d3dx9math.h

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/*
 *
 * Copyright (C) Microsoft Corporation. All Rights Reserved.
 *
 * File: d3dx9math.h
 * Content: D3DX math types and functions
 */

#include "d3dx9.h"

#ifndef __D3DX9MATH_H__
#define __D3DX9MATH_H__

#include <math.h>
#if _MSC_VER >= 1200
#pragma warning(push)
#endif

/*
 *
 * General purpose utilities
 *
 */
#define D3DX_PI ((FLOAT) 3.141592654f)
#define D3DX_1BYPI ((FLOAT) 0.318309886f)

#define D3DXToRadian( degree ) ((degree) * (D3DX_PI / 180.0f))
#define D3DXToDegree( radian ) ((radian) * (180.0f / D3DX_PI))

/*
 *
 * 16 bit floating point numbers
 */

#define D3DX_16F_DIG 3 /* # of decimal digits of precision */
#define D3DX_16F_EPSILON 4.8875809e-4f /* smallest such that 1.0 + epsilon != 1.0 */
#define D3DX_16F_MANT_DIG 11 /* # of bits in mantissa */
#define D3DX_16F_MAX 6.550400e+004 /* max value */
#define D3DX_16F_MAX_10_EXP 4 /* max decimal exponent */
#define D3DX_16F_MAX_EXP 15 /* max binary exponent */
#define D3DX_16F_MIN 6.1035156e-5f /* min positive value */
#define D3DX_16F_MIN_10_EXP (-4) /* min decimal exponent */
#define D3DX_16F_MIN_EXP (-14) /* min binary exponent */
#define D3DX_16F_RADIX 2 /* exponent radix */
#define D3DX_16F_ROUNDS 1 /* addition rounding: near */


typedef struct D3DXFLOAT16
{
#ifdef __cplusplus
public:
 D3DXFLOAT16() {};
 D3DXFLOAT16( FLOAT );
 D3DXFLOAT16( CONST D3DXFLOAT16& );

 /* casting */
 operator FLOAT ();

 /* binary operators */
 BOOL operator == ( CONST D3DXFLOAT16& ) const;
 BOOL operator != ( CONST D3DXFLOAT16& ) const;

protected:
#endif /*__cplusplus */
 WORD value;
} D3DXFLOAT16, *LPD3DXFLOAT16;



/*===========================================================================
 *
 * Vectors
 *
 *===========================================================================
 */


/*
 * 2D Vector
 */
typedef struct D3DXVECTOR2
{
#ifdef __cplusplus
public:
 D3DXVECTOR2() {};
 D3DXVECTOR2( CONST FLOAT * );
 D3DXVECTOR2( CONST D3DXFLOAT16 * );
 D3DXVECTOR2( FLOAT x, FLOAT y );

 /* casting */
 operator FLOAT* ();
 operator CONST FLOAT* () const;

 /* assignment operators */
 D3DXVECTOR2& operator += ( CONST D3DXVECTOR2& );
 D3DXVECTOR2& operator -= ( CONST D3DXVECTOR2& );
 D3DXVECTOR2& operator *= ( FLOAT );
 D3DXVECTOR2& operator /= ( FLOAT );

 /* unary operators */
 D3DXVECTOR2 operator + () const;
 D3DXVECTOR2 operator - () const;

 /* binary operators */
 D3DXVECTOR2 operator + ( CONST D3DXVECTOR2& ) const;
 D3DXVECTOR2 operator - ( CONST D3DXVECTOR2& ) const;
 D3DXVECTOR2 operator * ( FLOAT ) const;
 D3DXVECTOR2 operator / ( FLOAT ) const;

 friend D3DXVECTOR2 operator * ( FLOAT, CONST D3DXVECTOR2& );

 BOOL operator == ( CONST D3DXVECTOR2& ) const;
 BOOL operator != ( CONST D3DXVECTOR2& ) const;


public:
#endif /*__cplusplus */
 FLOAT x, y;
} D3DXVECTOR2, *LPD3DXVECTOR2;

/*
 * 2D Vector (16 bit)
 */

typedef struct D3DXVECTOR2_16F
{
#ifdef __cplusplus
public:
 D3DXVECTOR2_16F() {};
 D3DXVECTOR2_16F( CONST FLOAT * );
 D3DXVECTOR2_16F( CONST D3DXFLOAT16 * );
 D3DXVECTOR2_16F( CONST D3DXFLOAT16 &x, CONST D3DXFLOAT16 &y );

 /* casting */
 operator D3DXFLOAT16* ();
 operator CONST D3DXFLOAT16* () const;

 /* binary operators */
 BOOL operator == ( CONST D3DXVECTOR2_16F& ) const;
 BOOL operator != ( CONST D3DXVECTOR2_16F& ) const;

public:
#endif /*__cplusplus */
 D3DXFLOAT16 x, y;

} D3DXVECTOR2_16F, *LPD3DXVECTOR2_16F;

/*--------------------------
 * 3D Vector
 *--------------------------
 */
#ifdef __cplusplus
typedef struct D3DXVECTOR3 : public D3DVECTOR
{
public:
 D3DXVECTOR3() {};
 D3DXVECTOR3( CONST FLOAT * );
 D3DXVECTOR3( CONST D3DVECTOR& );
 D3DXVECTOR3( CONST D3DXFLOAT16 * );
 D3DXVECTOR3( FLOAT x, FLOAT y, FLOAT z );

 /* casting */
 operator FLOAT* ();
 operator CONST FLOAT* () const;

 /* assignment operators */
 D3DXVECTOR3& operator += ( CONST D3DXVECTOR3& );
 D3DXVECTOR3& operator -= ( CONST D3DXVECTOR3& );
 D3DXVECTOR3& operator *= ( FLOAT );
 D3DXVECTOR3& operator /= ( FLOAT );

 /* unary operators */
 D3DXVECTOR3 operator + () const;
 D3DXVECTOR3 operator - () const;

 /* binary operators */
 D3DXVECTOR3 operator + ( CONST D3DXVECTOR3& ) const;
 D3DXVECTOR3 operator - ( CONST D3DXVECTOR3& ) const;
 D3DXVECTOR3 operator * ( FLOAT ) const;
 D3DXVECTOR3 operator / ( FLOAT ) const;

 friend D3DXVECTOR3 operator * ( FLOAT, CONST struct D3DXVECTOR3& );

 BOOL operator == ( CONST D3DXVECTOR3& ) const;
 BOOL operator != ( CONST D3DXVECTOR3& ) const;

} D3DXVECTOR3, *LPD3DXVECTOR3;

#else /* !__cplusplus */
typedef struct _D3DVECTOR D3DXVECTOR3, *LPD3DXVECTOR3;
#endif /* !__cplusplus */

/*--------------------------
 * 3D Vector (16 bit)
 *--------------------------
 */

typedef struct D3DXVECTOR3_16F
{
#ifdef __cplusplus
public:
 D3DXVECTOR3_16F() {};
 D3DXVECTOR3_16F( CONST FLOAT * );
 D3DXVECTOR3_16F( CONST D3DVECTOR& );
 D3DXVECTOR3_16F( CONST D3DXFLOAT16 * );
 D3DXVECTOR3_16F( CONST D3DXFLOAT16 &x, CONST D3DXFLOAT16 &y, CONST D3DXFLOAT16 &z );

 /* casting */
 operator D3DXFLOAT16* ();
 operator CONST D3DXFLOAT16* () const;

 /* binary operators */
 BOOL operator == ( CONST D3DXVECTOR3_16F& ) const;
 BOOL operator != ( CONST D3DXVECTOR3_16F& ) const;

public:
#endif /*__cplusplus */
 D3DXFLOAT16 x, y, z;

} D3DXVECTOR3_16F, *LPD3DXVECTOR3_16F;

/*--------------------------
 * 4D Vector
 *--------------------------
 */
typedef struct D3DXVECTOR4
{
#ifdef __cplusplus
public:
 D3DXVECTOR4() {};
 D3DXVECTOR4( CONST FLOAT* );
 D3DXVECTOR4( CONST D3DXFLOAT16* );
 D3DXVECTOR4( CONST D3DVECTOR& xyz, FLOAT w );
 D3DXVECTOR4( FLOAT x, FLOAT y, FLOAT z, FLOAT w );

 /* casting */
 operator FLOAT* ();
 operator CONST FLOAT* () const;

 /* assignment operators */
 D3DXVECTOR4& operator += ( CONST D3DXVECTOR4& );
 D3DXVECTOR4& operator -= ( CONST D3DXVECTOR4& );
 D3DXVECTOR4& operator *= ( FLOAT );
 D3DXVECTOR4& operator /= ( FLOAT );

 /* unary operators */
 D3DXVECTOR4 operator + () const;
 D3DXVECTOR4 operator - () const;

 /* binary operators */
 D3DXVECTOR4 operator + ( CONST D3DXVECTOR4& ) const;
 D3DXVECTOR4 operator - ( CONST D3DXVECTOR4& ) const;
 D3DXVECTOR4 operator * ( FLOAT ) const;
 D3DXVECTOR4 operator / ( FLOAT ) const;

 friend D3DXVECTOR4 operator * ( FLOAT, CONST D3DXVECTOR4& );

 BOOL operator == ( CONST D3DXVECTOR4& ) const;
 BOOL operator != ( CONST D3DXVECTOR4& ) const;

public:
#endif /*__cplusplus */
 FLOAT x, y, z, w;
} D3DXVECTOR4, *LPD3DXVECTOR4;


/*--------------------------
 * 4D Vector (16 bit)
 *--------------------------
 */
typedef struct D3DXVECTOR4_16F
{
#ifdef __cplusplus
public:
 D3DXVECTOR4_16F() {};
 D3DXVECTOR4_16F( CONST FLOAT * );
 D3DXVECTOR4_16F( CONST D3DXFLOAT16* );
 D3DXVECTOR4_16F( CONST D3DXVECTOR3_16F& xyz, CONST D3DXFLOAT16& w );
 D3DXVECTOR4_16F( CONST D3DXFLOAT16& x, CONST D3DXFLOAT16& y, CONST D3DXFLOAT16& z, CONST D3DXFLOAT16& w );

 /* casting */
 operator D3DXFLOAT16* ();
 operator CONST D3DXFLOAT16* () const;

 /* binary operators */
 BOOL operator == ( CONST D3DXVECTOR4_16F& ) const;
 BOOL operator != ( CONST D3DXVECTOR4_16F& ) const;

public:
#endif /* __cplusplus */
 D3DXFLOAT16 x, y, z, w;

} D3DXVECTOR4_16F, *LPD3DXVECTOR4_16F;

/*===========================================================================
 *
 * Matrices
 *
 *===========================================================================
 */
#ifdef __cplusplus
typedef struct D3DXMATRIX : public D3DMATRIX
{
public:
 D3DXMATRIX() {};
 D3DXMATRIX( CONST FLOAT * );
 D3DXMATRIX( CONST D3DMATRIX& );
 D3DXMATRIX( CONST D3DXFLOAT16 * );
 D3DXMATRIX( FLOAT _11, FLOAT _12, FLOAT _13, FLOAT _14,
 FLOAT _21, FLOAT _22, FLOAT _23, FLOAT _24,
 FLOAT _31, FLOAT _32, FLOAT _33, FLOAT _34,
 FLOAT _41, FLOAT _42, FLOAT _43, FLOAT _44 );


 /* access grants */
 FLOAT& operator () ( UINT Row, UINT Col );
 FLOAT operator () ( UINT Row, UINT Col ) const;

 /* casting operators */
 operator FLOAT* ();
 operator CONST FLOAT* () const;

 /* assignment operators */
 D3DXMATRIX& operator *= ( CONST D3DXMATRIX& );
 D3DXMATRIX& operator += ( CONST D3DXMATRIX& );
 D3DXMATRIX& operator -= ( CONST D3DXMATRIX& );
 D3DXMATRIX& operator *= ( FLOAT );
 D3DXMATRIX& operator /= ( FLOAT );

 /* unary operators */
 D3DXMATRIX operator + () const;
 D3DXMATRIX operator - () const;

 /* binary operators */
 D3DXMATRIX operator * ( CONST D3DXMATRIX& ) const;
 D3DXMATRIX operator + ( CONST D3DXMATRIX& ) const;
 D3DXMATRIX operator - ( CONST D3DXMATRIX& ) const;
 D3DXMATRIX operator * ( FLOAT ) const;
 D3DXMATRIX operator / ( FLOAT ) const;

 friend D3DXMATRIX operator * ( FLOAT, CONST D3DXMATRIX& );

 BOOL operator == ( CONST D3DXMATRIX& ) const;
 BOOL operator != ( CONST D3DXMATRIX& ) const;

} D3DXMATRIX, *LPD3DXMATRIX;

#else /* !__cplusplus */
typedef struct _D3DMATRIX D3DXMATRIX, *LPD3DXMATRIX;
#endif /* !__cplusplus */


/*---------------------------------------------------------------------------
 * Aligned Matrices
 *
 * This class helps keep matrices 16-byte aligned as preferred by P4 cpus.
 * It aligns matrices on the stack and on the heap or in global scope.
 * It does this using __declspec(align(16)) which works on VC7 and on VC 6
 * with the processor pack. Unfortunately there is no way to detect the
 * latter so this is turned on only on VC7. On other compilers this is the
 * the same as D3DXMATRIX.
 *
 * Using this class on a compiler that does not actually do the alignment
 * can be dangerous since it will not expose bugs that ignore alignment.
 * E.g if an object of this class in inside a struct or class, and some code
 * memcopys data in it assuming tight packing. This could break on a compiler
 * that eventually start aligning the matrix.
 *---------------------------------------------------------------------------
 */
#ifdef __cplusplus
typedef struct _D3DXMATRIXA16 : public D3DXMATRIX
{
 _D3DXMATRIXA16() {}
 _D3DXMATRIXA16( CONST FLOAT * );
 _D3DXMATRIXA16( CONST D3DMATRIX& );
 _D3DXMATRIXA16( CONST D3DXFLOAT16 * );
 _D3DXMATRIXA16( FLOAT _11, FLOAT _12, FLOAT _13, FLOAT _14,
 FLOAT _21, FLOAT _22, FLOAT _23, FLOAT _24,
 FLOAT _31, FLOAT _32, FLOAT _33, FLOAT _34,
 FLOAT _41, FLOAT _42, FLOAT _43, FLOAT _44 );

 /* new operators */
 void* operator new ( size_t );
 void* operator new[] ( size_t );

 /* delete operators */
 void operator delete ( void* ); /* These are NOT virtual; Do not */
 void operator delete[] ( void* ); /* cast to D3DXMATRIX and delete. */

 /* assignment operators */
 _D3DXMATRIXA16& operator = ( CONST D3DXMATRIX& );

} _D3DXMATRIXA16;

#else /* !__cplusplus */
typedef D3DXMATRIX _D3DXMATRIXA16;
#endif /* !__cplusplus */

#if _MSC_VER >= 1300 /* VC7 */
#define D3DX_ALIGN16 __declspec(align(16))
#else
#define D3DX_ALIGN16 /* Earlier compiler may not understand this, do nothing. */
#endif

typedef D3DX_ALIGN16 _D3DXMATRIXA16 D3DXMATRIXA16, *LPD3DXMATRIXA16;

/*
 *
 * Quaternions
 */

typedef struct D3DXQUATERNION
{
#ifdef __cplusplus
public:
 D3DXQUATERNION() {}
 D3DXQUATERNION( CONST FLOAT * );
 D3DXQUATERNION( CONST D3DXFLOAT16 * );
 D3DXQUATERNION( FLOAT x, FLOAT y, FLOAT z, FLOAT w );

 /* casting */
 operator FLOAT* ();
 operator CONST FLOAT* () const;

 /* assignment operators */
 D3DXQUATERNION& operator += ( CONST D3DXQUATERNION& );
 D3DXQUATERNION& operator -= ( CONST D3DXQUATERNION& );
 D3DXQUATERNION& operator *= ( CONST D3DXQUATERNION& );
 D3DXQUATERNION& operator *= ( FLOAT );
 D3DXQUATERNION& operator /= ( FLOAT );

 /* unary operators */
 D3DXQUATERNION operator + () const;
 D3DXQUATERNION operator - () const;

 /* binary operators */
 D3DXQUATERNION operator + ( CONST D3DXQUATERNION& ) const;
 D3DXQUATERNION operator - ( CONST D3DXQUATERNION& ) const;
 D3DXQUATERNION operator * ( CONST D3DXQUATERNION& ) const;
 D3DXQUATERNION operator * ( FLOAT ) const;
 D3DXQUATERNION operator / ( FLOAT ) const;

 friend D3DXQUATERNION operator * (FLOAT, CONST D3DXQUATERNION& );

 BOOL operator == ( CONST D3DXQUATERNION& ) const;
 BOOL operator != ( CONST D3DXQUATERNION& ) const;

#endif /* __cplusplus */
 FLOAT x, y, z, w;
} D3DXQUATERNION, *LPD3DXQUATERNION;

/*
 *
 * Planes
 */
typedef struct D3DXPLANE
{
#ifdef __cplusplus
public:
 D3DXPLANE() {}
 D3DXPLANE( CONST FLOAT* );
 D3DXPLANE( CONST D3DXFLOAT16* );
 D3DXPLANE( FLOAT a, FLOAT b, FLOAT c, FLOAT d );

 /* casting */
 operator FLOAT* ();
 operator CONST FLOAT* () const;

 /* assignment operators */
 D3DXPLANE& operator *= ( FLOAT );
 D3DXPLANE& operator /= ( FLOAT );

 /* unary operators */
 D3DXPLANE operator + () const;
 D3DXPLANE operator - () const;

 /* binary operators */
 D3DXPLANE operator * ( FLOAT ) const;
 D3DXPLANE operator / ( FLOAT ) const;

 friend D3DXPLANE operator * ( FLOAT, CONST D3DXPLANE& );

 BOOL operator == ( CONST D3DXPLANE& ) const;
 BOOL operator != ( CONST D3DXPLANE& ) const;

#endif /*__cplusplus */
 FLOAT a, b, c, d;
} D3DXPLANE, *LPD3DXPLANE;


/*
 *
 * Colors
 *
 */

typedef struct D3DXCOLOR
{
#ifdef __cplusplus
public:
 D3DXCOLOR() {}
 D3DXCOLOR( DWORD argb );
 D3DXCOLOR( CONST FLOAT * );
 D3DXCOLOR( CONST D3DXFLOAT16 * );
 D3DXCOLOR( CONST D3DCOLORVALUE& );
 D3DXCOLOR( FLOAT r, FLOAT g, FLOAT b, FLOAT a );

 /* casting */
 operator DWORD () const;

 operator FLOAT* ();
 operator CONST FLOAT* () const;

 operator D3DCOLORVALUE* ();
 operator CONST D3DCOLORVALUE* () const;

 operator D3DCOLORVALUE& ();
 operator CONST D3DCOLORVALUE& () const;

 /* assignment operators */
 D3DXCOLOR& operator += ( CONST D3DXCOLOR& );
 D3DXCOLOR& operator -= ( CONST D3DXCOLOR& );
 D3DXCOLOR& operator *= ( FLOAT );
 D3DXCOLOR& operator /= ( FLOAT );

 /* unary operators */
 D3DXCOLOR operator + () const;
 D3DXCOLOR operator - () const;

 /* binary operators */
 D3DXCOLOR operator + ( CONST D3DXCOLOR& ) const;
 D3DXCOLOR operator - ( CONST D3DXCOLOR& ) const;
 D3DXCOLOR operator * ( FLOAT ) const;
 D3DXCOLOR operator / ( FLOAT ) const;

 friend D3DXCOLOR operator * ( FLOAT, CONST D3DXCOLOR& );

 BOOL operator == ( CONST D3DXCOLOR& ) const;
 BOOL operator != ( CONST D3DXCOLOR& ) const;

#endif /* __cplusplus */
 FLOAT r, g, b, a;
} D3DXCOLOR, *LPD3DXCOLOR;

/*
 *
 * D3DX math functions:
 *
 * NOTE:
 * * All these functions can take the same object as in and out parameters.
 *
 * * Out parameters are typically also returned as return values, so that
 * the output of one function may be used as a parameter to another.
 */

/*
 * Float16
 */

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

/* Converts an array 32-bit floats to 16-bit floats */
D3DXFLOAT16* WINAPI D3DXFloat32To16Array
 ( D3DXFLOAT16 *pOut, CONST FLOAT *pIn, UINT n );

/* Converts an array 16-bit floats to 32-bit floats */
FLOAT* WINAPI D3DXFloat16To32Array
 ( FLOAT *pOut, CONST D3DXFLOAT16 *pIn, UINT n );

#ifdef __cplusplus
}
#endif

/*
 * 2D Vector
 */

/* inline */

FLOAT D3DXVec2Length
 ( CONST D3DXVECTOR2 *pV );

FLOAT D3DXVec2LengthSq
 ( CONST D3DXVECTOR2 *pV );

FLOAT D3DXVec2Dot
 ( CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );

/* Z component of ((x1,y1,0) cross (x2,y2,0)) */
FLOAT D3DXVec2CCW
 ( CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );

D3DXVECTOR2* D3DXVec2Add
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );

D3DXVECTOR2* D3DXVec2Subtract
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );

/* Minimize each component. x = min(x1, x2), y = min(y1, y2) */
D3DXVECTOR2* D3DXVec2Minimize
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );

/* Maximize each component. x = max(x1, x2), y = max(y1, y2) */
D3DXVECTOR2* D3DXVec2Maximize
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );

D3DXVECTOR2* D3DXVec2Scale
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV, FLOAT s );

/* Linear interpolation. V1 + s(V2-V1) */
D3DXVECTOR2* D3DXVec2Lerp
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2,
 FLOAT s );

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

D3DXVECTOR2* WINAPI D3DXVec2Normalize
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV );

/* Hermite interpolation between position V1, tangent T1 (when s == 0)
 * and position V2, tangent T2 (when s == 1). */
D3DXVECTOR2* WINAPI D3DXVec2Hermite
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pT1,
 CONST D3DXVECTOR2 *pV2, CONST D3DXVECTOR2 *pT2, FLOAT s );

/* CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1) */
D3DXVECTOR2* WINAPI D3DXVec2CatmullRom
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV0, CONST D3DXVECTOR2 *pV1,
 CONST D3DXVECTOR2 *pV2, CONST D3DXVECTOR2 *pV3, FLOAT s );

/* Barycentric coordinates. V1 + f(V2-V1) + g(V3-V1) */
D3DXVECTOR2* WINAPI D3DXVec2BaryCentric
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2,
 CONST D3DXVECTOR2 *pV3, FLOAT f, FLOAT g);

/* Transform (x, y, 0, 1) by matrix. */
D3DXVECTOR4* WINAPI D3DXVec2Transform
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR2 *pV, CONST D3DXMATRIX *pM );

/* Transform (x, y, 0, 1) by matrix, project result back into w=1. */
D3DXVECTOR2* WINAPI D3DXVec2TransformCoord
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV, CONST D3DXMATRIX *pM );

/* Transform (x, y, 0, 0) by matrix. */
D3DXVECTOR2* WINAPI D3DXVec2TransformNormal
 ( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV, CONST D3DXMATRIX *pM );

/* Transform Array (x, y, 0, 1) by matrix. */
D3DXVECTOR4* WINAPI D3DXVec2TransformArray
 ( D3DXVECTOR4 *pOut, UINT OutStride, CONST D3DXVECTOR2 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n);

/* Transform Array (x, y, 0, 1) by matrix, project result back into w=1. */
D3DXVECTOR2* WINAPI D3DXVec2TransformCoordArray
 ( D3DXVECTOR2 *pOut, UINT OutStride, CONST D3DXVECTOR2 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );

/* Transform Array (x, y, 0, 0) by matrix. */
D3DXVECTOR2* WINAPI D3DXVec2TransformNormalArray
 ( D3DXVECTOR2 *pOut, UINT OutStride, CONST D3DXVECTOR2 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );



#ifdef __cplusplus
}
#endif

/*
 * 3D Vector
 */

/* inline */

FLOAT D3DXVec3Length
 ( CONST D3DXVECTOR3 *pV );

FLOAT D3DXVec3LengthSq
 ( CONST D3DXVECTOR3 *pV );

FLOAT D3DXVec3Dot
 ( CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );

D3DXVECTOR3* D3DXVec3Cross
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );

D3DXVECTOR3* D3DXVec3Add
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );

D3DXVECTOR3* D3DXVec3Subtract
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );

/* Minimize each component. x = min(x1, x2), y = min(y1, y2), ... */
D3DXVECTOR3* D3DXVec3Minimize
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );

/* Maximize each component. x = max(x1, x2), y = max(y1, y2), ... */
D3DXVECTOR3* D3DXVec3Maximize
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );

D3DXVECTOR3* D3DXVec3Scale
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, FLOAT s);

/* Linear interpolation. V1 + s(V2-V1) */
D3DXVECTOR3* D3DXVec3Lerp
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2,
 FLOAT s );

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

D3DXVECTOR3* WINAPI D3DXVec3Normalize
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV );

/* Hermite interpolation between position V1, tangent T1 (when s == 0)
 * and position V2, tangent T2 (when s == 1). */
D3DXVECTOR3* WINAPI D3DXVec3Hermite
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pT1,
 CONST D3DXVECTOR3 *pV2, CONST D3DXVECTOR3 *pT2, FLOAT s );

/* CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1) */
D3DXVECTOR3* WINAPI D3DXVec3CatmullRom
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV0, CONST D3DXVECTOR3 *pV1,
 CONST D3DXVECTOR3 *pV2, CONST D3DXVECTOR3 *pV3, FLOAT s );

/* Barycentric coordinates. V1 + f(V2-V1) + g(V3-V1) */
D3DXVECTOR3* WINAPI D3DXVec3BaryCentric
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2,
 CONST D3DXVECTOR3 *pV3, FLOAT f, FLOAT g);

/* Transform (x, y, z, 1) by matrix. */
D3DXVECTOR4* WINAPI D3DXVec3Transform
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DXMATRIX *pM );

/* Transform (x, y, z, 1) by matrix, project result back into w=1. */
D3DXVECTOR3* WINAPI D3DXVec3TransformCoord
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DXMATRIX *pM );

/* Transform (x, y, z, 0) by matrix. If you transforming a normal by a
 * non-affine matrix, the matrix you pass to this function should be the
 * transpose of the inverse of the matrix you would use to transform a coord.
 */
D3DXVECTOR3* WINAPI D3DXVec3TransformNormal
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DXMATRIX *pM );


/* Transform Array (x, y, z, 1) by matrix. */
D3DXVECTOR4* WINAPI D3DXVec3TransformArray
 ( D3DXVECTOR4 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );

/* Transform Array (x, y, z, 1) by matrix, project result back into w=1. */
D3DXVECTOR3* WINAPI D3DXVec3TransformCoordArray
 ( D3DXVECTOR3 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );

/* Transform (x, y, z, 0) by matrix. If you transforming a normal by a
 * non-affine matrix, the matrix you pass to this function should be the
 * transpose of the inverse of the matrix you would use to transform a coord.
 */
D3DXVECTOR3* WINAPI D3DXVec3TransformNormalArray
 ( D3DXVECTOR3 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );

/* Project vector from object space into screen space */
D3DXVECTOR3* WINAPI D3DXVec3Project
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DVIEWPORT9 *pViewport,
 CONST D3DXMATRIX *pProjection, CONST D3DXMATRIX *pView, CONST D3DXMATRIX *pWorld);

/* Project vector from screen space into object space */
D3DXVECTOR3* WINAPI D3DXVec3Unproject
 ( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DVIEWPORT9 *pViewport,
 CONST D3DXMATRIX *pProjection, CONST D3DXMATRIX *pView, CONST D3DXMATRIX *pWorld);

/* Project vector Array from object space into screen space */
D3DXVECTOR3* WINAPI D3DXVec3ProjectArray
 ( D3DXVECTOR3 *pOut, UINT OutStride,CONST D3DXVECTOR3 *pV, UINT VStride,CONST D3DVIEWPORT9 *pViewport,
 CONST D3DXMATRIX *pProjection, CONST D3DXMATRIX *pView, CONST D3DXMATRIX *pWorld, UINT n);

/* Project vector Array from screen space into object space */
D3DXVECTOR3* WINAPI D3DXVec3UnprojectArray
 ( D3DXVECTOR3 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DVIEWPORT9 *pViewport,
 CONST D3DXMATRIX *pProjection, CONST D3DXMATRIX *pView, CONST D3DXMATRIX *pWorld, UINT n);


#ifdef __cplusplus
}
#endif

/*
 * 4D Vector
 */

/* inline */

FLOAT D3DXVec4Length
 ( CONST D3DXVECTOR4 *pV );

FLOAT D3DXVec4LengthSq
 ( CONST D3DXVECTOR4 *pV );

FLOAT D3DXVec4Dot
 ( CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2 );

D3DXVECTOR4* D3DXVec4Add
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2);

D3DXVECTOR4* D3DXVec4Subtract
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2);

/* Minimize each component. x = min(x1, x2), y = min(y1, y2), ... */
D3DXVECTOR4* D3DXVec4Minimize
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2);

/* Maximize each component. x = max(x1, x2), y = max(y1, y2), ... */
D3DXVECTOR4* D3DXVec4Maximize
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2);

D3DXVECTOR4* D3DXVec4Scale
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV, FLOAT s);

/* Linear interpolation. V1 + s(V2-V1) */
D3DXVECTOR4* D3DXVec4Lerp
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2,
 FLOAT s );

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

/* Cross-product in 4 dimensions. */
D3DXVECTOR4* WINAPI D3DXVec4Cross
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2,
 CONST D3DXVECTOR4 *pV3);

D3DXVECTOR4* WINAPI D3DXVec4Normalize
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV );

/* Hermite interpolation between position V1, tangent T1 (when s == 0)
 * and position V2, tangent T2 (when s == 1). */
D3DXVECTOR4* WINAPI D3DXVec4Hermite
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pT1,
 CONST D3DXVECTOR4 *pV2, CONST D3DXVECTOR4 *pT2, FLOAT s );

/* CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1) */
D3DXVECTOR4* WINAPI D3DXVec4CatmullRom
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV0, CONST D3DXVECTOR4 *pV1,
 CONST D3DXVECTOR4 *pV2, CONST D3DXVECTOR4 *pV3, FLOAT s );

/* Barycentric coordinates. V1 + f(V2-V1) + g(V3-V1) */
D3DXVECTOR4* WINAPI D3DXVec4BaryCentric
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV1, CONST D3DXVECTOR4 *pV2,
 CONST D3DXVECTOR4 *pV3, FLOAT f, FLOAT g);

/* Transform vector by matrix. */
D3DXVECTOR4* WINAPI D3DXVec4Transform
 ( D3DXVECTOR4 *pOut, CONST D3DXVECTOR4 *pV, CONST D3DXMATRIX *pM );

/* Transform vector array by matrix. */
D3DXVECTOR4* WINAPI D3DXVec4TransformArray
 ( D3DXVECTOR4 *pOut, UINT OutStride, CONST D3DXVECTOR4 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );

#ifdef __cplusplus
}
#endif


/*
 * 4D Matrix
 */

/* inline */

D3DXMATRIX* D3DXMatrixIdentity
 ( D3DXMATRIX *pOut );

BOOL D3DXMatrixIsIdentity
 ( CONST D3DXMATRIX *pM );


/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

FLOAT WINAPI D3DXMatrixDeterminant
 ( CONST D3DXMATRIX *pM );

HRESULT WINAPI D3DXMatrixDecompose
 ( D3DXVECTOR3 *pOutScale, D3DXQUATERNION *pOutRotation,
 D3DXVECTOR3 *pOutTranslation, CONST D3DXMATRIX *pM );

D3DXMATRIX* WINAPI D3DXMatrixTranspose
 ( D3DXMATRIX *pOut, CONST D3DXMATRIX *pM );

/* Matrix multiplication. The result represents the transformation M2
 * followed by the transformation M1. (Out = M1 * M2) */
D3DXMATRIX* WINAPI D3DXMatrixMultiply
 ( D3DXMATRIX *pOut, CONST D3DXMATRIX *pM1, CONST D3DXMATRIX *pM2 );

/* Matrix multiplication, followed by a transpose. (Out = T(M1 * M2)) */
D3DXMATRIX* WINAPI D3DXMatrixMultiplyTranspose
 ( D3DXMATRIX *pOut, CONST D3DXMATRIX *pM1, CONST D3DXMATRIX *pM2 );

/* Calculate inverse of matrix. Inversion my fail, in which case NULL will
 * be returned. The determinant of pM is also returned it pfDeterminant
 * is non-NULL. */
D3DXMATRIX* WINAPI D3DXMatrixInverse
 ( D3DXMATRIX *pOut, FLOAT *pDeterminant, CONST D3DXMATRIX *pM );

/* Build a matrix which scales by (sx, sy, sz) */
D3DXMATRIX* WINAPI D3DXMatrixScaling
 ( D3DXMATRIX *pOut, FLOAT sx, FLOAT sy, FLOAT sz );

/* Build a matrix which translates by (x, y, z) */
D3DXMATRIX* WINAPI D3DXMatrixTranslation
 ( D3DXMATRIX *pOut, FLOAT x, FLOAT y, FLOAT z );

/* Build a matrix which rotates around the X axis */
D3DXMATRIX* WINAPI D3DXMatrixRotationX
 ( D3DXMATRIX *pOut, FLOAT Angle );

/* Build a matrix which rotates around the Y axis */
D3DXMATRIX* WINAPI D3DXMatrixRotationY
 ( D3DXMATRIX *pOut, FLOAT Angle );

/* Build a matrix which rotates around the Z axis */
D3DXMATRIX* WINAPI D3DXMatrixRotationZ
 ( D3DXMATRIX *pOut, FLOAT Angle );

/* Build a matrix which rotates around an arbitrary axis */
D3DXMATRIX* WINAPI D3DXMatrixRotationAxis
 ( D3DXMATRIX *pOut, CONST D3DXVECTOR3 *pV, FLOAT Angle );

/* Build a matrix from a quaternion */
D3DXMATRIX* WINAPI D3DXMatrixRotationQuaternion
 ( D3DXMATRIX *pOut, CONST D3DXQUATERNION *pQ);

/* Yaw around the Y axis, a pitch around the X axis,
 * and a roll around the Z axis. */
D3DXMATRIX* WINAPI D3DXMatrixRotationYawPitchRoll
 ( D3DXMATRIX *pOut, FLOAT Yaw, FLOAT Pitch, FLOAT Roll );

/* Build transformation matrix. NULL arguments are treated as identity.
 * Mout = Msc-1 * Msr-1 * Ms * Msr * Msc * Mrc-1 * Mr * Mrc * Mt */
D3DXMATRIX* WINAPI D3DXMatrixTransformation
 ( D3DXMATRIX *pOut, CONST D3DXVECTOR3 *pScalingCenter,
 CONST D3DXQUATERNION *pScalingRotation, CONST D3DXVECTOR3 *pScaling,
 CONST D3DXVECTOR3 *pRotationCenter, CONST D3DXQUATERNION *pRotation,
 CONST D3DXVECTOR3 *pTranslation);

/* Build 2D transformation matrix in XY plane. NULL arguments are treated as identity.
 * Mout = Msc-1 * Msr-1 * Ms * Msr * Msc * Mrc-1 * Mr * Mrc * Mt */
D3DXMATRIX* WINAPI D3DXMatrixTransformation2D
 ( D3DXMATRIX *pOut, CONST D3DXVECTOR2* pScalingCenter,
 FLOAT ScalingRotation, CONST D3DXVECTOR2* pScaling,
 CONST D3DXVECTOR2* pRotationCenter, FLOAT Rotation,
 CONST D3DXVECTOR2* pTranslation);

/* Build affine transformation matrix. NULL arguments are treated as identity.
 * Mout = Ms * Mrc-1 * Mr * Mrc * Mt */
D3DXMATRIX* WINAPI D3DXMatrixAffineTransformation
 ( D3DXMATRIX *pOut, FLOAT Scaling, CONST D3DXVECTOR3 *pRotationCenter,
 CONST D3DXQUATERNION *pRotation, CONST D3DXVECTOR3 *pTranslation);

/* Build 2D affine transformation matrix in XY plane. NULL arguments are treated as identity.
 * Mout = Ms * Mrc-1 * Mr * Mrc * Mt */
D3DXMATRIX* WINAPI D3DXMatrixAffineTransformation2D
 ( D3DXMATRIX *pOut, FLOAT Scaling, CONST D3DXVECTOR2* pRotationCenter,
 FLOAT Rotation, CONST D3DXVECTOR2* pTranslation);

/* Build a lookat matrix. (right-handed) */
D3DXMATRIX* WINAPI D3DXMatrixLookAtRH
 ( D3DXMATRIX *pOut, CONST D3DXVECTOR3 *pEye, CONST D3DXVECTOR3 *pAt,
 CONST D3DXVECTOR3 *pUp );

/* Build a lookat matrix. (left-handed) */
D3DXMATRIX* WINAPI D3DXMatrixLookAtLH
 ( D3DXMATRIX *pOut, CONST D3DXVECTOR3 *pEye, CONST D3DXVECTOR3 *pAt,
 CONST D3DXVECTOR3 *pUp );

/* Build a perspective projection matrix. (right-handed) */
D3DXMATRIX* WINAPI D3DXMatrixPerspectiveRH
 ( D3DXMATRIX *pOut, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf );

/* Build a perspective projection matrix. (left-handed) */
D3DXMATRIX* WINAPI D3DXMatrixPerspectiveLH
 ( D3DXMATRIX *pOut, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf );

/* Build a perspective projection matrix. (right-handed) */
D3DXMATRIX* WINAPI D3DXMatrixPerspectiveFovRH
 ( D3DXMATRIX *pOut, FLOAT fovy, FLOAT Aspect, FLOAT zn, FLOAT zf );

/* Build a perspective projection matrix. (left-handed) */
D3DXMATRIX* WINAPI D3DXMatrixPerspectiveFovLH
 ( D3DXMATRIX *pOut, FLOAT fovy, FLOAT Aspect, FLOAT zn, FLOAT zf );

/* Build a perspective projection matrix. (right-handed) */
D3DXMATRIX* WINAPI D3DXMatrixPerspectiveOffCenterRH
 ( D3DXMATRIX *pOut, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn,
 FLOAT zf );

/* Build a perspective projection matrix. (left-handed) */
D3DXMATRIX* WINAPI D3DXMatrixPerspectiveOffCenterLH
 ( D3DXMATRIX *pOut, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn,
 FLOAT zf );

/* Build an ortho projection matrix. (right-handed) */
D3DXMATRIX* WINAPI D3DXMatrixOrthoRH
 ( D3DXMATRIX *pOut, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf );

/* Build an ortho projection matrix. (left-handed) */
D3DXMATRIX* WINAPI D3DXMatrixOrthoLH
 ( D3DXMATRIX *pOut, FLOAT w, FLOAT h, FLOAT zn, FLOAT zf );

/* Build an ortho projection matrix. (right-handed) */
D3DXMATRIX* WINAPI D3DXMatrixOrthoOffCenterRH
 ( D3DXMATRIX *pOut, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn,
 FLOAT zf );

/* Build an ortho projection matrix. (left-handed) */
D3DXMATRIX* WINAPI D3DXMatrixOrthoOffCenterLH
 ( D3DXMATRIX *pOut, FLOAT l, FLOAT r, FLOAT b, FLOAT t, FLOAT zn,
 FLOAT zf );

/* Build a matrix which flattens geometry into a plane, as if casting
 * a shadow from a light. */
D3DXMATRIX* WINAPI D3DXMatrixShadow
 ( D3DXMATRIX *pOut, CONST D3DXVECTOR4 *pLight,
 CONST D3DXPLANE *pPlane );

/* Build a matrix which reflects the coordinate system about a plane */
D3DXMATRIX* WINAPI D3DXMatrixReflect
 ( D3DXMATRIX *pOut, CONST D3DXPLANE *pPlane );

#ifdef __cplusplus
}
#endif

/*
 * Quaternion
 */

/* inline */

FLOAT D3DXQuaternionLength
 ( CONST D3DXQUATERNION *pQ );

/* Length squared, or "norm" */
FLOAT D3DXQuaternionLengthSq
 ( CONST D3DXQUATERNION *pQ );

FLOAT D3DXQuaternionDot
 ( CONST D3DXQUATERNION *pQ1, CONST D3DXQUATERNION *pQ2 );

/* (0, 0, 0, 1) */
D3DXQUATERNION* D3DXQuaternionIdentity
 ( D3DXQUATERNION *pOut );

BOOL D3DXQuaternionIsIdentity
 ( CONST D3DXQUATERNION *pQ );

/* (-x, -y, -z, w) */
D3DXQUATERNION* D3DXQuaternionConjugate
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ );

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

/* Compute a quaternin's axis and angle of rotation. Expects unit quaternions. */
void WINAPI D3DXQuaternionToAxisAngle
 ( CONST D3DXQUATERNION *pQ, D3DXVECTOR3 *pAxis, FLOAT *pAngle );

/* Build a quaternion from a rotation matrix. */
D3DXQUATERNION* WINAPI D3DXQuaternionRotationMatrix
 ( D3DXQUATERNION *pOut, CONST D3DXMATRIX *pM);

/* Rotation about arbitrary axis. */
D3DXQUATERNION* WINAPI D3DXQuaternionRotationAxis
 ( D3DXQUATERNION *pOut, CONST D3DXVECTOR3 *pV, FLOAT Angle );

/* Yaw around the Y axis, a pitch around the X axis,
 * and a roll around the Z axis. */
D3DXQUATERNION* WINAPI D3DXQuaternionRotationYawPitchRoll
 ( D3DXQUATERNION *pOut, FLOAT Yaw, FLOAT Pitch, FLOAT Roll );

/* Quaternion multiplication. The result represents the rotation Q2
 * followed by the rotation Q1. (Out = Q2 * Q1) */
D3DXQUATERNION* WINAPI D3DXQuaternionMultiply
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ1,
 CONST D3DXQUATERNION *pQ2 );

D3DXQUATERNION* WINAPI D3DXQuaternionNormalize
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ );

/* Conjugate and re-norm */
D3DXQUATERNION* WINAPI D3DXQuaternionInverse
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ );

/* Expects unit quaternions.
 * if q = (cos(theta), sin(theta) * v); ln(q) = (0, theta * v) */
D3DXQUATERNION* WINAPI D3DXQuaternionLn
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ );

/* Expects pure quaternions. (w == 0) w is ignored in calculation.
 * if q = (0, theta * v); exp(q) = (cos(theta), sin(theta) * v) */
D3DXQUATERNION* WINAPI D3DXQuaternionExp
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ );

/* Spherical linear interpolation between Q1 (t == 0) and Q2 (t == 1).
 * Expects unit quaternions. */
D3DXQUATERNION* WINAPI D3DXQuaternionSlerp
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ1,
 CONST D3DXQUATERNION *pQ2, FLOAT t );

/* Spherical quadrangle interpolation.
 * Slerp(Slerp(Q1, C, t), Slerp(A, B, t), 2t(1-t)) */
D3DXQUATERNION* WINAPI D3DXQuaternionSquad
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ1,
 CONST D3DXQUATERNION *pA, CONST D3DXQUATERNION *pB,
 CONST D3DXQUATERNION *pC, FLOAT t );

/* Setup control points for spherical quadrangle interpolation
 * from Q1 to Q2. The control points are chosen in such a way
 * to ensure the continuity of tangents with adjacent segments. */
void WINAPI D3DXQuaternionSquadSetup
 ( D3DXQUATERNION *pAOut, D3DXQUATERNION *pBOut, D3DXQUATERNION *pCOut,
 CONST D3DXQUATERNION *pQ0, CONST D3DXQUATERNION *pQ1,
 CONST D3DXQUATERNION *pQ2, CONST D3DXQUATERNION *pQ3 );

/* Barycentric interpolation.
 * Slerp(Slerp(Q1, Q2, f+g), Slerp(Q1, Q3, f+g), g/(f+g)) */
D3DXQUATERNION* WINAPI D3DXQuaternionBaryCentric
 ( D3DXQUATERNION *pOut, CONST D3DXQUATERNION *pQ1,
 CONST D3DXQUATERNION *pQ2, CONST D3DXQUATERNION *pQ3,
 FLOAT f, FLOAT g );

#ifdef __cplusplus
}
#endif


/*
 * Plane
*/

/* inline */

/* ax + by + cz + dw */
FLOAT D3DXPlaneDot
 ( CONST D3DXPLANE *pP, CONST D3DXVECTOR4 *pV);

/* ax + by + cz + d */
FLOAT D3DXPlaneDotCoord
 ( CONST D3DXPLANE *pP, CONST D3DXVECTOR3 *pV);

/* ax + by + cz */
FLOAT D3DXPlaneDotNormal
 ( CONST D3DXPLANE *pP, CONST D3DXVECTOR3 *pV);

D3DXPLANE* D3DXPlaneScale
 (D3DXPLANE *pOut, CONST D3DXPLANE *pP, FLOAT s);

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

/* Normalize plane (so that |a,b,c| == 1) */
D3DXPLANE* WINAPI D3DXPlaneNormalize
 ( D3DXPLANE *pOut, CONST D3DXPLANE *pP);

/* Find the intersection between a plane and a line. If the line is
 * parallel to the plane, NULL is returned. */
D3DXVECTOR3* WINAPI D3DXPlaneIntersectLine
 ( D3DXVECTOR3 *pOut, CONST D3DXPLANE *pP, CONST D3DXVECTOR3 *pV1,
 CONST D3DXVECTOR3 *pV2);

/* Construct a plane from a point and a normal */
D3DXPLANE* WINAPI D3DXPlaneFromPointNormal
 ( D3DXPLANE *pOut, CONST D3DXVECTOR3 *pPoint, CONST D3DXVECTOR3 *pNormal);

/* Construct a plane from 3 points */
D3DXPLANE* WINAPI D3DXPlaneFromPoints
 ( D3DXPLANE *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2,
 CONST D3DXVECTOR3 *pV3);

/* Transform a plane by a matrix. The vector (a,b,c) must be normal.
 * M should be the inverse transpose of the transformation desired. */
D3DXPLANE* WINAPI D3DXPlaneTransform
 ( D3DXPLANE *pOut, CONST D3DXPLANE *pP, CONST D3DXMATRIX *pM );

/* Transform an array of planes by a matrix. The vectors (a,b,c) must be normal.
 * M should be the inverse transpose of the transformation desired. */
D3DXPLANE* WINAPI D3DXPlaneTransformArray
 ( D3DXPLANE *pOut, UINT OutStride, CONST D3DXPLANE *pP, UINT PStride, CONST D3DXMATRIX *pM, UINT n );

#ifdef __cplusplus
}
#endif

/*
 * Color
 */

/* inline */

/* (1-r, 1-g, 1-b, a) */
D3DXCOLOR* D3DXColorNegative
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC);

D3DXCOLOR* D3DXColorAdd
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC1, CONST D3DXCOLOR *pC2);

D3DXCOLOR* D3DXColorSubtract
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC1, CONST D3DXCOLOR *pC2);

D3DXCOLOR* D3DXColorScale
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC, FLOAT s);

/* (r1*r2, g1*g2, b1*b2, a1*a2) */
D3DXCOLOR* D3DXColorModulate
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC1, CONST D3DXCOLOR *pC2);

/* Linear interpolation of r,g,b, and a. C1 + s(C2-C1) */
D3DXCOLOR* D3DXColorLerp
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC1, CONST D3DXCOLOR *pC2, FLOAT s);

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

/* Interpolate r,g,b between desaturated color and color.
 * DesaturatedColor + s(Color - DesaturatedColor) */
D3DXCOLOR* WINAPI D3DXColorAdjustSaturation
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC, FLOAT s);

/* Interpolate r,g,b between 50% grey and color. Grey + s(Color - Grey) */
D3DXCOLOR* WINAPI D3DXColorAdjustContrast
 (D3DXCOLOR *pOut, CONST D3DXCOLOR *pC, FLOAT c);

#ifdef __cplusplus
}
#endif

/*
 * Misc
*/

#ifdef __cplusplus
extern "C" {
#endif

/* Calculate Fresnel term given the cosine of theta (likely obtained by
 * taking the dot of two normals), and the refraction index of the material. */
FLOAT WINAPI D3DXFresnelTerm
 (FLOAT CosTheta, FLOAT RefractionIndex);

#ifdef __cplusplus
}
#endif

/*
 *
 * Matrix Stack
 */

typedef interface ID3DXMatrixStack ID3DXMatrixStack;
typedef interface ID3DXMatrixStack *LPD3DXMATRIXSTACK;

/* {C7885BA7-F990-4fe7-922D-8515E477DD85} */
DEFINE_GUID(IID_ID3DXMatrixStack,
0xc7885ba7, 0xf990, 0x4fe7, 0x92, 0x2d, 0x85, 0x15, 0xe4, 0x77, 0xdd, 0x85);


#undef INTERFACE
#define INTERFACE ID3DXMatrixStack

DECLARE_INTERFACE_(ID3DXMatrixStack, IUnknown)
{
 /* IUnknown methods */
 STDMETHOD(QueryInterface)(THIS_ REFIID riid, LPVOID * ppvObj) PURE;
 STDMETHOD_(ULONG,AddRef)(THIS) PURE;
 STDMETHOD_(ULONG,Release)(THIS) PURE;

 /* ID3DXMatrixStack methods */

 /* Pops the top of the stack, returns the current top
 * *after* popping the top. */
 STDMETHOD(Pop)(THIS) PURE;

 /* Pushes the stack by one, duplicating the current matrix. */
 STDMETHOD(Push)(THIS) PURE;

 /* Loads identity in the current matrix. */
 STDMETHOD(LoadIdentity)(THIS) PURE;

 /* Loads the given matrix into the current matrix */
 STDMETHOD(LoadMatrix)(THIS_ CONST D3DXMATRIX* pM ) PURE;

 /* Right-Multiplies the given matrix to the current matrix.
 * (transformation is about the current world origin) */
 STDMETHOD(MultMatrix)(THIS_ CONST D3DXMATRIX* pM ) PURE;

 /* Left-Multiplies the given matrix to the current matrix
 * (transformation is about the local origin of the object) */
 STDMETHOD(MultMatrixLocal)(THIS_ CONST D3DXMATRIX* pM ) PURE;

 /* Right multiply the current matrix with the computed rotation
 * matrix, counterclockwise about the given axis with the given angle.
 * (rotation is about the current world origin) */
 STDMETHOD(RotateAxis)
 (THIS_ CONST D3DXVECTOR3* pV, FLOAT Angle) PURE;

 /* Left multiply the current matrix with the computed rotation
 * matrix, counterclockwise about the given axis with the given angle.
 * (rotation is about the local origin of the object) */
 STDMETHOD(RotateAxisLocal)
 (THIS_ CONST D3DXVECTOR3* pV, FLOAT Angle) PURE;

 /* Right multiply the current matrix with the computed rotation
 * matrix. All angles are counterclockwise. (rotation is about the
 * current world origin)

 * The rotation is composed of a yaw around the Y axis, a pitch around
 * the X axis, and a roll around the Z axis.
 */
 STDMETHOD(RotateYawPitchRoll)
 (THIS_ FLOAT Yaw, FLOAT Pitch, FLOAT Roll) PURE;

 /* Left multiply the current matrix with the computed rotation
 * matrix. All angles are counterclockwise. (rotation is about the
 * local origin of the object)

 * The rotation is composed of a yaw around the Y axis, a pitch around
 * the X axis, and a roll around the Z axis.
 */
 STDMETHOD(RotateYawPitchRollLocal)
 (THIS_ FLOAT Yaw, FLOAT Pitch, FLOAT Roll) PURE;

 /* Right multiply the current matrix with the computed scale
 * matrix. (transformation is about the current world origin) */
 STDMETHOD(Scale)(THIS_ FLOAT x, FLOAT y, FLOAT z) PURE;

 /* Left multiply the current matrix with the computed scale
 * matrix. (transformation is about the local origin of the object) */
 STDMETHOD(ScaleLocal)(THIS_ FLOAT x, FLOAT y, FLOAT z) PURE;

 /* Right multiply the current matrix with the computed translation
 * matrix. (transformation is about the current world origin) */
 STDMETHOD(Translate)(THIS_ FLOAT x, FLOAT y, FLOAT z ) PURE;

 /* Left multiply the current matrix with the computed translation
 * matrix. (transformation is about the local origin of the object) */
 STDMETHOD(TranslateLocal)(THIS_ FLOAT x, FLOAT y, FLOAT z) PURE;

 /* Obtain the current matrix at the top of the stack */
 STDMETHOD_(D3DXMATRIX*, GetTop)(THIS) PURE;
};

#ifdef __cplusplus
extern "C" {
#endif

HRESULT WINAPI
 D3DXCreateMatrixStack(
 DWORD Flags,
 LPD3DXMATRIXSTACK* ppStack);

#ifdef __cplusplus
}
#endif

/*
 *
 * Spherical Harmonic Runtime Routines
 *
 * NOTE:
 * * Most of these functions can take the same object as in and out parameters.
 * The exceptions are the rotation functions.
 *
 * * Out parameters are typically also returned as return values, so that
 * the output of one function may be used as a parameter to another.
 */

/* non-inline */
#ifdef __cplusplus
extern "C" {
#endif

/*
 *
 * Basic Spherical Harmonic math routines
 */

#define D3DXSH_MINORDER 2
#define D3DXSH_MAXORDER 6

FLOAT* WINAPI D3DXSHEvalDirection
 ( FLOAT *pOut, UINT Order, CONST D3DXVECTOR3 *pDir );

FLOAT* WINAPI D3DXSHRotate
 ( FLOAT *pOut, UINT Order, CONST D3DXMATRIX *pMatrix, CONST FLOAT *pIn );

FLOAT* WINAPI D3DXSHRotateZ
 ( FLOAT *pOut, UINT Order, FLOAT Angle, CONST FLOAT *pIn );

FLOAT* WINAPI D3DXSHAdd
 ( FLOAT *pOut, UINT Order, CONST FLOAT *pA, CONST FLOAT *pB );

FLOAT* WINAPI D3DXSHScale
 ( FLOAT *pOut, UINT Order, CONST FLOAT *pIn, CONST FLOAT Scale );

FLOAT WINAPI D3DXSHDot
 ( UINT Order, CONST FLOAT *pA, CONST FLOAT *pB );

FLOAT* WINAPI D3DXSHMultiply2( FLOAT *pOut, CONST FLOAT *pF, CONST FLOAT *pG);
FLOAT* WINAPI D3DXSHMultiply3( FLOAT *pOut, CONST FLOAT *pF, CONST FLOAT *pG);
FLOAT* WINAPI D3DXSHMultiply4( FLOAT *pOut, CONST FLOAT *pF, CONST FLOAT *pG);
FLOAT* WINAPI D3DXSHMultiply5( FLOAT *pOut, CONST FLOAT *pF, CONST FLOAT *pG);
FLOAT* WINAPI D3DXSHMultiply6( FLOAT *pOut, CONST FLOAT *pF, CONST FLOAT *pG);

/*
 *
 * Basic Spherical Harmonic lighting routines
 */

HRESULT WINAPI D3DXSHEvalDirectionalLight
 ( UINT Order, CONST D3DXVECTOR3 *pDir,
 FLOAT RIntensity, FLOAT GIntensity, FLOAT BIntensity,
 FLOAT *pROut, FLOAT *pGOut, FLOAT *pBOut );

HRESULT WINAPI D3DXSHEvalSphericalLight
 ( UINT Order, CONST D3DXVECTOR3 *pPos, FLOAT Radius,
 FLOAT RIntensity, FLOAT GIntensity, FLOAT BIntensity,
 FLOAT *pROut, FLOAT *pGOut, FLOAT *pBOut );

HRESULT WINAPI D3DXSHEvalConeLight
 ( UINT Order, CONST D3DXVECTOR3 *pDir, FLOAT Radius,
 FLOAT RIntensity, FLOAT GIntensity, FLOAT BIntensity,
 FLOAT *pROut, FLOAT *pGOut, FLOAT *pBOut );

HRESULT WINAPI D3DXSHEvalHemisphereLight
 ( UINT Order, CONST D3DXVECTOR3 *pDir, D3DXCOLOR Top, D3DXCOLOR Bottom,
 FLOAT *pROut, FLOAT *pGOut, FLOAT *pBOut );

/*
 *
 * Basic Spherical Harmonic projection routines
 */

/*
 *
 * D3DXSHProjectCubeMap:
 * --------------------
 * Projects a function represented on a cube map into spherical harmonics.
 *
 * Parameters:
 * Order
 * Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
 * pCubeMap
 * CubeMap that is going to be projected into spherical harmonics
 * pROut
 * Output SH vector for Red.
 * pGOut
 * Output SH vector for Green
 * pBOut
 * Output SH vector for Blue
 */

HRESULT WINAPI D3DXSHProjectCubeMap
 ( UINT uOrder, LPDIRECT3DCUBETEXTURE9 pCubeMap,
 FLOAT *pROut, FLOAT *pGOut, FLOAT *pBOut );


#ifdef __cplusplus
}
#endif

#if 0
#include "d3dx9math.inl"
#endif

#if _MSC_VER >= 1200
#pragma warning(pop)
#endif

#endif /* __D3DX9MATH_H__ */