矩陣類型及其操作

在Direct3D中，頂點坐標變換通常是借助于矩陣實現的，因此下面首先介紹在Direct3D中提供的各種矩陣類型和相關的矩陣運算函數。

1、D3DMATRIX矩陣類型

D3DMATRIX是Direct3D中最簡單的矩陣類型，其定義如下：

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;

顯然，D3DMATIX中存放的是一個4x4的二維浮點數組，可以通過_ij的格式訪問該數組中的每個元素，i表示該元素的行數，j表示該元素的列數。例如，_34表示第三行、第四列的元素。

2、D3DXMATRIX矩陣類型

該類型矩陣定義如下：

#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

3、D3DXMATRIXA16矩陣類型

D3DXMATRIXA16稱為16字節對齊矩陣（16-byte aligned matrix），它是從矩陣D3DXMATRIX中繼承而來的，其定義如下：

typedef D3DX_ALIGN16 _D3DXMATRIXA16 D3DXMATRIXA16, *LPD3DXMATRIXA16;

//---------------------------------------------------------------------------
// 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

當使用了Intel Pentium 4運行一個D3DX數學函數時，16字節對齊矩陣D3DXMATRIXA16為完成相應操作進行了優化。當使用VC++.net或使用安裝了processor pack的VC6++時，將開啟字節對齊功能。但不幸的是，編譯器無法探測到是否安裝了processor pack，所以字節對齊僅僅只對VC++.net默認開啟。對于其他編譯器，16字節對齊矩陣D3DXMATRIXA16將被當作D3DXMATRIX進行操作。

經過擴展后的結構體D3DXMATRIX和D3DXMATRIXA16對許多運算符進行了重載，所以可以直接進行轉換運算、賦值運算以及多種一元、二元運算，大大方便了矩陣類型變量的運算。

4、常見的矩陣運算函數

因為矩陣的運算相對比較復雜，所以Direct3D提供了一組矩陣運算函數，例如，通過函數D3DXMatrixTranslation()構造一個平移矩陣；通過函數D3DXMatrixRotationX()、D3DXMatrixRotationY()和D3DXMatrixRotationZ()構造繞x、y和z軸轉動一定角度的矩陣；通過函數D3DXMatrixScaling()構造一個縮放矩陣；通過函數D3DXMatrxiIdentity()將一個矩陣單位化；通過函數D3DXMatrixMultiply()計算兩個矩陣的積；通過函數D3DXMatrixInverse()求原矩陣的逆矩陣；通過函數D3DXMatrixTranspose()計算原矩陣的轉置矩陣。