Vector3.h

Go to the documentation of this file.

/*
 * Copyright (c) Meta Platforms, Inc. and affiliates.
 *
 * This source code is licensed under the MIT license found in the
 * LICENSE file in the root directory of this source tree.
 */
 
#ifndef META_OCEAN_MATH_VECTOR3_H
#define META_OCEAN_MATH_VECTOR3_H
 
#include "ocean/math/Math.h"
#include "ocean/math/Numeric.h"
#include "ocean/math/Vector2.h"
 
#include <type_traits>
#include <vector>
 
namespace Ocean
{
 
// Forward declaration.
template <typename T> class VectorT3;
 
/**
 * Definition of a 3D vector.
 * @see VectorT3
 * @ingroup math
 */
using Vector3 = VectorT3<Scalar>;
 
/**
 * Definition of a 3D vector with double values.
 * @see VectorT3
 * @ingroup math
 */
using VectorD3 = VectorT3<double>;
 
/**
 * Definition of a 3D vector with float values.
 * @see VectorT3
 * @ingroup math
 */
using VectorF3 = VectorT3<float>;
 
/**
 * Definition of a 3D vector with integer values.
 * @see VectorT3
 * @ingroup math
 */
using VectorI3 = VectorT3<int>;
 
/**
 * Definition of a typename alias for vectors with VectorT3 objects.
 * @see VectorT3
 * @ingroup math
 */
template <typename T>
using VectorsT3 = std::vector<VectorT3<T>>;
 
/**
 * Definition of a vector holding Vector3 objects.
 * @see Vector3
 * @ingroup math
 */
using Vectors3 = std::vector<Vector3>;
 
/**
 * Definition of a vector holding VectorD3 objects.
 * @see VectorD3
 * @ingroup math
 */
using VectorsD3 = std::vector<VectorD3>;
 
/**
 * Definition of a vector holding VectorF3 objects.
 * @see VectorF3
 * @ingroup math
 */
using VectorsF3 = std::vector<VectorF3>;
 
/**
 * Definition of a vector holding VectorI3 objects.
 * @see VectorI3
 * @ingroup math
 */
using VectorsI3 = std::vector<VectorI3>;
 
/**
 * This class implements a vector with three elements.
 * The element order is: (x, y, z).
 * @tparam T Data type of the vector elements.
 * @see Vector3, VectorF3, VectorD3.
 * @ingroup math
 */
template <typename T>
class VectorT3
{
    public:
 
        /**
         * Definition of the used data type.
         */
        using Type = T;
 
    public:
 
        /**
         * Creates a new 3D vector with undefined elements.
         * Beware: The elements are neither zero nor a specific value!
         * This is useful in situations where VectorT3 objects are created (e.g, by a large array or vector)
         * and their values are assigned in a function afterwards.
         */
        inline VectorT3() noexcept;
 
        /**
         * Creates a new 3D vector.
         * @param setToHomogeneous Determines whether a homogeneous vector (0, 0, 1) will be created, otherwise the vector is initialized with zeros
         */
        inline explicit VectorT3(const bool setToHomogeneous) noexcept;
 
        /**
         * Creates a new 3D vector with three given elements.
         * @param x X value
         * @param y Y value
         * @param z Z value
         */
        inline VectorT3(const T& x, const T& y, const T& z) noexcept;
 
        /**
         * Creates a new 3D vector with a given array of elements.
         * @param valueArray Array with at least three elements
         */
        inline explicit VectorT3(const T* valueArray) noexcept;
 
        /**
         * Creates a new 3D vector with a given 2D vector defining the first two elements and a single value defining the third element.
         * @param vector 2D vector defining the first two elements (X and Y value)
         * @param z Z value defining the third element
         */
        inline explicit VectorT3(const VectorT2<T>& vector, const T& z = 0) noexcept;
 
        /**
         * Copies a vector.
         * @param vector 3D vector that is copied
         */
        VectorT3(const VectorT3<T>& vector) noexcept = default;
 
        /**
         * Copies a vector with different element data type than T.
         * @param vector The 3D vector to copy
         * @tparam U The element data type of the second vector
         */
        template <typename U>
        inline explicit VectorT3(const VectorT3<U>& vector) noexcept;
 
        /**
         * Returns the cross product of two vectors.
         * The cross product of two parallel vectors (or of at least one zero vector) results in a zero vector.
         * @param vector The right vector
         * @return The resulting cross product of both vectors
         * @see isParallel().
         */
        inline VectorT3<T> cross(const VectorT3<T>& vector) const;
 
        /**
         * Returns the normalized vector.
         * Beware: This function does not throw an exception if this vector cannot be normalized.<br>
         * Thus, ensure that this vector is not zero before calling this function.<br>
         * Or even better, use different normalization functions like: normalizedOrZero(), normalizedOrValue(), or normalize().<br>
         * In case, the vector cannot be normalized, an uninitialized vector will be returned (due to performance reasons).
         * @return This vector as unit vector (vector with length 1)
         * @see normalizedOrZero(), normalizedOrValue(), normalize().
         */
        inline VectorT3<T> normalized() const;
 
        /**
         * Returns the normalized vector.
         * If this vector cannot be normalized the zero vector is returned.
         * @return Vector with length 1
         */
        inline VectorT3<T> normalizedOrZero() const;
 
        /**
         * Returns the normalized vector.
         * If this vector cannot be normalized the given vector is returned.
         * @param value Vector that will be returned if the vector cannot be normalized
         * @return Vector with length 1
         */
        inline VectorT3<T> normalizedOrValue(const VectorT3<T>& value) const;
 
        /**
         * Normalizes this vector
         * @return True, if the vector could be normalized
         */
        inline bool normalize();
 
        /**
         * Returns the length of the vector.
         * @return Vector length
         */
        inline T length() const;
 
        /**
         * Returns the square of the vector length.
         * @return Square of vector length
         */
        inline T sqr() const;
 
        /**
         * Returns the distance between this 3D position and a second 3D position.
         * @param right Second 3D position
         * @return Distance between the two points
         */
        inline T distance(const VectorT3<T>& right) const;
 
        /**
         * Returns the square distance between this 3D position and a second 3D position.
         * @param right Second 3D position
         * @return Square distance between the two points
         */
        inline T sqrDistance(const VectorT3<T>& right) const;
 
        /**
         * Returns the angle between this vector and a second vectors.
         * Beware: This vector must not be zero.<br>
         * Beware: This function does not throw an exception if one or both vectors are zero.<br>
         * In case, the angle cannot be determined -1 will be returned.
         * @param right Second vector, must not be zero
         * @return Angle between both vectors in radian, with range [0, PI], -1 in case of an error
         */
        T angle(const VectorT3<T>& right) const;
 
        /**
         * Returns the reflected vector of this vector corresponding to a given normal vector.
         * The dot product between this vector and the normal vector must be positive.<br>
         * @param normal The normal vector used to determine the reflection vector for
         * @return Resulting reflection vector
         */
        VectorT3<T> reflect(const VectorT3<T>& normal) const;
 
        /**
         * Returns the refracted vector of this vector corresponding to a given normal vector.
         * The dot product between this vector and the normal vector must be positive.<br>
         * @param normal The normal vector used to determine the refracted vector for
         * @param index Refraction index that is the ratio between the leaving and the entering refraction index, an index lower than 1 describes the transition from a thin into a thick medium, with range (0, infinity)
         * @return Resulting refracted vector
         */
        VectorT3<T> refract(const VectorT3<T>& normal, const T index) const;
 
        /**
         * Returns a vector that is perpendicular to this vector.
         * If this vector is a zero vector, than the resulting vector will be arbitrary.
         * @return Resulting perpendicular vector, a unity vector is not guaranteed
         */
        VectorT3<T> perpendicular() const;
 
        /**
         * Returns whether two vectors are parallel.
         * A zero vector will not be parallel.
         * @param right The right vector
         * @return True, if so
         * @see cross().
         */
        bool isParallel(const VectorT3<T>& right) const;
 
        /**
         * Returns whether two vectors are orthogonal.
         * A zero vector will not be orthogonal.
         * @param right The right vector
         * @return True, if so
         */
        inline bool isOrthogonal(const VectorT3<T>& right) const;
 
        /**
         * Returns the x value.
         * @return X value
         */
        inline const T& x() const noexcept;
 
        /**
         * Returns the x value.
         * @return X value
         */
        inline T& x() noexcept;
 
        /**
         * Returns the y value.
         * @return Y value
         */
        inline const T& y() const noexcept;
 
        /**
         * Returns the y value.
         * @return Y value
         */
        inline T& y() noexcept;
 
        /**
         * Returns the z value.
         * @return Z value
         */
        inline const T& z() const noexcept;
 
        /**
         * Returns the z value.
         * @return Z value
         */
        inline T& z() noexcept;
 
        /**
         * Returns the x and y component of the vector as new 2D vector.
         * @return New 2D vector
         */
        inline VectorT2<T> xy() const noexcept;
 
        /**
         * Returns an pointer to the vector elements.
         * @return Pointer to elements
         */
        inline const T* data() const noexcept;
 
        /**
         * Returns an pointer to the vector elements.
         * @return Pointer to elements
         */
        inline T* data() noexcept;
 
        /**
         * Returns whether this vector is a null vector up to a small epsilon.
         * @return True, if so
         */
        inline bool isNull() const;
 
        /**
         * Returns whether this vector is a unit vector (whether the vector has the length 1).
         * @param eps Epsilon to be used, with range [0, infinity)
         * @return True, if so
         */
        inline bool isUnit(const T eps = NumericT<T>::eps()) const;
 
        /**
         * Returns whether two vectors are equal up to a specified epsilon.
         * @param vector Second vector
         * @param eps Epsilon to be used
         * @return True, if so
         */
        inline bool isEqual(const VectorT3<T>& vector, const T eps) const;
 
        /**
         * Copy assigns a vector
         * @param vector 3D vector that is copied
         */
        VectorT3<T>& operator=(const VectorT3<T>& vector) = default;
 
        /**
         * Returns whether two vectors are identical up to a small epsilon.
         * @param vector Right vector
         * @return True, if so
         */
        inline bool operator==(const VectorT3<T>& vector) const;
 
        /**
         * Returns whether two vectors are not identical up to a small epsilon.
         * @param vector Right vector
         * @return True, if so
         */
        inline bool operator!=(const VectorT3<T>& vector) const;
 
        /**
         * Adds two vectors.
         * @param vector Right vector
         * @return Sum vector
         */
        inline VectorT3<T> operator+(const VectorT3<T>& vector) const;
 
        /**
         * Adds and assigns two vectors.
         * @param vector Right vector
         * @return Reference to this vector
         */
        inline VectorT3<T>& operator+=(const VectorT3<T>& vector);
 
        /**
         * Subtracts two vectors.
         * @param vector Right vector
         * @return Difference vector
         */
        inline VectorT3<T> operator-(const VectorT3<T>& vector) const;
 
        /**
         * Subtracts and assigns two vectors.
         * @param vector Right vector
         * @return Reference to this vector
         */
        inline VectorT3<T>& operator-=(const VectorT3<T>& vector);
 
        /**
         * Returns the negated vector.
         * @return Negated vector
         */
        inline VectorT3<T> operator-() const;
 
        /**
         * Returns the dot product of two vectors.
         * @param vector Right vector
         * @return Dot product
         */
        inline T operator*(const VectorT3<T>& vector) const;
 
        /**
         * Multiplies this vector with a scalar.
         * @param value Scalar value
         * @return Resulting vector
         */
        inline VectorT3<T> operator*(const T& value) const;
 
        /**
         * Multiplies and assigns this vector with a scalar.
         * @param value Scalar value
         * @return Reference to this vector
         */
        inline VectorT3<T>& operator*=(const T& value);
 
        /**
         * Divides this vector by a scalar.
         * Beware: This function does not throw an exception if the given value is zero.<br>
         * Thus, ensure that given value is not zero before calling this function.<br>
         * In case, the given value is zero, the result is undefined.
         * @param value Scalar value to be used as denominator, must not be zero
         * @return Resulting vector
         */
        inline VectorT3<T> operator/(const T& value) const;
 
        /**
         * Divides and assigns this vector by a scalar.
         * Beware: This function does not throw an exception if the given value is zero.<br>
         * Thus, ensure that given value is not zero before calling this function.<br>
         * In case, the given value is zero, the result is undefined.
         * @param value Scalar value to be used as denominator, must not be zero
         * @return Reference to this vector
         */
        inline VectorT3<T>& operator/=(const T& value);
 
        /**
         * Compares two vector objects and returns whether the left vector represents a smaller value than the right vector.
         * First the first component of both vectors are compared, if these values are equal then the next components are compares and so on.<br>
         * @param vector The second vector to compare
         * @return True, if so
         */
        inline bool operator<(const VectorT3<T>& vector) const;
 
        /**
         * Element access operator.
         * @param index The index of the element to access, with range [0, 2]
         * @return Element of the vector
         */
        inline const T& operator[](const unsigned int index) const noexcept;
 
        /**
         * Element access operator.
         * @param index The index of the element to access, with range [0, 2]
         * @return Element of the vector
         */
        inline T& operator[](const unsigned int index) noexcept;
 
        /**
         * Element access operator.
         * @param index The index of the element to access, with range [0, 2]
         * @return Element of the vector
         */
        inline const T& operator()(const unsigned int index) const noexcept;
 
        /**
         * Element access operator.
         * @param index The index of the element to access, with range [0, 2]
         * @return Element of the vector
         */
        inline T& operator()(const unsigned int index) noexcept;
 
        /**
         * Access operator.
         * @return Pointer to the elements
         */
        inline const T* operator()() const noexcept;
 
        /**
         * Access operator.
         * @return Pointer to the elements
         */
        inline T* operator()() noexcept;
 
        /**
         * Hash function.
         * @param vector The vector for which the hash value will be determined
         * @return The resulting hash value
         */
        inline size_t operator()(const VectorT3<T>& vector) const;
 
        /**
         * Returns a 3D vector with all elements set to NumericT::minValue().
         * @return The resulting 3D vector
         */
        static inline VectorT3<T> minValue();
 
        /**
         * Returns a 3D vector with all elements set to NumericT::maxValue().
         * @return The resulting 3D vector
         */
        static inline VectorT3<T> maxValue();
 
        /**
         * Converts vectors with specific data type to vectors with different data type.
         * @param vectors The vectors to convert
         * @return The converted vectors
         * @tparam U The element data type of the vectors to convert
         */
        template <typename U>
        static inline std::vector<VectorT3<T>> vectors2vectors(std::vector<VectorT3<U>>&& vectors);
 
        /**
         * Converts vectors with specific data type to vectors with different data type.
         * @param vectors The vectors to convert
         * @return The converted vectors
         * @tparam U The element data type of the vectors to convert
         */
        template <typename U>
        static inline std::vector<VectorT3<T>> vectors2vectors(const std::vector<VectorT3<U>>& vectors);
 
        /**
         * Converts vectors with specific data type to vectors with different data type.
         * @param vectors The vectors to convert
         * @param size The number of vector to convert
         * @return The converted vectors
         * @tparam U The element data type of the vectors to convert
         */
        template <typename U>
        static inline std::vector<VectorT3<T>> vectors2vectors(const VectorT3<U>* vectors, const size_t size);
 
    protected:
 
        /// The three values of the vector, with element order x, y, z.
        T values_[3];
};
 
template <typename T>
inline VectorT3<T>::VectorT3() noexcept
{
    static_assert(std::is_arithmetic<T>::value, "VectorT3 only supports arithmetic types");
    // nothing to do here
}
 
template <typename T>
inline VectorT3<T>::VectorT3(const bool setToHomogeneous) noexcept
{
    if (setToHomogeneous)
    {
        values_[0] = T(0.0);
        values_[1] = T(0.0);
        values_[2] = T(1.0);
    }
    else
    {
        values_[0] = T(0.0);
        values_[1] = T(0.0);
        values_[2] = T(0.0);
    }
}
 
template <typename T>
inline VectorT3<T>::VectorT3(const T& x, const T& y, const T& z) noexcept
{
    values_[0] = x;
    values_[1] = y;
    values_[2] = z;
}
 
template <typename T>
inline VectorT3<T>::VectorT3(const T* valueArray) noexcept
{
    memcpy(values_, valueArray, sizeof(T) * 3);
}
 
template <typename T>
inline VectorT3<T>::VectorT3(const VectorT2<T>& vector, const T& z) noexcept
{
    values_[0] = vector[0];
    values_[1] = vector[1];
    values_[2] = z;
}
 
template <typename T>
template <typename U>
inline VectorT3<T>::VectorT3(const VectorT3<U>& vector) noexcept
{
    values_[0] = T(vector[0]);
    values_[1] = T(vector[1]);
    values_[2] = T(vector[2]);
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::cross(const VectorT3<T>& vector) const
{
    return VectorT3<T>(values_[1] * vector.values_[2] - values_[2] * vector.values_[1],
                        values_[2] * vector.values_[0] - values_[0] * vector.values_[2],
                        values_[0] * vector.values_[1] - values_[1] * vector.values_[0]);
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::normalized() const
{
    const T len = length();
    if (NumericT<T>::isEqualEps(len))
    {
        ocean_assert(false && "Division by zero!");
        return VectorT3<T>();
    }
 
    const T factor = T(1) / len;
    return VectorT3<T>(values_[0] * factor, values_[1] * factor, values_[2] * factor);
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::normalizedOrZero() const
{
    const T len = length();
 
    if (NumericT<T>::isEqualEps(len))
    {
        return *this;
    }
 
    const T factor = T(1) / len;
    return VectorT3<T>(values_[0] * factor, values_[1] * factor, values_[2] * factor);
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::normalizedOrValue(const VectorT3<T>& value) const
{
    const T len = length();
 
    if (NumericT<T>::isEqualEps(len))
    {
        return value;
    }
 
    const T factor = T(1) / len;
    return VectorT3<T>(values_[0] * factor, values_[1] * factor, values_[2] * factor);
}
 
template <typename T>
inline bool VectorT3<T>::normalize()
{
    const T len = length();
    if (NumericT<T>::isEqualEps(len))
    {
        return false;
    }
 
    const T factor = T(1) / len;
    values_[0] *= factor;
    values_[1] *= factor;
    values_[2] *= factor;
 
    return true;
}
 
template <typename T>
inline T VectorT3<T>::length() const
{
    return NumericT<T>::sqrt(values_[0] * values_[0] + values_[1] * values_[1] + values_[2] * values_[2]);
}
 
template <typename T>
inline T VectorT3<T>::sqr() const
{
    return values_[0] * values_[0] + values_[1] * values_[1] + values_[2] * values_[2];
}
 
template <typename T>
inline T VectorT3<T>::distance(const VectorT3<T>& right) const
{
    return NumericT<T>::sqrt(NumericT<T>::sqr(values_[0] - right.values_[0]) + NumericT<T>::sqr(values_[1] - right.values_[1]) + NumericT<T>::sqr(values_[2] - right.values_[2]));
}
 
template <typename T>
inline T VectorT3<T>::sqrDistance(const VectorT3<T>& right) const
{
    return NumericT<T>::sqr(values_[0] - right.values_[0]) + NumericT<T>::sqr(values_[1] - right.values_[1]) + NumericT<T>::sqr(values_[2] - right.values_[2]);
}
 
template <typename T>
T VectorT3<T>::angle(const VectorT3<T>& right) const
{
    // a * b = cos * |a| * |b|
    // cos = (a * b) / (|a| * |b|)
    // we separate the sqrt determinations to receive a higher accuracy
 
    const T thisLength = length();
    const T rightLength = right.length();
 
    if (NumericT<T>::isEqualEps(thisLength) || NumericT<T>::isEqualEps(rightLength))
    {
        ocean_assert(false && "Invalid vector!");
        return T(-1);
    }
 
    const T dot = values_[0] * right.values_[0] + values_[1] * right.values_[1] + values_[2] * right.values_[2];
 
    return NumericT<T>::acos((dot / thisLength) / rightLength);
}
 
template <typename T>
VectorT3<T> VectorT3<T>::reflect(const VectorT3<T>& normal) const
{
    ocean_assert(NumericT<T>::isNotEqualEps(normal.length()));
    ocean_assert(*this * normal >= 0);
 
#ifdef OCEAN_DEBUG
    const VectorT3<T> result(normal * ((normal * *this) * 2) - *this);
    ocean_assert(int(angle(normal) * 100) == int(result.angle(normal) * 100));
    ocean_assert(result * normal >= 0);
    ocean_assert(NumericT<T>::isWeakEqual(length(), result.length()));
#endif // OCEAN_DEBUG
 
    return normal * ((normal * *this) * 2) - *this;
}
 
template <typename T>
VectorT3<T> VectorT3<T>::refract(const VectorT3<T>& normal, const T index) const
{
    ocean_assert(NumericT<T>::isNotEqualEps(normal.length()));
    ocean_assert(*this * normal >= 0);
    ocean_assert(index > T(0));
 
    const T dot = normal * *this;
 
    const T sqrtValue = T(1) - (index * index) * (T(1) - dot * dot);
 
    // check whether a total internal reflection occurs
    if (sqrtValue < T(0))
    {
        return reflect(normal);
    }
 
#ifdef OCEAN_DEBUG
    const VectorT3<T> result(normal * (index * dot - NumericT<T>::sqrt(sqrtValue)) - *this * index);
    const T angle0 = angle(normal);
    const T angle1 = result.angle(-normal);
    const T sin0 = NumericT<T>::sin(angle0);
    const T sin1 = NumericT<T>::sin(angle1);
    ocean_assert(NumericT<T>::isNotEqualEps(sin1));
    ocean_assert(NumericT<T>::isWeakEqual(index, sin0 / sin1));
    ocean_assert(NumericT<T>::isWeakEqual(length(), result.length()));
#endif // OCEAN_DEBUG
 
    return normal * (index * dot - NumericT<T>::sqrt(T(1) - (index * index) * (T(1) - dot * dot))) - *this * index;
}
 
template <typename T>
VectorT3<T> VectorT3<T>::perpendicular() const
{
    if (NumericT<T>::isNotEqualEps(values_[0]) || NumericT<T>::isNotEqualEps(values_[2]))
    {
        return cross(VectorT3<T>(0, 1, 0));
    }
 
    if (NumericT<T>::isNotEqualEps(values_[1]))
    {
        return cross(VectorT3<T>(1, 0, 0));
    }
 
    ocean_assert(isNull());
    return VectorT3<T>(1, 0, 0);
}
 
template <typename T>
bool VectorT3<T>::isParallel(const VectorT3<T>& right) const
{
#ifdef OCEAN_DEBUG
    if (std::is_same<double, Scalar>::value)
    {
        const VectorT3<T> normalizedThis(normalizedOrZero());
        const VectorT3<T> normalizedRight(right.normalizedOrZero());
 
        const T dotProduct = normalizedThis * normalizedRight;
 
        const bool debugResult = NumericT<T>::isEqual(dotProduct, 1) || NumericT<T>::isEqual(dotProduct, -1);
        const VectorT3<T> crossVector = cross(right);
 
        ocean_assert_accuracy(debugResult == (!isNull() && !right.isNull() && crossVector.isNull()));
    }
#endif
 
    return !isNull() && !right.isNull() && cross(right).isNull();
}
 
template <typename T>
inline bool VectorT3<T>::isOrthogonal(const VectorT3<T>& right) const
{
    return NumericT<T>::isEqualEps(values_[0] * right.values_[0] + values_[1] * right.values_[1] + values_[2] * right.values_[2]);
}
 
template <typename T>
inline const T& VectorT3<T>::x() const noexcept
{
    return values_[0];
}
 
template <typename T>
inline T& VectorT3<T>::x() noexcept
{
    return values_[0];
}
 
template <typename T>
inline const T& VectorT3<T>::y() const noexcept
{
    return values_[1];
}
 
template <typename T>
inline T& VectorT3<T>::y() noexcept
{
    return values_[1];
}
 
template <typename T>
inline const T& VectorT3<T>::z() const noexcept
{
    return values_[2];
}
 
template <typename T>
inline T& VectorT3<T>::z() noexcept
{
    return values_[2];
}
 
template <typename T>
inline VectorT2<T> VectorT3<T>::xy() const noexcept
{
    return VectorT2<T>(values_[0], values_[1]);
}
 
template <typename T>
inline const T* VectorT3<T>::data() const noexcept
{
    return values_;
}
 
template <typename T>
inline T* VectorT3<T>::data() noexcept
{
    return values_;
}
 
template <typename T>
inline bool VectorT3<T>::isNull() const
{
    return NumericT<T>::isEqualEps(values_[0]) && NumericT<T>::isEqualEps(values_[1])
        && NumericT<T>::isEqualEps(values_[2]);
}
 
template <typename T>
inline bool VectorT3<T>::isUnit(const T eps) const
{
    return NumericT<T>::isEqual(length(), T(1), eps);
}
 
template <typename T>
inline bool VectorT3<T>::isEqual(const VectorT3<T>& vector, const T eps) const
{
    return NumericT<T>::isEqual(values_[0], vector.values_[0], eps)
            && NumericT<T>::isEqual(values_[1], vector.values_[1], eps)
            && NumericT<T>::isEqual(values_[2], vector.values_[2], eps);
}
 
template <typename T>
inline bool VectorT3<T>::operator==(const VectorT3<T>& vector) const
{
    return NumericT<T>::isEqual(values_[0], vector.values_[0])
        && NumericT<T>::isEqual(values_[1], vector.values_[1])
        && NumericT<T>::isEqual(values_[2], vector.values_[2]);
}
 
template <typename T>
inline bool VectorT3<T>::operator!=(const VectorT3<T>& vector) const
{
    return NumericT<T>::isNotEqual(values_[0], vector.values_[0])
        || NumericT<T>::isNotEqual(values_[1], vector.values_[1])
        || NumericT<T>::isNotEqual(values_[2], vector.values_[2]);
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::operator+(const VectorT3<T>& vector) const
{
    return VectorT3<T>(values_[0] + vector.values_[0], values_[1] + vector.values_[1], values_[2] + vector.values_[2]);
}
 
template <typename T>
inline VectorT3<T>& VectorT3<T>::operator+=(const VectorT3<T>& vector)
{
    values_[0] += vector.values_[0];
    values_[1] += vector.values_[1];
    values_[2] += vector.values_[2];
 
    return *this;
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::operator-(const VectorT3<T>& vector) const
{
    return VectorT3<T>(values_[0] - vector.values_[0], values_[1] - vector.values_[1], values_[2] - vector.values_[2]);
}
 
template <typename T>
inline VectorT3<T>& VectorT3<T>::operator-=(const VectorT3<T>& vector)
{
    values_[0] -= vector.values_[0];
    values_[1] -= vector.values_[1];
    values_[2] -= vector.values_[2];
 
    return *this;
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::operator-() const
{
    return VectorT3<T>(-values_[0], -values_[1], -values_[2]);
}
 
template <typename T>
inline T VectorT3<T>::operator*(const VectorT3<T>& vector) const
{
    return values_[0] * vector.values_[0] + values_[1] * vector.values_[1] + values_[2] * vector.values_[2];
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::operator*(const T& value) const
{
    return VectorT3<T>(values_[0] * value, values_[1] * value, values_[2] * value);
}
 
template <typename T>
inline VectorT3<T>& VectorT3<T>::operator*=(const T& value)
{
    values_[0] *= value;
    values_[1] *= value;
    values_[2] *= value;
 
    return *this;
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::operator/(const T& value) const
{
    ocean_assert(NumericT<T>::isNotEqualEps(value));
    T factor = T(1) / value;
 
    return VectorT3<T>(values_[0] * factor, values_[1] * factor, values_[2] * factor);
}
 
template <typename T>
inline VectorT3<T>& VectorT3<T>::operator/=(const T& value)
{
    ocean_assert(NumericT<T>::isNotEqualEps(value));
 
    T factor = T(1) / value;
 
    values_[0] *= factor;
    values_[1] *= factor;
    values_[2] *= factor;
 
    return *this;
}
 
template <typename T>
inline bool VectorT3<T>::operator<(const VectorT3<T>& right) const
{
    return values_[0] < right.values_[0]
            || (values_[0] == right.values_[0] && (values_[1] < right.values_[1]
            || (values_[1] == right.values_[1] && values_[2] < right.values_[2])));
}
 
template <typename T>
inline const T& VectorT3<T>::operator[](const unsigned int index) const noexcept
{
    ocean_assert(index < 3u);
    return values_[index];
}
 
template <typename T>
inline T& VectorT3<T>::operator[](const unsigned int index) noexcept
{
    ocean_assert(index < 3u);
    return values_[index];
}
 
template <typename T>
inline const T& VectorT3<T>::operator()(const unsigned int index) const noexcept
{
    ocean_assert(index < 3u);
    return values_[index];
}
 
template <typename T>
inline T& VectorT3<T>::operator()(const unsigned int index) noexcept
{
    ocean_assert(index < 3u);
    return values_[index];
}
 
template <typename T>
inline const T* VectorT3<T>::operator()() const noexcept
{
    return values_;
}
 
template <typename T>
inline T* VectorT3<T>::operator()() noexcept
{
    return values_;
}
 
template <typename T>
inline size_t VectorT3<T>::operator()(const VectorT3<T>& vector) const
{
    size_t seed = std::hash<T>{}(vector.x());
    seed ^= std::hash<T>{}(vector.y()) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
    seed ^= std::hash<T>{}(vector.z()) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
 
    return seed;
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::minValue()
{
    return VectorT3<T>(NumericT<T>::minValue(), NumericT<T>::minValue(), NumericT<T>::minValue());
}
 
template <typename T>
inline VectorT3<T> VectorT3<T>::maxValue()
{
    return VectorT3<T>(NumericT<T>::maxValue(), NumericT<T>::maxValue(), NumericT<T>::maxValue());
}
 
template <>
template <>
inline std::vector<VectorT3<float>> VectorT3<float>::vectors2vectors(std::vector<VectorT3<float>>&& vectors)
{
    return std::move(vectors);
}
 
template <>
template <>
inline std::vector<VectorT3<double>> VectorT3<double>::vectors2vectors(std::vector<VectorT3<double>>&& vectors)
{
    return std::move(vectors);
}
 
template <typename T>
template <typename U>
inline std::vector<VectorT3<T>> VectorT3<T>::vectors2vectors(std::vector<VectorT3<U>>&& vectors)
{
    std::vector<VectorT3<T>> result;
    result.reserve(vectors.size());
 
    for (typename std::vector<VectorT3<U>>::const_iterator i = vectors.cbegin(); i != vectors.cend(); ++i)
    {
        result.emplace_back(*i);
    }
 
    return result;
}
 
template <>
template <>
inline std::vector<VectorT3<float>> VectorT3<float>::vectors2vectors(const std::vector<VectorT3<float>>& vectors)
{
    return vectors;
}
 
template <>
template <>
inline std::vector<VectorT3<double>> VectorT3<double>::vectors2vectors(const std::vector<VectorT3<double>>& vectors)
{
    return vectors;
}
 
template <typename T>
template <typename U>
inline std::vector<VectorT3<T>> VectorT3<T>::vectors2vectors(const std::vector<VectorT3<U>>& vectors)
{
    std::vector<VectorT3<T>> result;
    result.reserve(vectors.size());
 
    for (typename std::vector<VectorT3<U>>::const_iterator i = vectors.cbegin(); i != vectors.cend(); ++i)
    {
        result.emplace_back(*i);
    }
 
    return result;
}
 
template <typename T>
template <typename U>
inline std::vector<VectorT3<T>> VectorT3<T>::vectors2vectors(const VectorT3<U>* vectors, const size_t size)
{
    std::vector< VectorT3<T>> result;
    result.reserve(size);
 
    for (size_t n = 0; n < size; ++n)
    {
        result.emplace_back(vectors[n]);
    }
 
    return result;
}
 
template <typename T>
std::ostream& operator<<(std::ostream& stream, const VectorT3<T>& vector)
{
    stream << "[" << vector.x() << ", " << vector.y() << ", " << vector.z() << "]";
 
    return stream;
}
 
template <bool tActive, typename T>
MessageObject<tActive>& operator<<(MessageObject<tActive>& messageObject, const VectorT3<T>& vector)
{
    return messageObject << "[" << vector.x() << ", " << vector.y() << ", " << vector.z() << "]";
}
 
template <bool tActive, typename T>
MessageObject<tActive>& operator<<(MessageObject<tActive>&& messageObject, const VectorT3<T>& vector)
{
    return messageObject << "[" << vector.x() << ", " << vector.y() << ", " << vector.z() << "]";
}
 
}
 
#endif // META_OCEAN_MATH_VECTOR3_H