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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 ((FLOAT) 3.141592654f)
#define D3DX_1BYPI ((FLOAT) 0.318309886f)
#define D3DXToRadian( degree ) ((degree) * (D3DX_PI / 180.0f))
#define D3DXToDegree( radian ) ((radian) * (180.0f / D3DX_PI))
//===========================================================================
//
// 16 bit floating point numbers
//
//===========================================================================
#define D3DX_16F_DIG 3 // # of decimal digits of precision
#define D3DX_16F_EPSILON 4.8875809e-4f // smallest such that 1.0 + epsilon != 1.0
#define D3DX_16F_MANT_DIG 11 // # of bits in mantissa
#define D3DX_16F_MAX 6.550400e+004 // max value
#define D3DX_16F_MAX_10_EXP 4 // max decimal exponent
#define D3DX_16F_MAX_EXP 15 // max binary exponent
#define D3DX_16F_MIN 6.1035156e-5f // min positive value
#define D3DX_16F_MIN_10_EXP (-4) // min decimal exponent
#define D3DX_16F_MIN_EXP (-12) // min binary exponent
#define D3DX_16F_RADIX 2 // exponent radix
#define D3DX_16F_ROUNDS 1 // addition rounding: near
typedef struct D3DXFLOAT16
{
#ifdef __cplusplus
public:
D3DXFLOAT16() {};
D3DXFLOAT16( FLOAT );
D3DXFLOAT16( CONST D3DXFLOAT16& );
// casting
operator FLOAT ();
// binary operators
BOOL operator == ( CONST D3DXFLOAT16& ) const;
BOOL operator != ( CONST D3DXFLOAT16& ) const;
protected:
#endif //__cplusplus
WORD value;
} D3DXFLOAT16, *LPD3DXFLOAT16;
//===========================================================================
//
// Vectors
//
//===========================================================================
//--------------------------
// 2D Vector
//--------------------------
typedef struct D3DXVECTOR2
{
#ifdef __cplusplus
public:
D3DXVECTOR2() {};
D3DXVECTOR2( CONST FLOAT * );
D3DXVECTOR2( CONST D3DXFLOAT16 * );
D3DXVECTOR2( FLOAT x, FLOAT y );
// casting
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXVECTOR2& operator += ( CONST D3DXVECTOR2& );
D3DXVECTOR2& operator -= ( CONST D3DXVECTOR2& );
D3DXVECTOR2& operator *= ( FLOAT );
D3DXVECTOR2& operator /= ( FLOAT );
// unary operators
D3DXVECTOR2 operator + () const;
D3DXVECTOR2 operator - () const;
// binary operators
D3DXVECTOR2 operator + ( CONST D3DXVECTOR2& ) const;
D3DXVECTOR2 operator - ( CONST D3DXVECTOR2& ) const;
D3DXVECTOR2 operator * ( FLOAT ) const;
D3DXVECTOR2 operator / ( FLOAT ) const;
friend D3DXVECTOR2 operator * ( FLOAT, CONST D3DXVECTOR2& );
BOOL operator == ( CONST D3DXVECTOR2& ) const;
BOOL operator != ( CONST D3DXVECTOR2& ) const;
public:
#endif //__cplusplus
FLOAT x, y;
} D3DXVECTOR2, *LPD3DXVECTOR2;
//--------------------------
// 2D Vector (16 bit)
//--------------------------
typedef struct D3DXVECTOR2_16F
{
#ifdef __cplusplus
public:
D3DXVECTOR2_16F() {};
D3DXVECTOR2_16F( CONST FLOAT * );
D3DXVECTOR2_16F( CONST D3DXFLOAT16 * );
D3DXVECTOR2_16F( CONST D3DXFLOAT16 &x, CONST D3DXFLOAT16 &y );
// casting
operator D3DXFLOAT16* ();
operator CONST D3DXFLOAT16* () const;
// binary operators
BOOL operator == ( CONST D3DXVECTOR2_16F& ) const;
BOOL operator != ( CONST D3DXVECTOR2_16F& ) const;
public:
#endif //__cplusplus
D3DXFLOAT16 x, y;
} D3DXVECTOR2_16F, *LPD3DXVECTOR2_16F;
//--------------------------
// 3D Vector
//--------------------------
#ifdef __cplusplus
typedef struct D3DXVECTOR3 : public D3DVECTOR
{
public:
D3DXVECTOR3() {};
D3DXVECTOR3( CONST FLOAT * );
D3DXVECTOR3( CONST D3DVECTOR& );
D3DXVECTOR3( CONST D3DXFLOAT16 * );
D3DXVECTOR3( FLOAT x, FLOAT y, FLOAT z );
// casting
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXVECTOR3& operator += ( CONST D3DXVECTOR3& );
D3DXVECTOR3& operator -= ( CONST D3DXVECTOR3& );
D3DXVECTOR3& operator *= ( FLOAT );
D3DXVECTOR3& operator /= ( FLOAT );
// unary operators
D3DXVECTOR3 operator + () const;
D3DXVECTOR3 operator - () const;
// binary operators
D3DXVECTOR3 operator + ( CONST D3DXVECTOR3& ) const;
D3DXVECTOR3 operator - ( CONST D3DXVECTOR3& ) const;
D3DXVECTOR3 operator * ( FLOAT ) const;
D3DXVECTOR3 operator / ( FLOAT ) const;
friend D3DXVECTOR3 operator * ( FLOAT, CONST struct D3DXVECTOR3& );
BOOL operator == ( CONST D3DXVECTOR3& ) const;
BOOL operator != ( CONST D3DXVECTOR3& ) const;
} D3DXVECTOR3, *LPD3DXVECTOR3;
#else //!__cplusplus
typedef struct _D3DVECTOR D3DXVECTOR3, *LPD3DXVECTOR3;
#endif //!__cplusplus
//--------------------------
// 3D Vector (16 bit)
//--------------------------
typedef struct D3DXVECTOR3_16F
{
#ifdef __cplusplus
public:
D3DXVECTOR3_16F() {};
D3DXVECTOR3_16F( CONST FLOAT * );
D3DXVECTOR3_16F( CONST D3DVECTOR& );
D3DXVECTOR3_16F( CONST D3DXFLOAT16 * );
D3DXVECTOR3_16F( CONST D3DXFLOAT16 &x, CONST D3DXFLOAT16 &y, CONST D3DXFLOAT16 &z );
// casting
operator D3DXFLOAT16* ();
operator CONST D3DXFLOAT16* () const;
// binary operators
BOOL operator == ( CONST D3DXVECTOR3_16F& ) const;
BOOL operator != ( CONST D3DXVECTOR3_16F& ) const;
public:
#endif //__cplusplus
D3DXFLOAT16 x, y, z;
} D3DXVECTOR3_16F, *LPD3DXVECTOR3_16F;
//--------------------------
// 4D Vector
//--------------------------
typedef struct D3DXVECTOR4
{
#ifdef __cplusplus
public:
D3DXVECTOR4() {};
D3DXVECTOR4( CONST FLOAT* );
D3DXVECTOR4( CONST D3DXFLOAT16* );
D3DXVECTOR4( CONST D3DVECTOR& xyz, FLOAT w );
D3DXVECTOR4( FLOAT x, FLOAT y, FLOAT z, FLOAT w );
// casting
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXVECTOR4& operator += ( CONST D3DXVECTOR4& );
D3DXVECTOR4& operator -= ( CONST D3DXVECTOR4& );
D3DXVECTOR4& operator *= ( FLOAT );
D3DXVECTOR4& operator /= ( FLOAT );
// unary operators
D3DXVECTOR4 operator + () const;
D3DXVECTOR4 operator - () const;
// binary operators
D3DXVECTOR4 operator + ( CONST D3DXVECTOR4& ) const;
D3DXVECTOR4 operator - ( CONST D3DXVECTOR4& ) const;
D3DXVECTOR4 operator * ( FLOAT ) const;
D3DXVECTOR4 operator / ( FLOAT ) const;
friend D3DXVECTOR4 operator * ( FLOAT, CONST D3DXVECTOR4& );
BOOL operator == ( CONST D3DXVECTOR4& ) const;
BOOL operator != ( CONST D3DXVECTOR4& ) const;
public:
#endif //__cplusplus
FLOAT x, y, z, w;
} D3DXVECTOR4, *LPD3DXVECTOR4;
//--------------------------
// 4D Vector (16 bit)
//--------------------------
typedef struct D3DXVECTOR4_16F
{
#ifdef __cplusplus
public:
D3DXVECTOR4_16F() {};
D3DXVECTOR4_16F( CONST FLOAT * );
D3DXVECTOR4_16F( CONST D3DXFLOAT16* );
D3DXVECTOR4_16F( CONST D3DXVECTOR3_16F& xyz, CONST D3DXFLOAT16& w );
D3DXVECTOR4_16F( CONST D3DXFLOAT16& x, CONST D3DXFLOAT16& y, CONST D3DXFLOAT16& z, CONST D3DXFLOAT16& w );
// casting
operator D3DXFLOAT16* ();
operator CONST D3DXFLOAT16* () const;
// binary operators
BOOL operator == ( CONST D3DXVECTOR4_16F& ) const;
BOOL operator != ( CONST D3DXVECTOR4_16F& ) const;
public:
#endif //__cplusplus
D3DXFLOAT16 x, y, z, w;
} D3DXVECTOR4_16F, *LPD3DXVECTOR4_16F;
//===========================================================================
//
// Matrices
//
//===========================================================================
#ifdef __cplusplus
typedef struct D3DXMATRIX : public D3DMATRIX
{
public:
D3DXMATRIX() {};
D3DXMATRIX( CONST FLOAT * );
D3DXMATRIX( CONST D3DMATRIX& );
D3DXMATRIX( CONST D3DXFLOAT16 * );
D3DXMATRIX( FLOAT _11, FLOAT _12, FLOAT _13, FLOAT _14,
FLOAT _21, FLOAT _22, FLOAT _23, FLOAT _24,
FLOAT _31, FLOAT _32, FLOAT _33, FLOAT _34,
FLOAT _41, FLOAT _42, FLOAT _43, FLOAT _44 );
// access grants
FLOAT& operator () ( UINT Row, UINT Col );
FLOAT operator () ( UINT Row, UINT Col ) const;
// casting operators
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXMATRIX& operator *= ( CONST D3DXMATRIX& );
D3DXMATRIX& operator += ( CONST D3DXMATRIX& );
D3DXMATRIX& operator -= ( CONST D3DXMATRIX& );
D3DXMATRIX& operator *= ( FLOAT );
D3DXMATRIX& operator /= ( FLOAT );
// unary operators
D3DXMATRIX operator + () const;
D3DXMATRIX operator - () const;
// binary operators
D3DXMATRIX operator * ( CONST D3DXMATRIX& ) const;
D3DXMATRIX operator + ( CONST D3DXMATRIX& ) const;
D3DXMATRIX operator - ( CONST D3DXMATRIX& ) const;
D3DXMATRIX operator * ( FLOAT ) const;
D3DXMATRIX operator / ( FLOAT ) const;
friend D3DXMATRIX operator * ( FLOAT, CONST D3DXMATRIX& );
BOOL operator == ( CONST D3DXMATRIX& ) const;
BOOL operator != ( CONST D3DXMATRIX& ) const;
} D3DXMATRIX, *LPD3DXMATRIX;
#else //!__cplusplus
typedef struct _D3DMATRIX D3DXMATRIX, *LPD3DXMATRIX;
#endif //!__cplusplus
//---------------------------------------------------------------------------
// Aligned Matrices
//
// This class helps keep matrices 16-byte aligned as preferred by P4 cpus.
// It aligns matrices on the stack and on the heap or in global scope.
// It does this using __declspec(align(16)) which works on VC7 and on VC 6
// with the processor pack. Unfortunately there is no way to detect the
// latter so this is turned on only on VC7. On other compilers this is the
// the same as D3DXMATRIX.
//
// Using this class on a compiler that does not actually do the alignment
// can be dangerous since it will not expose bugs that ignore alignment.
// E.g if an object of this class in inside a struct or class, and some code
// memcopys data in it assuming tight packing. This could break on a compiler
// that eventually start aligning the matrix.
//---------------------------------------------------------------------------
#ifdef __cplusplus
typedef struct _D3DXMATRIXA16 : public D3DXMATRIX
{
_D3DXMATRIXA16() {};
_D3DXMATRIXA16( CONST FLOAT * );
_D3DXMATRIXA16( CONST D3DMATRIX& );
_D3DXMATRIXA16( CONST D3DXFLOAT16 * );
_D3DXMATRIXA16( FLOAT _11, FLOAT _12, FLOAT _13, FLOAT _14,
FLOAT _21, FLOAT _22, FLOAT _23, FLOAT _24,
FLOAT _31, FLOAT _32, FLOAT _33, FLOAT _34,
FLOAT _41, FLOAT _42, FLOAT _43, FLOAT _44 );
// new operators
void* operator new ( size_t );
void* operator new[] ( size_t );
// delete operators
void operator delete ( void* ); // These are NOT virtual; Do not
void operator delete[] ( void* ); // cast to D3DXMATRIX and delete.
// assignment operators
_D3DXMATRIXA16& operator = ( CONST D3DXMATRIX& );
} _D3DXMATRIXA16;
#else //!__cplusplus
typedef D3DXMATRIX _D3DXMATRIXA16;
#endif //!__cplusplus
#if _MSC_VER >= 1300 // VC7
#define D3DX_ALIGN16 __declspec(align(16))
#else
#define D3DX_ALIGN16 // Earlier compiler may not understand this, do nothing.
#endif
typedef D3DX_ALIGN16 _D3DXMATRIXA16 D3DXMATRIXA16, *LPD3DXMATRIXA16;
//===========================================================================
//
// Quaternions
//
//===========================================================================
typedef struct D3DXQUATERNION
{
#ifdef __cplusplus
public:
D3DXQUATERNION() {};
D3DXQUATERNION( CONST FLOAT * );
D3DXQUATERNION( CONST D3DXFLOAT16 * );
D3DXQUATERNION( FLOAT x, FLOAT y, FLOAT z, FLOAT w );
// casting
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXQUATERNION& operator += ( CONST D3DXQUATERNION& );
D3DXQUATERNION& operator -= ( CONST D3DXQUATERNION& );
D3DXQUATERNION& operator *= ( CONST D3DXQUATERNION& );
D3DXQUATERNION& operator *= ( FLOAT );
D3DXQUATERNION& operator /= ( FLOAT );
// unary operators
D3DXQUATERNION operator + () const;
D3DXQUATERNION operator - () const;
// binary operators
D3DXQUATERNION operator + ( CONST D3DXQUATERNION& ) const;
D3DXQUATERNION operator - ( CONST D3DXQUATERNION& ) const;
D3DXQUATERNION operator * ( CONST D3DXQUATERNION& ) const;
D3DXQUATERNION operator * ( FLOAT ) const;
D3DXQUATERNION operator / ( FLOAT ) const;
friend D3DXQUATERNION operator * (FLOAT, CONST D3DXQUATERNION& );
BOOL operator == ( CONST D3DXQUATERNION& ) const;
BOOL operator != ( CONST D3DXQUATERNION& ) const;
#endif //__cplusplus
FLOAT x, y, z, w;
} D3DXQUATERNION, *LPD3DXQUATERNION;
//===========================================================================
//
// Planes
//
//===========================================================================
typedef struct D3DXPLANE
{
#ifdef __cplusplus
public:
D3DXPLANE() {};
D3DXPLANE( CONST FLOAT* );
D3DXPLANE( CONST D3DXFLOAT16* );
D3DXPLANE( FLOAT a, FLOAT b, FLOAT c, FLOAT d );
// casting
operator FLOAT* ();
operator CONST FLOAT* () const;
// assignment operators
D3DXPLANE& operator *= ( FLOAT );
D3DXPLANE& operator /= ( FLOAT );
// unary operators
D3DXPLANE operator + () const;
D3DXPLANE operator - () const;
// binary operators
D3DXPLANE operator * ( FLOAT ) const;
D3DXPLANE operator / ( FLOAT ) const;
friend D3DXPLANE operator * ( FLOAT, CONST D3DXPLANE& );
BOOL operator == ( CONST D3DXPLANE& ) const;
BOOL operator != ( CONST D3DXPLANE& ) const;
#endif //__cplusplus
FLOAT a, b, c, d;
} D3DXPLANE, *LPD3DXPLANE;
//===========================================================================
//
// Colors
//
//===========================================================================
typedef struct D3DXCOLOR
{
#ifdef __cplusplus
public:
D3DXCOLOR() {};
D3DXCOLOR( 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
( FLOAT *pOut, CONST D3DXFLOAT16 *pIn, UINT n );
#ifdef __cplusplus
}
#endif
//--------------------------
// 2D Vector
//--------------------------
// inline
FLOAT D3DXVec2Length
( CONST D3DXVECTOR2 *pV );
FLOAT D3DXVec2LengthSq
( CONST D3DXVECTOR2 *pV );
FLOAT D3DXVec2Dot
( CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );
// Z component of ((x1,y1,0) cross (x2,y2,0))
FLOAT D3DXVec2CCW
( CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );
D3DXVECTOR2* D3DXVec2Add
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );
D3DXVECTOR2* D3DXVec2Subtract
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );
// Minimize each component. x = min(x1, x2), y = min(y1, y2)
D3DXVECTOR2* D3DXVec2Minimize
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );
// Maximize each component. x = max(x1, x2), y = max(y1, y2)
D3DXVECTOR2* D3DXVec2Maximize
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2 );
D3DXVECTOR2* D3DXVec2Scale
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV, FLOAT s );
// Linear interpolation. V1 + s(V2-V1)
D3DXVECTOR2* D3DXVec2Lerp
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2,
FLOAT s );
// non-inline
#ifdef __cplusplus
extern "C" {
#endif
D3DXVECTOR2* WINAPI D3DXVec2Normalize
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV );
// Hermite interpolation between position V1, tangent T1 (when s == 0)
// and position V2, tangent T2 (when s == 1).
D3DXVECTOR2* WINAPI D3DXVec2Hermite
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pT1,
CONST D3DXVECTOR2 *pV2, CONST D3DXVECTOR2 *pT2, FLOAT s );
// CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1)
D3DXVECTOR2* WINAPI D3DXVec2CatmullRom
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV0, CONST D3DXVECTOR2 *pV1,
CONST D3DXVECTOR2 *pV2, CONST D3DXVECTOR2 *pV3, FLOAT s );
// Barycentric coordinates. V1 + f(V2-V1) + g(V3-V1)
D3DXVECTOR2* WINAPI D3DXVec2BaryCentric
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV1, CONST D3DXVECTOR2 *pV2,
CONST D3DXVECTOR2 *pV3, FLOAT f, FLOAT g);
// Transform (x, y, 0, 1) by matrix.
D3DXVECTOR4* WINAPI D3DXVec2Transform
( D3DXVECTOR4 *pOut, CONST D3DXVECTOR2 *pV, CONST D3DXMATRIX *pM );
// Transform (x, y, 0, 1) by matrix, project result back into w=1.
D3DXVECTOR2* WINAPI D3DXVec2TransformCoord
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV, CONST D3DXMATRIX *pM );
// Transform (x, y, 0, 0) by matrix.
D3DXVECTOR2* WINAPI D3DXVec2TransformNormal
( D3DXVECTOR2 *pOut, CONST D3DXVECTOR2 *pV, CONST D3DXMATRIX *pM );
// Transform Array (x, y, 0, 1) by matrix.
D3DXVECTOR4* WINAPI D3DXVec2TransformArray
( D3DXVECTOR4 *pOut, UINT OutStride, CONST D3DXVECTOR2 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n);
// Transform Array (x, y, 0, 1) by matrix, project result back into w=1.
D3DXVECTOR2* WINAPI D3DXVec2TransformCoordArray
( D3DXVECTOR2 *pOut, UINT OutStride, CONST D3DXVECTOR2 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );
// Transform Array (x, y, 0, 0) by matrix.
D3DXVECTOR2* WINAPI D3DXVec2TransformNormalArray
( D3DXVECTOR2 *pOut, UINT OutStride, CONST D3DXVECTOR2 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );
#ifdef __cplusplus
}
#endif
//--------------------------
// 3D Vector
//--------------------------
// inline
FLOAT D3DXVec3Length
( CONST D3DXVECTOR3 *pV );
FLOAT D3DXVec3LengthSq
( CONST D3DXVECTOR3 *pV );
FLOAT D3DXVec3Dot
( CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );
D3DXVECTOR3* D3DXVec3Cross
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );
D3DXVECTOR3* D3DXVec3Add
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );
D3DXVECTOR3* D3DXVec3Subtract
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );
// Minimize each component. x = min(x1, x2), y = min(y1, y2), ...
D3DXVECTOR3* D3DXVec3Minimize
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );
// Maximize each component. x = max(x1, x2), y = max(y1, y2), ...
D3DXVECTOR3* D3DXVec3Maximize
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2 );
D3DXVECTOR3* D3DXVec3Scale
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, FLOAT s);
// Linear interpolation. V1 + s(V2-V1)
D3DXVECTOR3* D3DXVec3Lerp
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2,
FLOAT s );
// non-inline
#ifdef __cplusplus
extern "C" {
#endif
D3DXVECTOR3* WINAPI D3DXVec3Normalize
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV );
// Hermite interpolation between position V1, tangent T1 (when s == 0)
// and position V2, tangent T2 (when s == 1).
D3DXVECTOR3* WINAPI D3DXVec3Hermite
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pT1,
CONST D3DXVECTOR3 *pV2, CONST D3DXVECTOR3 *pT2, FLOAT s );
// CatmullRom interpolation between V1 (when s == 0) and V2 (when s == 1)
D3DXVECTOR3* WINAPI D3DXVec3CatmullRom
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV0, CONST D3DXVECTOR3 *pV1,
CONST D3DXVECTOR3 *pV2, CONST D3DXVECTOR3 *pV3, FLOAT s );
// Barycentric coordinates. V1 + f(V2-V1) + g(V3-V1)
D3DXVECTOR3* WINAPI D3DXVec3BaryCentric
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV1, CONST D3DXVECTOR3 *pV2,
CONST D3DXVECTOR3 *pV3, FLOAT f, FLOAT g);
// Transform (x, y, z, 1) by matrix.
D3DXVECTOR4* WINAPI D3DXVec3Transform
( D3DXVECTOR4 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DXMATRIX *pM );
// Transform (x, y, z, 1) by matrix, project result back into w=1.
D3DXVECTOR3* WINAPI D3DXVec3TransformCoord
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DXMATRIX *pM );
// Transform (x, y, z, 0) by matrix. If you transforming a normal by a
// non-affine matrix, the matrix you pass to this function should be the
// transpose of the inverse of the matrix you would use to transform a coord.
D3DXVECTOR3* WINAPI D3DXVec3TransformNormal
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST D3DXMATRIX *pM );
// Transform Array (x, y, z, 1) by matrix.
D3DXVECTOR4* WINAPI D3DXVec3TransformArray
( D3DXVECTOR4 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );
// Transform Array (x, y, z, 1) by matrix, project result back into w=1.
D3DXVECTOR3* WINAPI D3DXVec3TransformCoordArray
( D3DXVECTOR3 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );
// Transform (x, y, z, 0) by matrix. If you transforming a normal by a
// non-affine matrix, the matrix you pass to this function should be the
// transpose of the inverse of the matrix you would use to transform a coord.
D3DXVECTOR3* WINAPI D3DXVec3TransformNormalArray
( D3DXVECTOR3 *pOut, UINT OutStride, CONST D3DXVECTOR3 *pV, UINT VStride, CONST D3DXMATRIX *pM, UINT n );
// Project vector from object space into screen space
D3DXVECTOR3* WINAPI D3DXVec3Project
( D3DXVECTOR3 *pOut, CONST D3DXVECTOR3 *pV, CONST 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
( 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
( 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
( 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 );
//============================================================================
//
// 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,
FLOAT *pROut, FLOAT *pGOut, 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,
FLOAT *pROut, FLOAT *pGOut, 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,
FLOAT *pROut, FLOAT *pGOut, 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,
FLOAT *pROut, FLOAT *pGOut, 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);
#ifdef __cplusplus
}
#endif
#include "D3DX10math.inl"
#if _MSC_VER >= 1200
#pragma warning(pop)
#else
#pragma warning(default:4201)
#endif
#endif // __D3DX9MATH_H__