function.h File Reference

Math functions and function templates on simple types or generic container and vector concepts. More...

Go to the source code of this file.

Classes
struct	mi::math::functor::Operator_equal_equal
	Functor for the equality comparison operator, ==. More...
struct	mi::math::functor::Operator_not_equal
	Functor for the inequality comparison operator, !=. More...
struct	mi::math::functor::Operator_less
	Functor for the less-than comparison operator, <. More...
struct	mi::math::functor::Operator_less_equal
	Functor for the less-than-or-equal comparison operator, <=. More...
struct	mi::math::functor::Operator_greater
	Functor for the greater-than comparison operator, >. More...
struct	mi::math::functor::Operator_greater_equal
	Functor for the greater-than-or-equal comparison operator, >=. More...
struct	mi::math::functor::Operator_plus
	Functor for the plus operator, +. More...
struct	mi::math::functor::Operator_minus
	Functor for the minus operator, -, unary and binary. More...
struct	mi::math::functor::Operator_multiply
	Functor for the multiplication operator, *. More...
struct	mi::math::functor::Operator_divide
	Functor for the division operator, /. More...
struct	mi::math::functor::Operator_and_and
	Functor for the logical and operator, &&. More...
struct	mi::math::functor::Operator_or_or
	Functor for the logical or operator, ||. More...
struct	mi::math::functor::Operator_xor
	Functor for the xor operator, ^. More...
struct	mi::math::functor::Operator_not
	Functor for the logical not operator, !. More...
struct	mi::math::functor::Operator_pre_incr
	Functor for the pre-increment operator, ++. More...
struct	mi::math::functor::Operator_post_incr
	Functor for the post-increment operator, ++. More...
struct	mi::math::functor::Operator_pre_decr
	Functor for the pre-decrement operator, --. More...
struct	mi::math::functor::Operator_post_decr
	Functor for the post-decrement operator, --. More...

Namespaces
	mi
	Common namespace for APIs of NVIDIA Advanced Rendering Center GmbH.
	mi::math
	Namespace for the Math API.
	mi::math::functor
	Namespace for basic math functors in the Math API.
	mi::math::general
	Namespace for generic functions in the Math API.

Constant Groups
	mi
	Common namespace for APIs of NVIDIA Advanced Rendering Center GmbH.
	mi::math
	Namespace for the Math API.
	mi::math::functor
	Namespace for basic math functors in the Math API.
	mi::math::general
	Namespace for generic functions in the Math API.

Functions
template<class Vector , class ResultVector , class UnaryFunctor >
void	mi::math::general::transform (const Vector &vec, ResultVector &result, UnaryFunctor f)
	Generic transform function that applies a unary functor (return value). More...
template<class Vector1 , class Vector2 , class ResultVector , class BinaryFunctor >
void	mi::math::general::transform (const Vector1 &vec1, const Vector2 &vec2, ResultVector &result, BinaryFunctor f)
	Generic transform function that applies a binary functor (return value). More...
template<class Scalar , class Vector , class ResultVector , class BinaryFunctor >
void	mi::math::general::transform_left_scalar (const Scalar &s, const Vector &vec, ResultVector &result, BinaryFunctor f)
	Generic transform function that applies a binary functor (return value, LHS scalar). More...
template<class Scalar , class Vector , class ResultVector , class BinaryFunctor >
void	mi::math::general::transform_right_scalar (const Vector &vec, const Scalar &s, ResultVector &result, BinaryFunctor f)
	Generic transform function that applies a binary functor (return value, RHS scalar). More...
template<class Vector , class UnaryFunctor >
void	mi::math::general::for_each (Vector &vec, UnaryFunctor f)
	Generic transform function that applies a unary functor (in-place). More...
template<class Vector1 , class Vector2 , class BinaryFunctor >
void	mi::math::general::for_each (Vector1 &vec1, const Vector2 &vec2, BinaryFunctor f)
	Generic transform function that applies a binary functor (in-place). More...
Float32	mi::math::exp (Float32 s)
	Returns the constant e to the power of s (exponential function). More...
Float64	mi::math::exp (Float64 s)
	Returns the constant e to the power of s (exponential function). More...
Float32	mi::math::log (Float32 s)
	Returns the natural logarithm of s. More...
Float64	mi::math::log (Float64 s)
	Returns the natural logarithm of s. More...
Float32	mi::math::fast_sqrt (Float32 i)
	A fast implementation of sqrt(x) for floats. More...
Float32	mi::math::fast_exp (Float32 x)
	A fast implementation of exp for floats. More...
Float32	mi::math::fast_pow2 (Float32 x)
	A fast implementation of pow(2,x) for floats. More...
Float32	mi::math::fast_log2 (Float32 i)
	A fast implementation of log2(x) for floats. More...
Float32	mi::math::fast_pow (Float32 b, Float32 e)
	A fast implementation of pow(x,y) for floats. More...
Float32	mi::math::acos (Float32 s)
	Returns the arc cosine of s in radians. More...
Float64	mi::math::acos (Float64 s)
	Returns the arc cosine of s in radians. More...
bool	mi::math::all (Uint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Uint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Uint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Uint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Sint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Float32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::all (Float64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Uint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint8 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint16 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Sint64 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Float32 v)
	Returns true if v is not equal to zero. More...
bool	mi::math::any (Float64 v)
	Returns true if v is not equal to zero. More...
Float32	mi::math::asin (Float32 s)
	Returns the arc sine of s in radians. More...
Float64	mi::math::asin (Float64 s)
	Returns the arc sine of s in radians. More...
Float32	mi::math::atan (Float32 s)
	Returns the arc tangent of s. More...
Float64	mi::math::atan (Float64 s)
	Returns the arc tangent of s. More...
Float32	mi::math::atan2 (Float32 s, Float32 t)
	Returns the arc tangent of s / t. More...
Float64	mi::math::atan2 (Float64 s, Float64 t)
	Returns the arc tangent of s / t. More...
Float32	mi::math::ceil (Float32 s)
	Returns the smallest integral value that is not less than s. More...
Float64	mi::math::ceil (Float64 s)
	Returns the smallest integral value that is not less than s. More...
Uint8	mi::math::clamp (Uint8 s, Uint8 low, Uint8 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Uint16	mi::math::clamp (Uint16 s, Uint16 low, Uint16 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Uint32	mi::math::clamp (Uint32 s, Uint32 low, Uint32 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Uint64	mi::math::clamp (Uint64 s, Uint64 low, Uint64 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint8	mi::math::clamp (Sint8 s, Sint8 low, Sint8 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint16	mi::math::clamp (Sint16 s, Sint16 low, Sint16 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint32	mi::math::clamp (Sint32 s, Sint32 low, Sint32 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Sint64	mi::math::clamp (Sint64 s, Sint64 low, Sint64 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Float32	mi::math::clamp (Float32 s, Float32 low, Float32 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Float64	mi::math::clamp (Float64 s, Float64 low, Float64 high)
	Returns the value s if it is in the range [low, high], the value low if s < low, or the value high if s > high. More...
Float32	mi::math::cos (Float32 a)
	Returns the cosine of a. The angle a is specified in radians. More...
Float64	mi::math::cos (Float64 a)
	Returns the cosine of a. The angle a is specified in radians. More...
Float32	mi::math::degrees (Float32 r)
	Converts radians r to degrees. More...
Float64	mi::math::degrees (Float64 r)
	Converts radians r to degrees. More...
Float32	mi::math::exp2 (Float32 s)
	Returns the constant 2 to the power of s (exponential function). More...
Float64	mi::math::exp2 (Float64 s)
	Returns the constant 2 to the power of s (exponential function). More...
Float32	mi::math::floor (Float32 s)
	Returns the largest integral value that is not greater than s. More...
Float64	mi::math::floor (Float64 s)
	Returns the largest integral value that is not greater than s. More...
Float32	mi::math::fmod (Float32 a, Float32 b)
	Returns a modulo b, in other words, the remainder of a/b. More...
Float64	mi::math::fmod (Float64 a, Float64 b)
	Returns a modulo b, in other words, the remainder of a/b. More...
Float32	mi::math::frac (Float32 s)
	Returns the positive fractional part of s. More...
Float64	mi::math::frac (Float64 s)
	Returns the positive fractional part of s. More...
bool	mi::math::is_approx_equal (Float32 left, Float32 right, Float32 e)
	Compares the two given values for equality within the given epsilon. More...
bool	mi::math::is_approx_equal (Float64 left, Float64 right, Float64 e)
	Compares the two given values for equality within the given epsilon. More...
Float32	mi::math::log2 (Float32 s)
	Returns the base 2 logarithm of s. More...
Float64	mi::math::log2 (Float64 s)
	Returns the base 2 logarithm of s. More...
Float32	mi::math::log10 (Float32 s)
	Returns the base 10 logarithm of s. More...
Float64	mi::math::log10 (Float64 s)
	Returns the base 10 logarithm of s. More...
Float32	mi::math::lerp (Float32 s1, Float32 s2, Float32 t)
	Returns the linear interpolation between s1 and s2, i.e., it returns (1-t) * s1 + t * s2. More...
Float64	mi::math::lerp (Float64 s1, Float64 s2, Float64 t)
	Returns the linear interpolation between s1 and s2, i.e., it returns (1-t) * s1 + t * s2. More...
Float32	mi::math::modf (Float32 s, Float32 &i)
	Returns the fractional part of s and stores the integral part of s in i. More...
Float64	mi::math::modf (Float64 s, Float64 &i)
	Returns the fractional part of s and stores the integral part of s in i. More...
Uint32	mi::math::pow (Uint32 a, Uint32 b)
	Returns a to the power of b. More...
Uint64	mi::math::pow (Uint64 a, Uint64 b)
	Returns a to the power of b. More...
Sint32	mi::math::pow (Sint32 a, Sint32 b)
	Returns a to the power of b. More...
Sint64	mi::math::pow (Sint64 a, Sint64 b)
	Returns a to the power of b. More...
Float32	mi::math::pow (Float32 a, Float32 b)
	Returns a to the power of b. More...
Float64	mi::math::pow (Float64 a, Float64 b)
	Returns a to the power of b. More...
Float32	mi::math::radians (Float32 d)
	Converts degrees d to radians. More...
Float64	mi::math::radians (Float64 d)
	Converts degrees d to radians. More...
Float32	mi::math::round (Float32 s)
	Returns s rounded to the nearest integer value. More...
Float64	mi::math::round (Float64 s)
	Returns s rounded to the nearest integer value. More...
Float32	mi::math::rsqrt (Float32 s)
	Returns the reciprocal of the square root of s. More...
Float64	mi::math::rsqrt (Float64 s)
	Returns the reciprocal of the square root of s. More...
Float32	mi::math::saturate (Float32 s)
	Returns the value s clamped to the range [0,1]. More...
Float64	mi::math::saturate (Float64 s)
	Returns the value s clamped to the range [0,1]. More...
Sint8	mi::math::sign (Sint8 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Sint16	mi::math::sign (Sint16 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Sint32	mi::math::sign (Sint32 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Sint64	mi::math::sign (Sint64 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Float32	mi::math::sign (Float32 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
Float64	mi::math::sign (Float64 s)
	Returns -1 if s<0, 0 if s==0, and +1 if s>0. More...
bool	mi::math::sign_bit (Sint8 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Sint16 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Sint32 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Sint64 s)
	Returns true if s<0 and false if s>= 0. More...
bool	mi::math::sign_bit (Float32 s)
	Extracts the sign bit of a single-precision floating point number. More...
bool	mi::math::sign_bit (Float64 s)
	Extracts the sign bit of a double-precision floating point number. More...
bool	mi::math::isnan (const Float32 x)
	Checks a single-precision floating point number for "not a number". More...
bool	mi::math::isnan (const Float64 x)
	Checks a double-precision floating point number for "not a number". More...
bool	mi::math::isinfinite (const Float32 x)
	Checks a single-precision floating point number for "infinity". More...
bool	mi::math::isinfinite (const Float64 x)
	Checks a double-precision floating point number for "infinity". More...
bool	mi::math::isfinite (const Float32 x)
	Checks a single-precision floating point number for neither "not a number" nor "infinity". More...
bool	mi::math::isfinite (const Float64 x)
	Checks a double-precision floating point number for neither "not a number" nor "infinity". More...
Float32	mi::math::sin (Float32 a)
	Returns the sine of a. The angle a is specified in radians. More...
Float64	mi::math::sin (Float64 a)
	Returns the sine of a. The angle a is specified in radians. More...
void	mi::math::sincos (Float32 a, Float32 &s, Float32 &c)
	Computes the sine s and cosine c of angle a simultaneously. More...
void	mi::math::sincos (Float64 a, Float64 &s, Float64 &c)
	Computes the sine s and cosine c of angle a simultaneously. More...
Float32	mi::math::smoothstep (Float32 a, Float32 b, Float32 x)
	Returns 0 if x is less than a and 1 if x is greater than b. More...
Float64	mi::math::smoothstep (Float64 a, Float64 b, Float64 x)
	Returns 0 if x is less than a and 1 if x is greater than b. More...
Float32	mi::math::sqrt (Float32 s)
	Returns the square root of s. More...
Float64	mi::math::sqrt (Float64 s)
	Returns the square root of s. More...
Float32	mi::math::step (Float32 a, Float32 x)
	Returns 0 if x is less than a and 1 otherwise. More...
Float64	mi::math::step (Float64 a, Float64 x)
	Returns 0 if x is less than a and 1 otherwise. More...
Float32	mi::math::tan (Float32 a)
	Returns the tangent of a. The angle a is specified in radians. More...
Float64	mi::math::tan (Float64 a)
	Returns the tangent of a. The angle a is specified in radians. More...
void	mi::math::to_rgbe (const Float32 color[3], Uint32 &rgbe)
	Encodes a color into RGBE representation. More...
void	mi::math::to_rgbe (const Float32 color[3], Uint8 rgbe[4])
	Encodes a color into RGBE representation. More...
void	mi::math::from_rgbe (const Uint8 rgbe[4], Float32 color[3])
	Decodes a color from RGBE representation. More...
void	mi::math::from_rgbe (const Uint32 rgbe, Float32 color[3])
	Decodes a color from RGBE representation. More...
Sint32	mi::math::dot (Sint32 a, Sint32 b)
	Returns the inner product (a.k.a. dot or scalar product) of two integers. More...
Float32	mi::math::dot (Float32 a, Float32 b)
	Returns the inner product (a.k.a. dot or scalar product) of two scalars. More...
Float64	mi::math::dot (Float64 a, Float64 b)
	Returns the inner product (a.k.a. dot or scalar product) of two scalars. More...
template<class V >
V::value_type	mi::math::dot (const V &lhs, const V &rhs)
	Returns the inner product (a.k.a. dot or scalar product) of two vectors. More...
template<class V >
V::value_type	mi::math::square_length (const V &v)
	Returns the squared Euclidean norm of the vector v. More...
Float32	mi::math::length (Float32 a)
	Returns the Euclidean norm of the scalar a (its absolute value). More...
Float64	mi::math::length (Float64 a)
	Returns the Euclidean norm of the scalar a (its absolute value). More...
template<class V >
V::value_type	mi::math::length (const V &v)
	Returns the Euclidean norm of the vector v. More...
template<class V >
V::value_type	mi::math::square_euclidean_distance (const V &lhs, const V &rhs)
	Returns the squared Euclidean distance from the vector lhs to the vector rhs. More...
template<class V >
V::value_type	mi::math::euclidean_distance (const V &lhs, const V &rhs)
	Returns the Euclidean distance from the vector lhs to the vector rhs. More...
template<class V >
void	mi::math::set_bounds (V &v, const V &low, const V &high)
	Bounds the value of vector v elementwise to the given low and high vector values. More...
template<class V >
bool	mi::math::is_equal (const V &lhs, const V &rhs)
	Returns true if vector lhs is elementwise equal to vector rhs, and false otherwise. More...
template<class V >
Comparison_result	mi::math::lexicographically_compare (const V &lhs, const V &rhs)
	Compares two vectors lexicographically. More...
template<class V >
bool	mi::math::lexicographically_less (const V &lhs, const V &rhs)
	Returns true if vector lhs is lexicographically less than vector rhs, and false otherwise. More...

Detailed Description

Math functions and function templates on simple types or generic container and vector concepts.

See Math Functions.