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In hidden surface removal, how does the Z-buffer algorithm work vs. painter's algorithm?

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In short painter's algorithm can't deal with intersecting geometry.

Suppose that you draw a plane angled away from the camera, and a plane angled towards the camera. The planes intersect in an 'X' shape.

Camera ------> X

With painter's algorithm no such ordering exists that will render the shape exactly. You would only see whichever plane you decided to draw last.

The Z-Buffer or Depth-Buffer stores the nearest depth per each pixel relative from the camera. If another triangle is rasterized and has a depth less than the current depth buffer value it is accepted, if it's depth is greater, it is rejected. This is called a depth test.

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    $\begingroup$ The painter's algorithm can also fail with nonintersecting geometry if there are cycles in the occlusion relation. For example, consider three rods arranged on the ground in a triangle such that each rod is resting on the one clockwise from it. Viewed from above, there is no rod that can be drawn first. $\endgroup$
    – user106
    Dec 2, 2018 at 10:41
  • $\begingroup$ Painter's algorithm WILL work with overlaps etc provided you take the steps described by Newell, Newell & Sancha. en.wikipedia.org/wiki/Newell%27s_algorithm $\endgroup$
    – Simon F
    Dec 4, 2018 at 9:16
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  • In the painter's algorithm, you first sort all graphics elements on depth (deepest first) and then one-by-one fully paint them into the image on top of each other. That way, deeper elements are obscured by less deep element. (Intersecting graphics element require special attention.)

  • In the depth-buffering algorithm, you store the current depth of each pixel in the image (in addition to other pixel info), and fully paint each graphics element pixel-by-pixel, where an image pixel is updated only if its depth is more than that of the new pixel.

So, there is a time-memory tradeoff:

  • The painter's algorithm requires an extra sorting step (costs time), but avoids storing additional (depth) information per pixel (saves memory).
  • Depth-buffering avoids sorting (saves time), but stores extra (depth) information per pixel (costs memory).
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