#ifndef __RIMATH_H

#define __RIMATH_H

/*------------------------------------------------------------------------

 *

 * OpenVG 1.1 Reference Implementation

 * -----------------------------------

 *

 * Copyright (c) 2007 The Khronos Group Inc.

 * Portions copyright (c) 2010 Nokia Corporation and/or its subsidiary(-ies).

 *

 * Permission is hereby granted, free of charge, to any person obtaining a

 * copy of this software and /or associated documentation files

 * (the "Materials "), to deal in the Materials without restriction,

 * including without limitation the rights to use, copy, modify, merge,

 * publish, distribute, sublicense, and/or sell copies of the Materials,

 * and to permit persons to whom the Materials are 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 Materials.

 *

 * THE MATERIALS ARE 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 MATERIALS OR

 * THE USE OR OTHER DEALINGS IN THE MATERIALS.

 *

 *//**

 * \file

 * \brief	Math functions, Vector and Matrix classes.

 * \note

 *//*-------------------------------------------------------------------*/

#ifndef __RIDEFS_H

#include "riDefs.h"

#endif

#include <math.h>

namespace OpenVGRI

{

/*-------------------------------------------------------------------*//*!

* \brief

* \param

* \return

* \note

*//*-------------------------------------------------------------------*/

RI_INLINE int		RI_ISNAN(float a)

{

    RIfloatInt p;

    p.f = a;

    unsigned int exponent = (p.i>>23) & 0xff;

    unsigned int mantissa = p.i & 0x7fffff;

    if(exponent == 255 && mantissa)

        return 1;

    return 0;

}

#if (RI_MANTISSA_BITS > 23)

#error RI_MANTISSA_BITS is greater than 23

#elif (RI_EXPONENT_BITS > 8)

#error RI_EXPONENT_BITS is greater than 8

#elif (RI_MANTISSA_BITS != 23) || (RI_EXPONENT_BITS != 8)

class RIfloat

{

public:

    RIfloat() : v(0.0f)						{ removeBits(); }

    RIfloat(float a) : v(a)					{ removeBits(); }

    RIfloat(double a) : v((float)a)			{ removeBits(); }

    RIfloat(int a) : v((float)a)			{ removeBits(); }

    RIfloat(unsigned int a) : v((float)a)	{ removeBits(); }

    RIfloat&	operator=(const RIfloat &a)	{ v = a.v; removeBits(); return *this; }

    RIfloat&	operator+=(const RIfloat &a){ v += a.v; removeBits(); return *this; }

    RIfloat&	operator-=(const RIfloat &a){ v -= a.v; removeBits(); return *this; }

    RIfloat&	operator*=(const RIfloat &a){ v *= a.v; removeBits(); return *this; }

    RIfloat&	operator/=(const RIfloat &a){ v /= a.v; removeBits(); return *this; }

    RIfloat		operator-() const			{ return -v; }

    operator float() const					{ return v; }

    operator double() const					{ return (double)v; }

    operator int() const					{ return (int)v; }

    friend RIfloat	operator+(const RIfloat &a, const RIfloat &b);

    friend RIfloat	operator+(float a, const RIfloat &b);

    friend RIfloat	operator+(const RIfloat &a, float b);

    friend RIfloat	operator-(const RIfloat &a, const RIfloat &b);

    friend RIfloat	operator-(float a, const RIfloat &b);

    friend RIfloat	operator-(const RIfloat &a, float b);

    friend RIfloat	operator*(const RIfloat &a, const RIfloat &b);

    friend RIfloat	operator*(float a, const RIfloat &b);

    friend RIfloat	operator*(const RIfloat &a, float b);

    friend RIfloat	operator/(const RIfloat &a, const RIfloat &b);

    friend RIfloat	operator/(float a, const RIfloat &b);

    friend RIfloat	operator/(const RIfloat &a, float b);

    friend bool		operator<(const RIfloat &a, const RIfloat &b);

    friend bool		operator<(float a, const RIfloat &b);

    friend bool		operator<(const RIfloat &a, float b);

    friend bool		operator>(const RIfloat &a, const RIfloat &b);

    friend bool		operator>(float a, const RIfloat &b);

    friend bool		operator>(const RIfloat &a, float b);

    friend bool		operator<=(const RIfloat &a, const RIfloat &b);

    friend bool		operator<=(float a, const RIfloat &b);

    friend bool		operator<=(const RIfloat &a, float b);

    friend bool		operator>=(const RIfloat &a, const RIfloat &b);

    friend bool		operator>=(float a, const RIfloat &b);

    friend bool		operator>=(const RIfloat &a, float b);

    friend bool		operator==(const RIfloat &a, const RIfloat &b);

    friend bool		operator==(float a, const RIfloat &b);

    friend bool		operator==(const RIfloat &a, float b);

    friend bool		operator!=(const RIfloat &a, const RIfloat &b);

    friend bool		operator!=(float a, const RIfloat &b);

    friend bool		operator!=(const RIfloat &a, float b);

private:

    void	removeBits()

    {

        RIfloatInt p;

        p.f = v;

        unsigned int exponent = (p.i>>23) & 0xff;

        if(exponent == 0 || exponent == 255)

            return;	//zero, denormal, infinite, or NaN

        p.i &= ~((1<<(23-RI_MANTISSA_BITS))-1);

#if (RI_EXPONENT_BITS != 8)

        if (exponent > 127 + (1 << (RI_EXPONENT_BITS-1)))

            exponent = 127 + (1 << (RI_EXPONENT_BITS-1));

        if (exponent < 127 + 1 - (1 << (RI_EXPONENT_BITS-1)))

            exponent = 127 + 1 - (1 << (RI_EXPONENT_BITS-1));

        p.i &= ~(0xff<<23);

        p.i |= exponent<<23;

#endif

        v = p.f;

    }

    float		v;

};

RI_INLINE RIfloat operator+(const RIfloat &a, const RIfloat &b)	{ return RIfloat(a.v+b.v); }

RI_INLINE RIfloat operator+(float a, const RIfloat &b)			{ return RIfloat(a+b.v); }

RI_INLINE RIfloat operator+(const RIfloat &a, float b)			{ return RIfloat(a.v+b); }

RI_INLINE RIfloat operator-(const RIfloat &a, const RIfloat &b)	{ return RIfloat(a.v-b.v); }

RI_INLINE RIfloat operator-(float a, const RIfloat &b)			{ return RIfloat(a-b.v); }

RI_INLINE RIfloat operator-(const RIfloat &a, float b)			{ return RIfloat(a.v-b); }

RI_INLINE RIfloat operator*(const RIfloat &a, const RIfloat &b)	{ return RIfloat(a.v*b.v); }

RI_INLINE RIfloat operator*(float a, const RIfloat &b)			{ return RIfloat(a*b.v); }

RI_INLINE RIfloat operator*(const RIfloat &a, float b)			{ return RIfloat(a.v*b); }

RI_INLINE RIfloat operator/(const RIfloat &a, const RIfloat &b)	{ return RIfloat(a.v/b.v); }

RI_INLINE RIfloat operator/(float a, const RIfloat &b)			{ return RIfloat(a/b.v); }

RI_INLINE RIfloat operator/(const RIfloat &a, float b)			{ return RIfloat(a.v/b); }

RI_INLINE bool operator<(const RIfloat &a, const RIfloat &b)	{ return a.v < b.v ? true : false; }

RI_INLINE bool operator<(float a, const RIfloat &b)				{ return a < b.v ? true : false; }

RI_INLINE bool operator<(const RIfloat &a, float b)				{ return a.v < b ? true : false; }

RI_INLINE bool operator>(const RIfloat &a, const RIfloat &b)	{ return a.v > b.v ? true : false; }

RI_INLINE bool operator>(float a, const RIfloat &b)				{ return a > b.v ? true : false; }

RI_INLINE bool operator>(const RIfloat &a, float b)				{ return a.v > b ? true : false; }

RI_INLINE bool operator<=(const RIfloat &a, const RIfloat &b)	{ return a.v <= b.v ? true : false; }

RI_INLINE bool operator<=(float a, const RIfloat &b)			{ return a <= b.v ? true : false; }

RI_INLINE bool operator<=(const RIfloat &a, float b)			{ return a.v <= b ? true : false; }

RI_INLINE bool operator>=(const RIfloat &a, const RIfloat &b)	{ return a.v >= b.v ? true : false; }

RI_INLINE bool operator>=(float a, const RIfloat &b)			{ return a >= b.v ? true : false; }

RI_INLINE bool operator>=(const RIfloat &a, float b)			{ return a.v >= b ? true : false; }

RI_INLINE bool operator==(const RIfloat &a, const RIfloat &b)	{ return a.v == b.v ? true : false; }

RI_INLINE bool operator==(float a, const RIfloat &b)			{ return a == b.v ? true : false; }

RI_INLINE bool operator==(const RIfloat &a, float b)			{ return a.v == b ? true : false; }

RI_INLINE bool operator!=(const RIfloat &a, const RIfloat &b)	{ return a.v != b.v ? true : false; }

RI_INLINE bool operator!=(float a, const RIfloat &b)			{ return a != b.v ? true : false; }

RI_INLINE bool operator!=(const RIfloat &a, float b)			{ return a.v != b ? true : false; }

#else

typedef float RIfloat;

#endif

#define	RI_PI						3.141592654f

RI_INLINE RIfloat   RI_FRAC(RIfloat f)                          { return f - (RIfloat)(int)f; }

RI_INLINE int       RI_ROUND_TO_INT(RIfloat v)                  { return (v >= 0.0f) ? (int)(v+0.5f) : (int)(v-0.5f); }

RI_INLINE RIfloat	RI_MAX(RIfloat a, RIfloat b)				{ return (a > b) ? a : b; }

RI_INLINE int		RI_MAX(int a, int b)						{ return (a > b) ? a : b; }

RI_INLINE RIfloat	RI_MIN(RIfloat a, RIfloat b)				{ return (a < b) ? a : b; }

RI_INLINE int		RI_MIN(int a, int b)						{ return (a < b) ? a : b; }

RI_INLINE RIfloat	RI_CLAMP(RIfloat a, RIfloat l, RIfloat h)	{ if(RI_ISNAN(a)) return l; RI_ASSERT(l <= h); return (a < l) ? l : (a > h) ? h : a; }

RI_INLINE int       RI_CEIL(RIfloat a) {return (int)ceilf(a);}

RI_INLINE int       RI_FLOOR(RIfloat a) { return (int)floorf(a); }

RI_INLINE void		RI_SWAP(RIfloat &a, RIfloat &b)				{ RIfloat tmp = a; a = b; b = tmp; }

RI_INLINE RIfloat	RI_ABS(RIfloat a)							{ return (a < 0.0f) ? -a : a; }

RI_INLINE RIfloat	RI_SQR(RIfloat a)							{ return a * a; }

RI_INLINE RIfloat	RI_DEG_TO_RAD(RIfloat a)					{ return a * RI_PI / 180.0f; }

RI_INLINE RIfloat	RI_RAD_TO_DEG(RIfloat a)					{ return a * 180.0f/ RI_PI; }

RI_INLINE RIfloat	RI_MOD(RIfloat a, RIfloat b)				{ if(RI_ISNAN(a) || RI_ISNAN(b)) return 0.0f; RI_ASSERT(b >= 0.0f); if(b == 0.0f) return 0.0f; RIfloat f = (RIfloat)fmod(a, b); if(f < 0.0f) f += b; RI_ASSERT(f >= 0.0f && f <= b); return f; }

#define RI_ANY_SWAP(type, a, b) {type tmp = a; a = b; b = tmp;}

RI_INLINE void      RI_INT16_SWAP(RIint16 &a, RIint16 &b) {RIint16 tmp = a; a = b; b = tmp;}

RI_INLINE int       RI_INT_ABS(int a)                   { return (a >= 0) ? a : -a; }

RI_INLINE int		RI_INT_MAX(int a, int b)			{ return (a > b) ? a : b; }

RI_INLINE int		RI_INT_MIN(int a, int b)			{ return (a < b) ? a : b; }

RI_INLINE int       RI_INT_CLAMP(int a, int l, int h)   { return (a < l) ? l : (a > h) ? h : a; }

RI_INLINE void		RI_INT_SWAP(int &a, int &b)			{ int tmp = a; a = b; b = tmp; }

RI_INLINE int		RI_INT_MOD(int a, int b)			{ RI_ASSERT(b >= 0); if(!b) return 0; int i = a % b; if(i < 0) i += b; RI_ASSERT(i >= 0 && i < b); return i; }

RI_INLINE int		RI_INT_ADDSATURATE(int a, int b)	{ RI_ASSERT(b >= 0); int r = a + b; return (r >= a) ? r : RI_INT32_MAX; }

RI_INLINE RIfloat validateFloat(RIfloat f)

{

    //this function is used for all floating point input values

    if(RI_ISNAN(f)) return 0.0f;	//convert NaN to zero

    return RI_CLAMP(f, -RI_FLOAT_MAX, RI_FLOAT_MAX);	//clamp +-inf to +-RIfloat max

}

RI_INLINE int       RI_SHL(int a, int sh)

{

    RI_ASSERT(sh >= 0 && sh <= 31);

    int r = a << sh;

    RI_ASSERT(a >= 0 ? (r >= 0) : (r < 0));

    return r;

}

RI_INLINE int RI_SAT_SHL(RIint32 a, int sh)

{

    RI_ASSERT(sh >= 0 && sh <= 31);

    RIint64 r = ((RIint64)a) << sh;

    if (r > 0x7fffffff)

        return 0x7fffffff;

    else if (r < (long long)(int)0x80000000)

        return 0x80000000;

    return (RIint32)r;

}

RI_INLINE int RI_SHR(int a, int sh)

{

    RI_ASSERT(sh >= 0 && sh <= 31);

    int r = a >> sh;

    return r;

}

class Matrix3x3;

class Vector2;

class Vector3;

//==============================================================================================

//MatrixRxC, R = number of rows, C = number of columns

//indexing: matrix[row][column]

//Matrix3x3 inline functions cannot be inside the class because Vector3 is not defined yet when Matrix3x3 is defined

class Matrix3x3

{

public:

    RI_INLINE					Matrix3x3		();						//initialized to identity

    RI_INLINE					Matrix3x3		( const Matrix3x3& m );

    RI_INLINE					Matrix3x3		( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 );

    RI_INLINE					~Matrix3x3		();

    RI_INLINE Matrix3x3&		operator=		( const Matrix3x3& m );

    RI_INLINE Vector3&			operator[]		( int i );				//returns a row vector

    RI_INLINE const Vector3&	operator[]		( int i ) const;

    RI_INLINE void				set				( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 );

    RI_INLINE const Vector3		getRow			( int i ) const;

    RI_INLINE const Vector3		getColumn		( int i ) const;

    RI_INLINE void				setRow			( int i, const Vector3& v );

    RI_INLINE void				setColumn		( int i, const Vector3& v );

    RI_INLINE void				operator*=		( const Matrix3x3& m );

    RI_INLINE void				operator*=		( RIfloat f );

    RI_INLINE void				operator+=		( const Matrix3x3& m );

    RI_INLINE void				operator-=		( const Matrix3x3& m );

    RI_INLINE const Matrix3x3	operator-		() const;

    RI_INLINE void				identity		();

    RI_INLINE void				transpose		();

    bool						invert			();	//if the matrix is singular, returns false and leaves it unmodified

    RI_INLINE RIfloat				det				() const;

    RI_INLINE bool				isAffine		() const;

    RI_INLINE void              assertValid     () const;

    RI_INLINE void              validate        ();

private:

    RIfloat						matrix[3][3];

};

//==============================================================================================

class Vector2

{

public:

    RI_INLINE					Vector2			() : x(0.0f), y(0.0f)					{}

    RI_INLINE					Vector2			( const Vector2& v ) : x(v.x), y(v.y)	{}

    RI_INLINE					Vector2			( RIfloat fx, RIfloat fy ) : x(fx), y(fy)	{}

    RI_INLINE					~Vector2		()								{}

    RI_INLINE Vector2&			operator=		( const Vector2& v )			{ x = v.x; y = v.y; return *this; }

    RI_INLINE RIfloat&			operator[]		( int i )						{ RI_ASSERT(i>=0&&i<2); return (&x)[i]; }

    RI_INLINE const RIfloat&	operator[]		( int i ) const					{ RI_ASSERT(i>=0&&i<2); return (&x)[i]; }

    RI_INLINE void				set				( RIfloat fx, RIfloat fy )			{ x = fx; y = fy; }

    RI_INLINE void				operator*=		( RIfloat f )						{ x *= f; y *= f; }

    RI_INLINE void				operator+=		( const Vector2& v )			{ x += v.x; y += v.y; }

    RI_INLINE void				operator-=		( const Vector2& v )			{ x -= v.x; y -= v.y; }

    RI_INLINE const Vector2		operator-		() const						{ return Vector2(-x,-y); }

    //if the vector is zero, returns false and leaves it unmodified

    RI_INLINE bool				normalize		()								{ double l = (double)x*(double)x+(double)y*(double)y; if( l == 0.0 ) return false; l = 1.0 / sqrt(l); x = (RIfloat)((double)x * l); y = (RIfloat)((double)y * l); return true; }

    RI_INLINE RIfloat			length			() const						{ return (RIfloat)sqrt((double)x*(double)x+(double)y*(double)y); }

    RI_INLINE void				scale			( const Vector2& v )			{ x *= v.x; y *= v.y; }	//component-wise scale

    RI_INLINE void				negate			()								{ x = -x; y = -y; }

    RIfloat						x,y;

};

//==============================================================================================

class Vector3

{

public:

    RI_INLINE					Vector3			() : x(0.0f), y(0.0f), z(0.0f)							{}

    RI_INLINE					Vector3			( const Vector3& v ) : x(v.x), y(v.y), z(v.z)			{}

    RI_INLINE					Vector3			( RIfloat fx, RIfloat fy, RIfloat fz ) : x(fx), y(fy), z(fz)	{}

    RI_INLINE					~Vector3		()								{}

    RI_INLINE Vector3&			operator=		( const Vector3& v )			{ x = v.x; y = v.y; z = v.z; return *this; }

    RI_INLINE RIfloat&			operator[]		( int i )						{ RI_ASSERT(i>=0&&i<3); return (&x)[i]; }

    RI_INLINE const RIfloat&	operator[]		( int i ) const					{ RI_ASSERT(i>=0&&i<3); return (&x)[i]; }

    RI_INLINE void				set				( RIfloat fx, RIfloat fy, RIfloat fz ){ x = fx; y = fy; z = fz; }

    RI_INLINE void				operator*=		( RIfloat f )						{ x *= f; y *= f; z *= f; }

    RI_INLINE void				operator+=		( const Vector3& v )			{ x += v.x; y += v.y; z += v.z; }

    RI_INLINE void				operator-=		( const Vector3& v )			{ x -= v.x; y -= v.y; z -= v.z; }

    RI_INLINE const Vector3		operator-		() const						{ return Vector3(-x,-y,-z); }

    //if the vector is zero, returns false and leaves it unmodified

    RI_INLINE bool				normalize		()								{ double l = (double)x*(double)x+(double)y*(double)y+(double)z*(double)z; if( l == 0.0 ) return false; l = 1.0 / sqrt(l); x = (RIfloat)((double)x * l); y = (RIfloat)((double)y * l); z = (RIfloat)((double)z * l); return true; }

    RI_INLINE RIfloat			length			() const						{ return (RIfloat)sqrt((double)x*(double)x+(double)y*(double)y+(double)z*(double)z); }

    RI_INLINE void				scale			( const Vector3& v )			{ x *= v.x; y *= v.y; z *= v.z; }	//component-wise scale

    RI_INLINE void				negate			()								{ x = -x; y = -y; z = -z; }

    RIfloat						x,y,z;

};

//==============================================================================================

//Vector2 global functions

RI_INLINE bool			operator==	( const Vector2& v1, const Vector2& v2 )	{ return (v1.x == v2.x) && (v1.y == v2.y); }

RI_INLINE bool			operator!=	( const Vector2& v1, const Vector2& v2 )	{ return (v1.x != v2.x) || (v1.y != v2.y); }

RI_INLINE bool			isEqual		( const Vector2& v1, const Vector2& v2, RIfloat epsilon )	{ return RI_SQR(v2.x-v1.x) + RI_SQR(v2.y-v1.y) <= epsilon*epsilon; }

RI_INLINE bool			isZero		( const Vector2& v )						{ return (v.x == 0.0f) && (v.y == 0.0f); }

RI_INLINE const Vector2	operator*	( RIfloat f, const Vector2& v )				{ return Vector2(v.x*f,v.y*f); }

RI_INLINE const Vector2	operator*	( const Vector2& v, RIfloat f )				{ return Vector2(v.x*f,v.y*f); }

RI_INLINE const Vector2	operator+	( const Vector2& v1, const Vector2& v2 )	{ return Vector2(v1.x+v2.x, v1.y+v2.y); }

RI_INLINE const Vector2	operator-	( const Vector2& v1, const Vector2& v2 )	{ return Vector2(v1.x-v2.x, v1.y-v2.y); }

RI_INLINE RIfloat		dot			( const Vector2& v1, const Vector2& v2 )	{ return v1.x*v2.x+v1.y*v2.y; }

//if v is a zero vector, returns a zero vector

RI_INLINE const Vector2	normalize	( const Vector2& v )						{ double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y; if( l != 0.0 ) l = 1.0 / sqrt(l); return Vector2((RIfloat)((double)v.x * l), (RIfloat)((double)v.y * l)); }

//if onThis is a zero vector, returns a zero vector

RI_INLINE const Vector2	project		( const Vector2& v, const Vector2& onThis ) { RIfloat l = dot(onThis,onThis); if( l != 0.0f ) l = dot(v, onThis)/l; return onThis * l; }

RI_INLINE const Vector2	lerp		( const Vector2& v1, const Vector2& v2, RIfloat ratio )	{ return v1 + ratio * (v2 - v1); }

RI_INLINE const Vector2	scale		( const Vector2& v1, const Vector2& v2 )	{ return Vector2(v1.x*v2.x, v1.y*v2.y); }

//matrix * column vector. The input vector2 is implicitly expanded to (x,y,1)

RI_INLINE const Vector2 affineTransform( const Matrix3x3& m, const Vector2& v )	{ RI_ASSERT(m.isAffine()); return Vector2(v.x * m[0][0] + v.y * m[0][1] + m[0][2], v.x * m[1][0] + v.y * m[1][1] + m[1][2]); }

//matrix * column vector. The input vector2 is implicitly expanded to (x,y,0)

RI_INLINE const Vector2 affineTangentTransform(const Matrix3x3& m, const Vector2& v)	{ RI_ASSERT(m.isAffine()); return Vector2(v.x * m[0][0] + v.y * m[0][1], v.x * m[1][0] + v.y * m[1][1]); }

RI_INLINE const Vector2 perpendicularCW(const Vector2& v)						{ return Vector2(v.y, -v.x); }

RI_INLINE const Vector2 perpendicularCCW(const Vector2& v)						{ return Vector2(-v.y, v.x); }

RI_INLINE const Vector2 perpendicular(const Vector2& v, bool cw)				{ if(cw) return Vector2(v.y, -v.x); return Vector2(-v.y, v.x); }

//==============================================================================================

//Vector3 global functions

RI_INLINE bool			operator==	( const Vector3& v1, const Vector3& v2 )	{ return (v1.x == v2.x) && (v1.y == v2.y) && (v1.z == v2.z); }

RI_INLINE bool			operator!=	( const Vector3& v1, const Vector3& v2 )	{ return (v1.x != v2.x) || (v1.y != v2.y) || (v1.z != v2.z); }

RI_INLINE bool			isEqual		( const Vector3& v1, const Vector3& v2, RIfloat epsilon )	{ return RI_SQR(v2.x-v1.x) + RI_SQR(v2.y-v1.y) + RI_SQR(v2.z-v1.z) <= epsilon*epsilon; }

RI_INLINE const Vector3	operator*	( RIfloat f, const Vector3& v )				{ return Vector3(v.x*f,v.y*f,v.z*f); }

RI_INLINE const Vector3	operator*	( const Vector3& v, RIfloat f )				{ return Vector3(v.x*f,v.y*f,v.z*f); }

RI_INLINE const Vector3	operator+	( const Vector3& v1, const Vector3& v2 )	{ return Vector3(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z); }

RI_INLINE const Vector3	operator-	( const Vector3& v1, const Vector3& v2 )	{ return Vector3(v1.x-v2.x, v1.y-v2.y, v1.z-v2.z); }

RI_INLINE RIfloat		dot			( const Vector3& v1, const Vector3& v2 )	{ return v1.x*v2.x+v1.y*v2.y+v1.z*v2.z; }

RI_INLINE const Vector3	cross		( const Vector3& v1, const Vector3& v2 )	{ return Vector3( v1.y*v2.z-v1.z*v2.y, v1.z*v2.x-v1.x*v2.z, v1.x*v2.y-v1.y*v2.x ); }

//if v is a zero vector, returns a zero vector

RI_INLINE const Vector3	normalize	( const Vector3& v )						{ double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y+(double)v.z*(double)v.z; if( l != 0.0 ) l = 1.0 / sqrt(l); return Vector3((RIfloat)((double)v.x * l), (RIfloat)((double)v.y * l), (RIfloat)((double)v.z * l)); }

RI_INLINE const Vector3	lerp		( const Vector3& v1, const Vector3& v2, RIfloat ratio )	{ return v1 + ratio * (v2 - v1); }

RI_INLINE const Vector3	scale		( const Vector3& v1, const Vector3& v2 )	{ return Vector3(v1.x*v2.x, v1.y*v2.y, v1.z*v2.z); }

//==============================================================================================

//matrix * column vector

RI_INLINE const Vector3	operator*	( const Matrix3x3& m, const Vector3& v)		{ return Vector3( v.x*m[0][0]+v.y*m[0][1]+v.z*m[0][2], v.x*m[1][0]+v.y*m[1][1]+v.z*m[1][2], v.x*m[2][0]+v.y*m[2][1]+v.z*m[2][2] ); }

//==============================================================================================

//Matrix3x3 global functions

RI_INLINE bool				operator==	( const Matrix3x3& m1, const Matrix3x3& m2 )	{ for(int i=0;i<3;i++) for(int j=0;j<3;j++) if( m1[i][j] != m2[i][j] ) return false; return true; }

RI_INLINE bool				operator!=	( const Matrix3x3& m1, const Matrix3x3& m2 )	{ return !(m1 == m2); }

RI_INLINE const Matrix3x3	operator*	( const Matrix3x3& m1, const Matrix3x3& m2 )	{ Matrix3x3 t; for(int i=0;i<3;i++) for(int j=0;j<3;j++) t[i][j] = m1[i][0] * m2[0][j] + m1[i][1] * m2[1][j] + m1[i][2] * m2[2][j]; return t; }

RI_INLINE const Matrix3x3	operator*	( RIfloat f, const Matrix3x3& m )					{ Matrix3x3 t(m); t *= f; return t; }

RI_INLINE const Matrix3x3	operator*	( const Matrix3x3& m, RIfloat f )					{ Matrix3x3 t(m); t *= f; return t; }

RI_INLINE const Matrix3x3	operator+	( const Matrix3x3& m1, const Matrix3x3& m2 )	{ Matrix3x3 t(m1); t += m2; return t; }

RI_INLINE const Matrix3x3	operator-	( const Matrix3x3& m1, const Matrix3x3& m2 )	{ Matrix3x3 t(m1); t -= m2; return t; }

RI_INLINE const Matrix3x3	transpose	( const Matrix3x3& m )							{ Matrix3x3 t(m); t.transpose(); return t; }

// if the matrix is singular, returns it unmodified

RI_INLINE const Matrix3x3	invert		( const Matrix3x3& m )							{ Matrix3x3 t(m); t.invert(); return t; }

//==============================================================================================

//Matrix3x3 inline functions (cannot be inside the class because Vector3 is not defined yet when Matrix3x3 is defined)

RI_INLINE					Matrix3x3::Matrix3x3	()									{ identity(); }

RI_INLINE					Matrix3x3::Matrix3x3	( const Matrix3x3& m )				{ *this = m; }

RI_INLINE					Matrix3x3::Matrix3x3	( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 )	{ set(m00,m01,m02,m10,m11,m12,m20,m21,m22); }

RI_INLINE					Matrix3x3::~Matrix3x3	()									{}

RI_INLINE Matrix3x3&		Matrix3x3::operator=	( const Matrix3x3& m )				{ for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] = m.matrix[i][j]; return *this; }

RI_INLINE Vector3&			Matrix3x3::operator[]	( int i )							{ RI_ASSERT(i>=0&&i<3); return (Vector3&)matrix[i][0]; }

RI_INLINE const Vector3&	Matrix3x3::operator[]	( int i ) const						{ RI_ASSERT(i>=0&&i<3); return (const Vector3&)matrix[i][0]; }

RI_INLINE void				Matrix3x3::set			( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ) { matrix[0][0] = m00; matrix[0][1] = m01; matrix[0][2] = m02; matrix[1][0] = m10; matrix[1][1] = m11; matrix[1][2] = m12; matrix[2][0] = m20; matrix[2][1] = m21; matrix[2][2] = m22; }

RI_INLINE const Vector3		Matrix3x3::getRow		( int i ) const						{ RI_ASSERT(i>=0&&i<3); return Vector3(matrix[i][0], matrix[i][1], matrix[i][2]); }

RI_INLINE const Vector3		Matrix3x3::getColumn	( int i ) const						{ RI_ASSERT(i>=0&&i<3); return Vector3(matrix[0][i], matrix[1][i], matrix[2][i]); }

RI_INLINE void				Matrix3x3::setRow		( int i, const Vector3& v )			{ RI_ASSERT(i>=0&&i<3); matrix[i][0] = v.x; matrix[i][1] = v.y; matrix[i][2] = v.z; }

RI_INLINE void				Matrix3x3::setColumn	( int i, const Vector3& v )			{ RI_ASSERT(i>=0&&i<3); matrix[0][i] = v.x; matrix[1][i] = v.y; matrix[2][i] = v.z; }

RI_INLINE void				Matrix3x3::operator*=	( const Matrix3x3& m )				{ *this = *this * m; }

RI_INLINE void				Matrix3x3::operator*=	( RIfloat f )							{ for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] *= f; }

RI_INLINE void				Matrix3x3::operator+=	( const Matrix3x3& m )				{ for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] += m.matrix[i][j]; }

RI_INLINE void				Matrix3x3::operator-=	( const Matrix3x3& m )				{ for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] -= m.matrix[i][j]; }

RI_INLINE const Matrix3x3	Matrix3x3::operator-	() const							{ return Matrix3x3( -matrix[0][0],-matrix[0][1],-matrix[0][2], -matrix[1][0],-matrix[1][1],-matrix[1][2], -matrix[2][0],-matrix[2][1],-matrix[2][2]); }

RI_INLINE void				Matrix3x3::identity		()									{ for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] = (i == j) ? 1.0f : 0.0f; }

RI_INLINE void				Matrix3x3::transpose	()									{ RI_SWAP(matrix[1][0], matrix[0][1]); RI_SWAP(matrix[2][0], matrix[0][2]); RI_SWAP(matrix[2][1], matrix[1][2]); }

RI_INLINE RIfloat			Matrix3x3::det			() const							{ return matrix[0][0] * (matrix[1][1]*matrix[2][2] - matrix[2][1]*matrix[1][2]) + matrix[0][1] * (matrix[2][0]*matrix[1][2] - matrix[1][0]*matrix[2][2]) + matrix[0][2] * (matrix[1][0]*matrix[2][1] - matrix[2][0]*matrix[1][1]); }

RI_INLINE bool				Matrix3x3::isAffine		() const							{ if(matrix[2][0] == 0.0f && matrix[2][1] == 0.0f && matrix[2][2] == 1.0f) return true; return false; }

RI_INLINE void Matrix3x3::validate()

{

    for (int i = 0; i < 3; i++)

        for (int j = 0; j < 3; j++)

            matrix[i][j] = validateFloat(matrix[i][j]);

}

RI_INLINE void Matrix3x3::assertValid() const

{

#if defined(RI_DEBUG)

    for (int i = 0; i < 3; i++)

        for (int j = 0; j < 3; j++)

            RI_ASSERT(!RI_ISNAN(matrix[i][j]));

#endif

}

//==============================================================================================

}	//namespace OpenVGRI

#endif /* __RIMATH_H */