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矩阵类型及其操作

在Direct3D中，顶点坐标变换通常是借助于矩阵实现的，因此下面首先介绍在Direct3D中提供的各种矩阵类型和相关的矩阵运算函数。

1、D3DMATRIX矩阵类型

D3DMATRIX是Direct3D中最简单的矩阵类型，其定义如下：

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;

显然，D3DMATIX中存放的是一个4x4的二维浮点数组，可以通过_ij的格式访问该数组中的每个元素，i表示该元素的行数，j表示该元素的列数。例如，_34表示第三行、第四列的元素。

2、D3DXMATRIX矩阵类型

该类型矩阵定义如下：

#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矩阵类型

D3DXMATRIXA16称为16字节对齐矩阵（16-byte aligned matrix），它是从矩阵D3DXMATRIX中继承而来的，其定义如下：

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

当使用了Intel Pentium 4运行一个D3DX数学函数时，16字节对齐矩阵D3DXMATRIXA16为完成相应操作进行了优化。当使用VC++.net或使用安装了processor pack的VC6++时，将开启字节对齐功能。但不幸的是，编译器无法探测到是否安装了processor pack，所以字节对齐仅仅只对VC++.net默认开启。对于其他编译器，16字节对齐矩阵D3DXMATRIXA16将被当作D3DXMATRIX进行操作。

经过扩展后的结构体D3DXMATRIX和D3DXMATRIXA16对许多运算符进行了重载，所以可以直接进行转换运算、赋值运算以及多种一元、二元运算，大大方便了矩阵类型变量的运算。

4、常见的矩阵运算函数

因为矩阵的运算相对比较复杂，所以Direct3D提供了一组矩阵运算函数，例如，通过函数D3DXMatrixTranslation()构造一个平移矩阵；通过函数D3DXMatrixRotationX()、D3DXMatrixRotationY()和D3DXMatrixRotationZ()构造绕x、y和z轴转动一定角度的矩阵；通过函数D3DXMatrixScaling()构造一个缩放矩阵；通过函数D3DXMatrxiIdentity()将一个矩阵单位化；通过函数D3DXMatrixMultiply()计算两个矩阵的积；通过函数D3DXMatrixInverse()求原矩阵的逆矩阵；通过函数D3DXMatrixTranspose()计算原矩阵的转置矩阵。