The orthographic camera

The affine camera reduces to the case of orthographic (parallel) projection when $ {\bf M}$ represents the first two rows of a rotation matrix. The simplest form is

$\displaystyle {\bf T}_{orth} =
\left[ \begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 \\
\end{array}\right]
$

yielding,

$\displaystyle {\bf M}_{orth} = \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
\end{array}\right]$   and$\displaystyle \left[ \begin{array}{c}
x \\ y
\end{array}\right]
=
\left[ \begin{array}{c}
X \\ Y
\end{array}\right]
$

Figure 1: 1D image formation with image plane at $ Z = f$ . $ X_p,X_{wp}$ and $ X_{orth}$ are the perspective, weak-perspective and orthographic projections respectively.
\includegraphics[width=5.0in]{models.ps}


Subhashis Banerjee 2008-01-20