Namespaces
	internal

	mat3_internal

	pcg

Classes
class	AffineMap
	A general linear transform using homogeneous coordinates to perform rotation, scaling, shear and translation. More...

class	BaseStencil

class	BBox
	Axis-aligned bounding box. More...

struct	BIAS_SCHEME

struct	BIAS_SCHEME< FIRST_BIAS >

struct	BIAS_SCHEME< HJWENO5_BIAS >

struct	BIAS_SCHEME< SECOND_BIAS >

struct	BIAS_SCHEME< THIRD_BIAS >

struct	BIAS_SCHEME< WENO5_BIAS >

class	BoxStencil

class	CompoundMap
	Creates the composition of two maps, each of which could be a composition. In the case that each component of the composition classified as linear an acceleration AffineMap is stored. More...

struct	Conversion
	Dummy class for tag dispatch of conversion constructors. More...

class	Coord
	Signed (x, y, z) 32-bit integer coordinates. More...

class	CoordBBox
	Axis-aligned bounding box of signed integer coordinates. More...

struct	CPT
	Compute the closest-point transform to a level set. More...

struct	CPT_RANGE
	Compute the closest-point transform to a level set. More...

struct	Curl
	Compute the curl of a vector-valued grid using differencing of various orders in the space defined by the range of the map. More...

struct	Curl< UniformScaleMap, CD_2ND >
	Full template specialization of Curl. More...

struct	Curl< UniformScaleMap, DiffScheme >
	Partial template specialization of Curl. More...

struct	Curl< UniformScaleTranslateMap, CD_2ND >
	Full template specialization of Curl. More...

struct	Curl< UniformScaleTranslateMap, DiffScheme >
	Partial template specialization of Curl. More...

class	CurvatureStencil

struct	D1

struct	D1< BD_1ST >

struct	D1< BD_2ND >

struct	D1< BD_3RD >

struct	D1< BD_HJWENO5 >

struct	D1< BD_WENO5 >

struct	D1< CD_2ND >

struct	D1< CD_2NDT >

struct	D1< CD_4TH >

struct	D1< CD_6TH >

struct	D1< FD_1ST >

struct	D1< FD_2ND >

struct	D1< FD_3RD >

struct	D1< FD_HJWENO5 >

struct	D1< FD_WENO5 >

struct	D1Vec

struct	D1Vec< CD_2ND >

struct	D1Vec< CD_2NDT >

struct	D1Vec< CD_4TH >

struct	D1Vec< CD_6TH >

struct	D2

struct	D2< CD_FOURTH >

struct	D2< CD_SECOND >

struct	D2< CD_SIXTH >

class	DDA
	A Digital Differential Analyzer specialized for OpenVDB grids. More...

struct	Delta
	Delta for small floating-point offsets. More...

struct	Delta< double >

struct	Delta< float >

class	DenseStencil
	Dense stencil of a given width. More...

struct	Divergence
	Compute the divergence of a vector-valued grid using differencing of various orders, the result defined with respect to the range-space of the map. More...

struct	Divergence< ScaleMap, CD_2ND >

struct	Divergence< ScaleMap, DiffScheme >

struct	Divergence< ScaleTranslateMap, CD_2ND >

struct	Divergence< ScaleTranslateMap, DiffScheme >

struct	Divergence< TranslationMap, DiffScheme >

struct	Divergence< UniformScaleMap, CD_2ND >

struct	Divergence< UniformScaleMap, DiffScheme >

struct	Divergence< UniformScaleTranslateMap, CD_2ND >

struct	Divergence< UniformScaleTranslateMap, DiffScheme >

class	Extrema
	This class computes the minimum and maximum values of a population of floating-point values. More...

class	FourthOrderDenseStencil

class	GenericMap
	A wrapper that holds a MapBase::ConstPtr and exposes a reduced set of functionality needed by the mathematical operators. More...

struct	Gradient
	Center difference gradient operators, defined with respect to the range-space of the `map`. More...

struct	Gradient< ScaleMap, CD_2ND >

struct	Gradient< ScaleTranslateMap, CD_2ND >

struct	Gradient< TranslationMap, DiffScheme >

struct	Gradient< UniformScaleMap, CD_2ND >

struct	Gradient< UniformScaleTranslateMap, CD_2ND >

struct	GradientBiased
	Biased gradient operators, defined with respect to the range-space of the map. More...

struct	GradientNormSqrd

struct	GradientNormSqrd< UniformScaleMap, GradScheme >
	Partial template specialization of GradientNormSqrd. More...

struct	GradientNormSqrd< UniformScaleTranslateMap, GradScheme >
	Partial template specialization of GradientNormSqrd. More...

class	GradStencil

class	Histogram
	This class computes a histogram, with a fixed interval width, of a population of floating-point values. More...

struct	is_diagonal_jacobian

struct	is_double

struct	is_double< double >

struct	is_linear
	Map traits. More...

struct	is_linear< AffineMap >

struct	is_linear< CompoundMap< T1, T2 > >

struct	is_linear< ScaleMap >

struct	is_linear< ScaleTranslateMap >

struct	is_linear< TranslationMap >

struct	is_linear< UniformScaleMap >

struct	is_linear< UniformScaleTranslateMap >

struct	is_linear< UnitaryMap >

struct	is_scale

struct	is_scale< ScaleMap >

struct	is_scale_translate

struct	is_scale_translate< ScaleTranslateMap >

struct	is_uniform_diagonal_jacobian

struct	is_uniform_scale

struct	is_uniform_scale< UniformScaleMap >

struct	is_uniform_scale_translate

struct	is_uniform_scale_translate< TranslationMap >

struct	is_uniform_scale_translate< UniformScaleTranslateMap >

struct	is_vec3d

struct	is_vec3d< Vec3d >

struct	ISCurl
	Curl operator defined in index space using various first derivative schemes. More...

struct	ISDivergence
	Divergence operator defined in index space using various first derivative schemes. More...

struct	ISGradient
	Gradient operators defined in index space of various orders. More...

struct	ISGradientBiased
	Biased Gradient Operators, using upwinding defined by the `Vec3Bias` input. More...

struct	ISGradientNormSqrd

struct	ISLaplacian
	Laplacian defined in index space, using various center-difference stencils. More...

struct	ISLaplacian< CD_FOURTH >

struct	ISLaplacian< CD_SECOND >

struct	ISLaplacian< CD_SIXTH >

struct	ISMeanCurvature
	Compute the mean curvature in index space. More...

struct	ISOpMagnitude
	Adapter for vector-valued index-space operators to return the vector magnitude. More...

struct	Laplacian
	Compute the Laplacian at a given location in a grid using finite differencing of various orders. The result is defined in the range of the map. More...

struct	Laplacian< ScaleMap, DiffScheme >

struct	Laplacian< ScaleTranslateMap, DiffScheme >

struct	Laplacian< TranslationMap, DiffScheme >

struct	Laplacian< UniformScaleMap, DiffScheme >

struct	Laplacian< UniformScaleTranslateMap, DiffScheme >

struct	Laplacian< UnitaryMap, DiffScheme >

struct	LevelSetHDDA
	Helper class that implements Hierarchical Digital Differential Analyzers and is specialized for ray intersections with level sets. More...

struct	LevelSetHDDA< TreeT,-1 >
	Specialization of Hierarchical Digital Differential Analyzer class that intersects a ray against the voxels of a level set. More...

struct	MapAdapter
	Adapter to associate a map with a world-space operator, giving it the same call signature as an index-space operator. More...

class	MapBase
	Abstract base class for maps. More...

class	MapRegistry
	Threadsafe singleton object for accessing the map type-name dictionary. Associates a map type-name with a factory function. More...

class	Mat

class	Mat2

class	Mat3
	3x3 matrix class. More...

class	Mat4
	4x4 -matrix class. More...

struct	MeanCurvature
	Compute the mean curvature. More...

struct	MeanCurvature< TranslationMap, DiffScheme2, DiffScheme1 >

struct	MeanCurvature< UniformScaleMap, DiffScheme2, DiffScheme1 >

struct	MeanCurvature< UniformScaleTranslateMap, DiffScheme2, DiffScheme1 >

class	MinMax
	Templated class to compute the minimum and maximum values. More...

class	NineteenPointStencil

class	NonlinearFrustumMap
	This map is composed of three steps. First it will take a box of size (Lx X Ly X Lz) defined by a member data bounding box and map it into a frustum with near plane (1 X Ly/Lx) and prescribed depth Then this frustum is transformed by an internal second map: most often a uniform scale, but other effects can be achieved by accumulating translation, shear and rotation: these are all applied to the second map. More...

struct	OpMagnitude
	Adapter for vector-valued world-space operators to return the vector magnitude. More...

struct	promote

class	QuantizedUnitVec
	Unit vector occupying only 16 bits. More...

class	Quat

class	Rand01
	Simple generator of random numbers over the range [0, 1) More...

class	RandInt
	Simple random integer generator. More...

class	Ray

class	ScaleMap
	A specialized Affine transform that scales along the principal axis the scaling need not be uniform in the three-directions. More...

class	ScaleTranslateMap
	A specialized Affine transform that scales along the principal axis the scaling need not be uniform in the three-directions, and then translates the result. More...

class	SecondOrderDenseStencil

class	SevenPointStencil

class	SixthOrderDenseStencil

class	Stats
	This class computes statistics (minimum value, maximum value, mean, variance and standard deviation) of a population of floating-point values. More...

class	ThirteenPointStencil

struct	Tolerance
	Tolerance for floating-point comparison. More...

struct	Tolerance< double >

struct	Tolerance< float >

class	Transform

class	TranslationMap
	A specialized linear transform that performs a translation. More...

class	Tuple

class	UniformScaleMap
	A specialized Affine transform that scales along the principal axis the scaling is uniform in the three-directions. More...

class	UniformScaleTranslateMap
	A specialized Affine transform that uniformaly scales along the principal axis and then translates the result. More...

class	UnitaryMap
	A specialized linear transform that performs a unitary maping i.e. rotation and or reflection. More...

class	Vec2

class	Vec3

class	Vec4

class	VolumeHDDA
	Helper class that implements Hierarchical Digital Differential Analyzers for ray intersections against a generic volume. More...

class	VolumeHDDA< TreeT, RayT, 0 >
	Specialization of Hierarchical Digital Differential Analyzer class that intersects against the leafs or tiles of a generic volume. More...

class	WenoStencil
	This is a special 19-point stencil that supports optimal fifth-order WENO upwinding, second-order central differencing, Laplacian, and zero-crossing test. More...

Typedefs
using	half = internal::half

using	UnitaryAndTranslationMap = CompoundMap< UnitaryMap, TranslationMap >

using	SpectralDecomposedMap = CompoundMap< CompoundMap< UnitaryMap, ScaleMap >, UnitaryMap >

using	SymmetricMap = SpectralDecomposedMap

using	FullyDecomposedMap = CompoundMap< SymmetricMap, UnitaryAndTranslationMap >

using	PolarDecomposedMap = CompoundMap< SymmetricMap, UnitaryMap >

using	Mat3s = Mat3< float >

using	Mat3d = Mat3< double >

using	Mat3f = Mat3d

using	Mat4s = Mat4< float >

using	Mat4d = Mat4< double >

using	Mat4f = Mat4d

using	Random01 = Rand01< double, std::mt19937 >

using	RandomInt = RandInt< int, std::mt19937 >

using	Quats = Quat< float >

using	Quatd = Quat< double >

using	Vec2i = Vec2< int32_t >

using	Vec2ui = Vec2< uint32_t >

using	Vec2s = Vec2< float >

using	Vec2d = Vec2< double >

using	Vec3i = Vec3< int32_t >

using	Vec3ui = Vec3< uint32_t >

using	Vec3s = Vec3< float >

using	Vec3d = Vec3< double >

using	Vec4i = Vec4< int32_t >

using	Vec4ui = Vec4< uint32_t >

using	Vec4s = Vec4< float >

using	Vec4d = Vec4< double >

Enumerations
enum	DScheme { UNKNOWN_DS = -1, CD_2NDT = 0, CD_2ND, CD_4TH, CD_6TH, FD_1ST, FD_2ND, FD_3RD, BD_1ST, BD_2ND, BD_3RD, FD_WENO5, BD_WENO5, FD_HJWENO5, BD_HJWENO5 }
	Different discrete schemes used in the first derivatives. More...

enum	{ NUM_DS_SCHEMES = BD_HJWENO5 + 1 }

enum	DDScheme { UNKNOWN_DD = -1, CD_SECOND = 0, CD_FOURTH, CD_SIXTH }
	Different discrete schemes used in the second derivatives. More...

enum	{ NUM_DD_SCHEMES = CD_SIXTH + 1 }

enum	BiasedGradientScheme { UNKNOWN_BIAS = -1, FIRST_BIAS = 0, SECOND_BIAS, THIRD_BIAS, WENO5_BIAS, HJWENO5_BIAS }
	Biased Gradients are limited to non-centered differences. More...

enum	{ NUM_BIAS_SCHEMES = HJWENO5_BIAS + 1 }

enum	TemporalIntegrationScheme { UNKNOWN_TIS = -1, TVD_RK1, TVD_RK2, TVD_RK3 }
	Temporal integration schemes. More...

enum	{ NUM_TEMPORAL_SCHEMES = TVD_RK3 + 1 }

enum	Axis { X_AXIS = 0, Y_AXIS = 1, Z_AXIS = 2 }

enum	RotationOrder { XYZ_ROTATION = 0, XZY_ROTATION, YXZ_ROTATION, YZX_ROTATION, ZXY_ROTATION, ZYX_ROTATION, XZX_ROTATION, ZXZ_ROTATION }

Functions
template<>
auto	cwiseAdd (const math::Vec3< math::half > &v, const float s)

template<typename Vec3T >
std::ostream &	operator<< (std::ostream &os, const BBox< Vec3T > &b)

std::ostream &	operator<< (std::ostream &os, const Coord &xyz)

Coord	Abs (const Coord &xyz)

std::ostream &	operator<< (std::ostream &os, const CoordBBox &b)

template<typename RayT , Index Log2Dim>
std::ostream &	operator<< (std::ostream &os, const DDA< RayT, Log2Dim > &dda)
	Output streaming of the Ray class. More...

std::string	dsSchemeToString (DScheme dss)

DScheme	stringToDScheme (const std::string &s)

std::string	dsSchemeToMenuName (DScheme dss)

std::string	biasedGradientSchemeToString (BiasedGradientScheme bgs)

BiasedGradientScheme	stringToBiasedGradientScheme (const std::string &s)

std::string	biasedGradientSchemeToMenuName (BiasedGradientScheme bgs)

std::string	temporalIntegrationSchemeToString (TemporalIntegrationScheme tis)

TemporalIntegrationScheme	stringToTemporalIntegrationScheme (const std::string &s)

std::string	temporalIntegrationSchemeToMenuName (TemporalIntegrationScheme tis)

template<typename ValueType >
ValueType	WENO5 (const ValueType &v1, const ValueType &v2, const ValueType &v3, const ValueType &v4, const ValueType &v5, float scale2=0.01f)
	Implementation of nominally fifth-order finite-difference WENO. More...

template<typename Real >
Real	GodunovsNormSqrd (bool isOutside, Real dP_xm, Real dP_xp, Real dP_ym, Real dP_yp, Real dP_zm, Real dP_zp)

template<typename Real >
Real	GodunovsNormSqrd (bool isOutside, const Vec3< Real > &gradient_m, const Vec3< Real > &gradient_p)

OPENVDB_API SharedPtr< SymmetricMap >	createSymmetricMap (const Mat3d &m)
	Utility methods. More...

OPENVDB_API SharedPtr< FullyDecomposedMap >	createFullyDecomposedMap (const Mat4d &m)
	General decomposition of a Matrix into a Unitary (e.g. rotation) following a Symmetric (e.g. stretch & shear) More...

OPENVDB_API SharedPtr< PolarDecomposedMap >	createPolarDecomposedMap (const Mat3d &m)
	Decomposes a general linear into translation following polar decomposition. More...

OPENVDB_API SharedPtr< MapBase >	simplify (SharedPtr< AffineMap > affine)
	reduces an AffineMap to a ScaleMap or a ScaleTranslateMap when it can More...

OPENVDB_API Mat4d	approxInverse (const Mat4d &mat)
	Returns the left pseudoInverse of the input matrix when the 3x3 part is symmetric otherwise it zeros the 3x3 and reverses the translation. More...

template<class MatType >
MatType	rotation (const Quat< typename MatType::value_type > &q, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
	Return the rotation matrix specified by the given quaternion. More...

template<class MatType >
MatType	rotation (Axis axis, typename MatType::value_type angle)
	Return a matrix for rotation by angle radians about the given axis. More...

template<class MatType >
MatType	rotation (const Vec3< typename MatType::value_type > &_axis, typename MatType::value_type angle)
	Return a matrix for rotation by angle radians about the given axis. More...

template<class MatType >
Vec3< typename MatType::value_type >	eulerAngles (const MatType &mat, RotationOrder rotationOrder, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
	Return the Euler angles composing the given rotation matrix. More...

template<typename MatType , typename ValueType1 , typename ValueType2 >
MatType	rotation (const Vec3< ValueType1 > &_v1, const Vec3< ValueType2 > &_v2, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
	Return a rotation matrix that maps v1 onto v2 about the cross product of v1 and v2. More...

template<class MatType >
MatType	scale (const Vec3< typename MatType::value_type > &s)
	Return a matrix that scales by s. More...

template<class MatType >
Vec3< typename MatType::value_type >	getScale (const MatType &mat)
	Return a Vec3 representing the lengths of the passed matrix's upper 3×3's rows. More...

template<class MatType >
MatType	unit (const MatType &mat, typename MatType::value_type eps=1.0e-8)
	Return a copy of the given matrix with its upper 3×3 rows normalized. More...

template<class MatType >
MatType	unit (const MatType &in, typename MatType::value_type eps, Vec3< typename MatType::value_type > &scaling)
	Return a copy of the given matrix with its upper 3×3 rows normalized, and return the length of each of these rows in scaling. More...

template<class MatType >
MatType	shear (Axis axis0, Axis axis1, typename MatType::value_type shear)
	Set the matrix to a shear along axis0 by a fraction of axis1. More...

template<class MatType >
MatType	skew (const Vec3< typename MatType::value_type > &skew)
	Return a matrix as the cross product of the given vector. More...

template<class MatType >
MatType	aim (const Vec3< typename MatType::value_type > &direction, const Vec3< typename MatType::value_type > &vertical)
	Return an orientation matrix such that z points along direction, and y is along the direction / vertical plane. More...

template<class MatType >
MatType	snapMatBasis (const MatType &source, Axis axis, const Vec3< typename MatType::value_type > &direction)
	This function snaps a specific axis to a specific direction, preserving scaling. More...

template<class MatType >
MatType &	padMat4 (MatType &dest)
	Write 0s along Mat4's last row and column, and a 1 on its diagonal. More...

template<typename MatType >
void	sqrtSolve (const MatType &aA, MatType &aB, double aTol=0.01)
	Solve for A=B*B, given A. More...

template<typename MatType >
void	powSolve (const MatType &aA, MatType &aB, double aPower, double aTol=0.01)

template<typename MatType >
bool	isIdentity (const MatType &m)
	Determine if a matrix is an identity matrix. More...

template<typename MatType >
bool	isInvertible (const MatType &m)
	Determine if a matrix is invertible. More...

template<typename MatType >
bool	isSymmetric (const MatType &m)
	Determine if a matrix is symmetric. More...

template<typename MatType >
bool	isUnitary (const MatType &m)
	Determine if a matrix is unitary (i.e., rotation or reflection). More...

template<typename MatType >
bool	isDiagonal (const MatType &mat)
	Determine if a matrix is diagonal. More...

template<typename MatType >
MatType::ValueType	lInfinityNorm (const MatType &matrix)
	Return the L_∞ norm of an N×N matrix. More...

template<typename MatType >
MatType::ValueType	lOneNorm (const MatType &matrix)
	Return the L₁ norm of an N×N matrix. More...

template<typename MatType >
bool	polarDecomposition (const MatType &input, MatType &unitary, MatType &positive_hermitian, unsigned int MAX_ITERATIONS=100)
	Decompose an invertible 3×3 matrix into a unitary matrix followed by a symmetric matrix (positive semi-definite Hermitian), i.e., M = U * S. More...

template<unsigned SIZE, typename T >
bool	cwiseLessThan (const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)

template<unsigned SIZE, typename T >
bool	cwiseGreaterThan (const Mat< SIZE, T > &m0, const Mat< SIZE, T > &m1)

template<typename T0 , typename T1 >
Mat3< typename promote< T0, T1 >::type >	operator* (const Mat3< T0 > &m0, const Mat3< T1 > &m1)
	Multiply m0 by m1 and return the resulting matrix. More...

template<typename T >
Mat3< T >	outerProduct (const Vec3< T > &v1, const Vec3< T > &v2)

template<typename T , typename T0 >
Mat3< T >	powLerp (const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t)

template<typename T >
bool	diagonalizeSymmetricMatrix (const Mat3< T > &input, Mat3< T > &Q, Vec3< T > &D, unsigned int MAX_ITERATIONS=250)
	Use Jacobi iterations to decompose a symmetric 3x3 matrix (diagonalize and compute eigenvectors) More...

template<typename T >
Mat3< T >	Abs (const Mat3< T > &m)

template<typename Type1 , typename Type2 >
Mat3< Type1 >	cwiseAdd (const Mat3< Type1 > &m, const Type2 s)

template<typename T >
bool	cwiseLessThan (const Mat3< T > &m0, const Mat3< T > &m1)

template<typename T >
bool	cwiseGreaterThan (const Mat3< T > &m0, const Mat3< T > &m1)

template<typename T0 , typename T1 >
Vec3< T1 >	transformNormal (const Mat4< T0 > &m, const Vec3< T1 > &n)

template<typename T >
bool	isAffine (const Mat4< T > &m)

template<typename T >
bool	hasTranslation (const Mat4< T > &m)

template<typename T >
Mat4< T >	Abs (const Mat4< T > &m)

template<typename Type1 , typename Type2 >
Mat4< Type1 >	cwiseAdd (const Mat4< Type1 > &m, const Type2 s)

template<typename T >
bool	cwiseLessThan (const Mat4< T > &m0, const Mat4< T > &m1)

template<typename T >
bool	cwiseGreaterThan (const Mat4< T > &m0, const Mat4< T > &m1)

template<typename Type1 , typename Type2 >
auto	cwiseAdd (const Type1 &v, const Type2 s)
	Componentwise adder for POD types. More...

template<typename Type1 , typename Type2 >
bool	cwiseLessThan (const Type1 &a, const Type2 &b)
	Componentwise less than for POD types. More...

template<typename Type1 , typename Type2 >
bool	cwiseGreaterThan (const Type1 &a, const Type2 &b)
	Componentwise greater than for POD types. More...

template<typename T >
constexpr T	pi ()
	Pi constant taken from Boost to match old behaviour. More...

template<>
constexpr float	pi ()

template<>
constexpr double	pi ()

template<>
constexpr long double	pi ()

template<typename T >
T	negative (const T &val)
	Return the unary negation of the given value. More...

template<>
bool	negative (const bool &val)
	Return the negation of the given boolean. More...

template<>
std::string	negative (const std::string &val)
	Return the "negation" of the given string. More...

template<typename Type >
Type	Clamp (Type x, Type min, Type max)
	Return x clamped to [min, max]. More...

template<typename Type >
Type	Clamp01 (Type x)
	Return x clamped to [0, 1]. More...

template<typename Type >
bool	ClampTest01 (Type &x)
	Return `true` if x is outside [0,1]. More...

template<typename Type >
Type	SmoothUnitStep (Type x)
	Return 0 if x < 0, 1 if x > 1 or else (3 − 2 x) x². More...

template<typename Type >
Type	SmoothUnitStep (Type x, Type min, Type max)
	Return 0 if x < min, 1 if x > max or else (3 − 2 t) t², where t = (x − min)/(max − min). More...

template<typename Type >
bool	isZero (const Type &x)
	Return `true` if x is exactly equal to zero. More...

template<typename Type >
bool	isApproxZero (const Type &x)
	Return `true` if x is equal to zero to within the default floating-point comparison tolerance. More...

template<typename Type >
bool	isApproxZero (const Type &x, const Type &tolerance)
	Return `true` if x is equal to zero to within the given tolerance. More...

template<typename Type >
bool	isNegative (const Type &x)
	Return `true` if x is less than zero. More...

template<>
bool	isNegative< bool > (const bool &)

bool	isFinite (const float x)
	Return `true` if x is finite. More...

template<typename Type , typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0>
bool	isFinite (const Type &x)
	Return `true` if x is finite. More...

bool	isInfinite (const float x)
	Return `true` if x is an infinity value (either positive infinity or negative infinity). More...

template<typename Type , typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0>
bool	isInfinite (const Type &x)
	Return `true` if x is an infinity value (either positive infinity or negative infinity). More...

bool	isNan (const float x)
	Return `true` if x is a NaN (Not-A-Number) value. More...

template<typename Type , typename std::enable_if< std::is_arithmetic< Type >::value, int >::type = 0>
bool	isNan (const Type &x)
	Return `true` if x is a NaN (Not-A-Number) value. More...

template<typename Type >
bool	isApproxEqual (const Type &a, const Type &b, const Type &tolerance)
	Return `true` if a is equal to b to within the given tolerance. More...

template<typename Type >
bool	isApproxEqual (const Type &a, const Type &b)
	Return `true` if a is equal to b to within the default floating-point comparison tolerance. More...

template<>
bool	isApproxEqual< bool > (const bool &a, const bool &b)

template<>
bool	isApproxEqual< bool > (const bool &a, const bool &b, const bool &)

template<>
bool	isApproxEqual< std::string > (const std::string &a, const std::string &b)

template<>
bool	isApproxEqual< std::string > (const std::string &a, const std::string &b, const std::string &)

template<typename Type >
bool	isApproxLarger (const Type &a, const Type &b, const Type &tolerance)
	Return `true` if a is larger than b to within the given tolerance, i.e., if b - a < tolerance. More...

template<typename T0 , typename T1 >
bool	isExactlyEqual (const T0 &a, const T1 &b)
	Return `true` if a is exactly equal to b. More...

template<typename Type >
bool	isRelOrApproxEqual (const Type &a, const Type &b, const Type &absTol, const Type &relTol)

template<>
bool	isRelOrApproxEqual (const bool &a, const bool &b, const bool &, const bool &)

int32_t	floatToInt32 (const float f)

int64_t	doubleToInt64 (const double d)

bool	isUlpsEqual (const double aLeft, const double aRight, const int64_t aUnitsInLastPlace)

bool	isUlpsEqual (const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)

template<typename Type >
Type	Pow2 (Type x)
	Return x². More...

template<typename Type >
Type	Pow3 (Type x)
	Return x³. More...

template<typename Type >
Type	Pow4 (Type x)
	Return x⁴. More...

template<typename Type >
Type	Pow (Type x, int n)
	Return xⁿ. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b)
	Return the maximum of two values. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b, const Type &c)
	Return the maximum of three values. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b, const Type &c, const Type &d)
	Return the maximum of four values. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e)
	Return the maximum of five values. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f)
	Return the maximum of six values. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g)
	Return the maximum of seven values. More...

template<typename Type >
const Type &	Max (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h)
	Return the maximum of eight values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b)
	Return the minimum of two values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b, const Type &c)
	Return the minimum of three values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b, const Type &c, const Type &d)
	Return the minimum of four values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e)
	Return the minimum of five values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f)
	Return the minimum of six values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g)
	Return the minimum of seven values. More...

template<typename Type >
const Type &	Min (const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h)
	Return the minimum of eight values. More...

template<typename Type >
Type	Exp (const Type &x)
	Return e^x. More...

template<typename Type >
int	Sign (const Type &x)
	Return the sign of the given value as an integer (either -1, 0 or 1). More...

template<typename Type >
bool	SignChange (const Type &a, const Type &b)
	Return `true` if a and b have different signs. More...

template<typename Type >
bool	ZeroCrossing (const Type &a, const Type &b)
	Return `true` if the interval [a, b] includes zero, i.e., if either a or b is zero or if they have different signs. More...

template<typename Type >
Type	RoundUp (Type x, Type base)
	Return x rounded up to the nearest multiple of base. More...

template<typename Type >
Type	RoundDown (Type x, Type base)
	Return x rounded down to the nearest multiple of base. More...

template<typename Type >
Type	EuclideanRemainder (Type x)

template<typename Type >
Type	IntegerPart (Type x)
	Return the integer part of x. More...

template<typename Type >
Type	FractionalPart (Type x)
	Return the fractional part of x. More...

template<typename Type >
Type	Chop (Type x, Type delta)
	Return x if it is greater or equal in magnitude than delta. Otherwise, return zero. More...

template<typename Type >
Type	Truncate (Type x, unsigned int digits)
	Return x truncated to the given number of decimal digits. More...

template<typename T >
auto	PrintCast (const T &val) -> typename std::enable_if<!std::is_same< T, int8_t >::value &&!std::is_same< T, uint8_t >::value, const T & >::type
	8-bit integer values print to std::ostreams as characters. Cast them so that they print as integers instead. More...

int32_t	PrintCast (int8_t val)

uint32_t	PrintCast (uint8_t val)

template<typename Type >
Type	Inv (Type x)
	Return the inverse of x. More...

template<typename Vec3T >
size_t	MinIndex (const Vec3T &v)
	Return the index [0,1,2] of the smallest value in a 3D vector. More...

template<typename Vec3T >
size_t	MaxIndex (const Vec3T &v)
	Return the index [0,1,2] of the largest value in a 3D vector. More...

OPENVDB_API Vec3d	closestPointOnTriangleToPoint (const Vec3d &a, const Vec3d &b, const Vec3d &c, const Vec3d &p, Vec3d &uvw)
	Closest Point on Triangle to Point. Given a triangle `abc` and a point `p`, return the point on `abc` closest to `p` and the corresponding barycentric coordinates. More...

OPENVDB_API Vec3d	closestPointOnSegmentToPoint (const Vec3d &a, const Vec3d &b, const Vec3d &p, double &t)
	Closest Point on Line Segment to Point. Given segment `ab` and point `p`, return the point on `ab` closest to `p` and `t` the parametric distance to `b`. More...

template<typename T >
Quat< T >	slerp (const Quat< T > &q1, const Quat< T > &q2, T t, T tolerance=0.00001)
	Linear interpolation between the two quaternions. More...

template<typename S , typename T >
Quat< T >	operator* (S scalar, const Quat< T > &q)
	Multiply each element of the given quaternion by scalar and return the result. More...

template<typename T , typename T0 >
Mat3< T >	slerp (const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t)
	Interpolate between m1 and m2. Converts to quaternion form and uses slerp m1 and m2 must be rotation matrices! More...

template<typename T , typename T0 >
Mat3< T >	bezLerp (const Mat3< T0 > &m1, const Mat3< T0 > &m2, const Mat3< T0 > &m3, const Mat3< T0 > &m4, T t)

template<typename RealT >
std::ostream &	operator<< (std::ostream &os, const Ray< RealT > &r)
	Output streaming of the Ray class. More...

OPENVDB_API void	calculateBounds (const Transform &t, const Vec3d &minWS, const Vec3d &maxWS, Vec3d &minIS, Vec3d &maxIS)
	Calculate an axis-aligned bounding box in index space from an axis-aligned bounding box in world space. More...

OPENVDB_API std::ostream &	operator<< (std::ostream &, const Transform &)

template<typename ResolvedMapType , typename OpType >
void	doProcessTypedMap (Transform &transform, OpType &op)
	Helper function used internally by processTypedMap() More...

template<typename ResolvedMapType , typename OpType >
void	doProcessTypedMap (const Transform &transform, OpType &op)
	Helper function used internally by processTypedMap() More...

template<typename TransformType , typename OpType >
bool	processTypedMap (TransformType &transform, OpType &op)
	Utility function that, given a generic map pointer, calls a functor on the fully-resoved map. More...

template<int SIZE, typename T0 , typename T1 >
bool	operator< (const Tuple< SIZE, T0 > &t0, const Tuple< SIZE, T1 > &t1)

template<int SIZE, typename T0 , typename T1 >
bool	operator> (const Tuple< SIZE, T0 > &t0, const Tuple< SIZE, T1 > &t1)

template<int SIZE, typename T >
Tuple< SIZE, T >	Abs (const Tuple< SIZE, T > &t)

template<int SIZE, typename T >
bool	isNan (const Tuple< SIZE, T > &t)
	Return `true` if a Nan is present in the tuple. More...

template<int SIZE, typename T >
bool	isInfinite (const Tuple< SIZE, T > &t)
	Return `true` if an Inf is present in the tuple. More...

template<int SIZE, typename T >
bool	isFinite (const Tuple< SIZE, T > &t)
	Return `true` if no Nan or Inf values are present. More...

template<int SIZE, typename T >
bool	isZero (const Tuple< SIZE, T > &t)
	Return `true` if all elements are exactly equal to zero. More...

template<int SIZE, typename T >
std::ostream &	operator<< (std::ostream &ostr, const Tuple< SIZE, T > &classname)
	Write a Tuple to an output stream. More...

template<typename S , typename T >
Vec2< typename promote< S, T >::type >	operator* (S scalar, const Vec2< T > &v)
	Multiply each element of the given vector by scalar and return the result. More...

template<typename S , typename T >
Vec2< typename promote< S, T >::type >	operator* (const Vec2< T > &v, S scalar)
	Multiply each element of the given vector by scalar and return the result. More...

template<typename T0 , typename T1 >
Vec2< typename promote< T0, T1 >::type >	operator* (const Vec2< T0 > &v0, const Vec2< T1 > &v1)
	Multiply corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec2< typename promote< S, T >::type >	operator/ (S scalar, const Vec2< T > &v)
	Divide scalar by each element of the given vector and return the result. More...

template<typename S , typename T >
Vec2< typename promote< S, T >::type >	operator/ (const Vec2< T > &v, S scalar)
	Divide each element of the given vector by scalar and return the result. More...

template<typename T0 , typename T1 >
Vec2< typename promote< T0, T1 >::type >	operator/ (const Vec2< T0 > &v0, const Vec2< T1 > &v1)
	Divide corresponding elements of v0 and v1 and return the result. More...

template<typename T0 , typename T1 >
Vec2< typename promote< T0, T1 >::type >	operator+ (const Vec2< T0 > &v0, const Vec2< T1 > &v1)
	Add corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec2< typename promote< S, T >::type >	operator+ (const Vec2< T > &v, S scalar)
	Add scalar to each element of the given vector and return the result. More...

template<typename T0 , typename T1 >
Vec2< typename promote< T0, T1 >::type >	operator- (const Vec2< T0 > &v0, const Vec2< T1 > &v1)
	Subtract corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec2< typename promote< S, T >::type >	operator- (const Vec2< T > &v, S scalar)
	Subtract scalar from each element of the given vector and return the result. More...

template<typename T >
T	angle (const Vec2< T > &v1, const Vec2< T > &v2)

template<typename T >
bool	isApproxEqual (const Vec2< T > &a, const Vec2< T > &b)

template<typename T >
bool	isApproxEqual (const Vec2< T > &a, const Vec2< T > &b, const Vec2< T > &eps)

template<typename T >
Vec2< T >	Abs (const Vec2< T > &v)

template<typename T >
void	orthonormalize (Vec2< T > &v1, Vec2< T > &v2)

template<typename T >
Vec2< T >	minComponent (const Vec2< T > &v1, const Vec2< T > &v2)
	Return component-wise minimum of the two vectors. More...

template<typename T >
Vec2< T >	maxComponent (const Vec2< T > &v1, const Vec2< T > &v2)
	Return component-wise maximum of the two vectors. More...

template<typename T >
Vec2< T >	Exp (Vec2< T > v)
	Return a vector with the exponent applied to each of the components of the input vector. More...

template<typename T >
Vec2< T >	Log (Vec2< T > v)
	Return a vector with log applied to each of the components of the input vector. More...

template<typename T0 , typename T1 >
bool	operator== (const Vec3< T0 > &v0, const Vec3< T1 > &v1)
	Equality operator, does exact floating point comparisons. More...

template<typename T0 , typename T1 >
bool	operator!= (const Vec3< T0 > &v0, const Vec3< T1 > &v1)
	Inequality operator, does exact floating point comparisons. More...

template<typename S , typename T >
Vec3< typename promote< S, T >::type >	operator* (S scalar, const Vec3< T > &v)
	Multiply each element of the given vector by scalar and return the result. More...

template<typename S , typename T >
Vec3< typename promote< S, T >::type >	operator* (const Vec3< T > &v, S scalar)
	Multiply each element of the given vector by scalar and return the result. More...

template<typename T0 , typename T1 >
Vec3< typename promote< T0, T1 >::type >	operator* (const Vec3< T0 > &v0, const Vec3< T1 > &v1)
	Multiply corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec3< typename promote< S, T >::type >	operator/ (S scalar, const Vec3< T > &v)
	Divide scalar by each element of the given vector and return the result. More...

template<typename S , typename T >
Vec3< typename promote< S, T >::type >	operator/ (const Vec3< T > &v, S scalar)
	Divide each element of the given vector by scalar and return the result. More...

template<typename T0 , typename T1 >
Vec3< typename promote< T0, T1 >::type >	operator/ (const Vec3< T0 > &v0, const Vec3< T1 > &v1)
	Divide corresponding elements of v0 and v1 and return the result. More...

template<typename T0 , typename T1 >
Vec3< typename promote< T0, T1 >::type >	operator+ (const Vec3< T0 > &v0, const Vec3< T1 > &v1)
	Add corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec3< typename promote< S, T >::type >	operator+ (const Vec3< T > &v, S scalar)
	Add scalar to each element of the given vector and return the result. More...

template<typename T0 , typename T1 >
Vec3< typename promote< T0, T1 >::type >	operator- (const Vec3< T0 > &v0, const Vec3< T1 > &v1)
	Subtract corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec3< typename promote< S, T >::type >	operator- (const Vec3< T > &v, S scalar)
	Subtract scalar from each element of the given vector and return the result. More...

template<typename T >
T	angle (const Vec3< T > &v1, const Vec3< T > &v2)

template<typename T >
bool	isApproxEqual (const Vec3< T > &a, const Vec3< T > &b)

template<typename T >
bool	isApproxEqual (const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)

template<typename T >
Vec3< T >	Abs (const Vec3< T > &v)

template<typename T >
void	orthonormalize (Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)

template<typename T >
Vec3< T >	minComponent (const Vec3< T > &v1, const Vec3< T > &v2)
	Return component-wise minimum of the two vectors. More...

template<typename T >
Vec3< T >	maxComponent (const Vec3< T > &v1, const Vec3< T > &v2)
	Return component-wise maximum of the two vectors. More...

template<typename T >
Vec3< T >	Exp (Vec3< T > v)
	Return a vector with the exponent applied to each of the components of the input vector. More...

template<typename T >
Vec3< T >	Log (Vec3< T > v)
	Return a vector with log applied to each of the components of the input vector. More...

template<typename T0 , typename T1 >
bool	operator== (const Vec4< T0 > &v0, const Vec4< T1 > &v1)
	Equality operator, does exact floating point comparisons. More...

template<typename T0 , typename T1 >
bool	operator!= (const Vec4< T0 > &v0, const Vec4< T1 > &v1)
	Inequality operator, does exact floating point comparisons. More...

template<typename S , typename T >
Vec4< typename promote< S, T >::type >	operator* (S scalar, const Vec4< T > &v)
	Multiply each element of the given vector by scalar and return the result. More...

template<typename S , typename T >
Vec4< typename promote< S, T >::type >	operator* (const Vec4< T > &v, S scalar)
	Multiply each element of the given vector by scalar and return the result. More...

template<typename T0 , typename T1 >
Vec4< typename promote< T0, T1 >::type >	operator* (const Vec4< T0 > &v0, const Vec4< T1 > &v1)
	Multiply corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec4< typename promote< S, T >::type >	operator/ (S scalar, const Vec4< T > &v)
	Divide scalar by each element of the given vector and return the result. More...

template<typename S , typename T >
Vec4< typename promote< S, T >::type >	operator/ (const Vec4< T > &v, S scalar)
	Divide each element of the given vector by scalar and return the result. More...

template<typename T0 , typename T1 >
Vec4< typename promote< T0, T1 >::type >	operator/ (const Vec4< T0 > &v0, const Vec4< T1 > &v1)
	Divide corresponding elements of v0 and v1 and return the result. More...

template<typename T0 , typename T1 >
Vec4< typename promote< T0, T1 >::type >	operator+ (const Vec4< T0 > &v0, const Vec4< T1 > &v1)
	Add corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec4< typename promote< S, T >::type >	operator+ (const Vec4< T > &v, S scalar)
	Add scalar to each element of the given vector and return the result. More...

template<typename T0 , typename T1 >
Vec4< typename promote< T0, T1 >::type >	operator- (const Vec4< T0 > &v0, const Vec4< T1 > &v1)
	Subtract corresponding elements of v0 and v1 and return the result. More...

template<typename S , typename T >
Vec4< typename promote< S, T >::type >	operator- (const Vec4< T > &v, S scalar)
	Subtract scalar from each element of the given vector and return the result. More...

template<typename T >
bool	isApproxEqual (const Vec4< T > &a, const Vec4< T > &b)

template<typename T >
bool	isApproxEqual (const Vec4< T > &a, const Vec4< T > &b, const Vec4< T > &eps)

template<typename T >
Vec4< T >	Abs (const Vec4< T > &v)

template<typename T >
Vec4< T >	minComponent (const Vec4< T > &v1, const Vec4< T > &v2)
	Return component-wise minimum of the two vectors. More...

template<typename T >
Vec4< T >	maxComponent (const Vec4< T > &v1, const Vec4< T > &v2)
	Return component-wise maximum of the two vectors. More...

template<typename T >
Vec4< T >	Exp (Vec4< T > v)
	Return a vector with the exponent applied to each of the components of the input vector. More...

template<typename T >
Vec4< T >	Log (Vec4< T > v)
	Return a vector with log applied to each of the components of the input vector. More...


template<typename T >
Vec3< typename promote< T, typename Coord::ValueType >::type >	operator+ (const Vec3< T > &v0, const Coord &v1)
	Allow a Coord to be added to or subtracted from a Vec3. More...

template<typename T >
Vec3< typename promote< T, typename Coord::ValueType >::type >	operator+ (const Coord &v1, const Vec3< T > &v0)
	Allow a Coord to be added to or subtracted from a Vec3. More...


template<typename T >
Vec3< typename promote< T, Coord::ValueType >::type >	operator- (const Vec3< T > &v0, const Coord &v1)
	Allow a Coord to be subtracted from a Vec3. More...

template<typename T >
Vec3< typename promote< T, Coord::ValueType >::type >	operator- (const Coord &v1, const Vec3< T > &v0)
	Allow a Coord to be subtracted from a Vec3. More...


std::string	operator+ (const std::string &s, bool)
	Needed to support the `(zeroVal<ValueType>() + val)` idiom when `ValueType` is `std::string`. More...

std::string	operator+ (const std::string &s, int)
	Needed to support the `(zeroVal<ValueType>() + val)` idiom when `ValueType` is `std::string`. More...

std::string	operator+ (const std::string &s, float)
	Needed to support the `(zeroVal<ValueType>() + val)` idiom when `ValueType` is `std::string`. More...

std::string	operator+ (const std::string &s, double)
	Needed to support the `(zeroVal<ValueType>() + val)` idiom when `ValueType` is `std::string`. More...


int32_t	Abs (int32_t i)
	Return the absolute value of the given quantity. More...

int64_t	Abs (int64_t i)
	Return the absolute value of the given quantity. More...

float	Abs (float x)
	Return the absolute value of the given quantity. More...

double	Abs (double x)
	Return the absolute value of the given quantity. More...

long double	Abs (long double x)
	Return the absolute value of the given quantity. More...

uint32_t	Abs (uint32_t i)
	Return the absolute value of the given quantity. More...

uint64_t	Abs (uint64_t i)
	Return the absolute value of the given quantity. More...

bool	Abs (bool b)
	Return the absolute value of the given quantity. More...

template<typename T >
std::enable_if< std::is_same< T, size_t >::value, T >::type	Abs (T i)
	Return the absolute value of the given quantity. More...


float	Pow (float b, float e)
	Return b^e. More...

double	Pow (double b, double e)
	Return b^e. More...


float	Sin (const float &x)
	Return sin x. More...

double	Sin (const double &x)
	Return sin x. More...


float	Cos (const float &x)
	Return cos x. More...

double	Cos (const double &x)
	Return cos x. More...


float	Sqrt (float x)
	Return the square root of a floating-point value. More...

double	Sqrt (double x)
	Return the square root of a floating-point value. More...

long double	Sqrt (long double x)
	Return the square root of a floating-point value. More...


float	Cbrt (float x)
	Return the cube root of a floating-point value. More...

double	Cbrt (double x)
	Return the cube root of a floating-point value. More...

long double	Cbrt (long double x)
	Return the cube root of a floating-point value. More...


int	Mod (int x, int y)
	Return the remainder of x / y. More...

float	Mod (float x, float y)
	Return the remainder of x / y. More...

double	Mod (double x, double y)
	Return the remainder of x / y. More...

long double	Mod (long double x, long double y)
	Return the remainder of x / y. More...

template<typename Type >
Type	Remainder (Type x, Type y)
	Return the remainder of x / y. More...


float	RoundUp (float x)
	Return x rounded up to the nearest integer. More...

double	RoundUp (double x)
	Return x rounded up to the nearest integer. More...

long double	RoundUp (long double x)
	Return x rounded up to the nearest integer. More...


float	RoundDown (float x)
	Return x rounded down to the nearest integer. More...

double	RoundDown (double x)
	Return x rounded down to the nearest integer. More...

long double	RoundDown (long double x)
	Return x rounded down to the nearest integer. More...


float	Round (float x)
	Return x rounded to the nearest integer. More...

double	Round (double x)
	Return x rounded to the nearest integer. More...

long double	Round (long double x)
	Return x rounded to the nearest integer. More...


int	Floor (float x)
	Return the floor of x. More...

int	Floor (double x)
	Return the floor of x. More...

int	Floor (long double x)
	Return the floor of x. More...


int	Ceil (float x)
	Return the ceiling of x. More...

int	Ceil (double x)
	Return the ceiling of x. More...

int	Ceil (long double x)
	Return the ceiling of x. More...

Typedef Documentation

using FullyDecomposedMap = CompoundMap<SymmetricMap, UnitaryAndTranslationMap>

using half = internal::half

using Mat3d = Mat3<double>

using Mat3f = Mat3d

using Mat3s = Mat3<float>

using Mat4d = Mat4<double>

using Mat4f = Mat4d

using Mat4s = Mat4<float>

using PolarDecomposedMap = CompoundMap<SymmetricMap, UnitaryMap>

using Quatd = Quat<double>

using Quats = Quat<float>

using Random01 = Rand01<double, std::mt19937>

using RandomInt = RandInt<int, std::mt19937>

using SpectralDecomposedMap = CompoundMap<CompoundMap<UnitaryMap, ScaleMap>, UnitaryMap>

using SymmetricMap = SpectralDecomposedMap

using UnitaryAndTranslationMap = CompoundMap<UnitaryMap, TranslationMap>

using Vec2d = Vec2<double>

using Vec2i = Vec2<int32_t>

using Vec2s = Vec2<float>

using Vec2ui = Vec2<uint32_t>

using Vec3d = Vec3<double>

using Vec3i = Vec3<int32_t>

using Vec3s = Vec3<float>

using Vec3ui = Vec3<uint32_t>

using Vec4d = Vec4<double>

using Vec4i = Vec4<int32_t>

using Vec4s = Vec4<float>

using Vec4ui = Vec4<uint32_t>

Enumeration Type Documentation

anonymous enum

Enumerator
NUM_DS_SCHEMES

anonymous enum

Enumerator
NUM_DD_SCHEMES

anonymous enum

Enumerator
NUM_BIAS_SCHEMES

anonymous enum

Enumerator
NUM_TEMPORAL_SCHEMES

enum Axis

Enumerator
X_AXIS
Y_AXIS
Z_AXIS

enum BiasedGradientScheme

Biased Gradients are limited to non-centered differences.

Enumerator
UNKNOWN_BIAS
FIRST_BIAS
SECOND_BIAS
THIRD_BIAS
WENO5_BIAS
HJWENO5_BIAS

enum DDScheme

Different discrete schemes used in the second derivatives.

Enumerator
UNKNOWN_DD
CD_SECOND
CD_FOURTH
CD_SIXTH

enum DScheme

Different discrete schemes used in the first derivatives.

Enumerator
UNKNOWN_DS
CD_2NDT
CD_2ND
CD_4TH
CD_6TH
FD_1ST
FD_2ND
FD_3RD
BD_1ST
BD_2ND
BD_3RD
FD_WENO5
BD_WENO5
FD_HJWENO5
BD_HJWENO5

enum RotationOrder

Enumerator
XYZ_ROTATION
XZY_ROTATION
YXZ_ROTATION
YZX_ROTATION
ZXY_ROTATION
ZYX_ROTATION
XZX_ROTATION
ZXZ_ROTATION

enum TemporalIntegrationScheme

Temporal integration schemes.

Enumerator
UNKNOWN_TIS
TVD_RK1
TVD_RK2
TVD_RK3

Function Documentation

Tuple<SIZE, T> openvdb::v12_0::math::Abs ( const Tuple< SIZE, T > & t )

Returns: the absolute value of the given Tuple.

int32_t openvdb::v12_0::math::Abs ( int32_t i )

inline