...illustration
In Figure 1 we have drawn the image plane as though it were orthogonal to the z-axis $\hat\mathbf{z}$ indicating that the optical axis of the camera is (anti) parallel to $\hat\mathbf{z}$. In fact, the effective viewpoint $\mathbf{v}$ and the axis of symmetry of the mirror profile z(r) need not necessarily lie on the optical axis. Since perspective projection is rotationally symmetric with respect to any ray that passes through the pinhole $\mathbf{p}$, the camera could be rotated about $\mathbf{p}$ so that the optical axis is not parallel to the z-axis. Moreover, the image plane can be rotated independently so that it is no longer orthogonal to $\hat\mathbf{z}$. In this second case, the image plane would be non-frontal. This does not pose any additional problem since the mapping from a non-frontal image plane to a frontal image plane is one-to-one.
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Simon Baker
1/22/1998