General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at least arbitrary numeric value types) More...

#include <openvdb/Platform.h>
#include <openvdb/version.h>
#include <hboost/numeric/conversion/conversion_traits.hpp>
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <random>
#include <string>
#include <type_traits>

Include dependency graph for Math.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Classes
struct	openvdb::OPENVDB_VERSION_NAME::math::Tolerance< T >
	Tolerance for floating-point comparison. More...

struct	openvdb::OPENVDB_VERSION_NAME::math::Tolerance< float >

struct	openvdb::OPENVDB_VERSION_NAME::math::Tolerance< double >

struct	openvdb::OPENVDB_VERSION_NAME::math::Delta< T >
	Delta for small floating-point offsets. More...

struct	openvdb::OPENVDB_VERSION_NAME::math::Delta< float >

struct	openvdb::OPENVDB_VERSION_NAME::math::Delta< double >

class	openvdb::OPENVDB_VERSION_NAME::math::Rand01< FloatType, EngineType >
	Simple generator of random numbers over the range [0, 1) More...

class	openvdb::OPENVDB_VERSION_NAME::math::RandInt< IntType, EngineType >
	Simple random integer generator. More...

struct	openvdb::OPENVDB_VERSION_NAME::math::promote< S, T >

Namespaces
	openvdb

	openvdb::OPENVDB_VERSION_NAME

	openvdb::OPENVDB_VERSION_NAME::math

Macros
#define	OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN

#define	OPENVDB_NO_FP_EQUALITY_WARNING_END

#define	OPENVDB_IS_POD(Type)

#define	OPENVDB_EXACT_IS_APPROX_EQUAL(T)

Typedefs
using	openvdb::OPENVDB_VERSION_NAME::math::Random01 = Rand01< double, std::mt19937 >

using	openvdb::OPENVDB_VERSION_NAME::math::RandomInt = RandInt< int, std::mt19937 >

Enumerations
enum	openvdb::OPENVDB_VERSION_NAME::math::Axis { openvdb::OPENVDB_VERSION_NAME::math::X_AXIS = 0, openvdb::OPENVDB_VERSION_NAME::math::Y_AXIS = 1, openvdb::OPENVDB_VERSION_NAME::math::Z_AXIS = 2 }

enum	openvdb::OPENVDB_VERSION_NAME::math::RotationOrder { openvdb::OPENVDB_VERSION_NAME::math::XYZ_ROTATION = 0, openvdb::OPENVDB_VERSION_NAME::math::XZY_ROTATION, openvdb::OPENVDB_VERSION_NAME::math::YXZ_ROTATION, openvdb::OPENVDB_VERSION_NAME::math::YZX_ROTATION, openvdb::OPENVDB_VERSION_NAME::math::ZXY_ROTATION, openvdb::OPENVDB_VERSION_NAME::math::ZYX_ROTATION, openvdb::OPENVDB_VERSION_NAME::math::XZX_ROTATION, openvdb::OPENVDB_VERSION_NAME::math::ZXZ_ROTATION }

Functions
template<typename T >
constexpr T	openvdb::OPENVDB_VERSION_NAME::zeroVal ()
	Return the value of type T that corresponds to zero. More...

template<>
std::string	openvdb::OPENVDB_VERSION_NAME::zeroVal< std::string > ()
	Return the `std::string` value that corresponds to zero. More...

template<>
constexpr bool	openvdb::OPENVDB_VERSION_NAME::zeroVal< bool > ()
	Return the `bool` value that corresponds to zero. More...

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

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

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

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

template<>
constexpr float	openvdb::OPENVDB_VERSION_NAME::math::pi ()

template<>
constexpr double	openvdb::OPENVDB_VERSION_NAME::math::pi ()

template<>
constexpr long double	openvdb::OPENVDB_VERSION_NAME::math::pi ()

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

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

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

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

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

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

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

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

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

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

template<>
bool	openvdb::OPENVDB_VERSION_NAME::math::isNegative< bool > (const bool &)

bool	openvdb::OPENVDB_VERSION_NAME::math::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	openvdb::OPENVDB_VERSION_NAME::math::isFinite (const Type &x)
	Return `true` if x is finite. More...

bool	openvdb::OPENVDB_VERSION_NAME::math::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	openvdb::OPENVDB_VERSION_NAME::math::isInfinite (const Type &x)
	Return `true` if x is an infinity value (either positive infinity or negative infinity). More...

bool	openvdb::OPENVDB_VERSION_NAME::math::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	openvdb::OPENVDB_VERSION_NAME::math::isNan (const Type &x)
	Return `true` if x is a NaN (Not-A-Number) value. More...

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

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

template<>
bool	openvdb::OPENVDB_VERSION_NAME::math::isRelOrApproxEqual (const bool &a, const bool &b, const bool &, const bool &)

int32_t	openvdb::OPENVDB_VERSION_NAME::math::floatToInt32 (const float f)

int64_t	openvdb::OPENVDB_VERSION_NAME::math::doubleToInt64 (const double d)

bool	openvdb::OPENVDB_VERSION_NAME::math::isUlpsEqual (const double aLeft, const double aRight, const int64_t aUnitsInLastPlace)

bool	openvdb::OPENVDB_VERSION_NAME::math::isUlpsEqual (const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)

template<typename Type >
Type	openvdb::OPENVDB_VERSION_NAME::math::Pow2 (Type x)
	Return x². More...

template<typename Type >
Type	openvdb::OPENVDB_VERSION_NAME::math::Pow3 (Type x)
	Return x³. More...

template<typename Type >
Type	openvdb::OPENVDB_VERSION_NAME::math::Pow4 (Type x)
	Return x⁴. More...

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

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

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

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

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

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

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

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

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

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

template<typename Type >
Type	openvdb::OPENVDB_VERSION_NAME::math::EuclideanRemainder (Type x)

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

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

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

template<typename T >
auto	openvdb::OPENVDB_VERSION_NAME::math::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	openvdb::OPENVDB_VERSION_NAME::math::PrintCast (int8_t val)

uint32_t	openvdb::OPENVDB_VERSION_NAME::math::PrintCast (uint8_t val)

template<typename Type >
Type	openvdb::OPENVDB_VERSION_NAME::math::Inv (Type x)
	Return the inverse of x. More...

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

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


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

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

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

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


int32_t	openvdb::OPENVDB_VERSION_NAME::math::Abs (int32_t i)
	Return the absolute value of the given quantity. More...

int64_t	openvdb::OPENVDB_VERSION_NAME::math::Abs (int64_t i)
	Return the absolute value of the given quantity. More...

float	openvdb::OPENVDB_VERSION_NAME::math::Abs (float x)
	Return the absolute value of the given quantity. More...

double	openvdb::OPENVDB_VERSION_NAME::math::Abs (double x)
	Return the absolute value of the given quantity. More...

long double	openvdb::OPENVDB_VERSION_NAME::math::Abs (long double x)
	Return the absolute value of the given quantity. More...

uint32_t	openvdb::OPENVDB_VERSION_NAME::math::Abs (uint32_t i)
	Return the absolute value of the given quantity. More...

uint64_t	openvdb::OPENVDB_VERSION_NAME::math::Abs (uint64_t i)
	Return the absolute value of the given quantity. More...

bool	openvdb::OPENVDB_VERSION_NAME::math::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	openvdb::OPENVDB_VERSION_NAME::math::Abs (T i)
	Return the absolute value of the given quantity. More...


float	openvdb::OPENVDB_VERSION_NAME::math::Pow (float b, float e)
	Return b^e. More...

double	openvdb::OPENVDB_VERSION_NAME::math::Pow (double b, double e)
	Return b^e. More...


float	openvdb::OPENVDB_VERSION_NAME::math::Sin (const float &x)
	Return sin x. More...

double	openvdb::OPENVDB_VERSION_NAME::math::Sin (const double &x)
	Return sin x. More...


float	openvdb::OPENVDB_VERSION_NAME::math::Cos (const float &x)
	Return cos x. More...

double	openvdb::OPENVDB_VERSION_NAME::math::Cos (const double &x)
	Return cos x. More...


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

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

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


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

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

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


int	openvdb::OPENVDB_VERSION_NAME::math::Mod (int x, int y)
	Return the remainder of x / y. More...

float	openvdb::OPENVDB_VERSION_NAME::math::Mod (float x, float y)
	Return the remainder of x / y. More...

double	openvdb::OPENVDB_VERSION_NAME::math::Mod (double x, double y)
	Return the remainder of x / y. More...

long double	openvdb::OPENVDB_VERSION_NAME::math::Mod (long double x, long double y)
	Return the remainder of x / y. More...

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


float	openvdb::OPENVDB_VERSION_NAME::math::RoundUp (float x)
	Return x rounded up to the nearest integer. More...

double	openvdb::OPENVDB_VERSION_NAME::math::RoundUp (double x)
	Return x rounded up to the nearest integer. More...

long double	openvdb::OPENVDB_VERSION_NAME::math::RoundUp (long double x)
	Return x rounded up to the nearest integer. More...


float	openvdb::OPENVDB_VERSION_NAME::math::RoundDown (float x)
	Return x rounded down to the nearest integer. More...

double	openvdb::OPENVDB_VERSION_NAME::math::RoundDown (double x)
	Return x rounded down to the nearest integer. More...

long double	openvdb::OPENVDB_VERSION_NAME::math::RoundDown (long double x)
	Return x rounded down to the nearest integer. More...


float	openvdb::OPENVDB_VERSION_NAME::math::Round (float x)
	Return x rounded to the nearest integer. More...

double	openvdb::OPENVDB_VERSION_NAME::math::Round (double x)
	Return x rounded to the nearest integer. More...

long double	openvdb::OPENVDB_VERSION_NAME::math::Round (long double x)
	Return x rounded to the nearest integer. More...


int	openvdb::OPENVDB_VERSION_NAME::math::Floor (float x)
	Return the floor of x. More...

int	openvdb::OPENVDB_VERSION_NAME::math::Floor (double x)
	Return the floor of x. More...

int	openvdb::OPENVDB_VERSION_NAME::math::Floor (long double x)
	Return the floor of x. More...


int	openvdb::OPENVDB_VERSION_NAME::math::Ceil (float x)
	Return the ceiling of x. More...

int	openvdb::OPENVDB_VERSION_NAME::math::Ceil (double x)
	Return the ceiling of x. More...

int	openvdb::OPENVDB_VERSION_NAME::math::Ceil (long double x)
	Return the ceiling of x. More...

Detailed Description

General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at least arbitrary numeric value types)

Definition in file Math.h.

Macro Definition Documentation

#define OPENVDB_EXACT_IS_APPROX_EQUAL ( T )

Value:

template<> inline bool isApproxEqual<T>(const T& a, const T& b) { return a == b; } \

template<> inline bool isApproxEqual<T>(const T& a, const T& b, const T&) { return a == b; } \

a

GLboolean GLboolean GLboolean GLboolean a

Definition: glcorearb.h:1222

b

GLboolean GLboolean GLboolean b

Definition: glcorearb.h:1222

OBJ_MatchTransform::T

Definition at line 421 of file Math.h.

#define OPENVDB_IS_POD ( Type )

Value:

static_assert(std::is_standard_layout<Type>::value, \
    #Type" must be a POD type (satisfy StandardLayoutType.)"); \
static_assert(std::is_trivial<Type>::value, \
    #Type" must be a POD type (satisfy TrivialType.)");

Definition at line 56 of file Math.h.

#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN

Definition at line 48 of file Math.h.

#define OPENVDB_NO_FP_EQUALITY_WARNING_END

Definition at line 49 of file Math.h.

Classes

Namespaces

Macros

Typedefs

Enumerations

Functions

Detailed Description

Macro Definition Documentation