Coordonnées de la caméra: \(\mathrm{Cam}\)
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\(\mathrm{Cam}\times (1,0,0,0) = right\)
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\(\mathrm{Cam}\times (0,1,0,0) = up\)
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\(\mathrm{Cam}\times (0,0,1,0) = back\)
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\(\mathrm{Cam}\times (0,0,0,1) = eye\)
\(\mathrm{Cam}=\left(\begin{array}{cccc} | & | & | & | \\ right & up & back & eye \\ | & | & | & | \\ 0 & 0 & 0 & 1\end{array}\right)=\left(\begin{array}{cc} O & eye \\ 0 & 1 \end{array} \right)\)
View matrix: \(\mathrm{View}\)
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\(\mathrm{View}\times right = (1,0,0,0)\)
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\(\mathrm{View}\times up = (0,1,0,0)\)
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\(\mathrm{View}\times back = (0,0,1,0)\)
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\(\mathrm{View}\times eye = (0,0,0,1)\)
\(\mathrm{View}=\left(\begin{array}{cccc} ( \cdots & right & \cdots ) & - right \cdot eye \\ ( \dots & up & \cdots ) & - up \cdot eye \\ ( \cdots & -front & \cdots ) & - back \cdot eye \\ 0 & 0 & 0 & 1 \end{array}\right)=\left(\begin{array}{cc} O^T & -O^T\,eye \\ 0 & 1 \end{array} \right)\)
\(\mathrm{View}=\mathrm{Cam}^{-1}\)
