BansheeEngine/CamelotUtility/Include/CmMatrix3.h

/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2011 Torus Knot Software Ltd

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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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.
-----------------------------------------------------------------------------
*/
#pragma once

#include "CmPrerequisitesUtil.h"
#include "CmVector3.h"

namespace CamelotFramework
{
    class CM_UTILITY_EXPORT Matrix3
    {
	private:
		struct EulerAngleOrderData
		{
			int a, b, c;
			float sign;
		};

    public:
		Matrix3() {}

        Matrix3(const Matrix3& mat)
		{
			memcpy(m, mat.m, 9*sizeof(float));
		}

        Matrix3(float m00, float m01, float m02,
                float m10, float m11, float m12,
                float m20, float m21, float m22)
		{
			m[0][0] = m00;
			m[0][1] = m01;
			m[0][2] = m02;
			m[1][0] = m10;
			m[1][1] = m11;
			m[1][2] = m12;
			m[2][0] = m20;
			m[2][1] = m21;
			m[2][2] = m22;
		}

		/**
         * @brief	Construct a matrix from a quaternion.
         */
        explicit Matrix3(const Quaternion& quad)
        {
            fromQuaternion(quad);
        }

		/**
         * @brief	Construct a matrix that performs rotation and scale.
         */
        explicit Matrix3(const Quaternion& quad, const Vector3 scale)
        {
            fromQuaternion(quad);
			
			for (int row = 0; row < 3; row++)
			{
				for (int col = 0; col < 3; col++)
					m[row][col] = scale[row]*m[row][col];
			}
        }

		/**
         * @brief	Construct a matrix from an angle/axis.
         */
        explicit Matrix3(const Vector3& axis, const Radian& angle)
        {
            fromAxisAngle(axis, angle);
        }

        /**
         * @brief	Construct a matrix from 3 orthonormal local axes.
         */
        explicit Matrix3(const Vector3& xaxis, const Vector3& yaxis, const Vector3& zaxis)
        {
            fromAxes(xaxis, yaxis, zaxis);
        }

        /**
         * @brief	Construct a matrix from euler angles, XYZ ordering.
         * 			
		 * @see		Matrix3::fromEulerAngles
         */
		explicit Matrix3(const Radian& xAngle, const Radian& yAngle, const Radian& zAngle)
		{
			fromEulerAngles(xAngle, yAngle, zAngle);
		}

        /**
         * @brief	Construct a matrix from euler angles, custom ordering.
         * 			
		 * @see		Matrix3::fromEulerAngles
         */
		explicit Matrix3(const Radian& xAngle, const Radian& yAngle, const Radian& zAngle, EulerAngleOrder order)
		{
			fromEulerAngles(xAngle, yAngle, zAngle, order);
		}

		void swap(Matrix3& other)
		{
			std::swap(m[0][0], other.m[0][0]);
			std::swap(m[0][1], other.m[0][1]);
			std::swap(m[0][2], other.m[0][2]);
			std::swap(m[1][0], other.m[1][0]);
			std::swap(m[1][1], other.m[1][1]);
			std::swap(m[1][2], other.m[1][2]);
			std::swap(m[2][0], other.m[2][0]);
			std::swap(m[2][1], other.m[2][1]);
			std::swap(m[2][2], other.m[2][2]);
		}

        inline float* operator[] (size_t row) const
		{
			return (float*)m[row];
		}

        Vector3 getColumn(size_t col) const;
        void setColumn(size_t col, const Vector3& vec);

        Matrix3& operator= (const Matrix3& rhs)
		{
			memcpy(m, rhs.m, 9*sizeof(float));
			return *this;
		}
        bool operator== (const Matrix3& rhs) const;
        bool operator!= (const Matrix3& rhs) const;

        Matrix3 operator+ (const Matrix3& rhs) const;
        Matrix3 operator- (const Matrix3& rhs) const;
        Matrix3 operator* (const Matrix3& rhs) const;
        Matrix3 operator- () const;
		Matrix3 operator* (float rhs) const;

		friend Matrix3 operator* (float lhs, const Matrix3& rhs);

		Vector3 transform(const Vector3& vec) const;
        Matrix3 transpose () const;
        bool inverse(Matrix3& mat, float fTolerance = 1e-06f) const;
        Matrix3 inverse(float fTolerance = 1e-06f) const;
        float determinant() const;

        void singularValueDecomposition (Matrix3& matL, Vector3& matS, Matrix3& matR) const;
		void QDUDecomposition (Matrix3& matQ, Vector3& vecD, Vector3& vecU) const;

        /**
         * @brief	Gram-Schmidt orthonormalization (applied to columns of rotation matrix)
         */
        void orthonormalize();

        /**
         * @brief	Converts an orthonormal matrix to axis angle representation.
         *
         * @note	Matrix must be orthonormal.
         */
        void toAxisAngle(Vector3& axis, Radian& angle) const;

        /**
         * @brief	Creates a rotation matrix from an axis angle representation.
         */
        void fromAxisAngle(const Vector3& axis, const Radian& angle);

        /**
         * @brief	Converts an orthonormal matrix to quaternion representation.
         *
         * @note	Matrix must be orthonormal.
         */
        void toQuaternion(Quaternion& quat) const;

        /**
         * @brief	Creates a rotation matrix from a quaternion representation.
         */
        void fromQuaternion(const Quaternion& quat);

        /**
         * @brief	Creates a matrix from a three axes.
         */
		void fromAxes(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);

        /**
         * @brief	Extracts Pitch/Yaw/Roll rotations from this matrix.
         *
         * @param [in,out]	xAngle	Rotation about x axis. (AKA Pitch)
         * @param [in,out]	yAngle  Rotation about y axis. (AKA Yaw)
         * @param [in,out]	zAngle 	Rotation about z axis. (AKA Roll)
         *
         * @return	True if unique solution was found, false otherwise.
         * 			
		 * @note	Matrix must be orthonormal.
		 * 			
		 * 			Since different values will be returned depending in which order are the rotations applied, this method assumes
		 * 			they are applied in XYZ order. If you need a specific order, use the overloaded "toEulerAngles" method instead.
         */
        bool toEulerAngles(Radian& xAngle, Radian& yAngle, Radian& zAngle) const;

		/**
		 * @brief	Extracts Pitch/Yaw/Roll rotations from this matrix.
		 *
		 * @param	xAngle	Rotation about x axis. (AKA Pitch)
		 * @param	yAngle	Rotation about y axis. (AKA Yaw)
		 * @param	zAngle	Rotation about z axis. (AKA Roll)
		 * @param	order 	The order in which rotations will be extracted. 
		 * 					Different values can be retrieved depending on the order.
		 *
		 * @return	True if unique solution was found, false otherwise.
		 * 			
		 * @note	Matrix must be orthonormal.
		 */
		bool toEulerAngles(Radian& xAngle, Radian& yAngle, Radian& zAngle, EulerAngleOrder order) const;

        /**
         * @brief	Creates a rotation matrix from the provided Pitch/Yaw/Roll angles.
         *
		 * @param	xAngle	Rotation about x axis. (AKA Pitch)
		 * @param	yAngle	Rotation about y axis. (AKA Yaw)
		 * @param	zAngle	Rotation about z axis. (AKA Roll)
         *
         * @note	Matrix must be orthonormal.
		 * 			Since different values will be produced depending in which order are the rotations applied, this method assumes
		 * 			they are applied in XYZ order. If you need a specific order, use the overloaded "fromEulerAngles" method instead.
         */
        void fromEulerAngles(const Radian& xAngle, const Radian& yAngle, const Radian& zAngle);

        /**
         * @brief	Creates a rotation matrix from the provided Pitch/Yaw/Roll angles.
         *
		 * @param	xAngle	Rotation about x axis. (AKA Pitch)
		 * @param	yAngle	Rotation about y axis. (AKA Yaw)
		 * @param	zAngle	Rotation about z axis. (AKA Roll)
		 * @param	order 	The order in which rotations will be extracted.
		 * 					Different values can be retrieved depending on the order.
         *
         * @note	Matrix must be orthonormal.
         */
        void fromEulerAngles(const Radian& xAngle, const Radian& yAngle, const Radian& zAngle, EulerAngleOrder order);

        /**
         * @brief	Eigensolver, matrix must be symmetric.
         */
        void eigenSolveSymmetric(float eigenValues[3], Vector3 eigenVectors[3]) const;

        static const float EPSILON;
        static const Matrix3 ZERO;
        static const Matrix3 IDENTITY;

    protected:
		friend class Matrix4;

        // Support for eigensolver
        void tridiagonal (float diag[3], float subDiag[3]);
        bool QLAlgorithm (float diag[3], float subDiag[3]);

        // Support for singular value decomposition
        static const float SVD_EPSILON;
        static const unsigned int SVD_MAX_ITERS;
        static void bidiagonalize (Matrix3& matA, Matrix3& matL, Matrix3& matR);
        static void golubKahanStep (Matrix3& matA, Matrix3& matL, Matrix3& matR);

		// Euler angle conversions
		static const EulerAngleOrderData EA_LOOKUP[6];

        float m[3][3];
    };

	CM_ALLOW_MEMCPY_SERIALIZATION(Matrix3);
}