I am trying to re-implement the paper "A fresh perspective"
In this paper there is one paragraph on secion 2 that reads:
Usually, $z_s = z$ is the depth value of the point $P$, unchanged by $V_i$ . We extend the viewport transformations $V_i$ so that the cannonical depth of a point $z ∈ [0, 1] $ is linearly mapped to $z_s$ in an arbitrary, user specified range. While the relative depth values are preserved with respect to a single perspective view, this allows the powerful visual capability of intuitively altering the relative depths of points in a scene as one transitions between the mutiple linear perspectives.
I think I am not fully understanding the explanation.
If $z_s = z$ what does it mean that "the cannonical depth of a point $z ∈ [0, 1] $ is linearly mapped to $z_s$"?
We have $(x, y, z) = PM_i$, which I am assuming is the orthogonal normalization of space into the classic rendering box $[-1,1]^2\times [0, 1]$.
So $z$ is the depth before perspective and $z_s$ after perspective I think.
What exactly is the linear mapping described in the paper? I am very lost.
