Imath
<navlinks>
<page>

# Vec3

    #include <Imath/ImathVec.h>

The `Vec3` class template represents a 3D vector, with predefined typedefs for vectors of type `short`, `int`, `int64_t`, `float`, and `double`.

Note that the integer specializations of `Vec3` 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`. 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
    vec3_example()
    {
        Imath::V3f   a (1.0f, 2.0f, 3.0f);
        Imath::V3f   b; // b is uninitialized

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

        assert (a == b);

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

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

typedef Vec3<short> Imath::V3s

  Vec3 of short.

typedef Vec3<int> Imath::V3i

  Vec3 of integer.

typedef Vec3<int64_t> Imath::V3i64

  Vec3 of int64_t.

typedef Vec3<float> Imath::V3f

  Vec3 of float.

typedef Vec3<double> Imath::V3d

  Vec3 of double.

template<class T>
class Imath::Vec3

  3-element vector

  Subclassed by Imath::Color3< T >, Imath::Euler< T >

  Direct access to elements

  T x
  T y
  T z

  Constructors and Assignment

  inline Vec3() noexcept

    Uninitialized by default.

  inline explicit constexpr Vec3(T a) noexcept

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

  inline constexpr Vec3(T a, T b, T c) noexcept

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

  inline constexpr Vec3(const Vec3 &v) noexcept

    Copy constructor.

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

    Construct from Vec3 of another base type.

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

    Vec4 to Vec3 conversion: divide x, y and z by w, even if w is 0.

    The result depends on how the environment handles floating-point exceptions.

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

    Vec4 to Vec3 conversion: divide x, y and z by w.

    Throws an exception if w is zero or if division by w would overflow.

  inline constexpr const Vec3 &operator=(const Vec3 &v) noexcept

    Assignment.

  ~Vec3() noexcept = default

    Destructor.

  Compatibility with Sb

  template<class S>
  inline void setValue(S a, S b, S c) noexcept

    Set the value.

  template<class S>
  inline void setValue(const Vec3<S> &v) noexcept

    Set the value.

  template<class S>
  inline void getValue(S &a, S &b, S &c) const noexcept

    Return the value in `a`, `b`, and `c`

  template<class S>
  inline void getValue(Vec3<S> &v) const noexcept

    Return the value in `v`

  inline T *getValue() noexcept

    Return a raw pointer to the array of values.

  inline const T *getValue() const noexcept

    Return a raw pointer to the array of values.

  Arithmetic and Comparison

  template<class S>
  inline constexpr bool operator==(const Vec3<S> &v) const noexcept

    Equality.

  template<class S>
  inline constexpr bool operator!=(const Vec3<S> &v) const noexcept

    Inequality.

  inline constexpr bool equalWithAbsError(const Vec3<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 constexpr bool equalWithRelError(const Vec3<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 constexpr T dot(const Vec3 &v) const noexcept

    Dot product.

  inline constexpr T operator^(const Vec3 &v) const noexcept

    Dot product.

  inline constexpr Vec3 cross(const Vec3 &v) const noexcept

    Right-handed cross product.

  inline constexpr const Vec3 &operator%=(const Vec3 &v) noexcept

    Right-handed cross product.

  inline constexpr Vec3 operator%(const Vec3 &v) const noexcept

    Right-handed cross product.

  inline constexpr const Vec3 &operator+=(const Vec3 &v) noexcept

    Component-wise addition.

  inline constexpr Vec3 operator+(const Vec3 &v) const noexcept

    Component-wise addition.

  inline constexpr const Vec3 &operator-=(const Vec3 &v) noexcept

    Component-wise subtraction.

  inline constexpr Vec3 operator-(const Vec3 &v) const noexcept

    Component-wise subtraction.

  inline constexpr Vec3 operator-() const noexcept

    Component-wise multiplication by -1.

  inline constexpr const Vec3 &negate() noexcept

    Component-wise multiplication by -1.

  inline constexpr const Vec3 &operator*=(const Vec3 &v) noexcept

    Component-wise multiplication.

  inline constexpr const Vec3 &operator*=(T a) noexcept

    Component-wise multiplication.

  inline constexpr Vec3 operator*(const Vec3 &v) const noexcept

    Component-wise multiplication.

  inline constexpr Vec3 operator*(T a) const noexcept

    Component-wise multiplication.

  inline constexpr const Vec3 &operator/=(const Vec3 &v) noexcept

    Component-wise division.

  inline constexpr const Vec3 &operator/=(T a) noexcept

    Component-wise division.

  inline constexpr Vec3 operator/(const Vec3 &v) const noexcept

    Component-wise division.

  inline constexpr Vec3 operator/(T a) const noexcept

    Component-wise division.

  Query and Manipulation

  inline T length() const noexcept

    Return the Euclidean norm.

  inline constexpr T length2() const noexcept

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

    the dot product with itself.

  inline const Vec3 &normalize() noexcept

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

  inline const Vec3 &normalizeExc()

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

  inline const Vec3 &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 Vec3<T> normalized() const noexcept

    Return a normalized vector. Does not modify *this.

  inline Vec3<T> normalizedExc() const

    Return a normalized vector.

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

  inline Vec3<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 constexpr T baseTypeLowest() noexcept

    Largest possible negative value.

  static inline constexpr T baseTypeMax() noexcept

    Largest possible positive value.

  static inline constexpr T baseTypeSmallest() noexcept

    Smallest possible positive value.

  static inline constexpr 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 constexpr T &operator[](int i) noexcept

    Element access by index.

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

    Element access by index.

  Public Static Functions

  static inline constexpr unsigned int dimensions() noexcept

    Return the number of dimensions, i.e. 3.

template<class T>
std::ostream &Imath::operator<<(std::ostream &s, const Vec3<T> &v)

  Stream output, as “(x y z)”.

</page>