Direct3D数学基础函数

一、向量：1.直接相等加减直接D3DXVec3LengthD3DXVec3Normalize数乘直接[b]2.点乘D3DXVec3Dot[/b]点乘D3DXVec3Dot,主要计算夹角（投影角）V1( x1, y1).V2(x2, y2) = x1*x2 + y1*y2A.B = |A||B|Cos(θ)FLOAT D3DXVec3Dot( _In_ const D3DXVECTOR3 *pV1, _In_ const D3DXVECTOR3 *pV2);3.叉乘D3DXVec3Cross叉乘D3DXVec3Cross，主要计算平面的法向量|A x B| = |A||B|Sin(θ)a= [a1, a2, a3] =a1i+ a2j+ a3kb= [b1,b2,b3]=b1i+ b2j+ b3k ;则a × b= [a2b3-a3b2,a3b1-a1b3, a1b2-a2b1]D3DXVECTOR3* D3DXVec3Cross( _Inout_ D3DXVECTOR3 *pOut, _In_ const D3DXVECTOR3 *pV1, _In_ const D3DXVECTOR3 *pV2);二、矩阵：1.直接相等加减直接数乘直接矩阵乘以矩阵：

D3DXMATRIX* D3DXMatrixMultiply(
  _Inout_  D3DXMATRIX *pOut, // 矩阵相乘所得结果
  _In_     const D3DXMATRIX *pM1,// 输入矩阵1
  _In_     const D3DXMATRIX *pM2 // 输入矩阵2
);

2.单位/转置/逆矩阵单位矩阵：D3DXMatrixIdentityD3DXMATRIX* D3DXMatrixIdentity( _Inout_ D3DXMATRIX *pOut);转置D3DXMatrixTransposeD3DXMATRIX* D3DXMatrixTranspose( _Inout_ D3DXMATRIX *pOut, _In_ const D3DXMATRIX *pM);逆D3DXMatrixInverseD3DXMATRIX* D3DXMatrixInverse( _Inout_ D3DXMATRIX *pOut, _Inout_ FLOAT *pDeterminant, // 行列式的值，如果行列式值为NULL也是可以的，否则用伴随矩阵/行列式值求得矩阵的逆 _In_ const D3DXMATRIX *pM);3.平移D3DXMatrixTranslation

D3DXMATRIX* D3DXMatrixTranslation(
  _Inout_  D3DXMATRIX *pOut,
  _In_     FLOAT x,
  _In_     FLOAT y,
  _In_     FLOAT z
);

4.旋转D3DXMatrixRotationX/Y/Z

D3DXMATRIX* D3DXMatrixRotationX(
  _Inout_  D3DXMATRIX *pOut,
  _In_     FLOAT Angle // 弧度角，旋转方向是从旋转轴的正方向往原点看的顺时针方向
);

5.缩放D3DXMatrixScaling

D3DXMATRIX* D3DXMatrixScaling(
  _Inout_  D3DXMATRIX *pOut,
  _In_     FLOAT sx,
  _In_     FLOAT sy,
  _In_     FLOAT sz
);

6. 3D点/向量乘以矩阵实现真正物体变换点乘矩阵：D3DXVec3TransformCoord将结果向量第四个设置为1，D3DXVec3TransformNormal将结果向量第四个设置为0.

//Coordinate是坐标系，基于坐标点的变换，需要将向量解释为2D/3D点

//变换向量将第四位置为1，需要考虑平移(pV->x, pV->y, pV->z, 1)

D3DXVECTOR3* D3DXVec3TransformCoord(
  _Inout_  D3DXVECTOR3 *pOut,
  _In_     const D3DXVECTOR3 *pV,
  _In_     const D3DXMATRIX *pM // 都是考虑平移的矩阵
);

// Normal是法向量，就是纯向量的变换，向量是只有大小和方向的，需要将向量解释为2D/3D纯向量

//变换向量将第四位置为0，也就是忽略平移(pV->x, pV->y, pV->z, 0)

D3DXVECTOR3* D3DXVec3TransformNormal(
  _Inout_  D3DXVECTOR3 *pOut,
  _In_     const D3DXVECTOR3 *pV,
  _In_     const D3DXMATRIX *pM //都是考虑平移的矩阵
);

点数组和向量数组乘以矩阵：D3DXVec3TransformCoordArray/D3DXVec3TransformNormalArray.

D3DXVECTOR3* D3DXVec3TransformCoordArray(
  _Inout_  D3DXVECTOR3 *pOut,
  _In_     UINT OutStride, // 输出数组元素的字节步长,sizeof(D3DVECTOR3)或者sizeof(VERTTEX)都可以
  _In_     const D3DXVECTOR3 *pV,
  _In_     UINT VStride, // 输入数组元素的步长sizeof(D3DXVECTOR3)
  _In_     const D3DXMATRIX *pM,
  _In_     UINT n
);

D3DXVECTOR3* D3DXVec3TransformNormalArray(
  _Inout_  D3DXVECTOR3 *pOut,
  _In_     UINT OutStride,// 输出数组步长
  _In_     const D3DXVECTOR3 *pV,
  _In_     UINT VStride, // 输入数组步长
  _In_     const D3DXMATRIX *pM,
  _In_     UINT n
);

D3DXVec3TransformNormalArray参数和CoordArray一样。