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

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

yielding,

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

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.