vector.h File Reference

Description

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

Code Example

vector.h

‎/***************************************************************************************************
 * Copyright 2024 NVIDIA Corporation. All rights reserved.
 **************************************************************************************************/

#ifndef MI_MATH_VECTOR_H
#define MI_MATH_VECTOR_H

#include <mi/base/types.h>
#include <mi/math/assert.h>
#include <mi/math/function.h>

namespace mi {

namespace math {

enum From_iterator_tag {
    FROM_ITERATOR 
};


// Color and Vector can be converted into each other. To avoid cyclic dependencies among the
// headers, the Color_struct class is already defined here.

//------- POD struct that provides storage for color elements --------

struct Color_struct
{
    Float32 
               r;
    Float32 
               g;
    Float32 
               b;
    Float32 
               a;
};


//------- POD struct that provides storage for vector elements --------

template <typename T, Size DIM>
struct Vector_struct
{
    T elements[DIM]; 
};

template <typename T> struct Vector_struct<T, 1>
{
    T x;  
};

template <typename T> struct Vector_struct<T, 2>
{
    T x;  
    T y;  
};

template <typename T> struct Vector_struct<T, 3>
{
    T x;  
    T y;  
    T z;  
};

template <typename T> struct Vector_struct<T, 4>
{
    T x;  
    T y;  
    T z;  
    T w;  
};


//------ Indirect access to vector storage base ptr to keep Vector_struct a POD --

template <typename T, Size DIM>
inline T* vector_base_ptr( Vector_struct< T, DIM>& vec)
{
    return vec.elements;
}

template <typename T, Size DIM>
inline const T* vector_base_ptr( const Vector_struct< T, DIM>& vec)
{
    return vec.elements;
}

template <typename T>
inline T* vector_base_ptr( Vector_struct< T, 1>& vec)
{
    return &vec.x;
}

template <typename T>
inline const T* vector_base_ptr( const Vector_struct< T, 1>& vec)
{
    return &vec.x;
}

template <typename T>
inline T* vector_base_ptr( Vector_struct< T, 2>& vec)
{
    return &vec.x;
}

template <typename T>
inline const T* vector_base_ptr( const Vector_struct< T, 2>& vec)
{
    return &vec.x;
}

template <typename T>
inline T* vector_base_ptr( Vector_struct< T, 3>& vec)
{
    return &vec.x;
}

template <typename T>
inline const T* vector_base_ptr( const Vector_struct< T, 3>& vec)
{
    return &vec.x;
}

template <typename T>
inline T* vector_base_ptr( Vector_struct< T, 4>& vec)
{
    return &vec.x;
}

template <typename T>
inline const T* vector_base_ptr( const Vector_struct< T, 4>& vec)
{
    return &vec.x;
}

 // end group mi_math_vector_struct


//------ Generic Vector Class -------------------------------------------------

template < class T, Size DIM>
class Vector : public Vector_struct<T, DIM> //-V690 PVS
{
public:
    typedef Vector_struct< T, DIM> 
               Pod_type;      
    typedef Vector_struct< T, DIM> 
               storage_type;  

    typedef T           value_type;             
    typedef Size        
               size_type;              
    typedef Difference  
               difference_type;        
    typedef T *         pointer;                
    typedef const T *   const_pointer;          
    typedef T &         reference;              
    typedef const T &   const_reference;        

    static const Size 
               DIMENSION = DIM;          
    static const Size 
               SIZE      = DIM;          

    static inline Size 
               size()     { return SIZE; }

    static inline Size 
               max_size() { return SIZE; }

    inline T* begin() { return mi::math::vector_base_ptr( *this); }

    inline const T* begin() const { return mi::math::vector_base_ptr( *this); }

    inline T* end() { return begin() + DIM; }

    inline const T* end() const { return begin() + DIM; }

    inline Vector()
    {
#ifndef NDEBUG
        // In debug mode, default-constructed vectors are initialized with signaling NaNs or, if not
        // applicable, with a maximum value to increase the chances of diagnosing incorrect use of
        // an uninitialized vector.
        typedef mi::base::numeric_traits< T> Traits;
        T v = (Traits::has_signaling_NaN) ? Traits::signaling_NaN()
                                          : Traits::max MI_PREVENT_MACRO_EXPAND ();
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = v;
#endif
    }

#if (__cplusplus >= 201103L)
    Vector( const Vector<T,DIM>& vec ) = default;
#endif

    inline Vector( const Vector_struct< T, DIM>& vec )
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = mi::math::vector_base_ptr(vec)[i];
    }

    inline explicit Vector(T v)
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = v;
    }

    template <typename Iterator>
    inline Vector(From_iterator_tag, Iterator p)
    {
        for( Size i(0u); i < DIM; ++i, ++p)
            (*this)[i] = *p;
    }

    template <typename T2>
    inline explicit Vector( T2 const (& array)[DIM])
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = array[i];
    }

    template <typename T2>
    inline explicit Vector( const Vector< T2, DIM>& other)
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = T(other[i]);
    }

    template <typename T2>
    inline explicit Vector( const Vector_struct< T2, DIM>& other)
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = T(mi::math::vector_base_ptr(other)[i]);
    }

    inline Vector(T v1, T v2)
    {
        mi_static_assert(DIM == 2);
        begin()[0] = v1;
        begin()[1] = v2;
    }

    inline Vector(T v1, T v2, T v3)
    {
        mi_static_assert(DIM == 3);
        begin()[0] = v1;
        begin()[1] = v2;
        begin()[2] = v3;
    }

    inline Vector(T v1, const Vector< T, 2>& v2)
    {
        mi_static_assert(DIM == 3);
        begin()[0] = v1;
        begin()[1] = v2.x;
        begin()[2] = v2.y;
    }

    inline Vector(const Vector< T, 2>& v1, T v2)
    {
        mi_static_assert(DIM == 3);
        begin()[0] = v1.x;
        begin()[1] = v1.y;
        begin()[2] = v2;
    }

    inline Vector(T v1, T v2, T v3, T v4)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1;
        begin()[1] = v2;
        begin()[2] = v3;
        begin()[3] = v4;
    }

    inline Vector(T v1, T v2, const Vector< T, 2>& v3)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1;
        begin()[1] = v2;
        begin()[2] = v3.x;
        begin()[3] = v3.y;
    }


    inline Vector(T v1, const Vector< T, 2>& v2, T v3)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1;
        begin()[1] = v2.x;
        begin()[2] = v2.y;
        begin()[3] = v3;
    }

    inline Vector(const Vector< T, 2>& v1, T v2, T v3)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1.x;
        begin()[1] = v1.y;
        begin()[2] = v2;
        begin()[3] = v3;
    }

    inline Vector(const Vector< T, 2>& v1, const Vector< T, 2>& v2)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1.x;
        begin()[1] = v1.y;
        begin()[2] = v2.x;
        begin()[3] = v2.y;
    }

    inline Vector(T v1, const Vector< T, 3>& v2)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1;
        begin()[1] = v2.x;
        begin()[2] = v2.y;
        begin()[3] = v2.z;
    }

    inline Vector(const Vector< T, 3>& v1, T v2)
    {
        mi_static_assert(DIM == 4);
        begin()[0] = v1.x;
        begin()[1] = v1.y;
        begin()[2] = v1.z;
        begin()[3] = v2;
    }

    inline explicit Vector( const Color_struct& color)
    {
        mi_static_assert(DIM == 4);
        this->x = color.r;
        this->y = color.g;
        this->z = color.b;
        this->w = color.a;
    }

#if (__cplusplus >= 201103L)
    Vector& operator=( const Vector& other) = default;
#else
    inline Vector& operator=( const Vector& other)
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = other[i];
        return *this;
    }
#endif

    inline Vector& operator=( T s)
    {
        for( Size i(0u); i < DIM; ++i)
            (*this)[i] = s;
        return *this;
    }
    inline Vector& operator=( const Color_struct& color)
    {
        mi_static_assert(DIM == 4);
        this->x = color.r;
        this->y = color.g;
        this->z = color.b;
        this->w = color.a;
        return *this;
    }

    inline T& operator[](Size i)
    {
        mi_math_assert_msg(i < DIM, "precondition");
        return begin()[i];
    }

    inline const T& operator[](Size i) const
    {
        mi_math_assert_msg(i < DIM, "precondition");
        return begin()[i];
    }

    inline const T& get(Size i) const
    {
        mi_math_assert_msg(i < DIM, "precondition");
        return begin()[i];
    }

    inline void set(Size i, T value)
    {
        mi_math_assert_msg(i < DIM, "precondition");
        begin()[i] = value;
    }



    inline bool normalize()
    {
        const T rec_length = T(1) / length( *this);
        const bool result = isfinite( rec_length); //-V601 PVS
        if( result)
            (*this) *= rec_length;
        return result;
    }


    //------ Free comparison operators ==, !=, <, <=, >, >= for vectors --------

    inline bool operator==( Vector< T, DIM> rhs) const
    {
        return is_equal( *this, rhs);
    }

    inline bool operator!=( Vector< T, DIM> rhs) const
    {
        return is_not_equal( *this, rhs);
    }

    inline bool operator<( Vector<T,DIM> rhs) const
    {
        return lexicographically_less( *this, rhs);
    }

    inline bool operator<=( Vector<T,DIM> rhs) const
    {
        return lexicographically_less_or_equal( *this, rhs);
    }

    inline bool operator>( Vector< T, DIM> rhs) const
    {
        return lexicographically_greater( *this, rhs);
    }

    inline bool operator>=( Vector< T, DIM> rhs) const
    {
        return lexicographically_greater_or_equal( *this, rhs);
    }
};


//------ Free operators +=, -=, *=, /=, +, -, *, and / for vectors -------------

template <typename T, Size DIM>
inline Vector< T, DIM>& operator+=(
    Vector< T, DIM>&       lhs,
    const Vector_struct< T, DIM>& rhs)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(lhs)[i] += vector_base_ptr(rhs)[i];
    return lhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator-=(
    Vector< T, DIM>&       lhs,
    const Vector_struct< T, DIM>& rhs)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(lhs)[i] -= vector_base_ptr(rhs)[i];
    return lhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator*=(
    Vector< T, DIM>&       lhs,
    const Vector_struct< T, DIM>& rhs)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(lhs)[i] *= vector_base_ptr(rhs)[i];
    return lhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator%=(
    Vector< T, DIM>&       lhs,
    const Vector_struct< T, DIM>& rhs)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(lhs)[i] %= vector_base_ptr(rhs)[i];
    return lhs;
}

template <typename T, typename U, Size DIM>
inline Vector< T, DIM>& operator/=(
    Vector< T, DIM>&       lhs,
    const Vector_struct< U, DIM>& rhs)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(lhs)[i] = T(vector_base_ptr(lhs)[i] / vector_base_ptr(rhs)[i]);
    return lhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator+(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< T, DIM>& rhs)
{
    Vector< T, DIM> tmp( lhs);
    return tmp += rhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator-(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< T, DIM>& rhs)
{
    Vector< T, DIM> tmp( lhs);
    return tmp -= rhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator*(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< T, DIM>& rhs)
{
    Vector< T, DIM> tmp( lhs);
    return tmp *= rhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator%(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< T, DIM>& rhs)
{
    Vector< T, DIM> tmp( lhs);
    return tmp %= rhs;
}

template <typename T, typename U, Size DIM>
inline Vector< T, DIM> 
               operator/(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< U, DIM>& rhs)
{
    Vector< T, DIM> tmp(lhs);
    return tmp /= rhs;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator-( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> tmp;
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(tmp)[i] = -vector_base_ptr(v)[i];
    return tmp;
}


//------ Resolve ambiguity with hybrid operators -------------
// (Those operators should really be restricted to scalar types but that requires
// modern C++ which some users of this headers don't enable.)

template <typename T, Size DIM>
inline Vector< T, DIM>& operator+=(
    Vector< T, DIM>&       lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs += static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator-=(
    Vector< T, DIM>&       lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs -= static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator*=(
    Vector< T, DIM>&       lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs *= static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator%=(
    Vector< T, DIM>&       lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs %= static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, typename U, Size DIM>
inline Vector< T, DIM>& operator/=(
    Vector< T, DIM>&       lhs,
    const Vector< U, DIM>& rhs)
{
    return lhs /= static_cast<const Vector_struct< U, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator+(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs + static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator-(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs - static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator*(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs * static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator%(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    return lhs % static_cast<const Vector_struct< T, DIM>&>(rhs);
}

template <typename T, typename U, Size DIM>
inline Vector< T, DIM> 
               operator/(
    const Vector< T, DIM>& lhs,
    const Vector< U, DIM>& rhs)
{
    return lhs / static_cast<const Vector_struct< U, DIM>&>(rhs);
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               operator-( const Vector< T, DIM>& v)
{
    return -static_cast<const Vector_struct< T, DIM>&>(v);
}


//------ Free operator *=, /=, *, and / definitions for scalars ---------------

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM>& operator*=(
    Vector< T, DIM>& v,
    TT             s)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(v)[i] = T(vector_base_ptr(v)[i] * s);
    return v;
}

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM>& operator%=(
    Vector< T, DIM>& v,
    TT             s)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(v)[i] = T(vector_base_ptr(v)[i] % s);
    return v;
}

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM>& operator/=(
    Vector< T, DIM>&  v,
    TT              s)
{
    for( Size i(0u); i < DIM; ++i)
        vector_base_ptr(v)[i] = T(vector_base_ptr(v)[i] / s);
    return v;
}

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM> 
               operator*(
    const Vector_struct< T, DIM>& v,
    TT                   s)
{
    Vector< T, DIM> tmp( v);
    return tmp *= s;
}

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM> 
               operator*(
    TT                   s,
    const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> tmp(v);
    return tmp *= s;
}

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM> 
               operator%(
    const Vector_struct< T, DIM>& v,
    TT                   s)
{
    Vector< T, DIM> tmp(v);
    return tmp %= s;
}

template <typename T, typename TT, Size DIM>
inline Vector< T, DIM> 
               operator/(
    const Vector_struct< T, DIM>& v,
    TT                   s)
{
    Vector< T, DIM> tmp( v);
    return tmp /= s;
}


//------ Free operator ++, -- for vectors -------------------------------------

template <typename T, Size DIM>
inline Vector< T, DIM>& operator++( Vector< T, DIM>& vec)
{
    general::for_each( vec, functor::Operator_pre_incr());
    return vec;
}

template <typename T, Size DIM>
inline Vector< T, DIM>& operator--( Vector< T, DIM>& vec)
{
    general::for_each( vec, functor::Operator_pre_decr());
    return vec;
}


//------ Free operators !, &&, ||, ^ for bool vectors and bool scalars ---------

template <Size DIM>
inline Vector< bool, DIM> 
               operator&&(
    const Vector< bool, DIM>& lhs,
    const Vector< bool, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result, functor::Operator_and_and());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator&&(
    bool                    lhs,
    const Vector< bool, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform_left_scalar( lhs, rhs, result, functor::Operator_and_and());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator&&(
    const Vector< bool, DIM>& lhs,
    bool                    rhs)
{
    Vector< bool, DIM> result;
    general::transform_right_scalar( lhs, rhs, result, functor::Operator_and_and());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator||(
    const Vector< bool, DIM>& lhs,
    const Vector< bool, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform(lhs, rhs, result, functor::Operator_or_or());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator||(
    bool                    lhs,
    const Vector< bool, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform_left_scalar( lhs, rhs, result, functor::Operator_or_or());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator||(
    const Vector< bool, DIM>& lhs,
    bool                     rhs)
{
    Vector< bool, DIM> result;
    general::transform_right_scalar( lhs, rhs, result, functor::Operator_or_or());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator^(
    const Vector< bool, DIM>& lhs,
    const Vector< bool, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result, functor::Operator_xor());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator^(
    bool                    lhs,
    const Vector< bool, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform_left_scalar( lhs, rhs, result, functor::Operator_xor());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator^(
    const Vector< bool, DIM>& lhs,
    bool                    rhs)
{
    Vector< bool, DIM> result;
    general::transform_right_scalar( lhs, rhs, result, functor::Operator_xor());
    return result;
}

template <Size DIM>
inline Vector< bool, DIM> 
               operator!(
    const Vector< bool, DIM>& vec)
{
    Vector< bool, DIM> result;
    general::transform( vec, result, functor::Operator_not());
    return result;
}


//------ Elementwise comparison operators returning a bool vector. ------------

template <typename T, Size DIM>
inline Vector< bool, DIM> 
               elementwise_is_equal(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result,functor::Operator_equal_equal());
    return result;
}

template <typename T, Size DIM>
inline Vector< bool, DIM> 
               elementwise_is_not_equal(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result,functor::Operator_not_equal());
    return result;
}

template <typename T, Size DIM>
inline Vector< bool, DIM> 
               elementwise_is_less_than(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result,functor::Operator_less());
    return result;
}

template <typename T, Size DIM>
inline Vector< bool, DIM> 
               elementwise_is_less_than_or_equal(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result,functor::Operator_less_equal());
    return result;
}

template <typename T, Size DIM>
inline Vector< bool, DIM> 
               elementwise_is_greater_than(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result,functor::Operator_greater());
    return result;
}

template <typename T, Size DIM>
inline Vector< bool, DIM> 
               elementwise_is_greater_than_or_equal(
    const Vector< T, DIM>& lhs,
    const Vector< T, DIM>& rhs)
{
    Vector< bool, DIM> result;
    general::transform( lhs, rhs, result,functor::Operator_greater_equal());
    return result;
}


//------ Function Overloads for Vector Algorithms -----------------------------

template <typename T, Size DIM>
inline Vector< T, DIM> 
               abs( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = abs( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               acos( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = acos( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline bool all( const Vector_struct< T, DIM>& v)
{
    for( Size i = 0; i != DIM; ++i)
        if( !all(vector_base_ptr(v)[i]))
            return false;
    return true;
}

template <typename T, Size DIM>
inline bool any( const Vector_struct< T, DIM>& v)
{
    for( Size i = 0; i != DIM; ++i)
        if( any(vector_base_ptr(v)[i]))
           return true;
    return false;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               asin( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = asin( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               atan( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = atan( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               atan2( const Vector_struct< T, DIM>& v,  const Vector_struct< T, DIM>& w)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = atan2( vector_base_ptr(v)[i], vector_base_ptr(w)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               ceil( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = ceil( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               clamp(
    const Vector_struct< T, DIM>&  v,
    const Vector_struct< T, DIM>&  low,
    const Vector_struct< T, DIM>&  high)
{
    Vector< T, DIM> result;
    for( Size i = 0u; i < DIM; ++i)
        result[i] = clamp(
            vector_base_ptr(v)[i], vector_base_ptr(low)[i], vector_base_ptr(high)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               clamp(
    const Vector_struct< T, DIM>& v,
    const Vector_struct< T, DIM>& low,
    T                    high)
{
    Vector< T, DIM> result;
    for( Size i = 0u; i < DIM; ++i)
        result[i] = clamp( vector_base_ptr(v)[i], vector_base_ptr(low)[i], high);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               clamp(
    const Vector_struct< T, DIM>& v,
    T                    low,
    const Vector_struct< T, DIM>& high)
{
    Vector< T, DIM> result;
    for( Size i = 0u; i < DIM; ++i)
        result[i] = clamp( vector_base_ptr(v)[i], low, vector_base_ptr(high)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               clamp(
    const Vector_struct< T, DIM>& v,
    T                    low,
    T                    high)
{
    Vector< T, DIM> result;
    for( Size i = 0u; i < DIM; ++i)
        result[i] = clamp( vector_base_ptr(v)[i], low, high);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               cos( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = cos( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               degrees( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = degrees( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               elementwise_max(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< T, DIM>& rhs)
{
    Vector< T, DIM> r;
    for( Size i(0u); i < Vector<T,DIM>::DIMENSION; ++i)
        vector_base_ptr(r)[i] = base::max MI_PREVENT_MACRO_EXPAND (
            vector_base_ptr(lhs)[i], vector_base_ptr(rhs)[i] );
    return r;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               elementwise_min(
    const Vector_struct< T, DIM>& lhs,
    const Vector_struct< T, DIM>& rhs)
{
    Vector< T, DIM> r;
    for( Size i(0u); i < Vector<T,DIM>::DIMENSION; ++i)
        vector_base_ptr(r)[i] = base::min MI_PREVENT_MACRO_EXPAND (
            vector_base_ptr(lhs)[i], vector_base_ptr(rhs)[i] );
    return r;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               exp( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = exp( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               exp2( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = exp2( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               floor( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = floor( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               fmod( const Vector_struct< T, DIM>& a, const Vector_struct< T, DIM>& b)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = fmod( vector_base_ptr(a)[i], vector_base_ptr(b)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               fmod( const Vector_struct< T, DIM>& a, T b)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = fmod( vector_base_ptr(a)[i], b);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               frac( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = frac( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline bool is_approx_equal(
    const Vector_struct< T, DIM>& left,
    const Vector_struct< T, DIM>& right,
    T                    e)
{
    for( Size i = 0u; i < DIM; ++i)
        if( !is_approx_equal( vector_base_ptr(left)[i], vector_base_ptr(right)[i], e))
            return false;
    return true;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               lerp(
    const Vector_struct< T, DIM>& v1,  
    const Vector_struct< T, DIM>& v2,  
    const Vector_struct< T, DIM>& t)   
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = vector_base_ptr(v1)[i] * (T(1)-vector_base_ptr(t)[i])
                  + vector_base_ptr(v2)[i] * vector_base_ptr(t)[i];
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               lerp(
    const Vector_struct< T, DIM>& v1,  
    const Vector_struct< T, DIM>& v2,  
    T          t)             
{
    // equivalent to: return v1 * (T(1)-t) + v2 * t;
    Vector< T, DIM> result;
    T t2 = T(1) - t;
    for( Size i = 0; i != DIM; ++i)
        result[i] = vector_base_ptr(v1)[i] * t2 + vector_base_ptr(v2)[i] * t;
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               log( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = log( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               log2 
               MI_PREVENT_MACRO_EXPAND ( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = log2 
               MI_PREVENT_MACRO_EXPAND ( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               log10( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = log10( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               modf( const Vector_struct< T, DIM>& v, Vector< T, DIM>& i)
{
    Vector< T, DIM> result;
    for( Size j = 0; j != DIM; ++j)
        result[j] = modf( vector_base_ptr(v)[j], vector_base_ptr(i)[j]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               pow( const Vector_struct< T, DIM>& a, const Vector_struct< T, DIM>& b)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = pow( vector_base_ptr(a)[i], vector_base_ptr(b)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               pow( const Vector_struct< T, DIM>& a, T b)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = pow( vector_base_ptr(a)[i], b);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               radians( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = radians( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               round( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = round( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               rsqrt( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = rsqrt( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               saturate( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = saturate( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               sign( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = sign( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               sin( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = sin( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline void sincos( const Vector_struct< T, DIM>& a, Vector< T, DIM>& s, Vector< T, DIM>& c)
{
    for( Size i = 0; i != DIM; ++i)
        sincos( vector_base_ptr(a)[i], vector_base_ptr(s)[i], vector_base_ptr(c)[i]);
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               smoothstep(
    const Vector_struct< T, DIM>& a,
    const Vector_struct< T, DIM>& b,
    const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = smoothstep(
            vector_base_ptr(a)[i], vector_base_ptr(b)[i], vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               smoothstep(
    const Vector_struct< T, DIM>& a,
    const Vector_struct< T, DIM>& b,
    T x)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = smoothstep( vector_base_ptr(a)[i], vector_base_ptr(b)[i], x);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               sqrt( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = sqrt( vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               step( const Vector_struct< T, DIM>& a, const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = step( vector_base_ptr(a)[i], vector_base_ptr(v)[i]);
    return result;
}

template <typename T, Size DIM>
inline Vector< T, DIM> 
               tan( const Vector_struct< T, DIM>& v)
{
    Vector< T, DIM> result;
    for( Size i = 0; i != DIM; ++i)
        result[i] = tan( vector_base_ptr(v)[i]);
    return result;
}


//------ Geometric Vector Algorithms ------------------------------------------

template <typename T>
inline T cross(
    const Vector_struct< T, 2>& lhs,
    const Vector_struct< T, 2>& rhs)
{
    return lhs.x * rhs.y - lhs.y * rhs.x;
}

template <typename T>
inline Vector< T, 3> 
               cross(
    const Vector_struct< T, 3>& lhs,
    const Vector_struct< T, 3>& rhs)
{
    return Vector< T, 3>( lhs.y * rhs.z - lhs.z * rhs.y,
                        lhs.z * rhs.x - lhs.x * rhs.z,
                        lhs.x * rhs.y - lhs.y * rhs.x);
}

template <typename T>
inline void make_basis(
    const Vector< T, 3>& n,  
    Vector< T, 3>*       u,  
    Vector< T, 3>*       v)  
{
#ifdef mi_base_assert_enabled
    const T eps    = 1e-6f;       // smallest resolvable factor
#endif

    mi_math_assert_msg( u != 0, "precondition");
    mi_math_assert_msg( v != 0, "precondition");
    // Sanity check: the normal vector must be unit length.
    mi_math_assert_msg( abs( length(n) - 1.0f) < eps, "precondition");

    // Compute u.
    if( abs(n.x) < abs(n.y)) {
        // u = cross(x, n), x = (1, 0, 0)
        u->x = T(0);
        u->y = -n.z;
        u->z =  n.y;
    } else {
        // u = cross(y, n), y = (0, 1, 0)
        u->x =  n.z;
        u->y = T(0);
        u->z = -n.x;
    }
    u->normalize();

    // Compute v. Since *u and n are orthogonal and unit-length,
    // there is no need to normalize *v.
    *v = cross( *u, n);

    // Sanity check: make sure (u, n, v) is an orthogonal basis.
    mi_math_assert_msg( abs( dot( *u,  n)) < eps, "postcondition");
    mi_math_assert_msg( abs( dot( *u, *v)) < eps, "postcondition");
    mi_math_assert_msg( abs( dot(  n, *v)) < eps, "postcondition");
    // Sanity check: make sure u and v are unit length.
    mi_math_assert_msg( abs( length( *u) - T(1)) < eps, "postcondition");
    mi_math_assert_msg( abs( length( *v) - T(1)) < eps, "postcondition");
}

template <typename T>
inline void 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)     
{
    const T eps    = 1e-6f;       // smallest resolvable factor
    (void)eps;

    mi_math_assert_msg( t != 0, "precondition");
    mi_math_assert_msg( b != 0, "precondition");
    // Sanity check: the normal vector must be unit length.
    mi_math_assert_msg( abs( length( n) - 1.0f) < eps, "precondition");
    // Sanity check: the other vector lengths should be finite and non-zero
    mi_math_assert_msg( length( u) > 0., "precondition");
    mi_math_assert_msg( length( v) > 0., "precondition");
    mi_math_assert_msg( isfinite( length( u)), "precondition");
    mi_math_assert_msg( isfinite( length( v)), "precondition");

    // Compute b
    *b = cross(u,n);
    b->normalize();

    // Compute t. Since *b and n are orthogonal and unit-length,
    // there is no need to normalize *t.
    *t = cross(n,*b);

    // Check that b has the same orientation of v
    if( dot( *b,v) < T(0))
        *b = -*b;

    // Sanity check: make sure *u and t have the same orientation.
    mi_math_assert_msg( dot( u, *t) > T(0), "postcondition");
    // Sanity check: make sure (t, n, b) is an orthogonal basis.
    // We use a scaled epsilon in order to avoid false positives.
    mi_math_assert_msg( abs( dot( *t,  n)) < 20*eps, "postcondition");
    mi_math_assert_msg( abs( dot( *t, *b)) < 20*eps, "postcondition");
    mi_math_assert_msg( abs( dot(  n, *b)) < 20*eps, "postcondition");
    // Sanity check: make sure t and b are unit length.
    mi_math_assert_msg( abs( length( *t) - T(1)) < eps, "postcondition");
    mi_math_assert_msg( abs( length( *b) - T(1)) < eps, "postcondition");
}

template <typename T2, Size DIM2, typename T1, Size DIM1>
inline Vector< T2,  DIM2> 
               convert_vector(
    const Vector< T1,  DIM1>& v,
    const T2& fill = T2(0))
{
    const Size dim_min = base::min MI_PREVENT_MACRO_EXPAND ( DIM1, DIM2 );
    Vector< T2,  DIM2> result;
    for( Size i = 0; i < dim_min; ++i)
        result[i] = T2(v[i]);
    for( Size i = dim_min; i < DIM2; ++i)
        result[i] = fill;
    return result;
}
 // end group mi_math_vector

} // namespace math

} // namespace mi

#endif // MI_MATH_VECTOR_H

Namespaces

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

Classes

struct mi::math::Color_struct: Generic storage class template for an RGBA color representation storing four floating points elements. More...
class mi::math::Vector< T, DIM>: Fixed-size math vector class template with generic operations. 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...
struct mi::math::Vector_struct< T, DIM>: Generic storage class template for math vector representations storing DIM elements of type T. More...

Enumerations

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

Functions

template< typename T, Size> Vector < T , DIM > mi::math::abs ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise absolute values of the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::acos ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise arc cosine of the vector v. More...
template< typename T, Size>bool mi::math::all ( const Vector_struct < T , DIM >& v): Returns true if all of all elements of v returns true. More...
template< typename T, Size>bool mi::math::any ( const Vector_struct < T , DIM >& v): Returns true if any of any element of v returns true. More...
template< typename T, Size> Vector < T , DIM > mi::math::asin ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise arc sine of the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::atan ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise arc tangent of the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::atan2 ( const Vector_struct < T , DIM >& v, const Vector_struct < T , DIM >& w): Returns a vector with the elementwise arc tangent of the vector v / w. More...
template< typename T, Size> Vector < T , DIM > mi::math::ceil ( const Vector_struct < 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> Vector < T , DIM > mi::math::clamp ( const Vector_struct < T , DIM >& v, const Vector_struct < T , DIM >& low, const Vector_struct < T , DIM >& high): Returns the vector v elementwise clamped to the range [low, high]. More...
template< typename T, Size> Vector < T , DIM > mi::math::clamp ( const Vector_struct < T , DIM >& v, const Vector_struct < T , DIM >& low, T high): Returns the vector v elementwise clamped to the range [low, high]. More...
template< typename T, Size> Vector < T , DIM > mi::math::clamp ( const Vector_struct < T , DIM >& v, T low, const Vector_struct < T , DIM >& high): Returns the vector v elementwise clamped to the range [low, high]. More...
template< typename T, Size> Vector < T , DIM > mi::math::clamp ( const Vector_struct < T , DIM >& v, T low, T high): Returns the vector v elementwise clamped to the range [low, high]. More...
template< typename T2, Size, typename T1, Size> 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...
template< typename T, Size> Vector < T , DIM > mi::math::cos ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise cosine of the vector v. More...
template< typename T>T mi::math::cross ( const Vector_struct < T , 2 >& lhs, const Vector_struct < 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_struct < T , 3 >& lhs, const Vector_struct < T , 3 >& rhs): Returns the three-dimensional cross product result for the two vectors lhs and rhs. More...
template< typename T, Size> Vector < T , DIM > mi::math::degrees ( const Vector_struct < T , DIM >& v): Converts elementwise radians in v to degrees. More...
template< typename T, Size> 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> 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> 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> 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> 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> 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> Vector < T , DIM > mi::math::elementwise_max ( const Vector_struct < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Returns elementwise maximum of two vectors. More...
template< typename T, Size> Vector < T , DIM > mi::math::elementwise_min ( const Vector_struct < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Returns elementwise minimum of two vectors. More...
template< typename T, Size> Vector < T , DIM > mi::math::exp ( const Vector_struct < T , DIM >& v): Returns a vector with elementwise e to the power of the element in the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::exp2 ( const Vector_struct < T , DIM >& v): Returns a vector with elementwise 2 to the power of the element in the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::floor ( const Vector_struct < 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> Vector < T , DIM > mi::math::fmod ( const Vector_struct < T , DIM >& a, const Vector_struct < T , DIM >& b): Returns elementwise a modulo b, in other words, the remainder of a/b. More...
template< typename T, Size> Vector < T , DIM > mi::math::fmod ( const Vector_struct < T , DIM >& a, T b): Returns elementwise a modulo b, in other words, the remainder of a/b. More...
template< typename T, Size> Vector < T , DIM > mi::math::frac ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise positive fractional part of the vector v. More...
template< typename T, Size>bool mi::math::is_approx_equal ( const Vector_struct < T , DIM >& left, const Vector_struct < T , DIM >& right, T e): Compares the two given values elementwise for equality within the given epsilon. More...
template< typename T, Size> Vector < T , DIM > mi::math::lerp ( const Vector_struct < T , DIM >& v1, const Vector_struct < T , DIM >& v2, const Vector_struct < 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> Vector < T , DIM > mi::math::lerp ( const Vector_struct < T , DIM >& v1, const Vector_struct < 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> Vector < T , DIM > mi::math::log ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise natural logarithm of the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::log10 ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise base 10 logarithm of the vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::log2 ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise base 2 logarithm of the vector v. 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 T, Size> Vector < T , DIM > mi::math::modf ( const Vector_struct < 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< Size> 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> Vector < T , DIM > mi::math::operator% ( const Vector_struct < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Computes lhs modulo rhs elementwise and returns the new result. More...
template< typename T, Size> 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 TT, Size> Vector < T , DIM > mi::math::operator% ( const Vector_struct < T , DIM >& v, TT s): Computes v modulo s elementwise and returns the new result. More...
template< typename T, Size> Vector < T , DIM >& mi::math::operator%= ( Vector < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Computes lhs modulo rhs elementwise and returns the modified lhs. More...
template< typename T, Size> 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 TT, Size> 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< Size> 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> 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> 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< typename T, Size> Vector < T , DIM > mi::math::operator* ( const Vector_struct < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Multiplies rhs elementwise with lhs and returns the new result. More...
template< typename T, Size> 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, typename TT, Size> Vector < T , DIM > mi::math::operator* ( const Vector_struct < 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> Vector < T , DIM > mi::math::operator* ( TT s, const Vector_struct < T , DIM >& v): Multiplies the vector v elementwise with the scalar s and returns the new result. More...
template< typename T, Size> Vector < T , DIM >& mi::math::operator*= ( Vector < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Multiplies rhs elementwise with lhs and returns the modified lhs. More...
template< typename T, Size> 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, typename TT, Size> 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, Size> Vector < T , DIM > mi::math::operator+ ( const Vector_struct < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Adds lhs and rhs elementwise and returns the new result. More...
template< typename T, Size> 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> 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> Vector < T , DIM >& mi::math::operator+= ( Vector < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Adds rhs elementwise to lhs and returns the modified lhs. More...
template< typename T, Size> 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> Vector < T , DIM > mi::math::operator- ( const Vector_struct < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Subtracts rhs elementwise from lhs and returns the new result. More...
template< typename T, Size> Vector < T , DIM > mi::math::operator- ( const Vector_struct < T , DIM >& v): Negates the vector v elementwise and returns the new result. More...
template< typename T, Size> 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> 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, Size> Vector < T , DIM >& mi::math::operator-- ( Vector < T , DIM >& vec): Pre-decrements all elements of vec and returns the result. Modifies vec. More...
template< typename T, Size> Vector < T , DIM >& mi::math::operator-= ( Vector < T , DIM >& lhs, const Vector_struct < T , DIM >& rhs): Subtracts rhs elementwise from lhs and returns the modified lhs. More...
template< typename T, Size> 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, typename U, Size> Vector < T , DIM > mi::math::operator/ ( const Vector_struct < T , DIM >& lhs, const Vector_struct < U , DIM >& rhs): Divides rhs elementwise by lhs and returns the new result. More...
template< typename T, typename U, Size> 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, typename TT, Size> Vector < T , DIM > mi::math::operator/ ( const Vector_struct < T , DIM >& v, TT s): Divides the vector v elementwise by the scalar s and returns the new result. More...
template< typename T, typename U, Size> Vector < T , DIM >& mi::math::operator/= ( Vector < T , DIM >& lhs, const Vector_struct < U , DIM >& rhs): Divides lhs elementwise by rhs and returns the modified lhs. More...
template< typename T, typename U, Size> 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, typename TT, Size> 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< Size> 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> 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> 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> 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> 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> 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< typename T, Size> Vector < T , DIM > mi::math::pow ( const Vector_struct < T , DIM >& a, const Vector_struct < T , DIM >& b): Returns the vector a elementwise to the power of b. More...
template< typename T, Size> Vector < T , DIM > mi::math::pow ( const Vector_struct < T , DIM >& a, T b): Returns the vector a elementwise to the power of b. More...
template< typename T, Size> Vector < T , DIM > mi::math::radians ( const Vector_struct < T , DIM >& v): Converts elementwise degrees in v to radians. More...
template< typename T, Size> Vector < T , DIM > mi::math::round ( const Vector_struct < T , DIM >& v): Returns a vector with the elements of vector v rounded to nearest integers. More...
template< typename T, Size> Vector < T , DIM > mi::math::rsqrt ( const Vector_struct < T , DIM >& v): Returns the reciprocal of the square root of each element of v. More...
template< typename T, Size> Vector < T , DIM > mi::math::saturate ( const Vector_struct < T , DIM >& v): Returns the vector v clamped elementwise to the range [0,1]. More...
template< typename T, Size> Vector < T , DIM > mi::math::sign ( const Vector_struct < T , DIM >& v): Returns the elementwise sign of vector v. More...
template< typename T, Size> Vector < T , DIM > mi::math::sin ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise sine of the vector v. More...
template< typename T, Size>void mi::math::sincos ( const Vector_struct < 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> Vector < T , DIM > mi::math::smoothstep ( const Vector_struct < T , DIM >& a, const Vector_struct < T , DIM >& b, const Vector_struct < 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> Vector < T , DIM > mi::math::smoothstep ( const Vector_struct < T , DIM >& a, const Vector_struct < 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> Vector < T , DIM > mi::math::sqrt ( const Vector_struct < T , DIM >& v): Returns the square root of each element of v. More...
template< typename T, Size> Vector < T , DIM > mi::math::step ( const Vector_struct < T , DIM >& a, const Vector_struct < T , DIM >& v): Returns elementwise 0 if v is less than a and 1 otherwise. More...
template< typename T, Size> Vector < T , DIM > mi::math::tan ( const Vector_struct < T , DIM >& v): Returns a vector with the elementwise tangent of the vector v. More...
template< typename T, Size>T* mi::math::vector_base_ptr ( Vector_struct < T , DIM >& vec): Returns the base pointer to the vector data. More...
template< typename T, Size>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...

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