#ifndef Magnum_Math_Matrix3_h
#define Magnum_Math_Matrix3_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
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    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
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    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
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    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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*/

/** @file
 * @brief Class @ref Magnum::Math::Matrix3
 */

#include "Magnum/Math/Matrix.h"
#include "Magnum/Math/Vector3.h"

namespace Magnum { namespace Math {

/**
@brief 3x3 matrix
@tparam T   Underlying data type

Represents 2D transformation. See @ref matrix-vector and @ref transformations
for brief introduction.
@see @ref Magnum::Matrix3, @ref Magnum::Matrix3d, @ref DualComplex,
    @ref SceneGraph::MatrixTransformation2D
@configurationvalueref{Magnum::Math::Matrix3}
*/
template<class T> class Matrix3: public Matrix<3, T> {
    public:
        /**
         * @brief 2D translation matrix
         * @param vector    Translation vector
         *
         * @see translation() const, @ref DualComplex::translation(),
         *      @ref Matrix4::translation(const Vector3<T>&),
         *      @ref Vector2::xAxis(), @ref Vector2::yAxis()
         * @todoc Explicit reference when Doxygen can handle const
         */
        constexpr static Matrix3<T> translation(const Vector2<T>& vector) {
            return {{      T(1),       T(0), T(0)},
                    {      T(0),       T(1), T(0)},
                    {vector.x(), vector.y(), T(1)}};
        }

        /**
         * @brief 2D scaling matrix
         * @param vector    Scaling vector
         *
         * @see @ref rotationScaling(),
         *      @ref Matrix4::scaling(const Vector3<T>&),
         *      @ref Vector2::xScale(), @ref Vector2::yScale()
         */
        constexpr static Matrix3<T> scaling(const Vector2<T>& vector) {
            return {{vector.x(),       T(0), T(0)},
                    {      T(0), vector.y(), T(0)},
                    {      T(0),       T(0), T(1)}};
        }

        /**
         * @brief 2D rotation matrix
         * @param angle     Rotation angle (counterclockwise)
         *
         * @see rotation() const, @ref Complex::rotation(),
         *      @ref DualComplex::rotation(),
         *      @ref Matrix4::rotation(Rad, const Vector3<T>&)
         * @todoc Explicit reference when Doxygen can handle const
         */
        static Matrix3<T> rotation(Rad<T> angle);

        /**
         * @brief 2D reflection matrix
         * @param normal    Normal of the line through which to reflect
         *
         * Expects that the normal is normalized.
         * @see @ref Matrix4::reflection(), @ref Vector::isNormalized()
         */
        static Matrix3<T> reflection(const Vector2<T>& normal) {
            CORRADE_ASSERT(normal.isNormalized(),
                           "Math::Matrix3::reflection(): normal must be normalized", {});
            return from(Matrix<2, T>() - T(2)*normal*RectangularMatrix<1, 2, T>(normal).transposed(), {});
        }

        /**
         * @brief 2D projection matrix
         * @param size      Size of the view
         *
         * @see @ref Matrix4::orthographicProjection(),
         *      @ref Matrix4::perspectiveProjection()
         */
        static Matrix3<T> projection(const Vector2<T>& size) {
            return scaling(2.0f/size);
        }

        /**
         * @brief Create matrix from rotation/scaling part and translation part
         * @param rotationScaling   Rotation/scaling part (upper-left 2x2
         *      matrix)
         * @param translation       Translation part (first two elements of
         *      third column)
         *
         * @see @ref rotationScaling(), translation() const
         * @todoc Explicit reference when Doxygen can handle const
         */
        constexpr static Matrix3<T> from(const Matrix<2, T>& rotationScaling, const Vector2<T>& translation) {
            return {{rotationScaling[0], T(0)},
                    {rotationScaling[1], T(0)},
                    {       translation, T(1)}};
        }

        /** @copydoc Matrix::Matrix(ZeroType) */
        constexpr explicit Matrix3(typename Matrix<3, T>::ZeroType): Matrix<3, T>(Matrix<3, T>::Zero) {}

        /**
         * @brief Default constructor
         *
         * Creates identity matrix. You can also explicitly call this
         * constructor with `%Matrix3 m(Matrix3::Identity);`. Optional
         * parameter @p value allows you to specify value on diagonal.
         */
        constexpr /*implicit*/ Matrix3(typename Matrix<3, T>::IdentityType = (Matrix<3, T>::Identity), T value = T(1)): Matrix<3, T>(Matrix<3, T>::Identity, value) {}

        /** @brief %Matrix from column vectors */
        constexpr /*implicit*/ Matrix3(const Vector3<T>& first, const Vector3<T>& second, const Vector3<T>& third): Matrix<3, T>(first, second, third) {}

        /** @copydoc Matrix::Matrix(const RectangularMatrix<size, size, U>&) */
        template<class U> constexpr explicit Matrix3(const RectangularMatrix<3, 3, U>& other): Matrix<3, T>(other) {}

        /** @brief Construct matrix from external representation */
        template<class U, class V = decltype(Implementation::RectangularMatrixConverter<3, 3, T, U>::from(std::declval<U>()))> constexpr explicit Matrix3(const U& other): Matrix<3, T>(Implementation::RectangularMatrixConverter<3, 3, T, U>::from(other)) {}

        /** @brief Copy constructor */
        constexpr Matrix3(const RectangularMatrix<3, 3, T>& other): Matrix<3, 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(2) == Vector3<T>(T(0), T(0), T(1));
        }

        /**
         * @brief 2D rotation and scaling part of the matrix
         *
         * Upper-left 2x2 part of the matrix.
         * @see @ref from(const Matrix<2, T>&, const Vector2<T>&),
         *      rotation() const, @ref rotationNormalized(),
         *      @ref uniformScaling(), @ref rotation(Rad<T>),
         *      @ref Matrix4::rotationScaling()
         * @todoc Explicit reference when Doxygen can handle const
         */
        constexpr Matrix<2, T> rotationScaling() const {
            return {(*this)[0].xy(),
                    (*this)[1].xy()};
        }

        /**
         * @brief 2D 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 Matrix4::rotationNormalized()
         * @todo assert also orthogonality or this is good enough?
         * @todoc Explicit reference when Doxygen can handle const
         */
        Matrix<2, T> rotationNormalized() const {
            CORRADE_ASSERT((*this)[0].xy().isNormalized() && (*this)[1].xy().isNormalized(),
                           "Math::Matrix3::rotationNormalized(): the rotation part is not normalized", {});
            return {(*this)[0].xy(),
                    (*this)[1].xy()};
        }

        /**
         * @brief 2D rotation part of the matrix
         *
         * Normalized upper-left 2x2 part of the matrix. Expects uniform
         * scaling.
         * @see @ref rotationNormalized(), @ref rotationScaling(),
         *      @ref uniformScaling(), @ref rotation(Rad<T>),
         *      Matrix4::rotation() const
         * @todoc Explicit reference when Doxygen can handle const
         */
        Matrix<2, T> rotation() const {
            CORRADE_ASSERT(TypeTraits<T>::equals((*this)[0].xy().dot(), (*this)[1].xy().dot()),
                           "Math::Matrix3::rotation(): the matrix doesn't have uniform scaling", {});
            return {(*this)[0].xy().normalized(),
                    (*this)[1].xy().normalized()};
        }

        /**
         * @brief Uniform scaling part of the matrix, squared
         *
         * Squared length of vectors in upper-left 2x2 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 Vector2<T>&),
         *      @ref Matrix4::uniformScaling()
         * @todoc Explicit reference when Doxygen can handle const
         */
        T uniformScalingSquared() const {
            const T scalingSquared = (*this)[0].xy().dot();
            CORRADE_ASSERT(TypeTraits<T>::equals((*this)[1].xy().dot(), scalingSquared),
                           "Math::Matrix3::uniformScaling(): the matrix doesn't have uniform scaling", {});
            return scalingSquared;
        }

        /**
         * @brief Uniform scaling part of the matrix
         *
         * Length of vectors in upper-left 2x2 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 Vector2<T>&),
         *      @ref Matrix4::uniformScaling()
         * @todoc Explicit reference when Doxygen can handle const
         */
        T uniformScaling() const { return std::sqrt(uniformScalingSquared()); }

        /**
         * @brief Right-pointing 2D vector
         *
         * First two elements of first column.
         * @see @ref up(), @ref Vector2::xAxis(), @ref Matrix4::right()
         */
        Vector2<T>& right() { return (*this)[0].xy(); }
        constexpr Vector2<T> right() const { return (*this)[0].xy(); } /**< @overload */

        /**
         * @brief Up-pointing 2D vector
         *
         * First two elements of second column.
         * @see @ref right(), @ref Vector2::yAxis(), @ref Matrix4::up()
         */
        Vector2<T>& up() { return (*this)[1].xy(); }
        constexpr Vector2<T> up() const { return (*this)[1].xy(); } /**< @overload */

        /**
         * @brief 2D translation part of the matrix
         *
         * First two elements of third column.
         * @see @ref from(const Matrix<2, T>&, const Vector2<T>&),
         *      @ref translation(const Vector2<T>&),
         *      @ref Matrix4::translation()
         */
        Vector2<T>& translation() { return (*this)[2].xy(); }
        constexpr Vector2<T> translation() const { return (*this)[2].xy(); } /**< @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^{2,2})^T & (A^{2,2})^T \begin{pmatrix} a_{2,0} \\ a_{2,1} \end{pmatrix} \\ \begin{array}{cc} 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 Matrix4::invertedRigid()
         * @todoc Explicit reference when Doxygen can handle const
         */
        Matrix3<T> invertedRigid() const;

        /**
         * @brief Transform 2D vector with the matrix
         *
         * Unlike in @ref transformPoint(), translation is not involved in the
         * transformation. @f[
         *      \boldsymbol v' = \boldsymbol M \begin{pmatrix} v_x \\ v_y \\ 0 \end{pmatrix}
         * @f]
         * @see @ref Complex::transformVector(),
         *      @ref Matrix4::transformVector()
         * @todo extract 2x2 matrix and multiply directly? (benchmark that)
         */
        Vector2<T> transformVector(const Vector2<T>& vector) const {
            return ((*this)*Vector3<T>(vector, T(0))).xy();
        }

        /**
         * @brief Transform 2D 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 \\ 1 \end{pmatrix}
         * @f]
         * @see @ref DualComplex::transformPoint(),
         *      @ref Matrix4::transformPoint()
         */
        Vector2<T> transformPoint(const Vector2<T>& vector) const {
            return ((*this)*Vector3<T>(vector, T(1))).xy();
        }

        MAGNUM_RECTANGULARMATRIX_SUBCLASS_IMPLEMENTATION(3, 3, Matrix3<T>)
        MAGNUM_MATRIX_SUBCLASS_IMPLEMENTATION(3, Matrix3, Vector3)
};

MAGNUM_MATRIXn_OPERATOR_IMPLEMENTATION(3, Matrix3)

/** @debugoperator{Magnum::Math::Matrix3} */
template<class T> inline Corrade::Utility::Debug operator<<(Corrade::Utility::Debug debug, const Matrix3<T>& value) {
    return debug << static_cast<const Matrix<3, T>&>(value);
}

template<class T> Matrix3<T> Matrix3<T>::rotation(const Rad<T> angle) {
    const T sine = std::sin(T(angle));
    const T cosine = std::cos(T(angle));

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

template<class T> inline Matrix3<T> Matrix3<T>::invertedRigid() const {
    CORRADE_ASSERT(isRigidTransformation(),
        "Math::Matrix3::invertedRigid(): the matrix doesn't represent rigid transformation", {});

    Matrix<2, T> inverseRotation = rotationScaling().transposed();
    return from(inverseRotation, inverseRotation*-translation());
}

}}

namespace Corrade { namespace Utility {
    /** @configurationvalue{Magnum::Math::Matrix3} */
    template<class T> struct ConfigurationValue<Magnum::Math::Matrix3<T>>: public ConfigurationValue<Magnum::Math::Matrix<3, T>> {};
}}

#endif