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));
}
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typedef Vec3<short> Imath::V3s
Vec3 of short.
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typedef Vec3<int> Imath::V3i
Vec3 of integer.
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typedef Vec3<int64_t> Imath::V3i64
Vec3 of int64_t.
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typedef Vec3<float> Imath::V3f
Vec3 of float.
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typedef Vec3<double> Imath::V3d
Vec3 of double.
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template<class T>
class Vec3
3-element vector
Subclassed by Imath::Color3< T >, Imath::Euler< T >
Direct access to elements
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T x
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T y
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T z
Constructors and Assignment
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inline Vec3() noexcept
Uninitialized by default.
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inline explicit constexpr Vec3(T a) noexcept
Initialize to a scalar (a,a,a)
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inline constexpr Vec3(T a, T b, T c) noexcept
Initialize to given elements (a,b,c)
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inline constexpr Vec3(const Vec3 &v) noexcept
Copy constructor.
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template<class S>
inline constexpr Vec3(const Vec3<S> &v) noexcept
Construct from Vec3 of another base type.
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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.
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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.
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inline constexpr const Vec3 &operator=(const Vec3 &v) noexcept
Assignment.
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~Vec3() noexcept = default
Destructor.
Compatibility with Sb
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template<class S>
inline void setValue(S a, S b, S c) noexcept
Set the value.
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template<class S>
inline void setValue(const Vec3<S> &v) noexcept
Set the value.
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template<class S>
inline void getValue(S &a, S &b, S &c) const noexcept
Return the value in a, b, and c
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template<class S>
inline void getValue(Vec3<S> &v) const noexcept
Return the value in v
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inline T *getValue() noexcept
Return a raw pointer to the array of values.
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inline const T *getValue() const noexcept
Return a raw pointer to the array of values.
Arithmetic and Comparison
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template<class S>
inline constexpr bool operator==(const Vec3<S> &v) const noexcept
Equality.
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template<class S>
inline constexpr bool operator!=(const Vec3<S> &v) const noexcept
Inequality.
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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
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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])
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inline constexpr T dot(const Vec3 &v) const noexcept
Dot product.
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inline constexpr T operator^(const Vec3 &v) const noexcept
Dot product.
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inline constexpr Vec3 cross(const Vec3 &v) const noexcept
Right-handed cross product.
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inline constexpr const Vec3 &operator%=(const Vec3 &v) noexcept
Right-handed cross product.
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inline constexpr Vec3 operator%(const Vec3 &v) const noexcept
Right-handed cross product.
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inline constexpr const Vec3 &operator+=(const Vec3 &v) noexcept
Component-wise addition.
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inline constexpr Vec3 operator+(const Vec3 &v) const noexcept
Component-wise addition.
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inline constexpr const Vec3 &operator-=(const Vec3 &v) noexcept
Component-wise subtraction.
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inline constexpr Vec3 operator-(const Vec3 &v) const noexcept
Component-wise subtraction.
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inline constexpr Vec3 operator-() const noexcept
Component-wise multiplication by -1.
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inline constexpr const Vec3 &negate() noexcept
Component-wise multiplication by -1.
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inline constexpr const Vec3 &operator*=(const Vec3 &v) noexcept
Component-wise multiplication.
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inline constexpr const Vec3 &operator*=(T a) noexcept
Component-wise multiplication.
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inline constexpr Vec3 operator*(const Vec3 &v) const noexcept
Component-wise multiplication.
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inline constexpr Vec3 operator*(T a) const noexcept
Component-wise multiplication.
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inline constexpr const Vec3 &operator/=(const Vec3 &v) noexcept
Component-wise division.
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inline constexpr const Vec3 &operator/=(T a) noexcept
Component-wise division.
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inline constexpr Vec3 operator/(const Vec3 &v) const noexcept
Component-wise division.
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inline constexpr Vec3 operator/(T a) const noexcept
Component-wise division.
Query and Manipulation
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inline T length() const noexcept
Return the Euclidean norm.
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inline constexpr T length2() const noexcept
Return the square of the Euclidean norm, i.e.
the dot product with itself.
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inline const Vec3 &normalize() noexcept
Normalize in place. If length()==0, return a null vector.
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inline const Vec3 &normalizeExc()
Normalize in place. If length()==0, throw an exception.
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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.
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inline Vec3<T> normalized() const noexcept
Return a normalized vector. Does not modify *this.
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inline Vec3<T> normalizedExc() const
Return a normalized vector.
Does not modify *this. Throw an exception if length()==0.
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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
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static inline constexpr T baseTypeLowest() noexcept
Largest possible negative value.
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static inline constexpr T baseTypeMax() noexcept
Largest possible positive value.
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static inline constexpr T baseTypeSmallest() noexcept
Smallest possible positive value.
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static inline constexpr T baseTypeEpsilon() noexcept
Smallest possible e for which 1+e != 1.
Public Types
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typedef T BaseType
The base type: In templates that accept a parameter V, you can refer to T as V::BaseType
Public Functions
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inline constexpr T &operator[](int i) noexcept
Element access by index.
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inline constexpr const T &operator[](int i) const noexcept
Element access by index.
Public Static Functions
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static inline constexpr unsigned int dimensions() noexcept
Return the number of dimensions, i.e. 3.
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template<class T>
std::ostream &Imath::operator<<(std::ostream &s, const Vec3<T> &v)
Stream output, as “(x y z)”.
