples/RegistrationITKv3/ImageRegistration11.cxx, Examples/RegistrationITKv3/ImageRegistration14.cxx, Examples/RegistrationITKv3/ImageRegistration15.cxx, Examples/RegistrationITKv3/ImageRegistration18.cxx, Examples/RegistrationITKv3/ImageRegistration19.cxx, Examples/RegistrationITKv3/IterativeClosestPoint1.cxx, Examples/RegistrationITKv3/IterativeClosestPoint2.cxx, Examples/RegistrationITKv3/IterativeClosestPoint3.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/DetectEdgesWithCannyFilter/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, and SphinxExamples/src/IO/ImageBase/ReadUnknownImageType/Code.cxx.

Definition at line 53 of file itkMath.h.

Referenced by itk::TreeNodeChangeEvent< TTreeType >::CheckEvent(), itk::ProgressReporter::CompletedPixel(), 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::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().

constexpr double itk::Math::eps = vnl_math::eps
static
Examples:
Examples/DataRepresentation/Mesh/Mesh3.cxx, and SphinxExamples/src/Core/Common/DistanceBetweenPoints/Code.cxx.

Definition at line 94 of file itkMath.h.

Referenced by itk::MultiphaseFiniteDifferenceImageFilter< TInputImage, TFeatureImage, TOutputImage, TFunction, unsigned int >::MultiphaseFiniteDifferenceImageFilter(), itk::Function::Sheetness< TInputImage::PixelType, TOutputImage::PixelType >::operator()(), itk::Function::LocalStructure< TInputImage::PixelType, TOutputImage::PixelType >::operator()(), and itk::Function::Tubularness< TInputImage::PixelType, TOutputImage::PixelType >::operator()().

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

euler constant

Definition at line 91 of file itkMath.h.

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

Definition at line 97 of file itkMath.h.

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

Definition at line 98 of file itkMath.h.

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

\[ \log_e 10 \]

Definition at line 61 of file itkMath.h.

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

\[ \log_e 2 \]

Definition at line 59 of file itkMath.h.

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

\[ \log_{10} e \]

Definition at line 57 of file itkMath.h.

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

\[ \log_2 e \]

Definition at line 55 of file itkMath.h.

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

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

Definition at line 73 of file itkMath.h.

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

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

Definition at line 83 of file itkMath.h.

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

\[ \pi \]

Examples:
Examples/DataRepresentation/Mesh/PointSetWithVectors.cxx, Examples/DataRepresentation/Mesh/RGBPointSet.cxx, Examples/Filtering/SpatialObjectToImage1.cxx, Examples/Filtering/SpatialObjectToImage2.cxx, Examples/Filtering/SpatialObjectToImage3.cxx, Examples/RegistrationITKv3/ChangeInformationImageFilter.cxx, Examples/RegistrationITKv3/ImageRegistration13.cxx, Examples/RegistrationITKv3/ImageRegistration14.cxx, Examples/RegistrationITKv3/ImageRegistration5.cxx, Examples/RegistrationITKv3/ImageRegistration6.cxx, Examples/RegistrationITKv3/ImageRegistration7.cxx, Examples/RegistrationITKv3/ImageRegistration9.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/Filtering/ImageGrid/ChangeImageOriginSpacingOrDirection/Code.cxx, WikiExamples/ImageProcessing/UnaryFunctorImageFilter.cxx, WikiExamples/ImageSegmentation/ExtractContourWithSnakes.cxx, WikiExamples/Math/Pi.cxx, WikiExamples/Morphology/FlatStructuringElementRadiusIsParametric.cxx, WikiExamples/Registration/ExhaustiveOptimizer.cxx, and WikiExamples/Statistics/TextureFeatures.cxx.

Definition at line 63 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(), itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Sinc(), and itk::STLMeshIO::WritePointsTyped().

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

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

Definition at line 71 of file itkMath.h.

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

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

Definition at line 67 of file itkMath.h.

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

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

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

Definition at line 69 of file itkMath.h.

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

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

Definition at line 87 of file itkMath.h.

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

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

Definition at line 89 of file itkMath.h.

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

\[ \sqrt{2} \]

Definition at line 85 of file itkMath.h.

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

\[ \sqrt{2\pi} \]

Definition at line 79 of file itkMath.h.

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

Definition at line 95 of file itkMath.h.

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

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

Definition at line 75 of file itkMath.h.

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

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

Definition at line 81 of file itkMath.h.

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

\[ 2\pi \]

Examples:
Examples/Segmentation/HoughTransform2DCirclesImageFilter.cxx.

Definition at line 65 of file itkMath.h.

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