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 <openvdb/util/Assert.h>
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <random>
#include <string>
#include <type_traits>

Classes
struct	Tolerance< T >
	Tolerance for floating-point comparison. More...

struct	Tolerance< float >

struct	Tolerance< double >

struct	Delta< T >
	Delta for small floating-point offsets. More...

struct	Delta< float >

struct	Delta< double >

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

class	RandInt< IntType, EngineType >
	Simple random integer generator. More...

struct	promote< S, T, typename >

Namespaces
	openvdb

	openvdb::v12_0

	openvdb::v12_0::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	Random01 = Rand01< double, std::mt19937 >

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

Enumerations
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<typename T >
constexpr T	zeroVal ()
	Return the value of type T that corresponds to zero. More...

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

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

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...


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...

Detailed Description

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

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; } \

#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.)");

#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN

#define OPENVDB_NO_FP_EQUALITY_WARNING_END

Classes

Namespaces

Macros

Typedefs

Enumerations

Functions

Detailed Description

Macro Definition Documentation