magnum/src/Magnum/Math/Vector2.h

#ifndef Magnum_Math_Vector2_h
#define Magnum_Math_Vector2_h
/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
                2020, 2021, 2022, 2023 Vladimír Vondruš <mosra@centrum.cz>

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    copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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*/

/** @file
 * @brief Class @ref Magnum::Math::Vector2, function @ref Magnum::Math::cross()
 */

/* std::declval() is said to be in <utility> but libstdc++, libc++ and MSVC STL
   all have it directly in <type_traits> because it just makes sense */
#include <type_traits>

#include "Magnum/Math/Vector.h"

namespace Magnum { namespace Math {

/**
@brief 2D cross product

2D version of a cross product, also called a [perp-dot product](https://en.wikipedia.org/wiki/Vector_projection#Scalar_rejection),
equivalent to calling @ref cross(const Vector3<T>&, const Vector3<T>&) with Z
coordinate set to @cpp 0 @ce and extracting only Z coordinate from the result
(X and Y coordinates are always zero). Returns @cpp 0 @ce either when one of
the vectors is zero or they are parallel or antiparallel and @cpp 1 @ce when
two *normalized* vectors are perpendicular. @f[
    \boldsymbol a \times \boldsymbol b = \boldsymbol a_\bot \cdot \boldsymbol b = a_xb_y - a_yb_x
@f]

If @f$ \boldsymbol{a} @f$, @f$ \boldsymbol{b} @f$ and @f$ \boldsymbol{c} @f$
are corners of a triangle, @f$ \frac{1}{2}|(\boldsymbol{c} - \boldsymbol{b}) \times (\boldsymbol{a} - \boldsymbol{b})| @f$
is its area. Value of a 2D cross product is also related to a distance of a
point and a line, see
@ref Distance::linePoint(const Vector2<T>&, const Vector2<T>&, const Vector2<T>&)
for more information.
@see @ref Vector2::perpendicular(),
    @ref dot(const Vector<size, T>&, const Vector<size, T>&)
*/
template<class T> inline T cross(const Vector2<T>& a, const Vector2<T>& b) {
    return a._data[0]*b._data[1] - a._data[1]*b._data[0];
}

/**
@brief Two-component vector
@tparam T   Data type

See @ref matrix-vector for brief introduction.
@see @ref Magnum::Vector2, @ref Magnum::Vector3h, @ref Magnum::Vector2d,
    @ref Magnum::Vector2ub, @ref Magnum::Vector2b, @ref Magnum::Vector2us,
    @ref Magnum::Vector2s, @ref Magnum::Vector2ui, @ref Magnum::Vector2i
@configurationvalueref{Magnum::Math::Vector2}
*/
template<class T> class Vector2: public Vector<2, T> {
    public:
        /**
         * @brief Vector in a direction of X axis (right)
         *
         * Usable for translation in given axis, for example:
         *
         * @snippet MagnumMath.cpp Vector2-xAxis
         *
         * @see @ref yAxis(), @ref xScale(), @ref Matrix3::right()
         */
        constexpr static Vector2<T> xAxis(T length = T(1)) { return {length, T(0)}; }

        /**
         * @brief Vector in a direction of Y axis (up)
         *
         * See @ref xAxis() for more information.
         * @see @ref yScale(), @ref Matrix3::up()
         */
        constexpr static Vector2<T> yAxis(T length = T(1)) { return {T(0), length}; }

        /**
         * @brief Scaling vector in a direction of X axis (width)
         *
         * Usable for scaling along given direction, for example:
         *
         * @snippet MagnumMath.cpp Vector2-xScale
         *
         * @see @ref yScale(), @ref xAxis()
         */
        constexpr static Vector2<T> xScale(T scale) { return {scale, T(1)}; }

        /**
         * @brief Scaling vector in a direction of Y axis (height)
         *
         * See @ref xScale() for more information.
         * @see @ref yAxis()
         */
        constexpr static Vector2<T> yScale(T scale) { return {T(1), scale}; }

        /**
         * @brief Default constructor
         *
         * Equivalent to @ref Vector2(ZeroInitT).
         */
        constexpr /*implicit*/ Vector2() noexcept: Vector<2, T>{ZeroInit} {}

        /** @copydoc Vector::Vector(ZeroInitT) */
        constexpr explicit Vector2(ZeroInitT) noexcept: Vector<2, T>{ZeroInit} {}

        /** @copydoc Vector::Vector(NoInitT) */
        explicit Vector2(Magnum::NoInitT) noexcept: Vector<2, T>{Magnum::NoInit} {}

        /** @copydoc Vector::Vector(T) */
        constexpr explicit Vector2(T value) noexcept: Vector<2, T>(value) {}

        /**
         * @brief Constructor
         *
         * @f[
         *      \boldsymbol v = \begin{pmatrix} x \\ y \end{pmatrix}
         * @f]
         */
        constexpr /*implicit*/ Vector2(T x, T y) noexcept: Vector<2, T>(x, y) {}

        /** @copydoc Vector::Vector(const Vector<size, U>&) */
        template<class U> constexpr explicit Vector2(const Vector<2, U>& other) noexcept: Vector<2, T>(other) {}

        /** @brief Construct a vector from external representation */
        template<class U, class V =
            #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Causes ICE */
            decltype(Implementation::VectorConverter<2, T, U>::from(std::declval<U>()))
            #else
            decltype(Implementation::VectorConverter<2, T, U>())
            #endif
            >
        constexpr explicit Vector2(const U& other): Vector<2, T>(Implementation::VectorConverter<2, T, U>::from(other)) {}

        /** @brief Copy constructor */
        constexpr /*implicit*/ Vector2(const Vector<2, T>& other) noexcept: Vector<2, T>(other) {}

        /**
         * @brief X component
         *
         * @see @ref r()
         */
        T& x() { return Vector<2, T>::_data[0]; }
        constexpr T x() const { return Vector<2, T>::_data[0]; } /**< @overload */

        /**
         * @brief Y component
         *
         * @see @ref g()
         */
        T& y() { return Vector<2, T>::_data[1]; }
        constexpr T y() const { return Vector<2, T>::_data[1]; } /**< @overload */

        /**
         * @brief R component
         * @m_since_latest
         *
         * Equivalent to @ref x().
         */
        T& r() { return Vector<2, T>::_data[0]; }
        /**
         * @overload
         * @m_since_latest
         */
        constexpr T r() const { return Vector<2, T>::_data[0]; }

        /**
         * @brief Y component
         * @m_since_latest
         *
         * Equivalent to @ref y().
         */
        T& g() { return Vector<2, T>::_data[1]; }
        /**
         * @overload
         * @m_since_latest
         */
        constexpr T g() const { return Vector<2, T>::_data[1]; }

        /**
         * @brief Perpendicular vector
         *
         * Returns vector rotated 90° counterclockwise. Enabled only for signed
         * types. @f[
         *      \boldsymbol v_\bot = \begin{pmatrix} -v_y \\ v_x \end{pmatrix}
         * @f]
         * @see @ref cross(const Vector2<T>&, const Vector2<T>&),
         *      @ref dot(const Vector<size, T>&, const Vector<size, T>&),
         *      @ref Vector::operator-() const "operator-() const"
         */
        /* For some reason @ref operator-() const doesn't work since 1.8.17 */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        Vector2<T>
        #else
        template<class U = T> typename std::enable_if<std::is_signed<U>::value, Vector2<T>>::type
        #endif
        perpendicular() const { return {-y(), x()}; }

        /**
         * @brief Aspect ratio
         *
         * Returns quotient of the two elements. Enabled only for
         * floating-point types. @f[
         *      a = \frac{v_x}{v_y}
         * @f]
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        T
        #else
        template<class U = T> typename std::enable_if<std::is_floating_point<U>::value, T>::type
        #endif
        aspectRatio() const { return x()/y(); }

        MAGNUM_VECTOR_SUBCLASS_IMPLEMENTATION(2, Vector2)

    private:
        template<class U> friend U cross(const Vector2<U>&, const Vector2<U>&);
};

namespace Implementation {
    template<std::size_t, class> struct TypeForSize;
    template<class T> struct TypeForSize<2, T> { typedef Math::Vector2<typename T::Type> Type; };
    #ifndef MAGNUM_NO_MATH_STRICT_WEAK_ORDERING
    template<class T> struct StrictWeakOrdering<Vector2<T>>: StrictWeakOrdering<Vector<2, T>> {};
    #endif
}

}}

#endif