各种变换的原理----DX版本
DX 提供了D3DXMatrixPerspectiveLH,D3DXMatrixPerspectiveOffCenterLH以及D3DXMatrixPerspectiveFovLH来实现透视投影。提供了D3DXMatrixOrthoLH和D3DXMatrixOrthoOffCenterLH来实现正投影
(以上各函数都有右手坐标系下面的版本,只是把后面的LH改成RH)
先看D3DXMatrixPerspectiveLH
D3DXMatrixPerspectiveLH
Builds a left-handed perspective projection matrix
D3DXMATRIX * D3DXMatrixPerspectiveLH(D3DXMATRIX * pOut,FLOAT w,FLOAT h,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- w
- [in] Width of the view volume at the near view-plane.
- h
- [in] Height of the view volume at the near view-plane.
- zn
- [in] Z-value of the near view-plane.
- zf
- [in] Z-value of the far view-plane.
Return Values
Pointer to a D3DXMATRIX structure that is a left-handed perspective projection matrix.
这个函数的投影平面在z=n处
最后看下MSDN的结果
OK,为了完整把D3DXMatrixPerspectiveRH也推导下吧.囧....
D3DXMatrixPerspectiveRH
Builds a right-handed perspective projection matrix.
D3DXMATRIX * D3DXMatrixPerspectiveRH(D3DXMATRIX * pOut,FLOAT w,FLOAT h,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- w
- [in] Width of the view volume at the near view-plane.
- h
- [in] Height of the view volume at the near view-plane.
- zn
- [in] Z-value of the near view-plane.
- zf
- [in] Z-value of the far view-plane.
Return Values
Pointer to a D3DXMATRIX structure that is a right-handed perspective projection matrix.
这个函数的投影平面在z=-n处
最后看下MSDN的结果
再看下D3DXMatrixPerspectiveOffCenterLH
D3DXMatrixPerspectiveOffCenterLH
Builds a customized, left-handed perspective projection matrix.
D3DXMATRIX * D3DXMatrixPerspectiveOffCenterLH(D3DXMATRIX *pOut,FLOAT l,FLOAT r,FLOAT b,FLOAT t,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- l
- [in] Minimum x-value of the view volume.
- r
- [in] Maximum x-value of the view volume.
- b
- [in] Minimum y-value of the view volume.
- t
- [in] Maximum y-value of the view volume.
- zn
- [in] Minimum z-value of the view volume.
- zf
- [in] Maximum z-value of the view volume.
Return Values
Pointer to a D3DXMATRIX structure that is a customized, left-handed perspective projection matrix.
最后看下MSDN
接着看下D3DXMatrixPerspectiveOffCenterRH
D3DXMatrixPerspectiveOffCenterRH
Builds a customized, right-handed perspective projection matrix.
D3DXMATRIX * D3DXMatrixPerspectiveOffCenterRH(D3DXMATRIX *pOut,FLOAT l,FLOAT r,FLOAT b,FLOAT t,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- l
- [in] Minimum x-value of the view volume.
- r
- [in] Maximum x-value of the view volume.
- b
- [in] Minimum y-value of the view volume.
- t
- [in] Maximum y-value of the view volume.
- zn
- [in] Minimum z-value of the view volume.
- zf
- [in] Maximum z-value of the view volume.
Return Values
Pointer to a D3DXMATRIX structure that is a customized, right-handed perspective projection matrix.
看下MSDN
继续看D3DXMatrixPerspectiveFovLH
D3DXMatrixPerspectiveFovLH
Builds a left-handed perspective projection matrix based on a field of view.
D3DXMATRIX * D3DXMatrixPerspectiveFovLH(D3DXMATRIX *pOut,FLOAT fovy,FLOAT Aspect,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- fovy
- [in] Field of view in the y direction, in radians.
- Aspect
- [in] Aspect ratio, defined as view space width divided by height.
- zn
- [in] Z-value of the near view-plane.
- zf
- [in] Z-value of the far view-plane.
Return Values
Pointer to a D3DXMATRIX structure that is a left-handed perspective projection matrix.
看MSDN
继续看D3DXMatrixPerspectiveFovRH
D3DXMatrixPerspectiveFovRH
Builds a right-handed perspective projection matrix based on a field of view.
D3DXMATRIX * D3DXMatrixPerspectiveFovRH(D3DXMATRIX *pOut,FLOAT fovy,FLOAT Aspect,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- fovy
- [in] Field of view in the y direction, in radians.
- Aspect
- [in] Aspect ratio, defined as view space width divided by height.
- zn
- [in] Z-value of the near view-plane.
- zf
- [in] Z-value of the far view-plane.
Return Values
Pointer to a D3DXMATRIX structure that is a right-handed perspective projection matrix.
看结果
接着看几个正投影
先看D3DXMatrixOrthoLH
D3DXMatrixOrthoLH
Builds a left-handed orthographic projection matrix.
D3DXMATRIX * D3DXMatrixOrthoLH(D3DXMATRIX *pOut,FLOAT w,FLOAT h,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the resulting D3DXMATRIX.
- w
- [in] Width of the view volume.
- h
- [in] Height of the view volume.
- zn
- [in] Minimum z-value of the view volume which is referred to as z-near.
- zf
- [in] Maximum z-value of the view volume which is referred to as z-far.
Return Values
Pointer to the resulting D3DXMATRIX.
看结果
接着看D3DXMatrixOrthoRH
D3DXMatrixOrthoRH
Builds a right-handed orthographic projection matrix.
D3DXMATRIX * D3DXMatrixOrthoRH(D3DXMATRIX *pOut,FLOAT w,FLOAT h,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the resulting D3DXMATRIX.
- w
- [in] Width of the view volume.
- h
- [in] Height of the view volume.
- zn
- [in] Minimum z-value of the view volume.
- zf
- [in] Maximum z-value of the view volume.
Return Values
Pointer to the resulting D3DXMATRIX.
看结果
接着看D3DXMatrixOrthoOffCenterLH
D3DXMatrixOrthoOffCenterLH
Builds a customized, left-handed orthographic projection matrix.
D3DXMATRIX * D3DXMatrixOrthoOffCenterLH(D3DXMATRIX *pOut,FLOAT l,FLOAT r,FLOAT b,FLOAT t,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the resulting D3DXMATRIX.
- l
- [in] Minimum x-value of view volume.
- r
- [in] Maximum x-value of view volume.
- b
- [in] Minimum y-value of view volume.
- t
- [in] Maximum y-value of view volume.
- zn
- [in] Minimum z-value of the view volume.
- zf
- [in] Maximum z-value of the view volume.
Return Values
Pointer to the resulting D3DXMATRIX.
看结果
终于到最后一个了D3DXMatrixOrthoOffCenterRH
D3DXMatrixOrthoOffCenterRH
Builds a customized, right-handed orthographic projection matrix.
D3DXMATRIX * D3DXMatrixOrthoOffCenterRH(D3DXMATRIX *pOut,FLOAT l,FLOAT r,FLOAT b,FLOAT t,FLOAT zn,FLOAT zf );
Parameters
- pOut
- [in, out] Pointer to the resulting D3DXMATRIX.
- l
- [in] Minimum x-value of view volume.
- r
- [in] Maximum x-value of view volume.
- b
- [in] Minimum y-value of view volume.
- t
- [in] Maximum y-value of view volume.
- zn
- [in] Minimum z-value of the view volume.
- zf
- [in] Maximum z-value of the view volume.
Return Values
Pointer to the resulting D3DXMATRIX.
看结果
尼玛,终于搞完了,本来还有世界坐标到视图坐标的转换,标准设备坐标到视口的转换..今晚先到这里,伤不起啊,6点了,以后补上
继续补上,先看世界坐标到视图坐标的转换
先看D3DXMatrixLookAtLH
D3DXMatrixLookAtLH
Builds a left-handed, look-at matrix.
D3DXMATRIX * D3DXMatrixLookAtLH(D3DXMATRIX *pOut,CONST D3DXVECTOR3 *pEye,CONST D3DXVECTOR3 *pAt,CONST D3DXVECTOR3 *pUp );
Parameters
- pOut
- [in, out] Pointer to the D3DXMATRIX structure that is the result of the operation.
- pEye
- [in] Pointer to the D3DXVECTOR3 that defines the eye point. This value is used in translation.
- pAt
- [in] Pointer to the D3DXVECTOR3 structure that defines the camera look-at target.
- pUp
- [in] Pointer to the D3DXVECTOR3 structure that defines the current world's up, usually [0, 1, 0].
Return Values
Pointer to a D3DXMATRIX structure that is a left-handed, look-at matrix.
看结果
另外D3DXMatrixLookAtRH推导是一样的,只不过把Z''取负即可
接着看标准设备坐标到视口坐标的转换,DX提供了SetViewport方法来设置视口矩阵
IDirect3DDevice9::SetViewport
Sets the viewport parameters for the device.
HRESULT SetViewport(CONST D3DVIEWPORT9 * pViewport );
Parameters
- pViewport
- [in] Pointer to a D3DVIEWPORT9 structure, specifying the viewport parameters to set.
Return Values
If the method succeeds, the return value is D3D_OK. If the method fails, it will return D3DERR_INVALIDCALL. This will happen if pViewport is invalid, or if pViewport describes a region that cannot exist within the render target surface.
D3DVIEWPORT9结构体如下:
typedef struct D3DVIEWPORT9 {DWORD X;DWORD Y;DWORD Width;DWORD Height;float MinZ;float MaxZ;
} D3DVIEWPORT9, *LPD3DVIEWPORT9;
所以，视口变换
就是将
x''->x''':(-1,1)->(X,X+Width)
y''->y''':(-1,1)->(Y+Height,Y)//这里注意DX中视口坐标中的y值是从上到下递增的
z''->z''':(0,1)->(MinZ,MaxZ)
由于(x'',y'',z'')满足线性插值，所以设
x'''=A'x''+B'
y'''=A''y''+B''
z'''=A'''z''+B'''
代入变换条件可求得：
A'=Width/2 B'=Width/2+X
A''=-Height/2 B''=Height/2+Y
A'''=MaxZ-MinZ B'''=MinZ
所以视口矩阵为
也就是龙书上所说的
OK,渲染管线里面用到的变换基本上讲完了,当然还有神马旋转变换矩阵,镜像映射矩阵,平面投影矩阵到时候我会再开专题讲
敬请期待哦!
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