# Which stage of pipeline should I do culling and clipping and How should I reconstruct triangles after clipping

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Hi, I'm trying to implement graphic pipeline in software level. I have some problems with clipping and culling now.

Basically, there are two main concerns:

1. When should back-face culling take place? Eye coordinate, clipping coordinate or window coordinate? I initially made culling process in eye coordinate, thinking this way could relieve the burden of clipping process since many back-facing vertices have already been discarded. But later I realized that in this way vertices need to take 2 matrix multiplications , namely left multiply model-view matrix --> culling --> left multiply perspective matrix, which increases the overhead to some extent.

2. How do I do clipping and reconstruct triangle? As far as I know, clipping happens in clipping coordinate(after perspective transformation), in another word homogeneous coordinate in which every vertex is being determined whether no not it should be discarded  by comparing its x, y, z components with w component. So far so good, right? But after that I need to reconstruct those triangles which have one or two vertices been discarded. I googled that Liang-Barsky algorithm would be helpful in this case, but in clipping coordinate what clipping plane should I use? Should I just record clipped triangles and reconstruct them in NDC?

Any idea will be helpful. Thanks.

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Super quick answer, when I did this I clipped in screen space (2D) after back-face culling (also in screen space using winding).

You reconstruct the triangles with interpolation but you need to multiply/divide by w to account for the perspective correction.

While screen space might not be optimal, it is very easy, plus you only have to transform each vertex only once.

Good luck ;)

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Super quick answer, when I did this I clipped in screen space (2D) after back-face culling (also in screen space using winding).

You reconstruct the triangles with interpolation but you need to multiply/divide by w to account for the perspective correction.

While screen space might not be optimal, it is very easy, plus you only have to transform each vertex only once.

Good luck ;)

Thanks for the reply. I think I might try that out if there is no better suggestion.

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When I did the occlusion software rasterizer for Urho3D, I remember encountering some precision/overflow issues when clipping in screen space against the near plane. Basically, the X/Y coordinates could become huge if the near clipping plane was near 0. Therefore I switched to clipping in homogenous coordinates before perspective divide. When you reconstruct triangles in homogenous coords, just interpolate all of x,y,z,w after you find where an edge intersects with the clip plane in question. Note that clipping against all frustum planes can theoretically generate a large amount of new vertices & triangles.

If you want to check, the file in question is OcclusionBuffer.cpp.

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When I did the occlusion software rasterizer for Urho3D, I remember encountering some precision/overflow issues when clipping in screen space against the near plane. Basically, the X/Y coordinates could become huge if the near clipping plane was near 0. Therefore I switched to clipping in homogenous coordinates before perspective divide. When you reconstruct triangles in homogenous coords, just interpolate all of x,y,z,w after you find where an edge intersects with the clip plane in question. Note that clipping against all frustum planes can theoretically generate a large amount of new vertices & triangles.

If you want to check, the file in question is OcclusionBuffer.cpp.

Thanks, I just implemented clipping only with near plane which cares only about z value. As for x, y value, my workaround is to clamp the bounding-box in screen space for every triangle passed into rasterizer.

A confusion about reconstructing triangle in homogeneous coordinate. How do you know the clipping in homogeneous coordinate? I mean I have information of view frustum before projection transformation, but after that vertices are transformed into clipping coordinate, should I also do projection transformation on view frustum?

Sorry for my poor English, even myself no sure what I mean.

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After projection transform, the view volume is fixed (in Direct3D convention, left clip plane at X -1.0, far clip plane at Z 1.0, near clip at Z 0.0) so there should be no need to transform the frustum.

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After projection transform, the view volume is fixed (in Direct3D convention, left clip plane at X -1.0, far clip plane at Z 1.0, near clip at Z 0.0) so there should be no need to transform the frustum.

I think I get you. But is it a typo or something? because In your last post you said you did clipping in homogeneous coordinate before perspective divide, namely in clipping coordinate. But clipping coordinate doesn't have fixed view volume which is in NDC(normalized device coordinate).
Thanks, anyway.

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Ah, I took a bit of a shortcut. What I should have said that after projection & perspective divide the vertices sit inside the fixed view volume. But the end result is, that when you're clipping homogenous coordinates using 4-dimensional dot products, you can use those fixed clipping planes.

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Ah, I took a bit of a shortcut. What I should have said that after projection & perspective divide the vertices sit inside the fixed view volume. But the end result is, that when you're clipping homogenous coordinates using 4-dimensional dot products, you can use those fixed clipping planes.

After all these days, I still can't get clear about the clipping and reconstruction of triangle. Say triangle Tp has been left multiplied by perspective matrix but not yet divided by its fourth component w. Should I now do the clipping and reconstruction? if I do clipping and reconstruction in this stage, what clipping plane should I clip against?

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You can do it either way - mathematically they both will work, but they just use slightly different operations.  If you want to clip after the w-divide, then it is fairly simple to do since the view volume occupies the ranges that AgentC mentioned (x : [-1,1], y : [-1,1], z : [0,1]).  If you do it before w-divide, then you have to use a different type of clipping.  It is a bit of an involved derivation, but there is a pretty good explanation of it in Dave Eberly's book 3D Game Engine Design, 2nd edition.  If you get the book, look in chapter 2.4.

By doing the clipping before the divide, you are also able to do the perspective correct interpolation with the new vertices.