lovr-ODE/OPCODE/Ice/IceMatrix3x3.h

///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
 *	Contains code for 3x3 matrices.
 *	\file		IceMatrix3x3.h
 *	\author		Pierre Terdiman
 *	\date		April, 4, 2000
 */
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Include Guard
#ifndef __ICEMATRIX3X3_H__
#define __ICEMATRIX3X3_H__

	// Forward declarations
	class Quat;

	#define	MATRIX3X3_EPSILON		(1.0e-7f)

	class ICEMATHS_API Matrix3x3
	{
		public:
		//! Empty constructor
		inline_					Matrix3x3()									{}
		//! Constructor from 9 values
		inline_					Matrix3x3(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;
								}
		//! Copy constructor
		inline_					Matrix3x3(const Matrix3x3& mat)				{ CopyMemory(m, &mat.m, 9*sizeof(float));	}
		//! Destructor
		inline_					~Matrix3x3()								{}

		//! Assign values
		template<typename trotationfloat>
		inline_	void			Set(trotationfloat m00, trotationfloat m01, trotationfloat m02, 
									trotationfloat m10, trotationfloat m11, trotationfloat m12, 
									trotationfloat m20, trotationfloat m21, trotationfloat m22)
								{
									m[0][0] = (float)m00;	m[0][1] = (float)m01;	m[0][2] = (float)m02;
									m[1][0] = (float)m10;	m[1][1] = (float)m11;	m[1][2] = (float)m12;
									m[2][0] = (float)m20;	m[2][1] = (float)m21;	m[2][2] = (float)m22;
								}

		//! Sets the scale from a Point. The point is put on the diagonal.
		inline_	void			SetScale(const Point& p)					{ m[0][0] = p.x;	m[1][1] = p.y;	m[2][2] = p.z;	}

		//! Sets the scale from floats. Values are put on the diagonal.
		inline_	void			SetScale(float sx, float sy, float sz)		{ m[0][0] = sx;		m[1][1] = sy;	m[2][2] = sz;	}

		//! Scales from a Point. Each row is multiplied by a component.
		inline_	void			Scale(const Point& p)
								{
									m[0][0] *= p.x;	m[0][1] *= p.x;	m[0][2] *= p.x;
									m[1][0] *= p.y;	m[1][1] *= p.y;	m[1][2] *= p.y;
									m[2][0] *= p.z;	m[2][1] *= p.z;	m[2][2] *= p.z;
								}

		//! Scales from floats. Each row is multiplied by a value.
		inline_	void			Scale(float sx, float sy, float sz)
								{
									m[0][0] *= sx;	m[0][1] *= sx;	m[0][2] *= sx;
									m[1][0] *= sy;	m[1][1] *= sy;	m[1][2] *= sy;
									m[2][0] *= sz;	m[2][1] *= sz;	m[2][2] *= sz;
								}

		//! Copy from a Matrix3x3
		inline_	void			Copy(const Matrix3x3& source)				{ CopyMemory(m, source.m, 9*sizeof(float));			}

		// Row-column access
		//! Returns a row.
		inline_	void			GetRow(const udword r, Point& p)	const	{ p.x = m[r][0];	p.y = m[r][1];	p.z = m[r][2];	}
		//! Returns a row.
		inline_	const Point&	GetRow(const udword r)				const	{ return *(const Point*)&m[r][0];	}
		//! Returns a row.
		inline_	Point&			GetRow(const udword r)						{ return *(Point*)&m[r][0];			}
		//! Sets a row.
		inline_	void			SetRow(const udword r, const Point& p)		{ m[r][0] = p.x;	m[r][1] = p.y;	m[r][2] = p.z;	}
		//! Returns a column.
		inline_	void			GetCol(const udword c, Point& p)	const	{ p.x = m[0][c];	p.y = m[1][c];	p.z = m[2][c];	}
		//! Sets a column.
		inline_	void			SetCol(const udword c, const Point& p)		{ m[0][c] = p.x;	m[1][c] = p.y;	m[2][c] = p.z;	}

		//! Computes the trace. The trace is the sum of the 3 diagonal components.
		inline_	float			Trace()					const				{ return m[0][0] + m[1][1] + m[2][2];				}
		//! Clears the matrix.
		inline_	void			Zero()										{ ZeroMemory(&m, sizeof(m));						}
		//! Sets the identity matrix.
		inline_	void			Identity()									{ Zero(); m[0][0] = m[1][1] = m[2][2] = 1.0f; 		}
		//! Checks for identity
		inline_	bool			IsIdentity()			const
								{
									if(IR(m[0][0])!=IEEE_1_0)	return false;
									if(IR(m[0][1])!=0)			return false;
									if(IR(m[0][2])!=0)			return false;

									if(IR(m[1][0])!=0)			return false;
									if(IR(m[1][1])!=IEEE_1_0)	return false;
									if(IR(m[1][2])!=0)			return false;

									if(IR(m[2][0])!=0)			return false;
									if(IR(m[2][1])!=0)			return false;
									if(IR(m[2][2])!=IEEE_1_0)	return false;

									return true;
								}

		//! Checks matrix validity
		inline_	BOOL			IsValid()				const
								{
									for(udword j=0;j<3;j++)
									{
										for(udword i=0;i<3;i++)
										{
											if(!IsValidFloat(m[j][i]))	return FALSE;
										}
									}
									return TRUE;
								}

		//! Makes a skew-symmetric matrix (a.k.a. Star(*) Matrix)
		//!	[  0.0  -a.z   a.y ]
		//!	[  a.z   0.0  -a.x ]
		//!	[ -a.y   a.x   0.0 ]
		//! This is also called a "cross matrix" since for any vectors A and B,
		//! A^B = Skew(A) * B = - B * Skew(A);
		inline_	void			SkewSymmetric(const Point& a)
								{
									m[0][0] = 0.0f;
									m[0][1] = -a.z;
									m[0][2] = a.y;

									m[1][0] = a.z;
									m[1][1] = 0.0f;
									m[1][2] = -a.x;

									m[2][0] = -a.y;
									m[2][1] = a.x;
									m[2][2] = 0.0f;
								}

		//! Negates the matrix
		inline_	void			Neg()
								{
									m[0][0] = -m[0][0];	m[0][1] = -m[0][1];	m[0][2] = -m[0][2];
									m[1][0] = -m[1][0];	m[1][1] = -m[1][1];	m[1][2] = -m[1][2];
									m[2][0] = -m[2][0];	m[2][1] = -m[2][1];	m[2][2] = -m[2][2];
								}

		//! Neg from another matrix
		inline_	void			Neg(const Matrix3x3& mat)
								{
									m[0][0] = -mat.m[0][0];	m[0][1] = -mat.m[0][1];	m[0][2] = -mat.m[0][2];
									m[1][0] = -mat.m[1][0];	m[1][1] = -mat.m[1][1];	m[1][2] = -mat.m[1][2];
									m[2][0] = -mat.m[2][0];	m[2][1] = -mat.m[2][1];	m[2][2] = -mat.m[2][2];
								}

		//! Add another matrix
		inline_	void			Add(const Matrix3x3& mat)
								{
									m[0][0] += mat.m[0][0];	m[0][1] += mat.m[0][1];	m[0][2] += mat.m[0][2];
									m[1][0] += mat.m[1][0];	m[1][1] += mat.m[1][1];	m[1][2] += mat.m[1][2];
									m[2][0] += mat.m[2][0];	m[2][1] += mat.m[2][1];	m[2][2] += mat.m[2][2];
								}

		//! Sub another matrix
		inline_	void			Sub(const Matrix3x3& mat)
								{
									m[0][0] -= mat.m[0][0];	m[0][1]	-= mat.m[0][1];	m[0][2] -= mat.m[0][2];
									m[1][0] -= mat.m[1][0];	m[1][1] -= mat.m[1][1];	m[1][2] -= mat.m[1][2];
									m[2][0] -= mat.m[2][0];	m[2][1] -= mat.m[2][1];	m[2][2] -= mat.m[2][2];
								}
		//! Mac
		inline_	void			Mac(const Matrix3x3& a, const Matrix3x3& b, float s)
								{
									m[0][0] = a.m[0][0] + b.m[0][0] * s;
									m[0][1] = a.m[0][1] + b.m[0][1] * s;
									m[0][2] = a.m[0][2] + b.m[0][2] * s;

									m[1][0] = a.m[1][0] + b.m[1][0] * s;
									m[1][1] = a.m[1][1] + b.m[1][1] * s;
									m[1][2] = a.m[1][2] + b.m[1][2] * s;

									m[2][0] = a.m[2][0] + b.m[2][0] * s;
									m[2][1] = a.m[2][1] + b.m[2][1] * s;
									m[2][2] = a.m[2][2] + b.m[2][2] * s;
								}
		//! Mac
		inline_	void			Mac(const Matrix3x3& a, float s)
								{
									m[0][0] += a.m[0][0] * s;	m[0][1] += a.m[0][1] * s;	m[0][2] += a.m[0][2] * s;
									m[1][0] += a.m[1][0] * s;	m[1][1] += a.m[1][1] * s;	m[1][2] += a.m[1][2] * s;
									m[2][0] += a.m[2][0] * s;	m[2][1] += a.m[2][1] * s;	m[2][2] += a.m[2][2] * s;
								}

		//! this = A * s
		inline_	void			Mult(const Matrix3x3& a, float s)
								{
									m[0][0] = a.m[0][0] * s;	m[0][1] = a.m[0][1] * s;	m[0][2] = a.m[0][2] * s;
									m[1][0] = a.m[1][0] * s;	m[1][1] = a.m[1][1] * s;	m[1][2] = a.m[1][2] * s;
									m[2][0] = a.m[2][0] * s;	m[2][1] = a.m[2][1] * s;	m[2][2] = a.m[2][2] * s;
								}

		inline_	void			Add(const Matrix3x3& a, const Matrix3x3& b)
								{
									m[0][0] = a.m[0][0] + b.m[0][0];	m[0][1] = a.m[0][1] + b.m[0][1];	m[0][2] = a.m[0][2] + b.m[0][2];
									m[1][0] = a.m[1][0] + b.m[1][0];	m[1][1] = a.m[1][1] + b.m[1][1];	m[1][2] = a.m[1][2] + b.m[1][2];
									m[2][0] = a.m[2][0] + b.m[2][0];	m[2][1] = a.m[2][1] + b.m[2][1];	m[2][2] = a.m[2][2] + b.m[2][2];
								}

		inline_	void			Sub(const Matrix3x3& a, const Matrix3x3& b)
								{
									m[0][0] = a.m[0][0] - b.m[0][0];	m[0][1] = a.m[0][1] - b.m[0][1];	m[0][2] = a.m[0][2] - b.m[0][2];
									m[1][0] = a.m[1][0] - b.m[1][0];	m[1][1] = a.m[1][1] - b.m[1][1];	m[1][2] = a.m[1][2] - b.m[1][2];
									m[2][0] = a.m[2][0] - b.m[2][0];	m[2][1] = a.m[2][1] - b.m[2][1];	m[2][2] = a.m[2][2] - b.m[2][2];
								}

		//! this = a * b
		inline_	void			Mult(const Matrix3x3& a, const Matrix3x3& b)
								{
									m[0][0] = a.m[0][0] * b.m[0][0] + a.m[0][1] * b.m[1][0] + a.m[0][2] * b.m[2][0];
									m[0][1] = a.m[0][0] * b.m[0][1] + a.m[0][1] * b.m[1][1] + a.m[0][2] * b.m[2][1];
									m[0][2] = a.m[0][0] * b.m[0][2] + a.m[0][1] * b.m[1][2] + a.m[0][2] * b.m[2][2];
									m[1][0] = a.m[1][0] * b.m[0][0] + a.m[1][1] * b.m[1][0] + a.m[1][2] * b.m[2][0];
									m[1][1] = a.m[1][0] * b.m[0][1] + a.m[1][1] * b.m[1][1] + a.m[1][2] * b.m[2][1];
									m[1][2] = a.m[1][0] * b.m[0][2] + a.m[1][1] * b.m[1][2] + a.m[1][2] * b.m[2][2];
									m[2][0] = a.m[2][0] * b.m[0][0] + a.m[2][1] * b.m[1][0] + a.m[2][2] * b.m[2][0];
									m[2][1] = a.m[2][0] * b.m[0][1] + a.m[2][1] * b.m[1][1] + a.m[2][2] * b.m[2][1];
									m[2][2] = a.m[2][0] * b.m[0][2] + a.m[2][1] * b.m[1][2] + a.m[2][2] * b.m[2][2];
								}

		//! this = transpose(a) * b
		inline_	void			MultAtB(const Matrix3x3& a, const Matrix3x3& b)
								{
									m[0][0] = a.m[0][0] * b.m[0][0] + a.m[1][0] * b.m[1][0] + a.m[2][0] * b.m[2][0];
									m[0][1] = a.m[0][0] * b.m[0][1] + a.m[1][0] * b.m[1][1] + a.m[2][0] * b.m[2][1];
									m[0][2] = a.m[0][0] * b.m[0][2] + a.m[1][0] * b.m[1][2] + a.m[2][0] * b.m[2][2];
									m[1][0] = a.m[0][1] * b.m[0][0] + a.m[1][1] * b.m[1][0] + a.m[2][1] * b.m[2][0];
									m[1][1] = a.m[0][1] * b.m[0][1] + a.m[1][1] * b.m[1][1] + a.m[2][1] * b.m[2][1];
									m[1][2] = a.m[0][1] * b.m[0][2] + a.m[1][1] * b.m[1][2] + a.m[2][1] * b.m[2][2];
									m[2][0] = a.m[0][2] * b.m[0][0] + a.m[1][2] * b.m[1][0] + a.m[2][2] * b.m[2][0];
									m[2][1] = a.m[0][2] * b.m[0][1] + a.m[1][2] * b.m[1][1] + a.m[2][2] * b.m[2][1];
									m[2][2] = a.m[0][2] * b.m[0][2] + a.m[1][2] * b.m[1][2] + a.m[2][2] * b.m[2][2];
								}

		//! this = a * transpose(b)
		inline_	void			MultABt(const Matrix3x3& a, const Matrix3x3& b)
								{
									m[0][0] = a.m[0][0] * b.m[0][0] + a.m[0][1] * b.m[0][1] + a.m[0][2] * b.m[0][2];
									m[0][1] = a.m[0][0] * b.m[1][0] + a.m[0][1] * b.m[1][1] + a.m[0][2] * b.m[1][2];
									m[0][2] = a.m[0][0] * b.m[2][0] + a.m[0][1] * b.m[2][1] + a.m[0][2] * b.m[2][2];
									m[1][0] = a.m[1][0] * b.m[0][0] + a.m[1][1] * b.m[0][1] + a.m[1][2] * b.m[0][2];
									m[1][1] = a.m[1][0] * b.m[1][0] + a.m[1][1] * b.m[1][1] + a.m[1][2] * b.m[1][2];
									m[1][2] = a.m[1][0] * b.m[2][0] + a.m[1][1] * b.m[2][1] + a.m[1][2] * b.m[2][2];
									m[2][0] = a.m[2][0] * b.m[0][0] + a.m[2][1] * b.m[0][1] + a.m[2][2] * b.m[0][2];
									m[2][1] = a.m[2][0] * b.m[1][0] + a.m[2][1] * b.m[1][1] + a.m[2][2] * b.m[1][2];
									m[2][2] = a.m[2][0] * b.m[2][0] + a.m[2][1] * b.m[2][1] + a.m[2][2] * b.m[2][2];
								}

		//! Makes a rotation matrix mapping vector "from" to vector "to".
				Matrix3x3&		FromTo(const Point& from, const Point& to);

		//! Set a rotation matrix around the X axis.
		//!		 1		0		0
		//!	RX = 0		cx		sx
		//!		 0		-sx		cx
				void			RotX(float angle);
		//! Set a rotation matrix around the Y axis.
		//!		 cy		0		-sy
		//!	RY = 0		1		0
		//!		 sy		0		cy
				void			RotY(float angle);
		//! Set a rotation matrix around the Z axis.
		//!		 cz		sz		0
		//!	RZ = -sz	cz		0
		//!		 0		0		1
				void			RotZ(float angle);
		//!			cy		sx.sy		-sy.cx
		//!	RY.RX	0		cx			sx
		//!			sy		-sx.cy		cx.cy
				void			RotYX(float y, float x);

		//! Make a rotation matrix about an arbitrary axis
				Matrix3x3&		Rot(float angle, const Point& axis);

		//! Transpose the matrix.
				void			Transpose()
								{
									TSwap(m[1][0], m[0][1]);
									TSwap(m[2][0], m[0][2]);
									TSwap(m[2][1], m[1][2]);
								}

		//! this = Transpose(a)
				void			Transpose(const Matrix3x3& a)
								{
									m[0][0] = a.m[0][0];	m[0][1] = a.m[1][0];	m[0][2] = a.m[2][0];
									m[1][0] = a.m[0][1];	m[1][1] = a.m[1][1];	m[1][2] = a.m[2][1];
									m[2][0] = a.m[0][2];	m[2][1] = a.m[1][2];	m[2][2] = a.m[2][2];
								}

		//! Compute the determinant of the matrix. We use the rule of Sarrus.
				float			Determinant()					const
								{
									return (m[0][0]*m[1][1]*m[2][2] + m[0][1]*m[1][2]*m[2][0] + m[0][2]*m[1][0]*m[2][1])
										-  (m[2][0]*m[1][1]*m[0][2] + m[2][1]*m[1][2]*m[0][0] + m[2][2]*m[1][0]*m[0][1]);
								}
/*
		//! Compute a cofactor. Used for matrix inversion.
				float			CoFactor(ubyte row, ubyte column)	const
				{
					static const sdword gIndex[3+2] = { 0, 1, 2, 0, 1 };
					return	(m[gIndex[row+1]][gIndex[column+1]]*m[gIndex[row+2]][gIndex[column+2]] - m[gIndex[row+2]][gIndex[column+1]]*m[gIndex[row+1]][gIndex[column+2]]);
				}
*/
		//! Invert the matrix. Determinant must be different from zero, else matrix can't be inverted.
				Matrix3x3&		Invert()
								{
									float Det = Determinant();	// Must be !=0
									float OneOverDet = 1.0f / Det;

									Matrix3x3 Temp;
									Temp.m[0][0] = +(m[1][1] * m[2][2] - m[2][1] * m[1][2]) * OneOverDet;
									Temp.m[1][0] = -(m[1][0] * m[2][2] - m[2][0] * m[1][2]) * OneOverDet;
									Temp.m[2][0] = +(m[1][0] * m[2][1] - m[2][0] * m[1][1]) * OneOverDet;
									Temp.m[0][1] = -(m[0][1] * m[2][2] - m[2][1] * m[0][2]) * OneOverDet;
									Temp.m[1][1] = +(m[0][0] * m[2][2] - m[2][0] * m[0][2]) * OneOverDet;
									Temp.m[2][1] = -(m[0][0] * m[2][1] - m[2][0] * m[0][1]) * OneOverDet;
									Temp.m[0][2] = +(m[0][1] * m[1][2] - m[1][1] * m[0][2]) * OneOverDet;
									Temp.m[1][2] = -(m[0][0] * m[1][2] - m[1][0] * m[0][2]) * OneOverDet;
									Temp.m[2][2] = +(m[0][0] * m[1][1] - m[1][0] * m[0][1]) * OneOverDet;

									*this = Temp;

									return	*this;
								}

				Matrix3x3&		Normalize();

		//! this = exp(a)
				Matrix3x3&		Exp(const Matrix3x3& a);

void FromQuat(const Quat &q);
void FromQuatL2(const Quat &q, float l2);

		// Arithmetic operators
		//! Operator for Matrix3x3 Plus = Matrix3x3 + Matrix3x3;
		inline_	Matrix3x3		operator+(const Matrix3x3& mat)	const
								{
									return Matrix3x3(
									m[0][0] + mat.m[0][0],	m[0][1] + mat.m[0][1],	m[0][2] + mat.m[0][2],
									m[1][0] + mat.m[1][0],	m[1][1] + mat.m[1][1],	m[1][2] + mat.m[1][2],
									m[2][0] + mat.m[2][0],	m[2][1] + mat.m[2][1],	m[2][2] + mat.m[2][2]);
								}

		//! Operator for Matrix3x3 Minus = Matrix3x3 - Matrix3x3;
		inline_	Matrix3x3		operator-(const Matrix3x3& mat)	const
								{
									return Matrix3x3(
									m[0][0] - mat.m[0][0],	m[0][1] - mat.m[0][1],	m[0][2] - mat.m[0][2],
									m[1][0] - mat.m[1][0],	m[1][1] - mat.m[1][1],	m[1][2] - mat.m[1][2],
									m[2][0] - mat.m[2][0],	m[2][1] - mat.m[2][1],	m[2][2] - mat.m[2][2]);
								}

		//! Operator for Matrix3x3 Mul = Matrix3x3 * Matrix3x3;
		inline_	Matrix3x3		operator*(const Matrix3x3& mat)	const
								{
									return Matrix3x3(
									m[0][0]*mat.m[0][0] + m[0][1]*mat.m[1][0] + m[0][2]*mat.m[2][0],
									m[0][0]*mat.m[0][1] + m[0][1]*mat.m[1][1] + m[0][2]*mat.m[2][1],
									m[0][0]*mat.m[0][2] + m[0][1]*mat.m[1][2] + m[0][2]*mat.m[2][2],

									m[1][0]*mat.m[0][0] + m[1][1]*mat.m[1][0] + m[1][2]*mat.m[2][0],
									m[1][0]*mat.m[0][1] + m[1][1]*mat.m[1][1] + m[1][2]*mat.m[2][1],
									m[1][0]*mat.m[0][2] + m[1][1]*mat.m[1][2] + m[1][2]*mat.m[2][2],

									m[2][0]*mat.m[0][0] + m[2][1]*mat.m[1][0] + m[2][2]*mat.m[2][0],
									m[2][0]*mat.m[0][1] + m[2][1]*mat.m[1][1] + m[2][2]*mat.m[2][1],
									m[2][0]*mat.m[0][2] + m[2][1]*mat.m[1][2] + m[2][2]*mat.m[2][2]);
								}

		//! Operator for Point Mul = Matrix3x3 * Point;
		inline_	Point			operator*(const Point& v)		const		{ return Point(GetRow(0)|v, GetRow(1)|v, GetRow(2)|v); }

		//! Operator for Matrix3x3 Mul = Matrix3x3 * float;
		inline_	Matrix3x3		operator*(float s)				const
								{
									return Matrix3x3(
									m[0][0]*s,	m[0][1]*s,	m[0][2]*s,
									m[1][0]*s,	m[1][1]*s,	m[1][2]*s,
									m[2][0]*s,	m[2][1]*s,	m[2][2]*s);
								}

		//! Operator for Matrix3x3 Mul = float * Matrix3x3;
		inline_	friend Matrix3x3 operator*(float s, const Matrix3x3& mat)
								{
									return Matrix3x3(
									s*mat.m[0][0],	s*mat.m[0][1],	s*mat.m[0][2],
									s*mat.m[1][0],	s*mat.m[1][1],	s*mat.m[1][2],
									s*mat.m[2][0],	s*mat.m[2][1],	s*mat.m[2][2]);
								}

		//! Operator for Matrix3x3 Div = Matrix3x3 / float;
		inline_	Matrix3x3		operator/(float s)				const
								{
									if (s)	s = 1.0f / s;
									return Matrix3x3(
									m[0][0]*s,	m[0][1]*s,	m[0][2]*s,
									m[1][0]*s,	m[1][1]*s,	m[1][2]*s,
									m[2][0]*s,	m[2][1]*s,	m[2][2]*s);
								}

		//! Operator for Matrix3x3 Div = float / Matrix3x3;
		inline_	friend Matrix3x3 operator/(float s, const Matrix3x3& mat)
								{
									return Matrix3x3(
									s/mat.m[0][0],	s/mat.m[0][1],	s/mat.m[0][2],
									s/mat.m[1][0],	s/mat.m[1][1],	s/mat.m[1][2],
									s/mat.m[2][0],	s/mat.m[2][1],	s/mat.m[2][2]);
								}

		//! Operator for Matrix3x3 += Matrix3x3
		inline_	Matrix3x3&		operator+=(const Matrix3x3& mat)
								{
									m[0][0] += mat.m[0][0];		m[0][1] += mat.m[0][1];		m[0][2] += mat.m[0][2];
									m[1][0] += mat.m[1][0];		m[1][1] += mat.m[1][1];		m[1][2] += mat.m[1][2];
									m[2][0] += mat.m[2][0];		m[2][1] += mat.m[2][1];		m[2][2] += mat.m[2][2];
									return	*this;
								}

		//! Operator for Matrix3x3 -= Matrix3x3
		inline_	Matrix3x3&		operator-=(const Matrix3x3& mat)
								{
									m[0][0] -= mat.m[0][0];		m[0][1] -= mat.m[0][1];		m[0][2] -= mat.m[0][2];
									m[1][0] -= mat.m[1][0];		m[1][1] -= mat.m[1][1];		m[1][2] -= mat.m[1][2];
									m[2][0] -= mat.m[2][0];		m[2][1] -= mat.m[2][1];		m[2][2] -= mat.m[2][2];
									return	*this;
								}

		//! Operator for Matrix3x3 *= Matrix3x3
		inline_	Matrix3x3&		operator*=(const Matrix3x3& mat)
								{
									Point TempRow;

									GetRow(0, TempRow);
									m[0][0] = TempRow.x*mat.m[0][0] + TempRow.y*mat.m[1][0] + TempRow.z*mat.m[2][0];
									m[0][1] = TempRow.x*mat.m[0][1] + TempRow.y*mat.m[1][1] + TempRow.z*mat.m[2][1];
									m[0][2] = TempRow.x*mat.m[0][2] + TempRow.y*mat.m[1][2] + TempRow.z*mat.m[2][2];

									GetRow(1, TempRow);
									m[1][0] = TempRow.x*mat.m[0][0] + TempRow.y*mat.m[1][0] + TempRow.z*mat.m[2][0];
									m[1][1] = TempRow.x*mat.m[0][1] + TempRow.y*mat.m[1][1] + TempRow.z*mat.m[2][1];
									m[1][2] = TempRow.x*mat.m[0][2] + TempRow.y*mat.m[1][2] + TempRow.z*mat.m[2][2];

									GetRow(2, TempRow);
									m[2][0] = TempRow.x*mat.m[0][0] + TempRow.y*mat.m[1][0] + TempRow.z*mat.m[2][0];
									m[2][1] = TempRow.x*mat.m[0][1] + TempRow.y*mat.m[1][1] + TempRow.z*mat.m[2][1];
									m[2][2] = TempRow.x*mat.m[0][2] + TempRow.y*mat.m[1][2] + TempRow.z*mat.m[2][2];
									return	*this;
								}

		//! Operator for Matrix3x3 *= float
		inline_	Matrix3x3&		operator*=(float s)
								{
									m[0][0] *= s;	m[0][1] *= s;	m[0][2] *= s;
									m[1][0] *= s;	m[1][1] *= s;	m[1][2] *= s;
									m[2][0] *= s;	m[2][1] *= s;	m[2][2] *= s;
									return	*this;
								}

		//! Operator for Matrix3x3 /= float
		inline_	Matrix3x3&		operator/=(float s)
								{
									if (s)	s = 1.0f / s;
									m[0][0] *= s;	m[0][1] *= s;	m[0][2] *= s;
									m[1][0] *= s;	m[1][1] *= s;	m[1][2] *= s;
									m[2][0] *= s;	m[2][1] *= s;	m[2][2] *= s;
									return	*this;
								}

		// Cast operators
		//! Cast a Matrix3x3 to a Matrix4x4.
								operator Matrix4x4()	const;
		//! Cast a Matrix3x3 to a Quat.
								operator Quat()			const;

		inline_	const Point&	operator[](int row)		const	{ return *(const Point*)&m[row][0];	}
		inline_	Point&			operator[](int row)				{ return *(Point*)&m[row][0];		}

		public:

				float			m[3][3];
	};

#endif // __ICEMATRIX3X3_H__