magnum/src/Magnum/Math/Matrix4.h

#ifndef Magnum_Math_Matrix4_h
#define Magnum_Math_Matrix4_h
/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014
              Vladimír Vondruš <mosra@centrum.cz>

    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
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    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

/** @file
 * @brief Class @ref Magnum::Math::Matrix4
 */

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

#ifdef CORRADE_TARGET_WINDOWS /* I so HATE windef.h */
#undef near
#undef far
#endif

namespace Magnum { namespace Math {

/**
@brief 3D transformation matrix
@tparam T   Underlying data type

See @ref matrix-vector and @ref transformations for brief introduction.
@see @ref Magnum::Matrix4, @ref Magnum::Matrix4d, @ref Matrix4x4,
    @ref DualQuaternion, @ref SceneGraph::MatrixTransformation3D
@configurationvalueref{Magnum::Math::Matrix4}
 */
template<class T> class Matrix4: public Matrix4x4<T> {
    public:
        /**
         * @brief 3D translation
         * @param vector    Translation vector
         *
         * @see @ref translation(), @ref DualQuaternion::translation(),
         *      @ref Matrix3::translation(const Vector2<T>&),
         *      @ref Vector3::xAxis(), @ref Vector3::yAxis(),
         *      @ref Vector3::zAxis()
         */
        constexpr static Matrix4<T> translation(const Vector3<T>& vector) {
            return {{      T(1),       T(0),       T(0), T(0)},
                    {      T(0),       T(1),       T(0), T(0)},
                    {      T(0),       T(0),       T(1), T(0)},
                    {vector.x(), vector.y(), vector.z(), T(1)}};
        }

        /**
         * @brief 3D scaling
         * @param vector    Scaling vector
         *
         * @see @ref rotationScaling(),
         *      @ref Matrix3::scaling(const Vector2<T>&),
         *      @ref Vector3::xScale(), @ref Vector3::yScale(),
         *      @ref Vector3::zScale()
         */
        constexpr static Matrix4<T> scaling(const Vector3<T>& vector) {
            return {{vector.x(),       T(0),       T(0), T(0)},
                    {      T(0), vector.y(),       T(0), T(0)},
                    {      T(0),       T(0), vector.z(), T(0)},
                    {      T(0),       T(0),       T(0), T(1)}};
        }

        /**
         * @brief 3D rotation around arbitrary axis
         * @param angle             Rotation angle (counterclockwise)
         * @param normalizedAxis    Normalized rotation axis
         *
         * Expects that the rotation axis is normalized. If possible, use
         * faster alternatives like @ref rotationX(), @ref rotationY() and
         * @ref rotationZ().
         * @see rotation() const, @ref Quaternion::rotation(),
         *      @ref DualQuaternion::rotation(), @ref Matrix3::rotation(Rad),
         *      @ref Vector3::xAxis(), @ref Vector3::yAxis(),
         *      @ref Vector3::zAxis(), @ref Vector::isNormalized()
         * @todoc Explicit reference when Doxygen can handle const
         */
        static Matrix4<T> rotation(Rad<T> angle, const Vector3<T>& normalizedAxis);

        /**
         * @brief 3D rotation around X axis
         * @param angle Rotation angle (counterclockwise)
         *
         * Faster than calling `%Matrix4::rotation(angle, %Vector3::xAxis())`.
         * @see @ref rotation(Rad, const Vector3<T>&), @ref rotationY(),
         *      @ref rotationZ(), rotation() const,
         *      @ref Quaternion::rotation(), @ref Matrix3::rotation(Rad)
         * @todoc Explicit reference when Doxygen can handle const
         */
        static Matrix4<T> rotationX(Rad<T> angle);

        /**
         * @brief 3D rotation around Y axis
         * @param angle Rotation angle (counterclockwise)
         *
         * Faster than calling `%Matrix4::rotation(angle, %Vector3::yAxis())`.
         * @see @ref rotation(Rad, const Vector3<T>&), @ref rotationX(),
         *      @ref rotationZ(), rotation() const,
         *      @ref Quaternion::rotation(), @ref Matrix3::rotation(Rad)
         * @todoc Explicit reference when Doxygen can handle const
         */
        static Matrix4<T> rotationY(Rad<T> angle);

        /**
         * @brief 3D rotation matrix around Z axis
         * @param angle Rotation angle (counterclockwise)
         *
         * Faster than calling `%Matrix4::rotation(angle, %Vector3::zAxis())`.
         * @see @ref rotation(Rad, const Vector3<T>&), @ref rotationX(),
         *      @ref rotationY(), rotation() const,
         *      @ref Quaternion::rotation(), @ref Matrix3::rotation(Rad)
         * @todoc Explicit reference when Doxygen can handle const
         */
        static Matrix4<T> rotationZ(Rad<T> angle);

        /**
         * @brief 3D reflection matrix
         * @param normal    Normal of the plane through which to reflect
         *
         * Expects that the normal is normalized.
         * @see @ref Matrix3::reflection(), @ref Vector::isNormalized()
         */
        static Matrix4<T> reflection(const Vector3<T>& normal);

        /**
         * @brief 3D orthographic projection matrix
         * @param size      Size of the view
         * @param near      Near clipping plane
         * @param far       Far clipping plane
         *
         * @see @ref perspectiveProjection(), @ref Matrix3::projection()
         */
        static Matrix4<T> orthographicProjection(const Vector2<T>& size, T near, T far);

        /**
         * @brief 3D perspective projection matrix
         * @param size      Size of near clipping plane
         * @param near      Near clipping plane
         * @param far       Far clipping plane
         *
         * @see @ref orthographicProjection(), @ref Matrix3::projection()
         */
        static Matrix4<T> perspectiveProjection(const Vector2<T>& size, T near, T far);

        /**
         * @brief 3D perspective projection matrix
         * @param fov           Field of view angle (horizontal)
         * @param aspectRatio   Aspect ratio
         * @param near          Near clipping plane
         * @param far           Far clipping plane
         *
         * @see @ref orthographicProjection(), @ref Matrix3::projection()
         */
        static Matrix4<T> perspectiveProjection(Rad<T> fov, T aspectRatio, T near, T far) {
            const T xyScale = 2*std::tan(T(fov)/2)*near;
            return perspectiveProjection(Vector2<T>(xyScale, xyScale/aspectRatio), near, far);
        }

        /**
         * @brief Create matrix from rotation/scaling part and translation part
         * @param rotationScaling   Rotation/scaling part (upper-left 3x3
         *      matrix)
         * @param translation       Translation part (first three elements of
         *      fourth column)
         *
         * @see @ref rotationScaling(), translation() const
         * @todoc Explicit reference when Doxygen can handle const
         */
        constexpr static Matrix4<T> from(const Matrix3x3<T>& rotationScaling, const Vector3<T>& translation) {
            return {{rotationScaling[0], T(0)},
                    {rotationScaling[1], T(0)},
                    {rotationScaling[2], T(0)},
                    {       translation, T(1)}};
        }

        /** @copydoc Matrix::Matrix(ZeroType) */
        constexpr explicit Matrix4(typename Matrix4x4<T>::ZeroType): Matrix4x4<T>(Matrix4x4<T>::Zero) {}

        /**
         * @brief Default constructor
         *
         * Creates identity matrix. You can also explicitly call this
         * constructor with `%Matrix4 m(Matrix4::Identity);`. Optional
         * parameter @p value allows you to specify value on diagonal.
         */
        constexpr /*implicit*/ Matrix4(typename Matrix4x4<T>::IdentityType = (Matrix4x4<T>::Identity), T value = T(1)): Matrix4x4<T>(Matrix4x4<T>::Identity, value) {}

        /** @brief %Matrix from column vectors */
        constexpr /*implicit*/ Matrix4(const Vector4<T>& first, const Vector4<T>& second, const Vector4<T>& third, const Vector4<T>& fourth): Matrix4x4<T>(first, second, third, fourth) {}

        /** @copydoc Matrix::Matrix(const RectangularMatrix<size, size, U>&) */
        template<class U> constexpr explicit Matrix4(const RectangularMatrix<4, 4, U>& other): Matrix4x4<T>(other) {}

        /** @brief Construct matrix from external representation */
        template<class U, class V = decltype(Implementation::RectangularMatrixConverter<4, 4, T, U>::from(std::declval<U>()))> constexpr explicit Matrix4(const U& other): Matrix4x4<T>(Implementation::RectangularMatrixConverter<4, 4, T, U>::from(other)) {}

        /** @brief Copy constructor */
        constexpr Matrix4(const RectangularMatrix<4, 4, T>& other): Matrix4x4<T>(other) {}

        /**
         * @brief Check whether the matrix represents rigid transformation
         *
         * Rigid transformation consists only of rotation and translation (i.e.
         * no scaling or projection).
         * @see @ref isOrthogonal()
         */
        bool isRigidTransformation() const {
            return rotationScaling().isOrthogonal() && row(3) == Vector4<T>(T(0), T(0), T(0), T(1));
        }

        /**
         * @brief 3D rotation and scaling part of the matrix
         *
         * Upper-left 3x3 part of the matrix.
         * @see @ref from(const Matrix3x3<T>&, const Vector3<T>&),
         *      rotation() const, @ref rotationNormalized(),
         *      @ref uniformScaling(), @ref rotation(Rad, const Vector3<T>&),
         *      Matrix3::rotationScaling() const
         * @todoc Explicit reference when Doxygen can handle const
         */
        constexpr Matrix3x3<T> rotationScaling() const {
            return {(*this)[0].xyz(),
                    (*this)[1].xyz(),
                    (*this)[2].xyz()};
        }

        /**
         * @brief 3D rotation part of the matrix assuming there is no scaling
         *
         * Similar to @ref rotationScaling(), but additionally checks that the
         * base vectors are normalized.
         * @see rotation() const, @ref uniformScaling(),
         *      @ref Matrix3::rotationNormalized()
         * @todo assert also orthogonality or this is good enough?
         * @todoc Explicit reference when Doxygen can handle const
         */
        Matrix3x3<T> rotationNormalized() const {
            CORRADE_ASSERT((*this)[0].xyz().isNormalized() && (*this)[1].xyz().isNormalized() && (*this)[2].xyz().isNormalized(),
                           "Math::Matrix4::rotationNormalized(): the rotation part is not normalized", {});
            return {(*this)[0].xyz(),
                    (*this)[1].xyz(),
                    (*this)[2].xyz()};
        }

        /**
         * @brief 3D rotation part of the matrix
         *
         * Normalized upper-left 3x3 part of the matrix. Expects uniform
         * scaling.
         * @see @ref rotationNormalized(), @ref rotationScaling(),
         *      @ref uniformScaling(), @ref rotation(Rad, const Vector3<T>&),
         *      Matrix3::rotation() const
         * @todoc Explicit reference when Doxygen can handle const
         */
        Matrix3x3<T> rotation() const;

        /**
         * @brief Uniform scaling part of the matrix, squared
         *
         * Squared length of vectors in upper-left 3x3 part of the matrix.
         * Expects that the scaling is the same in all axes. Faster alternative
         * to @ref uniformScaling(), because it doesn't compute the square
         * root.
         * @see @ref rotationScaling(), rotation() const,
         *      @ref rotationNormalized(), @ref scaling(const Vector3<T>&),
         *      @ref Matrix3::uniformScaling()
         * @todoc Explicit reference when Doxygen can handle const
         */
        T uniformScalingSquared() const;

        /**
         * @brief Uniform scaling part of the matrix
         *
         * Length of vectors in upper-left 3x3 part of the matrix. Expects that
         * the scaling is the same in all axes. Use faster alternative
         * @ref uniformScalingSquared() where possible.
         * @see @ref rotationScaling(), rotation() const,
         *      @ref rotationNormalized(), @ref scaling(const Vector3<T>&),
         *      @ref Matrix3::uniformScaling()
         * @todoc Explicit reference when Doxygen can handle const
         */
        T uniformScaling() const { return std::sqrt(uniformScalingSquared()); }

        /**
         * @brief Right-pointing 3D vector
         *
         * First three elements of first column.
         * @see @ref up(), @ref backward(), @ref Vector3::xAxis(),
         *      @ref Matrix3::right()
         */
        Vector3<T>& right() { return (*this)[0].xyz(); }
        constexpr Vector3<T> right() const { return (*this)[0].xyz(); } /**< @overload */

        /**
         * @brief Up-pointing 3D vector
         *
         * First three elements of second column.
         * @see @ref right(), @ref backward(), @ref Vector3::yAxis(),
         *      @ref Matrix3::up()
         */
        Vector3<T>& up() { return (*this)[1].xyz(); }
        constexpr Vector3<T> up() const { return (*this)[1].xyz(); } /**< @overload */

        /**
         * @brief Backward-pointing 3D vector
         *
         * First three elements of third column.
         * @see @ref right(), @ref up(), @ref Vector3::yAxis()
         */
        Vector3<T>& backward() { return (*this)[2].xyz(); }
        constexpr Vector3<T> backward() const { return (*this)[2].xyz(); } /**< @overload */

        /**
         * @brief 3D translation part of the matrix
         *
         * First three elements of fourth column.
         * @see @ref from(const Matrix3x3<T>&, const Vector3<T>&),
         *      @ref translation(const Vector3<T>&),
         *      @ref Matrix3::translation()
         */
        Vector3<T>& translation() { return (*this)[3].xyz(); }
        constexpr Vector3<T> translation() const { return (*this)[3].xyz(); } /**< @overload */

        /**
         * @brief Inverted rigid transformation matrix
         *
         * Expects that the matrix represents rigid transformation.
         * Significantly faster than the general algorithm in @ref inverted(). @f[
         *      A^{-1} = \begin{pmatrix} (A^{3,3})^T & (A^{3,3})^T \begin{pmatrix} a_{3,0} \\ a_{3,1} \\ a_{3,2} \\ \end{pmatrix} \\ \begin{array}{ccc} 0 & 0 & 0 \end{array} & 1 \end{pmatrix}
         * @f]
         * @f$ A^{i, j} @f$ is matrix without i-th row and j-th column, see
         * @ref ij()
         * @see @ref isRigidTransformation(), @ref invertedOrthogonal(),
         *      @ref rotationScaling(), translation() const,
         *      @ref Matrix3::invertedRigid()
         * @todoc Explicit reference when Doxygen can handle const
         */
        Matrix4<T> invertedRigid() const;

        /**
         * @brief Transform 3D vector with the matrix
         *
         * Unlike in @ref transformVector(), translation is not involved in the
         * transformation. @f[
         *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ v_z \\ 0 \end{pmatrix}
         * @f]
         * @see @ref Quaternion::transformVector(),
         *      @ref Matrix3::transformVector()
         * @todo extract 3x3 matrix and multiply directly? (benchmark that)
         */
        Vector3<T> transformVector(const Vector3<T>& vector) const {
            return ((*this)*Vector4<T>(vector, T(0))).xyz();
        }

        /**
         * @brief Transform 3D point with the matrix
         *
         * Unlike in @ref transformVector(), translation is also involved in
         * the transformation. @f[
         *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ v_z \\ 1 \end{pmatrix}
         * @f]
         * @see @ref DualQuaternion::transformPoint(),
         *      @ref Matrix3::transformPoint()
         */
        Vector3<T> transformPoint(const Vector3<T>& vector) const {
            return ((*this)*Vector4<T>(vector, T(1))).xyz();
        }

        MAGNUM_RECTANGULARMATRIX_SUBCLASS_IMPLEMENTATION(4, 4, Matrix4<T>)
        MAGNUM_MATRIX_SUBCLASS_IMPLEMENTATION(4, Matrix4, Vector4)
};

MAGNUM_MATRIXn_OPERATOR_IMPLEMENTATION(4, Matrix4)

/** @debugoperator{Magnum::Math::Matrix4} */
template<class T> inline Corrade::Utility::Debug operator<<(Corrade::Utility::Debug debug, const Matrix4<T>& value) {
    return debug << static_cast<const Matrix4x4<T>&>(value);
}

template<class T> Matrix4<T> Matrix4<T>::rotation(const Rad<T> angle, const Vector3<T>& normalizedAxis) {
    CORRADE_ASSERT(normalizedAxis.isNormalized(),
                   "Math::Matrix4::rotation(): axis must be normalized", {});

    const T sine = std::sin(T(angle));
    const T cosine = std::cos(T(angle));
    const T oneMinusCosine = T(1) - cosine;

    const T xx = normalizedAxis.x()*normalizedAxis.x();
    const T xy = normalizedAxis.x()*normalizedAxis.y();
    const T xz = normalizedAxis.x()*normalizedAxis.z();
    const T yy = normalizedAxis.y()*normalizedAxis.y();
    const T yz = normalizedAxis.y()*normalizedAxis.z();
    const T zz = normalizedAxis.z()*normalizedAxis.z();

    return {
        {cosine + xx*oneMinusCosine,
            xy*oneMinusCosine + normalizedAxis.z()*sine,
                xz*oneMinusCosine - normalizedAxis.y()*sine,
                   T(0)},
        {xy*oneMinusCosine - normalizedAxis.z()*sine,
            cosine + yy*oneMinusCosine,
                yz*oneMinusCosine + normalizedAxis.x()*sine,
                   T(0)},
        {xz*oneMinusCosine + normalizedAxis.y()*sine,
            yz*oneMinusCosine - normalizedAxis.x()*sine,
                cosine + zz*oneMinusCosine,
                   T(0)},
        {T(0), T(0), T(0), T(1)}
    };
}

template<class T> Matrix4<T> Matrix4<T>::rotationX(const Rad<T> angle) {
    const T sine = std::sin(T(angle));
    const T cosine = std::cos(T(angle));

    return {{T(1),   T(0),   T(0), T(0)},
            {T(0), cosine,   sine, T(0)},
            {T(0),  -sine, cosine, T(0)},
            {T(0),   T(0),   T(0), T(1)}};
}

template<class T> Matrix4<T> Matrix4<T>::rotationY(const Rad<T> angle) {
    const T sine = std::sin(T(angle));
    const T cosine = std::cos(T(angle));

    return {{cosine, T(0),  -sine, T(0)},
            {  T(0), T(1),   T(0), T(0)},
            {  sine, T(0), cosine, T(0)},
            {  T(0), T(0),   T(0), T(1)}};
}

template<class T> Matrix4<T> Matrix4<T>::rotationZ(const Rad<T> angle) {
    const T sine = std::sin(T(angle));
    const T cosine = std::cos(T(angle));

    return {{cosine,   sine, T(0), T(0)},
            { -sine, cosine, T(0), T(0)},
            {  T(0),   T(0), T(1), T(0)},
            {  T(0),   T(0), T(0), T(1)}};
}

template<class T> Matrix4<T> Matrix4<T>::reflection(const Vector3<T>& normal) {
    CORRADE_ASSERT(normal.isNormalized(),
                    "Math::Matrix4::reflection(): normal must be normalized", {});
    return from(Matrix3x3<T>() - T(2)*normal*RectangularMatrix<1, 3, T>(normal).transposed(), {});
}

template<class T> Matrix4<T> Matrix4<T>::orthographicProjection(const Vector2<T>& size, const T near, const T far) {
    const Vector2<T> xyScale = T(2.0)/size;
    const T zScale = T(2.0)/(near-far);

    return {{xyScale.x(),        T(0),             T(0), T(0)},
            {       T(0), xyScale.y(),             T(0), T(0)},
            {       T(0),        T(0),           zScale, T(0)},
            {       T(0),        T(0), near*zScale-T(1), T(1)}};
}

template<class T> Matrix4<T> Matrix4<T>::perspectiveProjection(const Vector2<T>& size, const T near, const T far) {
    Vector2<T> xyScale = 2*near/size;
    T zScale = T(1.0)/(near-far);

    return {{xyScale.x(),        T(0),                 T(0),  T(0)},
            {       T(0), xyScale.y(),                 T(0),  T(0)},
            {       T(0),        T(0),    (far+near)*zScale, T(-1)},
            {       T(0),        T(0), T(2)*far*near*zScale,  T(0)}};
}

template<class T> inline Matrix3x3<T> Matrix4<T>::rotation() const {
    CORRADE_ASSERT(TypeTraits<T>::equals((*this)[0].xyz().dot(), (*this)[1].xyz().dot()) &&
                   TypeTraits<T>::equals((*this)[1].xyz().dot(), (*this)[2].xyz().dot()),
        "Math::Matrix4::rotation(): the matrix doesn't have uniform scaling", {});
    return {(*this)[0].xyz().normalized(),
            (*this)[1].xyz().normalized(),
            (*this)[2].xyz().normalized()};
}

template<class T> T Matrix4<T>::uniformScalingSquared() const {
    const T scalingSquared = (*this)[0].xyz().dot();
    CORRADE_ASSERT(TypeTraits<T>::equals((*this)[1].xyz().dot(), scalingSquared) &&
                   TypeTraits<T>::equals((*this)[2].xyz().dot(), scalingSquared),
        "Math::Matrix4::uniformScaling(): the matrix doesn't have uniform scaling", {});
    return scalingSquared;
}

template<class T> Matrix4<T> Matrix4<T>::invertedRigid() const {
    CORRADE_ASSERT(isRigidTransformation(),
        "Math::Matrix4::invertedRigid(): the matrix doesn't represent rigid transformation", {});

    Matrix3x3<T> inverseRotation = rotationScaling().transposed();
    return from(inverseRotation, inverseRotation*-translation());
}

}}

namespace Corrade { namespace Utility {
    /** @configurationvalue{Magnum::Math::Matrix4} */
    template<class T> struct ConfigurationValue<Magnum::Math::Matrix4<T>>: public ConfigurationValue<Magnum::Math::Matrix4x4<T>> {};
}}

#endif