matrix3x3.h

// © Copyright 2010 - 2014 BlackTopp Studios Inc.
/* This file is part of The Mezzanine Engine.

    The Mezzanine Engine is free software: you can redistribute it and/or modify
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    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with The Mezzanine Engine.  If not, see <http://www.gnu.org/licenses/>.
*/
/* The original authors have included a copy of the license specified above in the
   'Docs' folder. See 'gpl.txt'
*/
/* We welcome the use of the Mezzanine engine to anyone, including companies who wish to
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   However there are some practical restrictions, so if your project involves
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*/
#ifndef _matrix3x3_h
#define _matrix3x3_h

#include "vector3.h"
#include "quaternion.h"

class btMatrix3x3;

namespace Ogre
{
    class Matrix3;
}

namespace Mezzanine
{
    /// @class Matrix3x3
    /// @headerfile matrix3x3.h
    /// @brief This is a 3x3 Matrix class used for representing rotations and scaling in an object.
    /// @details The utility of this class overlaps with that of the Quaternion, for the most part the use of
    /// either class is a matter of preference.  The Mezzanine engine for the most part prefer's use of the
    /// Quaternion class since it deals with fewer numbers, but this class is still made available for others
    /// that may prefer it.
    class MEZZ_LIB Matrix3x3
    {
        public:
            /// @brief The Matrix.  Fo' Reals.
            Real Matrix[3][3];

            /// @brief Non-Initialization constructor.
            Matrix3x3();

            /// @brief Class destructor.
            ~Matrix3x3();

            ///////////////////////////////////////////////////////////////////////////////
            // Additional Constructors

            /// @brief Explict Initialization constructor.
            /// @details Provides initialization for every number in the matrix.
            Matrix3x3(const Real& XX, const Real& XY, const Real& XZ, const Real& YX, const Real& YY, const Real& YZ, const Real& ZX, const Real& ZY, const Real& ZZ);

            /// @brief Euler Initialization constructor.
            /// @param Yaw The number of degree's on the Yaw in Degrees to rotate.
            /// @param Pitch The number of degree's on the Pitch in Degrees to rotate.
            /// @param Roll The number of degree's on the Roll in Degrees to rotate.
            Matrix3x3(const Real& Yaw, const Real& Pitch, const Real& Roll);

            /// @brief Quaternion Initialization constructor.
            /// @param Rot The rotation to apply to this Matrix expressed as a Quaternion.
            Matrix3x3(const Quaternion& Rot);

            /// @brief Axis Angle Initialization constructor.
            /// @param Axis The axis on which to apply the rotation.
            /// @param Angle The amount of rotation to apply in Radians.
            Matrix3x3(const Vector3& Axis, const Real& Angle);

            /// @brief Bullet Matrix3x3 constructor.
            /// @param Mat The Bullet 3x3 Matrix.
            Matrix3x3(const btMatrix3x3& Mat);

            /// @brief Ogre Matrix3x3 constructor.
            /// @param Mat The Ogre 3x3 Matrix.
            Matrix3x3(const Ogre::Matrix3& Mat);

            ///////////////////////////////////////////////////////////////////////////////
            // Set From Other Data Functions

            /// @brief Sets the values for every number in the matrix.
            void SetValues(const Real& XX, const Real& XY, const Real& XZ, const Real& YX, const Real& YY, const Real& YZ, const Real& ZX, const Real& ZY, const Real& ZZ);

            /// @brief Sets the Matrix based on Euler angles.
            /// @param Yaw The number of degree's on the Yaw in Degrees to rotate.
            /// @param Pitch The number of degree's on the Pitch in Degrees to rotate.
            /// @param Roll The number of degree's on the Roll in Degrees to rotate.
            void SetFromEulerZYX(const Real& Yaw, const Real& Pitch, const Real& Roll);

            /// @brief Sets the Matrix from a quaternion.
            /// @param Rot The rotation to apply to this Matrix expressed as a Quaternion.
            void SetFromQuaternion(const Quaternion& Rot);

            /// @brief Sets the Matrix from an Axis Angle.
            /// @param Axis The axis on which to apply the rotation.
            /// @param Angle The amount of rotation to apply in Radians.
            void SetFromAxisAngle(const Vector3& Axis, const Real& Angle);

            /// @brief Sets all values in this Matrix to Identity values.
            /// @details Identity values for a 4x4 matrix is all zeros except for the values at [0][0], [1][1], [2][2], [3][3], which are set to one.
            void SetIdentity();

            /// @brief Sets all values in this Matrix to zero.
            void SetZero();

            ///////////////////////////////////////////////////////////////////////////////
            // Utility and Conversion Functions

            /// @brief Gets the Determinant of this Matrix.
            /// @return Returns a Real representing the Determinant of this Matrix.
            Real GetDeterminant() const;

            /// @brief Gets this Matrix as a Quaternion.
            /// @return Returns a Quaternion that expresses the same rotation as this Matrix.
            Quaternion GetAsQuaternion() const;

            /// @brief Gets the data from a Bullet Matrix3x3 and applies it to this.
            /// @param temp The Matrix3x3 to copy from.
            void ExtractBulletMatrix3x3(const btMatrix3x3& temp);

            /// @brief Gets a Bullet copy of this Matrix3x3.
            /// @return Returns a Bullet Matrix3x3 with the same values as this Matrix3x3.
            btMatrix3x3 GetBulletMatrix3x3() const;

            /// @brief Gets the data from an Ogre Matrix3x3 and applies it to this.
            /// @param temp The Matrix3x3 to copy from.
            void ExtractOgreMatrix3x3(const Ogre::Matrix3& temp);

            /// @brief Gets an Ogre copy of this Matrix3x3.
            /// @return Returns an Ogre Matrix3x3 with the same values as this Matrix3x3.
            Ogre::Matrix3 GetOgreMatrix3x3() const;

            ///////////////////////////////////////////////////////////////////////////////
            // Comparison Operators

            /// @brief Equality comparison operator.
            /// @param Other The other Matrix3x3 to compare against.
            /// @return Returns true if the two Matrix3x3's are equal, false otherwise.
            bool operator==(const Matrix3x3& Other) const;

            /// @brief Inequality comparison operator.
            /// @param Other The other Matrix3x3 to compare against.
            /// @return Returns true if the two Matrix3x3's are not equal, false otherwise.
            bool operator!=(const Matrix3x3& Other) const;

            ///////////////////////////////////////////////////////////////////////////////
            // Arithmetic Operators With Matrix3x3

            /// @brief Addition operator.
            /// @param Other The other Matrix3x3 to add to this.
            /// @return Returns a fresh Matrix3x3.
            Matrix3x3 operator+(const Matrix3x3& Other) const;

            /// @brief Subtraction operator.
            /// @param Other The other Matrix3x3 to subtract from this.
            /// @return Returns a fresh Matrix3x3.
            Matrix3x3 operator-(const Matrix3x3& Other) const;

            /// @brief Multiplication operator.
            /// @param Other The other Matrix3x3 to multiply this by.
            /// @return Returns a fresh Matrix3x3.
            Matrix3x3 operator*(const Matrix3x3& Other) const;

            /// @brief Addition Assignment operator.
            /// @param Other The other Matrix3x3 to add to this.
            /// @return Returns a reference to *this.
            Matrix3x3& operator+=(const Matrix3x3& Other);

            /// @brief Subtraction Assignment operator.
            /// @param Other The other Matrix3x3 to subtract from this.
            /// @return Returns a reference to *this.
            Matrix3x3& operator-=(const Matrix3x3& Other);

            /// @brief Multiplication Assignment operator.
            /// @param Other The other Matrix3x3 to add to this.
            /// @return Returns a reference to *this.
            Matrix3x3& operator*=(const Matrix3x3& Other);

            ///////////////////////////////////////////////////////////////////////////////
            // Arithmetic Operators With Other Datatypes

            /// @brief Multiply by Vector3 operator.
            /// @param Vec The Vector to be rotated.
            /// @return Returns a Vector3 with the rotation of this Matrix applied to it.
            Vector3 operator*(const Vector3& Vec) const;

            /// @brief Multiply by Real operator.
            /// @param Scaler The Real to multiply each member of this Matrix by.
            /// @return Returns a new Matrix3x3 that is a copy of this Matrix3x3 with each of it's members multiplied by the scaler.
            Matrix3x3 operator*(const Real& Scaler) const;

            /// @brief Multiply Assignment by Real operator.
            /// @param Scaler The Real to multiply each member of this Matrix by.
            /// @return Returns a reference to *this, being the modified Matrix3x3.
            Matrix3x3& operator*=(const Real& Scaler);

            ///////////////////////////////////////////////////////////////////////////////
            // Other Operators

            /// @brief Assignment operator.
            /// @param Other The other Matrix3x3 to copy from.
            void operator=(const Matrix3x3& Other);

            /// @brief Negative Unary operator.
            /// @return Returns a copy of this Matrix3x3 with each of it's members flipped.
            Matrix3x3 operator-() const;

            ///////////////////////////////////////////////////////////////////////////////
            // Fancy Math

            /// @brief Gets the Transpose of this Matrix.
            /// @todo I'm not gonna lie, I have no idea what the hell the Transpose of a 3x3 Matrix is or what it is used for...this doc could use a touchup.  In fact most of the doc's on this class could use a review.
            /// @return Returns a new Matrix3x3 that is a Transposed copy of this.
            Matrix3x3 Transpose() const;

            /// @brief Gets the Adjoint of this Matrix.
            /// @return Returns a new Matrix3x3 that is the Adjoint of this.
            Matrix3x3 Adjoint() const;

            /// @brief Gets the Inverse of this Matrix.
            /// @return Returns a new Matrix3x3 that is this Matrix inversed.
            Matrix3x3 Inverse() const;

            /// @brief Gets the cofactor between two sets of rows/columns.
            /// @param Row1 Row for the first Real of the calculated cofactor.
            /// @param Col1 Column for the first Real of the calculated cofactor.
            /// @param Row2 Row for the second Real of the calculated cofactor.
            /// @param Col2 Column for the second Real of the calculated cofactor.
            /// @return Returns the CoFactor of the provided rows/columns.
            Real CoFactor(const Whole& Row1, const Whole& Col1, const Whole& Row2, const Whole& Col2) const;

            /// @brief Scales this Matrix.
            /// @param Scaling A Vector3 containing the scaling to be applied to this Matrix.
            void SetScale(const Vector3& Scaling);

            /// @brief Checks to see if this Matrix has any scaling applied to it.
            /// @return Returns true if this Matrix is scaled, false otherwise.
            bool HasScaling() const;
    };//Matrix3x3
}//Mezzanine

#endif