3D projection

\begin{bmatrix} \mathbf{d}_x \\ \mathbf{d}_y \\ \mathbf{d}_z \\ \end{bmatrix}=\begin{bmatrix} 1 & 0 & 0 \\ 0 & {\cos ( \mathbf{- \theta}_x ) } & { - \sin ( \mathbf{- \theta}_x ) } \\ 0 & { \sin ( \mathbf{- \theta}_x ) } & { \cos ( \mathbf{- \theta}_x ) } \\ \end{bmatrix}\begin{bmatrix} { \cos ( \mathbf{- \theta}_y ) } & 0 & { \sin ( \mathbf{- \theta}_y ) } \\ 0 & 1 & 0 \\ { - \sin ( \mathbf{- \theta}_y ) } & 0 & { \cos ( \mathbf{- \theta}_y ) } \\ \end{bmatrix}\begin{bmatrix} { \cos ( \mathbf{- \theta}_z ) } & { - \sin ( \mathbf{- \theta}_z ) } & 0 \\ { \sin ( \mathbf{- \theta}_z ) } & { \cos ( \mathbf{- \theta}_z ) } & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}\left( {\begin{bmatrix} \mathbf{a}_x \\ \mathbf{a}_y \\ \mathbf{a}_z \\ \end{bmatrix} - \begin{bmatrix} \mathbf{c}_x \\ \mathbf{c}_y \\ \mathbf{c}_z \\ \end{bmatrix}} \right)

This representation corresponds to rotating by three Euler angles (more properly, Tait–Bryan angles), using the xyz convention, which can be interpreted either as "rotate about the extrinsic axes (axes of the scene) in the order z, y, x (reading right-to-left)" or "rotate about the intrinsic axes (axes of the camera) in the order x, y, z (reading left-to-right)". Note that if the camera is not rotated ( $\mathbf{\theta}_{x,y,z} = \langle 0,0,0\rangle$ ), then the matrices drop out (as identities), and this reduces to simply a shift: $\mathbf{d} = \mathbf{a} - \mathbf{c}.$

单词	Perspective Projection
释义	Perspective Projection 原声例句科技 Crash Course This type of 3D projection is called Perspective Projection. 这种类型的 3D 投影称为透视投影。英语百科 3D projection $\begin{bmatrix} \mathbf{d}_x \\ \mathbf{d}_y \\ \mathbf{d}_z \\ \end{bmatrix}=\begin{bmatrix} 1 & 0 & 0 \\ 0 & {\cos ( \mathbf{- \theta}_x ) } & { - \sin ( \mathbf{- \theta}_x ) } \\ 0 & { \sin ( \mathbf{- \theta}_x ) } & { \cos ( \mathbf{- \theta}_x ) } \\ \end{bmatrix}\begin{bmatrix} { \cos ( \mathbf{- \theta}_y ) } & 0 & { \sin ( \mathbf{- \theta}_y ) } \\ 0 & 1 & 0 \\ { - \sin ( \mathbf{- \theta}_y ) } & 0 & { \cos ( \mathbf{- \theta}_y ) } \\ \end{bmatrix}\begin{bmatrix} { \cos ( \mathbf{- \theta}_z ) } & { - \sin ( \mathbf{- \theta}_z ) } & 0 \\ { \sin ( \mathbf{- \theta}_z ) } & { \cos ( \mathbf{- \theta}_z ) } & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}\left( {\begin{bmatrix} \mathbf{a}_x \\ \mathbf{a}_y \\ \mathbf{a}_z \\ \end{bmatrix} - \begin{bmatrix} \mathbf{c}_x \\ \mathbf{c}_y \\ \mathbf{c}_z \\ \end{bmatrix}} \right)$ This representation corresponds to rotating by three Euler angles (more properly, Tait–Bryan angles), using the xyz convention, which can be interpreted either as "rotate about the extrinsic axes (axes of the scene) in the order z, y, x (reading right-to-left)" or "rotate about the intrinsic axes (axes of the camera) in the order x, y, z (reading left-to-right)". Note that if the camera is not rotated ( $\mathbf{\theta}_{x,y,z} = \langle 0,0,0\rangle$ ), then the matrices drop out (as identities), and this reduces to simply a shift: $\mathbf{d} = \mathbf{a} - \mathbf{c}.$
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Perspective Projection

3D projection