Transformation

旋转

$$R_{xyz}(\alpha,\beta,\gamma)=R_{x}(\alpha)R_{y}(\beta)R_{z}(\gamma)$$ $$R_{x}(\alpha)= \begin{bmatrix} 1&0&0&0\\ 0&cos{\alpha}&-sin{\alpha}&0\\ 0&sin{\alpha}&cos{\alpha}&0\\ 0&0&0&1\\ \end{bmatrix}$$ $$R_{y}(\beta)= \begin{bmatrix} cos{\beta}&0&sin{\beta}&0\\ 0&0&0&0\\ -sin{\beta}&0&cos{\beta}&0\\ 0&0&0&1\\ \end{bmatrix}$$ $$R_{z}(\gamma)= \begin{bmatrix} cos{\gamma}&-sin{\gamma}&0&0\\ sin{\gamma}&cos{\gamma}&0&0\\ 0&0&0&0\\ 0&0&0&1\\ \end{bmatrix}$$

缩放

$$S_{(s_x,s_y,s_z)}\begin{bmatrix} s_x&0&0&0\\ 0&s_y&0&0\\ 0&0&s_z&0\\ 0&0&0&1\\ \end{bmatrix}$$

齐次坐标

平移

$$T_{(t_x,t_y,t_z)}=\begin{bmatrix} 1&0&0&t_x\\ 0&1&0&t_y\\ 0&0&1&t_z\\ 0&0&0&1\\ \end{bmatrix}$$

模型变换Modeling

视图变换View

Camera Position
Camera LookAt
Camera UpDirection

投影变换Projection

Orthographic Projection

• Camera located at origin,looking at -Z,up at Y
• Drop Z coordinate
• Translate and scale the resulting rectangle to [-1,1]

Perspective Projection

参考

闫令琪的视频教程
闫令琪的视频教程