The way I understand 3D rendering, polygons are transformed using several matrices, and they are then clipped if they are not inside a certain box, before projecting the box onto the screen. Before transformation, the visible area is typically a frustum, and after transformation, I am guessing it's a cube. This cube makes the clipping math easier than a frustum would.

My question is, what's the 'standard' location/size for this clipping box? I can think of 3 possibilities: (0,0,0)-(1,1,1), (-0.5,-0.5,-0.5)-(0.5,0.5,0.5), (-1,-1,-1)-(1,1,1)

Or is there no standard?


Or is there no standard?

There isn't. OpenGL and D3D define clipping to happen in post-projective space, which is a 4D homogeneous coordinate system. So not a cube. But they use different post-projective spaces; the difference being the direction and range of the Z coordinate.

After the perspective divide (when you turn the 4D homogeneous space into a 3D space again), what you have in OpenGL is called normalized-device coordinates. This ranges from [-1, 1] in X, Y, and Z. In D3D, the equivalent space ranges from [-1, 1] in X and Y, but goes from [0, 1] in Z. Note that in both cases, clipping happened before then.

You can write a renderer that does clipping in whatever space you want. It's all just math in the end.

  • \$\begingroup\$ Am I right in understanding how it works though? I think that everything outside the final 3D box is clipped, though I see now that it is actually clipped before the 3D coordinates are used. The result is basically the same, no? \$\endgroup\$ Sep 29 '12 at 19:24
  • \$\begingroup\$ @KendallFrey here's a good paper on clipping in homogenous space if you're interested research.microsoft.com/pubs/73937/p245-blinn.pdf \$\endgroup\$
    – dreta
    Sep 29 '12 at 19:44

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