magnum/src/Magnum/Math/Frustum.h

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

    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
                2020, 2021, 2022, 2023, 2024, 2025, 2026
              Vladimír Vondruš <mosra@centrum.cz>
    Copyright © 2016, 2020 Jonathan Hale <squareys@googlemail.com>

    Permission is hereby granted, free of charge, to any person obtaining a
    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
    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

/** @file
 * @brief Class @ref Magnum::Math::Frustum
 */

/* 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 <Corrade/configure.h>
#ifndef CORRADE_SINGLES_NO_DEBUG
#include <Corrade/Utility/Debug.h>
#endif

#include "Magnum/Math/Matrix4.h"
#include "Magnum/Math/Vector4.h"

#ifdef CORRADE_TARGET_WINDOWS /* I so HATE windef.h */
/* far/near and FAR/NEAR are defined by minwindef.h, but the former are used by this file as variables.
   While they are all empty defines, the Windows headers expect FAR/NEAR to be defined and so we redefine them here.
   far/near are left undefined because they are not used directly in Windows headers.
   */
#undef near
#undef NEAR
#define NEAR
#undef far
#undef FAR
#define FAR
#endif

namespace Magnum { namespace Math {

namespace Implementation {
    template<class, class> struct FrustumConverter;
}

/**
@brief Camera frustum

Stores camera frustum planes in order left (index `0`), right (index `1`),
bottom (index `2`), top (index `3`), near (index `4`) and far (index `5`).
@see @ref Magnum::Frustum, @ref Magnum::Frustumd,
    @ref Intersection::pointFrustum(), @ref Intersection::rangeFrustum(),
    @ref Intersection::aabbFrustum(), @ref Intersection::sphereFrustum()
*/
template<class T> class Frustum {
    public:
        /** @brief Create a frustum from a projection matrix */
        static Frustum<T> fromMatrix(const Matrix4<T>& m) {
            return {m.row(3) + m.row(0),
                    m.row(3) - m.row(0),
                    m.row(3) + m.row(1),
                    m.row(3) - m.row(1),
                    m.row(3) + m.row(2),
                    m.row(3) - m.row(2)};
        }

        /**
         * @brief Default constructor
         *
         * Equivalent to @ref Frustum(IdentityInitT).
         */
        constexpr /*implicit*/ Frustum() noexcept: Frustum<T>{IdentityInit} {}

        /**
         * @brief Identity constructor
         *
         * Equivalent to creating a frustum from an identity matrix.
         * @see @ref fromMatrix()
         */
        constexpr explicit Frustum(IdentityInitT) noexcept;

        /** @brief Construct a frustum without initializing the contents */
        explicit Frustum(Magnum::NoInitT) noexcept: _data{Vector4<T>{Magnum::NoInit}, Vector4<T>{Magnum::NoInit}, Vector4<T>{Magnum::NoInit}, Vector4<T>{Magnum::NoInit}, Vector4<T>{Magnum::NoInit}, Vector4<T>{Magnum::NoInit}} {}

        /**
         * @brief Construct a frustum from plane equations
         *
         * The equations are in a form @f$ ax + by + cz + d = 0 @f$. You can
         * use @ref planeEquation() to calculate the coefficients from a normal
         * and a point.
         */
        constexpr /*implicit*/ Frustum(const Vector4<T>& left, const Vector4<T>& right, const Vector4<T>& bottom, const Vector4<T>& top, const Vector4<T>& near, const Vector4<T>& far) noexcept: _data{left, right, bottom, top, near, far} {}

        /**
         * @brief Construct a frustum from another of different type
         *
         * Performs only default casting on the values, no rounding or
         * anything else.
         */
        template<class U> constexpr explicit Frustum(const Frustum<U>& other) noexcept;

        /** @brief Construct a frustum from external representation */
        template<class U, class = decltype(Implementation::FrustumConverter<T, U>::from(std::declval<U>()))> constexpr explicit Frustum(const U& other) noexcept: Frustum<T>{Implementation::FrustumConverter<T, U>::from(other)} {}

        /** @brief Convert the frustum to external representation */
        template<class U, class = decltype(Implementation::FrustumConverter<T, U>::to(std::declval<Frustum<T>>()))> constexpr explicit operator U() const {
            return Implementation::FrustumConverter<T, U>::to(*this);
        }

        /**
         * @brief Equality comparison
         *
         * Done by comparing the underlying vectors, which internally uses
         * @ref TypeTraits::equals(), i.e. a fuzzy compare.
         */
        bool operator==(const Frustum<T>& other) const {
            for(std::size_t i = 0; i != 6; ++i)
                if(_data[i] != other._data[i]) return false;

            return true;
        }

        /**
         * @brief Non-equality comparison
         *
         * Done by comparing the underlying vectors, which internally uses
         * @ref TypeTraits::equals(), i.e. a fuzzy compare.
         */
        bool operator!=(const Frustum<T>& other) const {
            return !operator==(other);
        }

        /**
         * @brief Raw data
         *
         * Contrary to what Doxygen shows, returns reference to a
         * one-dimensional fixed-size array of 24 elements, i.e.
         * @cpp T(&)[24] @ce.
         * @see @ref operator[]()
         * @todoc Fix once there's a possibility to patch the signature in a
         *      post-processing step (https://github.com/mosra/m.css/issues/56)
         */
        #ifdef DOXYGEN_GENERATING_OUTPUT
        T* data();
        const T* data() const; /**< @overload */
        #else
        auto data() -> T(&)[24] {
            return reinterpret_cast<T(&)[24]>(_data);
        }
        /* Can't really be constexpr anymore, the only other solution is having
           an union with `T _rawData[24]` and return that, but in a constexpr
           context it'd mean we'd have to initialize it instead of `_data` in
           the constructor ... and then operator[]() could not be constexpr
           anymore. I can't think of a practical use case where constexpr
           data() would be needed and operator[]() could not be used instead.
           Similarly to RectangularMatrix::data(), having a statically sized
           array returned is a far more useful property than constexpr, so that
           wins. */
        auto data() const -> const T(&)[24] {
            return reinterpret_cast<const T(&)[24]>(_data);
        }
        #endif

        /**
         * @brief Plane at given index
         * @m_since{2020,06}
         *
         * Expects that @p i is less than @cpp 6 @ce.
         */
        CORRADE_CONSTEXPR14 Vector4<T>& operator[](std::size_t i) {
            CORRADE_DEBUG_ASSERT(i < 6, "Math::Frustum::operator[](): index" << i << "out of range",
                _data[i]);
            return _data[i];
        }

        /** @overload */
        /* returns const& so [][] operations are also constexpr */
        constexpr const Vector4<T>& operator[](std::size_t i) const {
            return CORRADE_CONSTEXPR_DEBUG_ASSERT(i < 6, "Math::Frustum::operator[](): index" << i << "out of range"), _data[i];
        }

        /**
         * @brief First plane
         * @m_since{2019,10}
         *
         * Together with @ref end() useful for range access, for example here
         * to check for a point/frustum intersection, similarly to
         * @ref Intersection::pointFrustum():
         *
         * @snippet Math.cpp Frustum-range
         */
        CORRADE_CONSTEXPR14 Vector4<T>* begin() { return _data; }

        /**
         * @overload
         * @m_since{2019,10}
         */
        constexpr const Vector4<T>* begin() const { return _data; }

        /**
         * @overload
         * @m_since{2019,10}
         */
        constexpr const Vector4<T>* cbegin() const { return _data; }

        /**
         * @brief (One after) last plane
         * @m_since{2019,10}
         */
        CORRADE_CONSTEXPR14 Vector4<T>* end() { return _data + 6; }

        /**
         * @overload
         * @m_since{2019,10}
         */
        constexpr const Vector4<T>* end() const { return _data + 6; }

        /**
         * @overload
         * @m_since{2019,10}
         */
        constexpr const Vector4<T>* cend() const { return _data + 6; }

        /**
         * @brief Left plane
         * @m_since{2020,06}
         */
        CORRADE_CONSTEXPR14 Vector4<T>& left() { return _data[0]; }
        constexpr Vector4<T> left() const { return _data[0]; } /**< @overload */

        /**
         * @brief Right plane
         * @m_since{2020,06}
         */
        CORRADE_CONSTEXPR14 Vector4<T>& right() { return _data[1]; }
        constexpr Vector4<T> right() const { return _data[1]; } /**< @overload */

        /**
         * @brief Bottom plane
         * @m_since{2020,06}
         */
        CORRADE_CONSTEXPR14 Vector4<T>& bottom() { return _data[2]; }
        constexpr Vector4<T> bottom() const { return _data[2]; } /**< @overload */

        /**
         * @brief Top plane
         * @m_since{2020,06}
         */
        CORRADE_CONSTEXPR14 Vector4<T>& top() { return _data[3]; }
        constexpr Vector4<T> top() const { return _data[3]; } /**< @overload */

        /**
         * @brief Near plane
         * @m_since{2020,06}
         */
        CORRADE_CONSTEXPR14 Vector4<T>& near() { return _data[4]; }
        constexpr Vector4<T> near() const { return _data[4]; } /**< @overload */

        /**
         * @brief Far plane
         * @m_since{2020,06}
         */
        CORRADE_CONSTEXPR14 Vector4<T>& far() { return _data[5]; }
        constexpr Vector4<T> far() const { return _data[5]; } /**< @overload */

    private:
        Vector4<T> _data[6];
};

#ifndef CORRADE_SINGLES_NO_DEBUG
/** @debugoperator{Frustum} */
template<class T> Debug& operator<<(Debug& debug, const Frustum<T>& value) {
    debug << "Frustum({" << Debug::nospace;
    for(std::size_t i = 0; i != 6; ++i) {
        if(i != 0) debug << Debug::nospace << "},\n        {" << Debug::nospace;
        for(std::size_t j = 0; j != 4; ++j) {
            if(j != 0) debug << Debug::nospace << ",";
            debug << value[i][j];
        }
    }
    return debug << Debug::nospace << "})";
}

/* Explicit instantiation for commonly used types */
#ifndef DOXYGEN_GENERATING_OUTPUT
extern template MAGNUM_EXPORT Debug& operator<<(Debug&, const Frustum<Float>&);
extern template MAGNUM_EXPORT Debug& operator<<(Debug&, const Frustum<Double>&);
#endif
#endif

template<class T> constexpr Frustum<T>::Frustum(IdentityInitT) noexcept: _data{
    { 1.0f,  0.0f,  0.0f, 1.0f},
    {-1.0f,  0.0f,  0.0f, 1.0f},
    { 0.0f,  1.0f,  0.0f, 1.0f},
    { 0.0f, -1.0f,  0.0f, 1.0f},
    { 0.0f,  0.0f,  1.0f, 1.0f},
    { 0.0f,  0.0f, -1.0f, 1.0f}} {}

template<class T> template<class U> constexpr Frustum<T>::Frustum(const Frustum<U>& other) noexcept: _data{
    Vector4<T>{other[0]},
    Vector4<T>{other[1]},
    Vector4<T>{other[2]},
    Vector4<T>{other[3]},
    Vector4<T>{other[4]},
    Vector4<T>{other[5]}} {}

#ifndef MAGNUM_NO_MATH_STRICT_WEAK_ORDERING
namespace Implementation {

template<class T> struct StrictWeakOrdering<Frustum<T>> {
    bool operator()(const Frustum<T>& a, const Frustum<T>& b) const {
        StrictWeakOrdering<Vector<4, T>> o;
        for(std::size_t i = 0; i < 6; ++i) {
            if(o(a[i], b[i]))
                return true;
            if(o(b[i], a[i]))
                return false;
        }

        return false; /* a and b are equivalent */
    }
};

}
#endif

}}

#endif