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//////////////////////////////////////////////////////////////////////////////
//
// Copyright (C) Microsoft Corporation. All Rights Reserved.
//
// File: d3dx8math.h
// Content: D3DX math types and functions
//
//////////////////////////////////////////////////////////////////////////////
#include "d3dx8.h"
#ifndef __D3DX8MATH_H__
#define __D3DX8MATH_H__
#include <math.h>
#pragma warning(disable:4201) // anonymous unions warning
//===========================================================================
//
// 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
//--------------------------
#ifdef __cplusplus
typedef struct D3DXVECTOR3 : public D3DVECTOR
{
public:
D3DXVECTOR3() {};
D3DXVECTOR3( CONST FLOAT * );
D3DXVECTOR3( CONST D3DVECTOR& );
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
//--------------------------
// 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
//
//===========================================================================
#ifdef __cplusplus
typedef struct D3DXMATRIX : public D3DMATRIX
{
public:
D3DXMATRIX() {};
D3DXMATRIX( CONST FLOAT * );
D3DXMATRIX( CONST D3DMATRIX& );
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
#ifdef __cplusplus
typedef struct _D3DXMATRIXA16 : public D3DXMATRIX
{
_D3DXMATRIXA16() {}
_D3DXMATRIXA16( CONST FLOAT * f): D3DXMATRIX(f) {}
_D3DXMATRIXA16( CONST D3DMATRIX& m): D3DXMATRIX(m) {}
_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 ) :
D3DXMATRIX(_11, _12, _13, _14,
_21, _22, _23, _24,
_31, _32, _33, _34,
_41, _42, _43, _44) {}
void* operator new(size_t s)
{
LPBYTE p = ::new BYTE[s + 16];
if (p)
{
BYTE offset = (BYTE)(16 - ((ULONG_PTR)p & 15));
p += offset;
p[-1] = offset;
}
return p;
};
void* operator new[](size_t s)
{
LPBYTE p = ::new BYTE[s + 16];
if (p)
{
BYTE offset = (BYTE)(16 - ((ULONG_PTR)p & 15));
p += offset;
p[-1] = offset;
}
return p;
};
// This is NOT a virtual operator. If you cast
// to D3DXMATRIX, do not delete using that
void operator delete(void* p)
{
if(p)
{
BYTE* pb = static_cast<BYTE*>(p);
pb -= pb[-1];
::delete [] pb;
}
};
// This is NOT a virtual operator. If you cast
// to D3DXMATRIX, do not delete using that
void operator delete[](void* p)
{
if(p)
{
BYTE* pb = static_cast<BYTE*>(p);
pb -= pb[-1];
::delete [] pb;
}
};
struct _D3DXMATRIXA16& operator=(CONST D3DXMATRIX& rhs)
{
memcpy(&_11, &rhs, sizeof(D3DXMATRIX));
return *this;
};
} _D3DXMATRIXA16;
#else //!__cplusplus
typedef D3DXMATRIX _D3DXMATRIXA16;
#endif //!__cplusplus
#if _MSC_FULL_VER >= 12008804 // First Processor Pack
#define _ALIGN_16 __declspec(align(16))
#else
#define _ALIGN_16
#endif
#define D3DXMATRIXA16 _ALIGN_16 _D3DXMATRIXA16
typedef D3DXMATRIXA16 *LPD3DXMATRIXA16;
//===========================================================================
//
// 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 );
// 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 );
#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 );
// Project vector from object space into screen space
D3DXVECTOR3* WINAPI D3DXVec3Project
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DVIEWPORT8 *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 D3DVIEWPORT8 *pViewport,
CONST D3DXMATRIX *pProjection, CONST D3DXMATRIX *pView, CONST D3DXMATRIX *pWorld);
#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 );
#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 );
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 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 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);
// 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 );
#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;
// {E3357330-CC5E-11d2-A434-00A0C90629A8}
DEFINE_GUID( IID_ID3DXMatrixStack,
0xe3357330, 0xcc5e, 0x11d2, 0xa4, 0x34, 0x0, 0xa0, 0xc9, 0x6, 0x29, 0xa8);
#undef INTERFACE
#define INTERFACE ID3DXMatrixStack
DECLARE_INTERFACE_(ID3DXMatrixStack, IUnknown)
{
//
// IUnknown methods
//
STDMETHOD(QueryInterface)(THIS_ REFIID riid, LPVOID * ppvObj) PURE;
STDMETHOD_(ULONG,AddRef)(THIS) PURE;
STDMETHOD_(ULONG,Release)(THIS) PURE;
//
// ID3DXMatrixStack methods
//
// Pops the top of the stack, returns the current top
// *after* popping the top.
STDMETHOD(Pop)(THIS) PURE;
// Pushes the stack by one, duplicating the current matrix.
STDMETHOD(Push)(THIS) PURE;
// Loads identity in the current matrix.
STDMETHOD(LoadIdentity)(THIS) PURE;
// Loads the given matrix into the current matrix
STDMETHOD(LoadMatrix)(THIS_ CONST D3DXMATRIX* pM ) PURE;
// Right-Multiplies the given matrix to the current matrix.
// (transformation is about the current world origin)
STDMETHOD(MultMatrix)(THIS_ CONST D3DXMATRIX* pM ) PURE;
// Left-Multiplies the given matrix to the current matrix
// (transformation is about the local origin of the object)
STDMETHOD(MultMatrixLocal)(THIS_ CONST D3DXMATRIX* pM ) PURE;
// Right multiply the current matrix with the computed rotation
// matrix, counterclockwise about the given axis with the given angle.
// (rotation is about the current world origin)
STDMETHOD(RotateAxis)
(THIS_ CONST D3DXVECTOR3* pV, FLOAT Angle) PURE;
// Left multiply the current matrix with the computed rotation
// matrix, counterclockwise about the given axis with the given angle.
// (rotation is about the local origin of the object)
STDMETHOD(RotateAxisLocal)
(THIS_ CONST D3DXVECTOR3* pV, FLOAT Angle) PURE;
// Right multiply the current matrix with the computed rotation
// matrix. All angles are counterclockwise. (rotation is about the
// current world origin)
// The rotation is composed of a yaw around the Y axis, a pitch around
// the X axis, and a roll around the Z axis.
STDMETHOD(RotateYawPitchRoll)
(THIS_ FLOAT Yaw, FLOAT Pitch, FLOAT Roll) PURE;
// Left multiply the current matrix with the computed rotation
// matrix. All angles are counterclockwise. (rotation is about the
// local origin of the object)
// The rotation is composed of a yaw around the Y axis, a pitch around
// the X axis, and a roll around the Z axis.
STDMETHOD(RotateYawPitchRollLocal)
(THIS_ FLOAT Yaw, FLOAT Pitch, FLOAT Roll) PURE;
// Right multiply the current matrix with the computed scale
// matrix. (transformation is about the current world origin)
STDMETHOD(Scale)(THIS_ FLOAT x, FLOAT y, FLOAT z) PURE;
// Left multiply the current matrix with the computed scale
// matrix. (transformation is about the local origin of the object)
STDMETHOD(ScaleLocal)(THIS_ FLOAT x, FLOAT y, FLOAT z) PURE;
// Right multiply the current matrix with the computed translation
// matrix. (transformation is about the current world origin)
STDMETHOD(Translate)(THIS_ FLOAT x, FLOAT y, FLOAT z ) PURE;
// Left multiply the current matrix with the computed translation
// matrix. (transformation is about the local origin of the object)
STDMETHOD(TranslateLocal)(THIS_ FLOAT x, FLOAT y, FLOAT z) PURE;
// Obtain the current matrix at the top of the stack
STDMETHOD_(D3DXMATRIX*, GetTop)(THIS) PURE;
};
#ifdef __cplusplus
extern "C" {
#endif
HRESULT WINAPI
D3DXCreateMatrixStack(
DWORD Flags,
LPD3DXMATRIXSTACK* ppStack);
#ifdef __cplusplus
}
#endif
#include "d3dx8math.inl"
#pragma warning(default:4201)
#endif // __D3DX8MATH_H__
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