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@ -26,7 +26,7 @@
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*/ |
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/** @file
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* @brief Class Magnum::Math::Vector |
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* @brief Class @ref Magnum::Math::Vector |
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*/ |
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#include <cmath> |
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@ -92,7 +92,9 @@ template<std::size_t size, class T> class Vector {
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* antiparallel. @f[ |
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* \boldsymbol a \cdot \boldsymbol b = \sum_{i=0}^{n-1} \boldsymbol a_i \boldsymbol b_i |
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* @f] |
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* @see dot() const, operator-(), Vector2::perpendicular() |
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* @see dot() const, @ref operator-(), |
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* @ref Vector2::perpendicular() |
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* @todoc Explicit reference when Doxygen can handle const |
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*/ |
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static T dot(const Vector<size, T>& a, const Vector<size, T>& b) { |
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return (a*b).sum(); |
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@ -104,7 +106,8 @@ template<std::size_t size, class T> class Vector {
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* Expects that both vectors are normalized. @f[ |
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* \theta = acos \left( \frac{\boldsymbol a \cdot \boldsymbol b}{|\boldsymbol a| |\boldsymbol b|} \right) = acos (\boldsymbol a \cdot \boldsymbol b) |
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* @f] |
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* @see isNormalized(), Quaternion::angle(), Complex::angle() |
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* @see @ref isNormalized(), @ref Quaternion::angle(), |
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* @ref Complex::angle() |
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*/ |
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static Rad<T> angle(const Vector<size, T>& normalizedA, const Vector<size, T>& normalizedB); |
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@ -202,7 +205,7 @@ template<std::size_t size, class T> class Vector {
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* @brief Raw data |
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* @return One-dimensional array of `size` length. |
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* |
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* @see operator[]() |
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* @see @ref operator[]() |
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*/ |
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T* data() { |
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#ifndef CORRADE_MSVC2013_COMPATIBILITY |
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@ -224,7 +227,7 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Value at given position |
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* |
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* @see data() |
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* @see @ref data() |
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*/ |
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T& operator[](std::size_t pos) { return _data[pos]; } |
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constexpr T operator[](std::size_t pos) const { return _data[pos]; } /**< @overload */ |
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@ -260,7 +263,7 @@ template<std::size_t size, class T> class Vector {
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* @f[ |
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* |\boldsymbol a \cdot \boldsymbol a - 0| < \epsilon^2 \cong \epsilon |
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* @f] |
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* @see dot(), normalized() |
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* @see @ref dot(), @ref normalized() |
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*/ |
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bool isZero() const { |
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return Implementation::isZeroSquared(dot()); |
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@ -272,7 +275,7 @@ template<std::size_t size, class T> class Vector {
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* The vector is normalized if it has unit length: @f[ |
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* |\boldsymbol a \cdot \boldsymbol a - 1| < 2 \epsilon + \epsilon^2 \cong 2 \epsilon |
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* @f] |
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* @see dot(), normalized() |
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* @see @ref dot(), @ref normalized() |
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*/ |
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bool isNormalized() const { |
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return Implementation::isNormalizedSquared(dot()); |
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@ -284,7 +287,7 @@ template<std::size_t size, class T> class Vector {
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* @f[ |
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* \boldsymbol b_i = -\boldsymbol a_i |
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* @f] |
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* @see Vector2::perpendicular() |
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* @see @ref Vector2::perpendicular() |
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*/ |
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Vector<size, T> operator-() const; |
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@ -305,7 +308,7 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Add vector |
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* |
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* @see operator+=(), sum() |
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* @see @ref operator+=(), @ref sum() |
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*/ |
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Vector<size, T> operator+(const Vector<size, T>& other) const { |
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return Vector<size, T>(*this) += other; |
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@ -328,7 +331,7 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Subtract vector |
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* |
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* @see operator-=() |
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* @see @ref operator-=() |
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*/ |
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Vector<size, T> operator-(const Vector<size, T>& other) const { |
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return Vector<size, T>(*this) -= other; |
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@ -340,8 +343,8 @@ template<std::size_t size, class T> class Vector {
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* The computation is done in-place. @f[ |
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* \boldsymbol a_i = b \boldsymbol a_i |
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* @f] |
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* @see operator*=(const Vector<size, T>&), |
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* operator*=(Vector<size, Integral>&, FloatingPoint) |
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* @see @ref operator*=(const Vector<size, T>&), |
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* @ref operator*=(Vector<size, Integral>&, FloatingPoint) |
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*/ |
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Vector<size, T>& operator*=(T number) { |
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for(std::size_t i = 0; i != size; ++i) |
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@ -353,9 +356,9 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Multiply vector with number |
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* |
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* @see operator*(const Vector<size, T>&) const, |
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* operator*=(T), operator*(T, const Vector<size, T>&), |
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* operator*(const Vector<size, Integral>&, FloatingPoint) |
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* @see @ref operator*(const Vector<size, T>&) const, |
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* @ref operator*=(T), operator*(T, const Vector<size, T>&), |
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* @ref operator*(const Vector<size, Integral>&, FloatingPoint) |
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*/ |
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Vector<size, T> operator*(T number) const { |
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return Vector<size, T>(*this) *= number; |
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@ -367,8 +370,8 @@ template<std::size_t size, class T> class Vector {
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* The computation is done in-place. @f[ |
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* \boldsymbol a_i = \frac{\boldsymbol a_i} b |
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* @f] |
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* @see operator/=(const Vector<size, T>&), |
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* operator/=(Vector<size, Integral>&, FloatingPoint) |
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* @see @ref operator/=(const Vector<size, T>&), |
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* @ref operator/=(Vector<size, Integral>&, FloatingPoint) |
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*/ |
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Vector<size, T>& operator/=(T number) { |
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for(std::size_t i = 0; i != size; ++i) |
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@ -380,9 +383,9 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Divide vector with number |
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* |
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* @see operator/(const Vector<size, T>&) const, |
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* operator/=(T), operator/(T, const Vector<size, T>&), |
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* operator/(const Vector<size, Integral>&, FloatingPoint) |
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* @see @ref operator/(const Vector<size, T>&) const, |
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* @ref operator/=(T), operator/(T, const Vector<size, T>&), |
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* @ref operator/(const Vector<size, Integral>&, FloatingPoint) |
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*/ |
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Vector<size, T> operator/(T number) const { |
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return Vector<size, T>(*this) /= number; |
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@ -394,8 +397,8 @@ template<std::size_t size, class T> class Vector {
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* The computation is done in-place. @f[ |
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* \boldsymbol a_i = \boldsymbol a_i \boldsymbol b_i |
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* @f] |
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* @see operator*=(T), |
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* operator*=(Vector<size, Integral>&, const Vector<size, FloatingPoint>&) |
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* @see @ref operator*=(T), |
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* @ref operator*=(Vector<size, Integral>&, const Vector<size, FloatingPoint>&) |
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*/ |
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Vector<size, T>& operator*=(const Vector<size, T>& other) { |
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for(std::size_t i = 0; i != size; ++i) |
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@ -407,8 +410,8 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Multiply vector component-wise |
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* |
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* @see operator*(T) const, operator*=(const Vector<size, T>&), |
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* operator*(const Vector<size, Integral>&, const Vector<size, FloatingPoint>&), |
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* @see @ref operator*(T) const, @ref operator*=(const Vector<size, T>&), |
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* @ref operator*(const Vector<size, Integral>&, const Vector<size, FloatingPoint>&), |
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* @ref product() |
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*/ |
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Vector<size, T> operator*(const Vector<size, T>& other) const { |
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@ -421,8 +424,8 @@ template<std::size_t size, class T> class Vector {
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* The computation is done in-place. @f[ |
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* \boldsymbol a_i = \frac{\boldsymbol a_i}{\boldsymbol b_i} |
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* @f] |
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* @see operator/=(T), |
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* operator/=(Vector<size, Integral>&, const Vector<size, FloatingPoint>&) |
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* @see @ref operator/=(T), |
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* @ref operator/=(Vector<size, Integral>&, const Vector<size, FloatingPoint>&) |
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*/ |
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Vector<size, T>& operator/=(const Vector<size, T>& other) { |
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for(std::size_t i = 0; i != size; ++i) |
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@ -434,8 +437,8 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Divide vector component-wise |
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* |
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* @see operator/(T) const, operator/=(const Vector<size, T>&), |
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* operator/(const Vector<size, Integral>&, const Vector<size, FloatingPoint>&) |
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* @see @ref operator/(T) const, @ref operator/=(const Vector<size, T>&), |
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* @ref operator/(const Vector<size, Integral>&, const Vector<size, FloatingPoint>&) |
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*/ |
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Vector<size, T> operator/(const Vector<size, T>& other) const { |
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return Vector<size, T>(*this) /= other; |
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@ -444,22 +447,24 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief Dot product of the vector |
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* |
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* Should be used instead of length() for comparing vector length with |
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* other values, because it doesn't compute the square root. @f[ |
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* Should be used instead of @ref length() for comparing vector length |
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* with other values, because it doesn't compute the square root. @f[ |
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* \boldsymbol a \cdot \boldsymbol a = \sum_{i=0}^{n-1} \boldsymbol a_i^2 |
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* @f] |
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* @see dot(const Vector<size, T>&, const Vector<size, T>&), isNormalized() |
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* @see @ref dot(const Vector<size, T>&, const Vector<size, T>&), |
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* @ref isNormalized() |
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*/ |
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T dot() const { return dot(*this, *this); } |
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/**
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* @brief %Vector length |
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* |
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* See also dot() const which is faster for comparing length with other |
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* values. @f[ |
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* See also @ref dot() const which is faster for comparing length with |
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* other values. @f[ |
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* |\boldsymbol a| = \sqrt{\boldsymbol a \cdot \boldsymbol a} |
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* @f] |
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* @see lengthInverted(), Math::sqrt(), normalized(), resized() |
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* @see @ref lengthInverted(), @ref Math::sqrt(), @ref normalized(), |
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* @ref resized() |
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* @todo something like std::hypot() for possibly better precision? |
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*/ |
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T length() const { return std::sqrt(dot()); } |
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@ -470,14 +475,15 @@ template<std::size_t size, class T> class Vector {
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* @f[ |
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* \frac{1}{|\boldsymbol a|} = \frac{1}{\sqrt{\boldsymbol a \cdot \boldsymbol a}} |
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* @f] |
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* @see length(), Math::sqrtInverted(), normalized(), resized() |
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* @see @ref length(), @ref Math::sqrtInverted(), @ref normalized(), |
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* @ref resized() |
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*/ |
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T lengthInverted() const { return T(1)/length(); } |
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/**
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* @brief Normalized vector (of unit length) |
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* |
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* @see isNormalized(), lengthInverted(), resized() |
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* @see @ref isNormalized(), @ref lengthInverted(), @ref resized() |
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*/ |
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Vector<size, T> normalized() const { return *this*lengthInverted(); } |
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@ -485,12 +491,12 @@ template<std::size_t size, class T> class Vector {
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* @brief Resized vector |
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* |
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* Convenience equivalent to the following code. Due to operation order |
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* this function is faster than the obvious way of sizing normalized() |
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* vector. |
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* this function is faster than the obvious way of sizing |
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* @ref normalized() vector. |
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* @code |
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* vec*(vec.lengthInverted()*length) // the brackets are important
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* @endcode |
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* @see normalized() |
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* @see @ref normalized() |
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*/ |
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Vector<size, T> resized(T length) const { |
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return *this*(lengthInverted()*length); |
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@ -502,7 +508,7 @@ template<std::size_t size, class T> class Vector {
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* Returns vector projected onto @p line. @f[ |
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* \boldsymbol a_1 = \frac{\boldsymbol a \cdot \boldsymbol b}{\boldsymbol b \cdot \boldsymbol b} \boldsymbol b |
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* @f] |
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* @see dot(), projectedOntoNormalized() |
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* @see @ref dot(), @ref projectedOntoNormalized() |
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*/ |
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Vector<size, T> projected(const Vector<size, T>& line) const { |
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return line*dot(*this, line)/line.dot(); |
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@ -511,26 +517,27 @@ template<std::size_t size, class T> class Vector {
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/**
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* @brief %Vector projected onto normalized line |
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* |
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* Slightly faster alternative to projected(), expects @p line to be |
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* normalized. @f[ |
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* Slightly faster alternative to @ref projected(), expects @p line to |
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* be normalized. @f[ |
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* \boldsymbol a_1 = \frac{\boldsymbol a \cdot \boldsymbol b}{\boldsymbol b \cdot \boldsymbol b} \boldsymbol b = |
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* (\boldsymbol a \cdot \boldsymbol b) \boldsymbol b |
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* @f] |
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* @see dot() |
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* @see dot() const |
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* @todoc Explicit reference when Doxygen can handle const |
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*/ |
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Vector<size, T> projectedOntoNormalized(const Vector<size, T>& line) const; |
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/**
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* @brief Sum of values in the vector |
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* |
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* @see operator+() |
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* @see @ref operator+() |
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*/ |
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T sum() const; |
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/**
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* @brief Product of values in the vector |
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* |
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* @see operator*(const Vector<size, T>&) const |
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* @see @ref operator*(const Vector<size, T>&) const |
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*/ |
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T product() const; |
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@ -575,7 +582,7 @@ template<std::size_t size, class T> class Vector {
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/** @relates Vector
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@brief Multiply number with vector |
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Same as Vector::operator*(T) const. |
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Same as @ref Vector::operator*(T) const. |
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*/ |
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template<std::size_t size, class T> inline Vector<size, T> operator*( |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -594,7 +601,7 @@ template<std::size_t size, class T> inline Vector<size, T> operator*(
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@f[ |
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\boldsymbol c_i = \frac b {\boldsymbol a_i} |
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@f] |
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@see Vector::operator/(T) const |
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@see @ref Vector::operator/(T) const |
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*/ |
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template<std::size_t size, class T> inline Vector<size, T> operator/( |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -883,8 +890,8 @@ operator>>(const Vector<size, Integral>& vector,
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/** @relates Vector
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@brief Multiply integral vector with floating-point number and assign |
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Similar to Vector::operator*=(T), except that the multiplication is done in |
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floating-point. The computation is done in-place. |
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Similar to @ref Vector::operator*=(T), except that the multiplication is done |
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in floating-point. The computation is done in-place. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -902,8 +909,8 @@ operator*=(Vector<size, Integral>& vector, FloatingPoint number) {
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/** @relates Vector
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@brief Multiply integral vector with floating-point number |
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Similar to Vector::operator*(T) const, except that the multiplication is done |
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in floating-point. |
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Similar to @ref Vector::operator*(T) const, except that the multiplication is |
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done in floating-point. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -919,7 +926,7 @@ operator*(const Vector<size, Integral>& vector, FloatingPoint number) {
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/** @relates Vector
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@brief Multiply floating-point number with integral vector |
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Same as operator*(const Vector<size, Integral>&, FloatingPoint). |
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Same as @ref operator*(const Vector<size, Integral>&, FloatingPoint). |
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*/ |
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template<std::size_t size, class FloatingPoint, class Integral> inline |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -934,7 +941,7 @@ operator*(FloatingPoint number, const Vector<size, Integral>& vector) {
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/** @relates Vector
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@brief Divide integral vector with floating-point number and assign |
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Similar to Vector::operator/=(T), except that the division is done in |
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Similar to @ref Vector::operator/=(T), except that the division is done in |
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floating-point. The computation is done in-place. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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@ -953,7 +960,7 @@ operator/=(Vector<size, Integral>& vector, FloatingPoint number) {
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/** @relates Vector
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@brief Divide integral vector with floating-point number |
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Similar to Vector::operator/(T) const, except that the division is done in |
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Similar to @ref Vector::operator/(T) const, except that the division is done in |
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floating-point. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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@ -970,7 +977,7 @@ operator/(const Vector<size, Integral>& vector, FloatingPoint number) {
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/** @relates Vector
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@brief Multiply integral vector with floating-point vector component-wise and assign |
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Similar to Vector::operator*=(const Vector<size, T>&), except that the |
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Similar to @ref Vector::operator*=(const Vector<size, T>&), except that the |
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multiplication is done in floating-point. The computation is done in-place. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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@ -989,10 +996,10 @@ operator*=(Vector<size, Integral>& a, const Vector<size, FloatingPoint>& b) {
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/** @relates Vector
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@brief Multiply integral vector with floating-point vector component-wise |
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Similar to Vector::operator*(const Vector<size, T>&) const, except that the |
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multiplication is done in floating-point. The result is always integral vector, |
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convert both arguments to the same floating-point type to have floating-point |
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result. |
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Similar to @ref Vector::operator*(const Vector<size, T>&) const, except that |
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the multiplication is done in floating-point. The result is always integral |
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vector, convert both arguments to the same floating-point type to have |
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floating-point result. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -1008,7 +1015,7 @@ operator*(const Vector<size, Integral>& a, const Vector<size, FloatingPoint>& b)
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/** @relates Vector
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@brief Multiply floating-point vector with integral vector component-wise |
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Same as operator*(const Vector<size, Integral>&, const Vector<size, FloatingPoint>&). |
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Same as @ref operator*(const Vector<size, Integral>&, const Vector<size, FloatingPoint>&). |
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*/ |
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template<std::size_t size, class FloatingPoint, class Integral> inline |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -1023,8 +1030,8 @@ operator*(const Vector<size, FloatingPoint>& a, const Vector<size, Integral>& b)
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/** @relates Vector
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@brief Divide integral vector with floating-point vector component-wise and assign |
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Similar to Vector::operator/=(const Vector<size, T>&), except that the division |
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is done in floating-point. The computation is done in-place. |
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Similar to @ref Vector::operator/=(const Vector<size, T>&), except that the |
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division is done in floating-point. The computation is done in-place. |
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*/ |
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template<std::size_t size, class Integral, class FloatingPoint> inline |
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#ifdef DOXYGEN_GENERATING_OUTPUT |
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@ -1042,8 +1049,8 @@ operator/=(Vector<size, Integral>& a, const Vector<size, FloatingPoint>& b) {
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/** @relates Vector
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@brief Divide integral vector with floating-point vector component-wise |
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Similar to Vector::operator/(const Vector<size, T>&) const, except that the |
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division is done in floating-point. The result is always integral vector, |
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Similar to @ref Vector::operator/(const Vector<size, T>&) const, except that |
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the division is done in floating-point. The result is always integral vector, |
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convert both arguments to the same floating-point type to have floating-point |
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result. |
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*/ |
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Vladimír Vondruš
12 years ago