Consider this figure for projection.

enter image description here There are two equations that give value for the xp and yp coordinates:

  • $x_p=x.\frac{(z_{vp}-z_{prp})}{h}+ x_{prp}.\frac{(z-z_{vp})}{h}$ and
  • $y_p=y.\frac{(z_{vp}-z_{prp})}{h}+ y_{prp}.\frac{(z-z_{vp})}{h}$

and then it explains in a paragraph: "Setting up matrix elements for obtaining the homogeneous-coordinate $x_h$ and $y_h$ values in the given equations is straightforward, but we must also structure the matrix to preserve depth (z-value) information. Otherwise, the z coordinates are distorted by the homogeneous-division parameter h. We can do this by setting up the matrix elements for the z transformation so as to normalize the perspective-projection $z_p$ coordinates. There are various ways that we could choose the matrix elements to produce the homogeneous coordinates and the normalized $z_p$ value for spatial position (x, y, z)."

So, I have some questions regarding this:

  • What does it mean to preserve depth(z-values)?
  • What does it mean to normalize the perspective-projection zp coordinates?
  • How to perform this normalization?
  • How does this normalization preserve z-values?


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