vector.h File Reference

Math vector class template of fixed dimension with arithmetic operators and generic functions. More...

Go to the source code of this file.

Classes
struct	mi::math::Color_struct
	Generic storage class template for an RGBA color representation storing four floating points elements. More...
struct	mi::math::Vector_struct< T, DIM >
	Generic storage class template for math vector representations storing DIM elements of type T. More...
struct	mi::math::Vector_struct< T, 1 >
	Specialization for dimension 1 to create x member. More...
struct	mi::math::Vector_struct< T, 2 >
	Specialization for dimension 2 to create x and y member. More...
struct	mi::math::Vector_struct< T, 3 >
	Specialization for dimension 3 to create x, y, and z members. More...
struct	mi::math::Vector_struct< T, 4 >
	Specialization for dimension 4 to create x, y, z, and w members. More...
class	mi::math::Vector< T, DIM >
	Fixed-size math vector class template with generic operations. More...
class	mi::math::Vector< T, DIM >
	Fixed-size math vector class template with generic operations. More...

Namespaces
	mi
	Common namespace for APIs of NVIDIA Advanced Rendering Center GmbH.
	mi::math
	Namespace for the Math API.

Constant Groups
	mi
	Common namespace for APIs of NVIDIA Advanced Rendering Center GmbH.
	mi::math
	Namespace for the Math API.

Enumerations
enum	mi::math::From_iterator_tag { mi::math::FROM_ITERATOR }
	Enum used for initializing a vector from an iterator. More...

Functions
template<typename T , Size DIM>
T *	mi::math::vector_base_ptr (Vector_struct< T, DIM > &vec)
	Returns the base pointer to the vector data. More...
template<typename T , Size DIM>
const T *	mi::math::vector_base_ptr (const Vector_struct< T, DIM > &vec)
	Returns the base pointer to the vector data. More...
template<typename T >
T *	mi::math::vector_base_ptr (Vector_struct< T, 1 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==1. More...
template<typename T >
const T *	mi::math::vector_base_ptr (const Vector_struct< T, 1 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==1. More...
template<typename T >
T *	mi::math::vector_base_ptr (Vector_struct< T, 2 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==2. More...
template<typename T >
const T *	mi::math::vector_base_ptr (const Vector_struct< T, 2 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==2. More...
template<typename T >
T *	mi::math::vector_base_ptr (Vector_struct< T, 3 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==3. More...
template<typename T >
const T *	mi::math::vector_base_ptr (const Vector_struct< T, 3 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==3. More...
template<typename T >
T *	mi::math::vector_base_ptr (Vector_struct< T, 4 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==4. More...
template<typename T >
const T *	mi::math::vector_base_ptr (const Vector_struct< T, 4 > &vec)
	Returns the base pointer to the vector data, specialization for DIM==4. More...
template<typename T , Size DIM>
Vector< T, DIM > &	mi::math::operator+= (Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Adds rhs elementwise to lhs and returns the modified lhs. More...
template<typename T , Size DIM>
Vector< T, DIM > &	mi::math::operator-= (Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Subtracts rhs elementwise from lhs and returns the modified lhs. More...
template<typename T , Size DIM>
Vector< T, DIM > &	mi::math::operator*= (Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Multiplies rhs elementwise with lhs and returns the modified lhs. More...
template<typename T , Size DIM>
Vector< T, DIM > &	mi::math::operator%= (Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Computes lhs modulo rhs elementwise and returns the modified lhs. More...
template<typename T , typename U , Size DIM>
Vector< T, DIM > &	mi::math::operator/= (Vector< T, DIM > &lhs, const Vector< U, DIM > &rhs)
	Divides lhs elementwise by rhs and returns the modified lhs. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::operator+ (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Adds lhs and rhs elementwise and returns the new result. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::operator- (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Subtracts rhs elementwise from lhs and returns the new result. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::operator* (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Multiplies rhs elementwise with lhs and returns the new result. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::operator% (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Computes lhs modulo rhs elementwise and returns the new result. More...
template<typename T , typename U , Size DIM>
Vector< T, DIM >	mi::math::operator/ (const Vector< T, DIM > &lhs, const Vector< U, DIM > &rhs)
	Divides rhs elementwise by lhs and returns the new result. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::operator- (const Vector< T, DIM > &v)
	Negates the vector v elementwise and returns the new result. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM > &	mi::math::operator*= (Vector< T, DIM > &v, TT s)
	Multiplies the vector v elementwise with the scalar s and returns the modified vector v. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM > &	mi::math::operator%= (Vector< T, DIM > &v, TT s)
	Computes v modulo s elementwise and returns the modified vector v. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM > &	mi::math::operator/= (Vector< T, DIM > &v, TT s)
	Divides the vector v elementwise by the scalar s and returns the modified vector v. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM >	mi::math::operator* (const Vector< T, DIM > &v, TT s)
	Multiplies the vector v elementwise with the scalar s and returns the new result. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM >	mi::math::operator* (TT s, const Vector< T, DIM > &v)
	Multiplies the vector v elementwise with the scalar s and returns the new result. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM >	mi::math::operator% (const Vector< T, DIM > &v, TT s)
	Computes v modulo s elementwise and returns the new result. More...
template<typename T , typename TT , Size DIM>
Vector< T, DIM >	mi::math::operator/ (const Vector< T, DIM > &v, TT s)
	Divides the vector v elementwise by the scalar s and returns the new result. More...
template<typename T , Size DIM>
Vector< T, DIM > &	mi::math::operator++ (Vector< T, DIM > &vec)
	Pre-increments all elements of vec and returns the result. Modifies vec. More...
template<typename T , Size DIM>
Vector< T, DIM > &	mi::math::operator-- (Vector< T, DIM > &vec)
	Pre-decrements all elements of vec and returns the result. Modifies vec. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator&& (const Vector< bool, DIM > &lhs, const Vector< bool, DIM > &rhs)
	Returns the elementwise logical and of two boolean vectors. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator&& (bool lhs, const Vector< bool, DIM > &rhs)
	Returns the elementwise logical and of a bool and a boolean vector. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator&& (const Vector< bool, DIM > &lhs, bool rhs)
	Returns the elementwise logical and of a boolean vector and a bool. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator|| (const Vector< bool, DIM > &lhs, const Vector< bool, DIM > &rhs)
	Returns the elementwise logical or of two boolean vectors. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator|| (bool lhs, const Vector< bool, DIM > &rhs)
	Returns the elementwise logical or of a bool and a boolean vector. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator|| (const Vector< bool, DIM > &lhs, bool rhs)
	Returns the elementwise logical or of a boolean vector and a bool. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator^ (const Vector< bool, DIM > &lhs, const Vector< bool, DIM > &rhs)
	Returns the elementwise logical xor of two boolean vectors. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator^ (bool lhs, const Vector< bool, DIM > &rhs)
	Returns the elementwise logical xor of a bool and a boolean vector. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator^ (const Vector< bool, DIM > &lhs, bool rhs)
	Returns the elementwise logical xor of a boolean vector and a bool. More...
template<Size DIM>
Vector< bool, DIM >	mi::math::operator! (const Vector< bool, DIM > &vec)
	Returns the elementwise logical not of a boolean vector. More...
template<typename T , Size DIM>
Vector< bool, DIM >	mi::math::elementwise_is_equal (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns the boolean vector result of an elementwise equality comparison. More...
template<typename T , Size DIM>
Vector< bool, DIM >	mi::math::elementwise_is_not_equal (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns the boolean vector result of an elementwise inequality comparison. More...
template<typename T , Size DIM>
Vector< bool, DIM >	mi::math::elementwise_is_less_than (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns the boolean vector result of an elementwise less-than comparison. More...
template<typename T , Size DIM>
Vector< bool, DIM >	mi::math::elementwise_is_less_than_or_equal (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns the boolean vector result of an elementwise less-than-or-equal comparison. More...
template<typename T , Size DIM>
Vector< bool, DIM >	mi::math::elementwise_is_greater_than (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns the boolean vector result of an elementwise greater-than comparison. More...
template<typename T , Size DIM>
Vector< bool, DIM >	mi::math::elementwise_is_greater_than_or_equal (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns the boolean vector result of an elementwise greater-than-or-equal comparison. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::abs (const Vector< T, DIM > &v)
	Returns a vector with the elementwise absolute values of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::acos (const Vector< T, DIM > &v)
	Returns a vector with the elementwise arc cosine of the vector v. More...
template<typename T , Size DIM>
bool	mi::math::all (const Vector< T, DIM > &v)
	Returns true if all of all elements of v returns true. More...
template<typename T , Size DIM>
bool	mi::math::any (const Vector< T, DIM > &v)
	Returns true if any of any element of v returns true. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::asin (const Vector< T, DIM > &v)
	Returns a vector with the elementwise arc sine of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::atan (const Vector< T, DIM > &v)
	Returns a vector with the elementwise arc tangent of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::atan2 (const Vector< T, DIM > &v, const Vector< T, DIM > &w)
	Returns a vector with the elementwise arc tangent of the vector v / w. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::ceil (const Vector< T, DIM > &v)
	Returns a vector with the elementwise smallest integral value that is not less than the element in vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::clamp (const Vector< T, DIM > &v, const Vector< T, DIM > &low, const Vector< T, DIM > &high)
	Returns the vector v elementwise clamped to the range [low, high]. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::clamp (const Vector< T, DIM > &v, const Vector< T, DIM > &low, T high)
	Returns the vector v elementwise clamped to the range [low, high]. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::clamp (const Vector< T, DIM > &v, T low, const Vector< T, DIM > &high)
	Returns the vector v elementwise clamped to the range [low, high]. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::clamp (const Vector< T, DIM > &v, T low, T high)
	Returns the vector v elementwise clamped to the range [low, high]. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::cos (const Vector< T, DIM > &v)
	Returns a vector with the elementwise cosine of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::degrees (const Vector< T, DIM > &v)
	Converts elementwise radians in v to degrees. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::elementwise_max (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns elementwise maximum of two vectors. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::elementwise_min (const Vector< T, DIM > &lhs, const Vector< T, DIM > &rhs)
	Returns elementwise minimum of two vectors. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::exp (const Vector< T, DIM > &v)
	Returns a vector with elementwise e to the power of the element in the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::exp2 (const Vector< T, DIM > &v)
	Returns a vector with elementwise 2 to the power of the element in the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::floor (const Vector< T, DIM > &v)
	Returns a vector with the elementwise largest integral value that is not greater than the element in vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::fmod (const Vector< T, DIM > &a, const Vector< T, DIM > &b)
	Returns elementwise a modulo b, in other words, the remainder of a/b. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::fmod (const Vector< T, DIM > &a, T b)
	Returns elementwise a modulo b, in other words, the remainder of a/b. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::frac (const Vector< T, DIM > &v)
	Returns a vector with the elementwise positive fractional part of the vector v. More...
template<typename T , Size DIM>
bool	mi::math::is_approx_equal (const Vector< T, DIM > &left, const Vector< T, DIM > &right, T e)
	Compares the two given values elementwise for equality within the given epsilon. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::lerp (const Vector< T, DIM > &v1, const Vector< T, DIM > &v2, const Vector< T, DIM > &t)
	Returns the elementwise linear interpolation between v1 and v2, i.e., it returns (1-t) * v1 + t * v2. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::lerp (const Vector< T, DIM > &v1, const Vector< T, DIM > &v2, T t)
	Returns the linear interpolation between v1 and v2, i.e., it returns (1-t) * v1 + t * v2. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::log (const Vector< T, DIM > &v)
	Returns a vector with the elementwise natural logarithm of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::log2 (const Vector< T, DIM > &v)
	Returns a vector with the elementwise base 2 logarithm of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::log10 (const Vector< T, DIM > &v)
	Returns a vector with the elementwise base 10 logarithm of the vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::modf (const Vector< T, DIM > &v, Vector< T, DIM > &i)
	Returns the elementwise fractional part of v and stores the elementwise integral part of v in i. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::pow (const Vector< T, DIM > &a, const Vector< T, DIM > &b)
	Returns the vector a elementwise to the power of b. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::pow (const Vector< T, DIM > &a, T b)
	Returns the vector a elementwise to the power of b. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::radians (const Vector< T, DIM > &v)
	Converts elementwise degrees in v to radians. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::round (const Vector< T, DIM > &v)
	Returns a vector with the elements of vector v rounded to nearest integers. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::rsqrt (const Vector< T, DIM > &v)
	Returns the reciprocal of the square root of each element of v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::saturate (const Vector< T, DIM > &v)
	Returns the vector v clamped elementwise to the range [0,1]. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::sign (const Vector< T, DIM > &v)
	Returns the elementwise sign of vector v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::sin (const Vector< T, DIM > &v)
	Returns a vector with the elementwise sine of the vector v. More...
template<typename T , Size DIM>
void	mi::math::sincos (const Vector< T, DIM > &a, Vector< T, DIM > &s, Vector< T, DIM > &c)
	Computes elementwise the sine s and cosine c of angles a simultaneously. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::smoothstep (const Vector< T, DIM > &a, const Vector< T, DIM > &b, const Vector< T, DIM > &v)
	Returns 0 if v is less than a and 1 if v is greater than b in an elementwise fashion. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::smoothstep (const Vector< T, DIM > &a, const Vector< T, DIM > &b, T x)
	Returns 0 if x is less than a and 1 if x is greater than b in an elementwise fashion. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::sqrt (const Vector< T, DIM > &v)
	Returns the square root of each element of v. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::step (const Vector< T, DIM > &a, const Vector< T, DIM > &v)
	Returns elementwise 0 if v is less than a and 1 otherwise. More...
template<typename T , Size DIM>
Vector< T, DIM >	mi::math::tan (const Vector< T, DIM > &v)
	Returns a vector with the elementwise tangent of the vector v. More...
template<typename T >
T	mi::math::cross (const Vector< T, 2 > &lhs, const Vector< T, 2 > &rhs)
	Returns the two-times-two determinant result for the two vectors lhs and rhs. More...
template<typename T >
Vector< T, 3 >	mi::math::cross (const Vector< T, 3 > &lhs, const Vector< T, 3 > &rhs)
	Returns the three-dimensional cross product result for the two vectors lhs and rhs. More...
template<typename T >
void	mi::math::make_basis (const Vector< T, 3 > &n, Vector< T, 3 > *u, Vector< T, 3 > *v)
	Computes a basis of 3D space with one given vector. More...
template<typename T >
void	mi::math::make_basis (const Vector< T, 3 > &n, const Vector< T, 3 > &u, const Vector< T, 3 > &v, Vector< T, 3 > *t, Vector< T, 3 > *b)
	Computes a basis of 3D space with one given vector, plane, and direction. More...
template<typename T2 , Size DIM2, typename T1 , Size DIM1>
Vector< T2, DIM2 >	mi::math::convert_vector (const Vector< T1, DIM1 > &v, const T2 &fill=T2(0))
	Converts the vector v of type Vector<T1, DIM1> to a vector of type Vector<T2, DIM2>. More...

Detailed Description

Math vector class template of fixed dimension with arithmetic operators and generic functions.

See Math Vector Class.