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BGFX Effects for (nearly) Everyone
==================================

By default, MAME outputs an idealized version of the video as it would be on the way to the arcade cabinet's monitor, with minimal modification of the output (primarily to stretch the game image back to the aspect ratio the monitor would traditionally have, usually 4:3) -- this works well, but misses some of the nostalgia factor. Arcade monitors were never ideal, even in perfect condition, and the nature of a CRT display distorts that image in ways that change the appearance significantly.

Modern LCD monitors simply do not look the same, and even computer CRT monitors cannot match the look of an arcade monitor without help.

That's where the new BGFX renderer with HLSL comes into the picture.

HLSL simulates most of the effects that a CRT arcade monitor has on the video, making the result look a lot more authentic. However, HLSL requires some effort on the user's part: the settings you use are going to be tailored to your PC's system specs, and especially the monitor you're using. Additionally, there were hundreds of thousands of monitors out there in arcades. Each was tuned and maintained differently, meaning there is no one correct appearance to judge by either. Basic guidelines will be provided here to help you, but you may also wish to ask for opinions on popular MAME-centric forums.


Resolution and Aspect Ratio
---------------------------

Resolution is a very important subject for HLSL settings. You will want MAME to be using the native resolution of your monitor to avoid additional distortion and lag created by your monitor upscaling the display image.

While most arcade machines used a 4:3 ratio display (or 3:4 for vertically oriented monitors like Pac-Man), it's difficult to find a consumer display that is 4:3 at this point. The good news is that that extra space on the sides isn't wasted. Many arcade cabinets used bezel artwork around the main display, and should you have the necessary artwork files, MAME will display that artwork. Turn the artwork view to Cropped for best results.

Some older LCD displays used a native resolution of 1280x1024 and were a 5:4 aspect ratio. There's not enough extra space to display artwork, and you'll end up with some very slight pillarboxing, but the results will be still be good and on-par with a 4:3 monitor.


Getting Started with BGFX
-------------------------

You will need to have followed the initial MAME setup instructions elsewhere in this manual before beginning. Official MAME distributions include BGFX as of 172, so you don't need to download any additional files.

Open your MAME.INI in your text editor of choice (e.g. Notepad), and make sure the following options are set correctly:

* **video bgfx**

Now, you may want to take a moment to look below at the Configuration Settings section to see how to set up these next options.

As referenced in :ref:`advanced-multi-CFG`, MAME has a order in which it processes INI files. The BGFX settings can be edited in MAME.INI, but to take full advantage of the power of MAME's config files, you'll want to copy the BGFX settings from MAME.INI to one of the other config files and make changes there.)

In particular, you will want the **bgfx_screen_chains** to be specific to each game.

Save your .INI file(s) and you're ready to begin.

Configuration Settings
----------------------

| **bgfx_path**
|
| 	This is where your BGFX shader files are stored. By default, this will be the BGFX folder in your MAME installation.
|
| **bgfx_backend**
|
|	Selects a rendering backend for BGFX to use. Possible choices include **d3d9**, **d3d11**, **opengl**, and **metal**. The default is **auto**, which will let MAME choose the best selection for you.
|
|	**d3d9** -- Direct3D 9.0 Renderer (Requires Windows XP or higher)
|	**d3d11** -- Direct3D 11.0 Renderer (Requires Windows Vista with D3D11 update or Windows 7 or higher)
|	**opengl** -- OpenGL Renderer (Requires OpenGL drivers, may work better on some poorly designed video cards, supported on Linux/Mac OS X)
|	**metal** -- Metal Apple Graphics API (Requires OS X 10.11 El Capitan or newer)
|
| **bgfx_debug**
|
|	Enables BGFX debugging features. Most users will not need to use this.
|
| **bgfx_screen_chains**
|
|	This dictates how to handle BGFX rendering on a per-display basis. Possible choices include **hlsl**, **unfiltered**, and **default**.
|
|	**default** -- default bilinear filterered output
|	**unfiltered** -- nearest neighbor unfiltered output
|	**hlsl** -- HLSL display simulation through shaders
|
|	We make a distinction between emulated device screens (which we'll call a **screen**) and physical displays (which we'll call a **window**, set by **-numscreens**) here. We use colons (:) to seperate windows, and commas (,) to seperate screens. Commas always go on the outside of the chain (see House Mannequin example)
|
|	On a combination of a single window, single screen case, such as Pac-Man on one physical PC monitor, you can specify one entry like:
|
|		**bgfx_screen_chains hlsl**
|
|	Things get only slightly more complicated when we get to multiple windows and multiple screens.
|
|	On a single window, multiple screen game, such as Darius on one physical PC monitor, specify multiple entries (one per window) like:
|
|		**bgfx_screen_chains hlsl,hlsl,hlsl**
|
|	This also works with single screen games where you are mirroring the output to more than one physical display. For instance, you could set up Pac-Man to have one unfiltered output for use with video broadcasting while a second display is set up HLSL for playing on.
|
|	On a mulitple window, multiple screen game, such as Darius on three physical PC monitors, specify multiple entries (one per window) like:
|
|		**bgfx_screen_chains hlsl:hlsl:hlsl**
|
|	Another example game would be Taisen Hot Gimmick, which used two CRTs to show individual player hands to just that player. If using two windows (two physical displays):
|
|		**bgfx_screen_chains hlsl:hlsl**
|
|	One more special case is that Nichibutsu had a special cocktail mahjongg cabinet that used a CRT in the middle along with two LCD displays to show each player their hand. We would want the LCDs to be unfiltered and untouched as they were, while the CRT would be improved through HLSL. Since we want to give each player their own full screen display (two physical monitors) along with the LCD, we'll go with:
|
|		**-numscreens 2 -view0 "Player 1" -view1 "Player 2" -video bgfx -bgfx_screen_chains hlsl,unfiltered,unfiltered:hlsl,unfiltered,unfiltered**
|
|	This sets up the view for each display respectively, keeping HLSL effect on the CRT for each window (physical display) while going unfiltered for the LCD screens.
|
|	If using only one window (one display), keep in mind the game still has three screens, so we would use:
|
|		**bgfx_screen_chains hlsl,unfiltered,unfiltered**
|
|
|	Note that the commas are on the outside edges, and any colons are in the middle.
|
| **bgfx_shadow_mask**
|
|	This specifies the shadow mask effect PNG file. By default this is **slot-mask.png**.
|
|


Tweaking BGFX HLSL Settings inside MAME
---------------------------------------

*Warning: Currently BGFX HLSL settings are not saved or loaded from any configuration files. This is expected to change in the future.*

Start by loading MAME with the game of your choice (e.g. **mame pacman**)

The tilde key (**~**) brings up the on-screen display options. Use up and down to go through the various settings, while left and right will allow you to change that setting. Results will be shown in real time as you're changing these settings.

Note that settings are individually changable on a per-screen basis.
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//////////////////////////////////////////////////////////////////////////////
//
//  Copyright (C) Microsoft Corporation.  All Rights Reserved.
//
//  File:       D3DX10math.h
//  Content:    D3DX10 math types and functions
//
//////////////////////////////////////////////////////////////////////////////

#include "D3DX10.h"

// D3DX10 and D3DX9 math look the same. You can include either one into your project.
// We are intentionally using the header define from D3DX9 math to prevent double-inclusion.
#ifndef __D3DX9MATH_H__
#define __D3DX9MATH_H__

#include <math.h>
#if _MSC_VER >= 1200
#pragma warning(push)
#endif
#pragma warning(disable:4201) // anonymous unions warning

//===========================================================================
//
// Type definitions from D3D9
//
//===========================================================================

#ifndef D3DVECTOR_DEFINED
typedef struct _D3DVECTOR {
    float x;
    float y;
    float z;
} D3DVECTOR;
#define D3DVECTOR_DEFINED
#endif

#ifndef D3DMATRIX_DEFINED
typedef struct _D3DMATRIX {
    union {
        struct {
            float        _11, _12, _13, _14;
            float        _21, _22, _23, _24;
            float        _31, _32, _33, _34;
            float        _41, _42, _43, _44;

        };
        float m[4][4];
    };
} D3DMATRIX;
#define D3DMATRIX_DEFINED
#endif

//===========================================================================
//
// General purpose utilities
//
//===========================================================================
#define D3DX_PI    (3.14159265358979323846)
#define D3DX_1BYPI ( 1.0 / D3DX_PI )

#define D3DXToRadian( degree ) ((degree) * (D3DX_PI / 180.0))
#define D3DXToDegree( radian ) ((radian) * (180.0 / 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
#define D3DX_16F_SIGN_MASK    0x8000
#define D3DX_16F_EXP_MASK     0x7C00
#define D3DX_16F_FRAC_MASK    0x03FF

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( UINT  argb );
    D3DXCOLOR( CONST FLOAT * );
    D3DXCOLOR( CONST D3DXFLOAT16 * );
    D3DXCOLOR( FLOAT r, FLOAT g, FLOAT b, FLOAT a );

    // casting
    operator UINT  () const;

    operator FLOAT* ();
    operator CONST FLOAT* () 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
    ( __out_ecount(n) FLOAT *pOut, __in_ecount(n) 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 D3D10_VIEWPORT *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 D3D10_VIEWPORT *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 D3D10_VIEWPORT *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 D3D10_VIEWPORT *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( 
        UINT                Flags, 
        LPD3DXMATRIXSTACK*  ppStack);

#ifdef __cplusplus
}
#endif

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

//============================================================================
//
//  Basic Spherical Harmonic math routines
//
//============================================================================

#define D3DXSH_MINORDER 2
#define D3DXSH_MAXORDER 6

//============================================================================
//
//  D3DXSHEvalDirection:
//  --------------------
//  Evaluates the Spherical Harmonic basis functions
//
//  Parameters:
//   pOut
//      Output SH coefficients - basis function Ylm is stored at l*l + m+l
//      This is the pointer that is returned.
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pDir
//      Direction to evaluate in - assumed to be normalized
//
//============================================================================

FLOAT* WINAPI D3DXSHEvalDirection
    (  FLOAT *pOut, UINT Order, CONST D3DXVECTOR3 *pDir );
    
//============================================================================
//
//  D3DXSHRotate:
//  --------------------
//  Rotates SH vector by a rotation matrix
//
//  Parameters:
//   pOut
//      Output SH coefficients - basis function Ylm is stored at l*l + m+l
//      This is the pointer that is returned (should not alias with pIn.)
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pMatrix
//      Matrix used for rotation - rotation sub matrix should be orthogonal
//      and have a unit determinant.
//   pIn
//      Input SH coeffs (rotated), incorect results if this is also output.
//
//============================================================================

FLOAT* WINAPI D3DXSHRotate
    ( __out_ecount(Order*Order) FLOAT *pOut, UINT Order, CONST D3DXMATRIX *pMatrix, CONST FLOAT *pIn );
    
//============================================================================
//
//  D3DXSHRotateZ:
//  --------------------
//  Rotates the SH vector in the Z axis by an angle
//
//  Parameters:
//   pOut
//      Output SH coefficients - basis function Ylm is stored at l*l + m+l
//      This is the pointer that is returned (should not alias with pIn.)
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   Angle
//      Angle in radians to rotate around the Z axis.
//   pIn
//      Input SH coeffs (rotated), incorect results if this is also output.
//
//============================================================================


FLOAT* WINAPI D3DXSHRotateZ
    ( FLOAT *pOut, UINT Order, FLOAT Angle, CONST FLOAT *pIn );
    
//============================================================================
//
//  D3DXSHAdd:
//  --------------------
//  Adds two SH vectors, pOut[i] = pA[i] + pB[i];
//
//  Parameters:
//   pOut
//      Output SH coefficients - basis function Ylm is stored at l*l + m+l
//      This is the pointer that is returned.
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pA
//      Input SH coeffs.
//   pB
//      Input SH coeffs (second vector.)
//
//============================================================================

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

//============================================================================
//
//  D3DXSHScale:
//  --------------------
//  Adds two SH vectors, pOut[i] = pA[i]*Scale;
//
//  Parameters:
//   pOut
//      Output SH coefficients - basis function Ylm is stored at l*l + m+l
//      This is the pointer that is returned.
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pIn
//      Input SH coeffs.
//   Scale
//      Scale factor.
//
//============================================================================

FLOAT* WINAPI D3DXSHScale
    ( __out_ecount(Order*Order) FLOAT *pOut, UINT Order, CONST FLOAT *pIn, CONST FLOAT Scale );
    
//============================================================================
//
//  D3DXSHDot:
//  --------------------
//  Computes the dot product of two SH vectors
//
//  Parameters:
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pA
//      Input SH coeffs.
//   pB
//      Second set of input SH coeffs.
//
//============================================================================

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

//============================================================================
//
//  D3DXSHMultiply[O]:
//  --------------------
//  Computes the product of two functions represented using SH (f and g), where:
//  pOut[i] = int(y_i(s) * f(s) * g(s)), where y_i(s) is the ith SH basis
//  function, f(s) and g(s) are SH functions (sum_i(y_i(s)*c_i)).  The order O
//  determines the lengths of the arrays, where there should always be O^2 
//  coefficients.  In general the product of two SH functions of order O generates
//  and SH function of order 2*O - 1, but we truncate the result.  This means
//  that the product commutes (f*g == g*f) but doesn't associate 
//  (f*(g*h) != (f*g)*h.
//
//  Parameters:
//   pOut
//      Output SH coefficients - basis function Ylm is stored at l*l + m+l
//      This is the pointer that is returned.
//   pF
//      Input SH coeffs for first function.
//   pG
//      Second set of input SH coeffs.
//
//============================================================================

__out_ecount(4)  FLOAT* WINAPI D3DXSHMultiply2(__out_ecount(4)  FLOAT *pOut,__in_ecount(4)  CONST FLOAT *pF,__in_ecount(4)  CONST FLOAT *pG);
__out_ecount(9)  FLOAT* WINAPI D3DXSHMultiply3(__out_ecount(9)  FLOAT *pOut,__in_ecount(9)  CONST FLOAT *pF,__in_ecount(9)  CONST FLOAT *pG);
__out_ecount(16) FLOAT* WINAPI D3DXSHMultiply4(__out_ecount(16) FLOAT *pOut,__in_ecount(16) CONST FLOAT *pF,__in_ecount(16) CONST FLOAT *pG);
__out_ecount(25) FLOAT* WINAPI D3DXSHMultiply5(__out_ecount(25) FLOAT *pOut,__in_ecount(25) CONST FLOAT *pF,__in_ecount(25) CONST FLOAT *pG);
__out_ecount(36) FLOAT* WINAPI D3DXSHMultiply6(__out_ecount(36) FLOAT *pOut,__in_ecount(36) CONST FLOAT *pF,__in_ecount(36) CONST FLOAT *pG);


//============================================================================
//
//  Basic Spherical Harmonic lighting routines
//
//============================================================================

//============================================================================
//
//  D3DXSHEvalDirectionalLight:
//  --------------------
//  Evaluates a directional light and returns spectral SH data.  The output 
//  vector is computed so that if the intensity of R/G/B is unit the resulting
//  exit radiance of a point directly under the light on a diffuse object with
//  an albedo of 1 would be 1.0.  This will compute 3 spectral samples, pROut
//  has to be specified, while pGout and pBout are optional.
//
//  Parameters:
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pDir
//      Direction light is coming from (assumed to be normalized.)
//   RIntensity
//      Red intensity of light.
//   GIntensity
//      Green intensity of light.
//   BIntensity
//      Blue intensity of light.
//   pROut
//      Output SH vector for Red.
//   pGOut
//      Output SH vector for Green (optional.)
//   pBOut
//      Output SH vector for Blue (optional.)        
//
//============================================================================

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

//============================================================================
//
//  D3DXSHEvalSphericalLight:
//  --------------------
//  Evaluates a spherical light and returns spectral SH data.  There is no 
//  normalization of the intensity of the light like there is for directional
//  lights, care has to be taken when specifiying the intensities.  This will 
//  compute 3 spectral samples, pROut has to be specified, while pGout and 
//  pBout are optional.
//
//  Parameters:
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pPos
//      Position of light - reciever is assumed to be at the origin.
//   Radius
//      Radius of the spherical light source.
//   RIntensity
//      Red intensity of light.
//   GIntensity
//      Green intensity of light.
//   BIntensity
//      Blue intensity of light.
//   pROut
//      Output SH vector for Red.
//   pGOut
//      Output SH vector for Green (optional.)
//   pBOut
//      Output SH vector for Blue (optional.)        
//
//============================================================================

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

//============================================================================
//
//  D3DXSHEvalConeLight:
//  --------------------
//  Evaluates a light that is a cone of constant intensity and returns spectral
//  SH data.  The output vector is computed so that if the intensity of R/G/B is
//  unit the resulting exit radiance of a point directly under the light oriented
//  in the cone direction on a diffuse object with an albedo of 1 would be 1.0.
//  This will compute 3 spectral samples, pROut has to be specified, while pGout
//  and pBout are optional.
//
//  Parameters:
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pDir
//      Direction light is coming from (assumed to be normalized.)
//   Radius
//      Radius of cone in radians.
//   RIntensity
//      Red intensity of light.
//   GIntensity
//      Green intensity of light.
//   BIntensity
//      Blue intensity of light.
//   pROut
//      Output SH vector for Red.
//   pGOut
//      Output SH vector for Green (optional.)
//   pBOut
//      Output SH vector for Blue (optional.)        
//
//============================================================================

HRESULT WINAPI D3DXSHEvalConeLight
    ( UINT Order, CONST D3DXVECTOR3 *pDir, FLOAT Radius,
      FLOAT RIntensity, FLOAT GIntensity, FLOAT BIntensity,
      __out_ecount_opt(Order*Order) FLOAT *pROut, 
      __out_ecount_opt(Order*Order) FLOAT *pGOut, 
      __out_ecount_opt(Order*Order) FLOAT *pBOut );
      
//============================================================================
//
//  D3DXSHEvalHemisphereLight:
//  --------------------
//  Evaluates a light that is a linear interpolant between two colors over the
//  sphere.  The interpolant is linear along the axis of the two points, not
//  over the surface of the sphere (ie: if the axis was (0,0,1) it is linear in
//  Z, not in the azimuthal angle.)  The resulting spherical lighting function
//  is normalized so that a point on a perfectly diffuse surface with no
//  shadowing and a normal pointed in the direction pDir would result in exit
//  radiance with a value of 1 if the top color was white and the bottom color
//  was black.  This is a very simple model where Top represents the intensity 
//  of the "sky" and Bottom represents the intensity of the "ground".
//
//  Parameters:
//   Order
//      Order of the SH evaluation, generates Order^2 coefs, degree is Order-1
//   pDir
//      Axis of the hemisphere.
//   Top
//      Color of the upper hemisphere.
//   Bottom
//      Color of the lower hemisphere.
//   pROut
//      Output SH vector for Red.
//   pGOut
//      Output SH vector for Green
//   pBOut
//      Output SH vector for Blue        
//
//============================================================================

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

// Math intersection functions

BOOL WINAPI D3DXIntersectTri 
(
    CONST D3DXVECTOR3 *p0,           // Triangle vertex 0 position
    CONST D3DXVECTOR3 *p1,           // Triangle vertex 1 position
    CONST D3DXVECTOR3 *p2,           // Triangle vertex 2 position
    CONST D3DXVECTOR3 *pRayPos,      // Ray origin
    CONST D3DXVECTOR3 *pRayDir,      // Ray direction
    FLOAT *pU,                         // Barycentric Hit Coordinates
    FLOAT *pV,                         // Barycentric Hit Coordinates
    FLOAT *pDist);                     // Ray-Intersection Parameter Distance

BOOL WINAPI
    D3DXSphereBoundProbe(
        CONST D3DXVECTOR3 *pCenter,
        FLOAT Radius,
        CONST D3DXVECTOR3 *pRayPosition,
        CONST D3DXVECTOR3 *pRayDirection);

BOOL WINAPI 
    D3DXBoxBoundProbe(
        CONST D3DXVECTOR3 *pMin, 
        CONST D3DXVECTOR3 *pMax,
        CONST D3DXVECTOR3 *pRayPosition,
        CONST D3DXVECTOR3 *pRayDirection);

HRESULT WINAPI 
    D3DXComputeBoundingSphere(
        CONST D3DXVECTOR3 *pFirstPosition,	// pointer to first position
        DWORD NumVertices, 
        DWORD dwStride,							// count in bytes to subsequent position vectors
        D3DXVECTOR3 *pCenter, 
        FLOAT *pRadius);

HRESULT WINAPI 
    D3DXComputeBoundingBox(
        CONST D3DXVECTOR3 *pFirstPosition,	// pointer to first position
        DWORD NumVertices, 
        DWORD dwStride,							// count in bytes to subsequent position vectors
        D3DXVECTOR3 *pMin, 
        D3DXVECTOR3 *pMax);


///////////////////////////////////////////////////////////////////////////
// CPU Optimization:
///////////////////////////////////////////////////////////////////////////

//-------------------------------------------------------------------------
// D3DX_CPU_OPTIMIZATION flags:
// ----------------------------
// D3DX_NOT_OPTIMIZED       Use Intel Pentium optimizations
// D3DX_3DNOW_OPTIMIZED     Use AMD 3DNow optimizations
// D3DX_SSE_OPTIMIZED       Use Intel Pentium III SSE optimizations
// D3DX_SSE2_OPTIMIZED      Use Intel Pentium IV SSE2 optimizations
//-------------------------------------------------------------------------


typedef enum _D3DX_CPU_OPTIMIZATION
{
    D3DX_NOT_OPTIMIZED = 0,
    D3DX_3DNOW_OPTIMIZED,
    D3DX_SSE2_OPTIMIZED,
    D3DX_SSE_OPTIMIZED
} D3DX_CPU_OPTIMIZATION;


//-------------------------------------------------------------------------
// D3DXCpuOptimizations:
// ---------------------
// Enables or disables CPU optimizations. Returns the type of CPU, which 
// was detected, and for which optimizations exist.
//
// Parameters:
//  Enable
//      TRUE to enable CPU optimizations. FALSE to disable.
//-------------------------------------------------------------------------

D3DX_CPU_OPTIMIZATION WINAPI 
    D3DXCpuOptimizations(BOOL Enable);

#ifdef __cplusplus
}
#endif


#include "D3DX10math.inl"

#if _MSC_VER >= 1200
#pragma warning(pop)
#else
#pragma warning(default:4201)
#endif

#endif // __D3DX9MATH_H__