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diff --git a/dxsdk/Include/d3dxmath.h b/dxsdk/Include/d3dxmath.h
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+++ b/dxsdk/Include/d3dxmath.h
@@ -0,0 +1,1092 @@
+//////////////////////////////////////////////////////////////////////////////
+//
+//  Copyright (C) Microsoft Corporation.  All Rights Reserved.
+//
+//  File:       d3dxmath.h
+//  Content:    D3DX math types and functions
+//
+//////////////////////////////////////////////////////////////////////////////
+
+#ifndef __D3DXMATH_H__
+#define __D3DXMATH_H__
+
+#include <d3d.h>
+#include <math.h>
+#include <limits.h>
+#include "d3dxerr.h"
+
+#ifndef D3DXINLINE
+#ifdef __cplusplus
+#define D3DXINLINE inline
+#else
+#define D3DXINLINE _inline
+#endif
+#endif
+
+#if _MSC_VER >= 1200
+#pragma warning(push)
+#endif
+#pragma warning(disable:4201) // anonymous unions warning
+
+
+
+typedef struct ID3DXMatrixStack *LPD3DXMATRIXSTACK;
+
+// {E3357330-CC5E-11d2-A434-00A0C90629A8}
+DEFINE_GUID( IID_ID3DXMatrixStack,
+             0xe3357330, 0xcc5e, 0x11d2, 0xa4, 0x34, 0x0, 0xa0, 0xc9, 0x6, 0x29, 0xa8);
+
+
+//===========================================================================
+//
+// 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))
+
+
+
+//===========================================================================
+//
+// Vectors
+//
+//===========================================================================
+
+//--------------------------
+// 2D Vector
+//--------------------------
+typedef struct D3DXVECTOR2
+{
+#ifdef __cplusplus
+public:
+    D3DXVECTOR2() {};
+    D3DXVECTOR2( const float * );
+    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;
+
+
+//--------------------------
+// 3D Vector
+//--------------------------
+typedef struct D3DXVECTOR3
+{
+#ifdef __cplusplus
+public:
+    D3DXVECTOR3() {};
+    D3DXVECTOR3( const float * );
+    D3DXVECTOR3( const D3DVECTOR& );
+    D3DXVECTOR3( float x, float y, float z );
+
+    // casting
+    operator float* ();
+    operator const float* () const;
+
+    operator D3DVECTOR* ();
+    operator const D3DVECTOR* () const;
+
+    operator D3DVECTOR& ();
+    operator const D3DVECTOR& () 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;
+
+public:
+#endif //__cplusplus
+    float x, y, z;
+} D3DXVECTOR3, *LPD3DXVECTOR3;
+
+
+//--------------------------
+// 4D Vector
+//--------------------------
+typedef struct D3DXVECTOR4
+{
+#ifdef __cplusplus
+public:
+    D3DXVECTOR4() {};
+    D3DXVECTOR4( const float* );
+    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;
+
+
+//===========================================================================
+//
+// Matrices
+//
+//===========================================================================
+typedef struct D3DXMATRIX
+{
+#ifdef __cplusplus
+public:
+    D3DXMATRIX() {};
+    D3DXMATRIX( const float * );
+    D3DXMATRIX( const D3DMATRIX& );
+    D3DXMATRIX( float m00, float m01, float m02, float m03,
+                float m10, float m11, float m12, float m13,
+                float m20, float m21, float m22, float m23,
+                float m30, float m31, float m32, float m33 );
+
+
+    // access grants
+    float& operator () ( UINT iRow, UINT iCol );
+    float  operator () ( UINT iRow, UINT iCol ) const;
+
+    // casting operators
+    operator float* ();
+    operator const float* () const;
+
+    operator D3DMATRIX* ();
+    operator const D3DMATRIX* () const;
+
+    operator D3DMATRIX& ();
+    operator const D3DMATRIX& () 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;
+
+
+#endif //__cplusplus
+
+    union
+    {
+        float m[4][4];
+#ifdef __cplusplus
+        struct
+        {
+            float m00, m01, m02, m03;
+            float m10, m11, m12, m13;
+            float m20, m21, m22, m23;
+            float m30, m31, m32, m33;
+        };
+#endif //__cplusplus
+    };
+} D3DXMATRIX, *LPD3DXMATRIX;
+
+
+//===========================================================================
+//
+//    Quaternions
+//
+//===========================================================================
+typedef struct D3DXQUATERNION
+{
+#ifdef __cplusplus
+public:
+    D3DXQUATERNION() {}
+    D3DXQUATERNION( const float * );
+    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( float a, float b, float c, float d );
+
+    // casting
+    operator float* ();
+    operator const float* () const;
+
+    // unary operators
+    D3DXPLANE operator + () const;
+    D3DXPLANE operator - () const;
+
+    // binary operators
+    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 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.
+//
+//===========================================================================
+
+//--------------------------
+// 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 );
+
+// Barycentric coordinates.  V1 + f(V2-V1) + g(V3-V1)
+D3DXVECTOR2* WINAPI D3DXVec2BaryCentric
+    ( D3DXVECTOR2 *pOut, const D3DXVECTOR2 *pV1, const D3DXVECTOR2 *pV2,
+      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 );
+
+#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 );
+
+// 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.
+D3DXVECTOR3* WINAPI D3DXVec3TransformNormal
+    ( D3DXVECTOR3 *pOut, const D3DXVECTOR3 *pV, const D3DXMATRIX *pM );
+
+#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 );
+
+// 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 );
+
+#ifdef __cplusplus
+}
+#endif
+
+
+//--------------------------
+// 4D Matrix
+//--------------------------
+
+// inline
+
+D3DXMATRIX* D3DXMatrixIdentity
+    ( D3DXMATRIX *pOut );
+
+BOOL D3DXMatrixIsIdentity
+    ( const D3DXMATRIX *pM );
+
+
+// non-inline
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+float WINAPI D3DXMatrixfDeterminant
+    ( 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 );
+
+D3DXMATRIX* WINAPI D3DXMatrixTranspose
+    ( D3DXMATRIX *pOut, const D3DXMATRIX *pM );
+
+// 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 *pfDeterminant, 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 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 a lookat matrix. (right-handed)
+D3DXMATRIX* WINAPI D3DXMatrixLookAt
+    ( 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 D3DXMatrixPerspective
+    ( 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 D3DXMatrixPerspectiveFov
+    ( 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 D3DXMatrixPerspectiveOffCenter
+    ( 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 D3DXMatrixOrtho
+    ( 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 D3DXMatrixOrthoOffCenter
+    ( 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 (s == 0) and Q2 (s == 1).
+// Expects unit quaternions.
+D3DXQUATERNION* WINAPI D3DXQuaternionSlerp
+    ( D3DXQUATERNION *pOut, const D3DXQUATERNION *pQ1,
+      const D3DXQUATERNION *pQ2, float t );
+
+// Spherical quadrangle interpolation.
+// Slerp(Slerp(Q1, Q4, t), Slerp(Q2, Q3, t), 2t(1-t))
+D3DXQUATERNION* WINAPI D3DXQuaternionSquad
+    ( D3DXQUATERNION *pOut, const D3DXQUATERNION *pQ1,
+      const D3DXQUATERNION *pQ2, const D3DXQUATERNION *pQ3,
+      const D3DXQUATERNION *pQ4, float t );
+
+// 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);
+
+// 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 must be an affine transform.
+D3DXPLANE* WINAPI D3DXPlaneTransform
+    ( D3DXPLANE *pOut, const D3DXPLANE *pP, const D3DXMATRIX *pM );
+
+#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
+
+
+
+
+
+
+//===========================================================================
+//
+//    Matrix Stack
+//
+//===========================================================================
+
+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
+
+#include "d3dxmath.inl"
+
+#if _MSC_VER >= 1200
+#pragma warning(pop)
+#else
+#pragma warning(default:4201)
+#endif
+
+#endif // __D3DXMATH_H__