OpenVDB 7.0.0

Classes | Namespaces | Macros | Typedefs | Enumerations | Functions
Math.h File Reference

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 <boost/numeric/conversion/conversion_traits.hpp>`
`#include <algorithm>`
`#include <cassert>`
`#include <cmath>`
`#include <cstdlib>`
`#include <random>`
`#include <string>`
`#include <type_traits>`

Go to the source code of this file.

## 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 >

## Namespaces
| openvdb
| openvdb::v7_0
| openvdb::v7_0::math

## Macros
#define | OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
#define | OPENVDB_NO_FP_EQUALITY_WARNING_END
#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 >
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<>
bool | zeroVal< bool > ()
| Return the `bool` value that corresponds to zero. 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)
std::string | operator+ (const std::string &s, float)
std::string | operator+ (const std::string &s, double)
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...
int32_t | Abs (int32_t i)
| Return the absolute value of the given quantity. More...
int64_t | Abs (int64_t i)
float | Abs (float x)
double | Abs (double x)
long double | Abs (long double x)
uint32_t | Abs (uint32_t i)
uint64_t | Abs (uint64_t i)
bool | Abs (bool b)
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)
| Return `true` if a is equal to b to within the default floating-point comparison tolerance. 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<>
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 aFloatValue)
int64_t | doubleToInt64 (const double aDoubleValue)
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...
float | Pow (float b, float e)
| Return be. More...
double | Pow (double b, double e)
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 ex. More...
float | Sin (const float &x)
| Return sin x. More...
double | Sin (const double &x)
float | Cos (const float &x)
| Return cos x. More...
double | Cos (const double &x)
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...
float | Sqrt (float x)
| Return the square root of a floating-point value. More...
double | Sqrt (double x)
long double | Sqrt (long double x)
float | Cbrt (float x)
| Return the cube root of a floating-point value. More...
double | Cbrt (double x)
long double | Cbrt (long double x)
int | Mod (int x, int y)
| Return the remainder of x / y. More...
float | Mod (float x, float y)
double | Mod (double x, double y)
long double | Mod (long double x, long double y)
template<typename Type >
Type | Remainder (Type x, Type y)
float | RoundUp (float x)
| Return x rounded up to the nearest integer. More...
double | RoundUp (double x)
long double | RoundUp (long double x)
template<typename Type >
Type | RoundUp (Type x, Type base)
| Return x rounded up to the nearest multiple of base. More...
float | RoundDown (float x)
| Return x rounded down to the nearest integer. More...
double | RoundDown (double x)
long double | RoundDown (long double x)
template<typename Type >
Type | RoundDown (Type x, Type base)
| Return x rounded down to the nearest multiple of base. More...
float | Round (float x)
| Return x rounded to the nearest integer. More...
double | Round (double x)
long double | Round (long double x)
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...
int | Floor (float x)
| Return the floor of x. More...
int | Floor (double x)
int | Floor (long double x)
int | Ceil (float x)
| Return the ceiling of x. More...
int | Ceil (double x)
int | Ceil (long double x)
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...

## 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

## ◆ OPENVDB_EXACT_IS_APPROX_EQUAL

#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; } \

## ◆ OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN

#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN

## ◆ OPENVDB_NO_FP_EQUALITY_WARNING_END

#define OPENVDB_NO_FP_EQUALITY_WARNING_END