title: Which stage of pipeline should I do culling and clipping and How should I reconstruct triangles after clipping
body: <p>I'm trying to implement graphic pipeline in software level. I have some problems with clipping and culling now.</p>
  
  <p>Basically, there are two main concerns:</p>
  
  <ol>
  <li><p>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.</p></li>
  <li><p>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?</p></li>
  </ol>
  
  <p>Any idea will be helpful. Thanks.</p>