Imath
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# Vec4

    #include <Imath/ImathVec.h>

The `Vec4` class template represents a 4D vector, with predefined typedefs for vectors of type `short`, `int`, `int64_t`, `float`, and `double`.

Note that the integer specializations of `Vec4` lack the `length()` and `normalize()` methods that are present in the `float` and `double` versions, because the results don’t fit into integer quantities.

There are also various utility functions that operate on vectors defined in `ImathVecAlgo.h` and described in Vector Functions.

Individual components of a vector `V` may be referenced as either `V[i]` or `V.x`, `V.y`, `V.z`, `V.w`. Obviously, the `[]` notation is more suited to looping over components, or in cases where a variable determines which coordinate is needed. However, when the coordinate is known, it can be more efficient to directly address the components, such as `V.y` rather than `V[1]`. While both appear to do the same thing (and indeed do generate the same machine operations for ordinary scalar code), when used inside loops that you hope to parallelize (either through compiler auto-vectorization or explicit hints such as `#pragma omp simd`), the function call and pointer casting of `operator[]` can confuse the compiler just enough to prevent vectorization of the loop.

Example:

    #include <Imath/ImathVec.h>
    #include <cassert>

    void
    vec4_example()
    {
        Imath::V4f   a (1.0f, 2.0f, 3.0f, 4.0f);
        Imath::V4f   b; // b is uninitialized

        b.x = a[0];
        b.y = a[1];
        b.z = a[2];
        b.w = a[3];

        assert (a == b);

        assert (a.length() == sqrt (a ^ a));

        a.normalize();
        assert (Imath::equalWithAbsError (a.length(), 1.0f, 1e-6f));
    }

typedef Vec4<short> Imath::V4s

  Vec4 of short.

typedef Vec4<int> Imath::V4i

  Vec4 of integer.

typedef Vec4<int64_t> Imath::V4i64

  Vec4 of int64_t.

typedef Vec4<float> Imath::V4f

  Vec4 of float.

typedef Vec4<double> Imath::V4d

  Vec4 of double.

template<class T>
class Vec4

  4-element vector

  Direct access to elements

  T x
  T y
  T z
  T w

  Constructors and Assignment

  inline Vec4() noexcept

    Uninitialized by default.

  inline explicit constexpr Vec4(T a) noexcept

    Initialize to a scalar `(a,a,a,a)`.

  inline constexpr Vec4(T a, T b, T c, T d) noexcept

    Initialize to given elements `(a,b,c,d)`.

  inline constexpr Vec4(const Vec4 &v) noexcept

    Copy constructor.

  template<class S>
  inline constexpr Vec4(const Vec4<S> &v) noexcept

    Construct from Vec4 of another base type.

  template<class S>
  inline explicit constexpr Vec4(const Vec3<S> &v) noexcept

    Vec3 to Vec4 conversion, sets w to 1.

  inline const Vec4 &operator=(const Vec4 &v) noexcept

    Assignment.

  ~Vec4() noexcept = default

    Destructor.

  Arithmetic and Comparison

  template<class S>
  inline bool operator==(const Vec4<S> &v) const noexcept

    Equality.

  template<class S>
  inline bool operator!=(const Vec4<S> &v) const noexcept

    Inequality.

  inline bool equalWithAbsError(const Vec4<T> &v, T e) const noexcept

    Compare two matrices and test if they are “approximately equal”:

    Returns:

      True if the coefficients of this and `m` are the same with an absolute error of no more than e, i.e., for all i, j:

          abs (this[i][j] - m[i][j]) <= e

  inline bool equalWithRelError(const Vec4<T> &v, T e) const noexcept

    Compare two matrices and test if they are “approximately equal”:

    Returns:

      True if the coefficients of this and m are the same with a relative error of no more than e, i.e., for all i, j:

          abs (this[i] - v[i][j]) <= e * abs (this[i][j])

  inline T dot(const Vec4 &v) const noexcept

    Dot product.

  inline T operator^(const Vec4 &v) const noexcept

    Dot product.

  inline const Vec4 &operator+=(const Vec4 &v) noexcept

    Component-wise addition.

  inline Vec4 operator+(const Vec4 &v) const noexcept

    Component-wise addition.

  inline const Vec4 &operator-=(const Vec4 &v) noexcept

    Component-wise subtraction.

  inline Vec4 operator-(const Vec4 &v) const noexcept

    Component-wise subtraction.

  inline Vec4 operator-() const noexcept

    Component-wise multiplication by -1.

  inline const Vec4 &negate() noexcept

    Component-wise multiplication by -1.

  inline const Vec4 &operator*=(const Vec4 &v) noexcept

    Component-wise multiplication.

  inline const Vec4 &operator*=(T a) noexcept

    Component-wise multiplication.

  inline Vec4 operator*(const Vec4 &v) const noexcept

    Component-wise multiplication.

  inline Vec4 operator*(T a) const noexcept

    Component-wise multiplication.

  inline const Vec4 &operator/=(const Vec4 &v) noexcept

    Component-wise division.

  inline const Vec4 &operator/=(T a) noexcept

    Component-wise division.

  inline Vec4 operator/(const Vec4 &v) const noexcept

    Component-wise division.

  inline Vec4 operator/(T a) const noexcept

    Component-wise division.

  Query and Manipulation

  inline T length() const noexcept

    Return the Euclidean norm.

  inline T length2() const noexcept

    Return the square of the Euclidean norm, i.e.

    the dot product with itself.

  inline const Vec4 &normalize() noexcept

    Normalize in place. If length()==0, return a null vector.

  inline const Vec4 &normalizeExc()

    Normalize in place. If length()==0, throw an exception.

  inline const Vec4 &normalizeNonNull() noexcept

    Normalize without any checks for length()==0.

    Slightly faster than the other normalization routines, but if v.length() is 0.0, the result is undefined.

  inline Vec4<T> normalized() const noexcept

    Return a normalized vector. Does not modify *this.

  inline Vec4<T> normalizedExc() const

    Return a normalized vector.

    Does not modify *this. Throw an exception if length()==0.

  inline Vec4<T> normalizedNonNull() const noexcept

    Return a normalized vector.

    Does not modify *this, and does not check for length()==0. Slightly faster than the other normalization routines, but if v.length() is 0.0, the result is undefined.

  Numeric Limits

  static inline T baseTypeLowest() noexcept

    Largest possible negative value.

  static inline T baseTypeMax() noexcept

    Largest possible positive value.

  static inline T baseTypeSmallest() noexcept

    Smallest possible positive value.

  static inline T baseTypeEpsilon() noexcept

    Smallest possible e for which 1+e != 1.

  Public Types

  typedef T BaseType

    The base type: In templates that accept a parameter `V`, you can refer to `T` as `V::BaseType`.

  Public Functions

  inline T &operator[](int i) noexcept

    Element access by index.

  inline const T &operator[](int i) const noexcept

    Element access by index.

  Public Static Functions

  static inline unsigned int dimensions() noexcept

    Return the number of dimensions, i.e. 4.

template<class T>
std::ostream &Imath::operator<<(std::ostream &s, const Vec4<T> &v)

  Stream output, as “(x y z w)”.

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