# Why does opengl perform clipping in clip coordinates?

Is there any reason why OpenGL performs primitives' clipping in clip coordinates? Can it be at least theoretically done in normalized device coordinates?

The space after clip space is normalized device coordinate space, which is obtained by dividing clip.xyz by clip.w. If W is zero... oops.

Oh sure, you could put a conditional test to see if W is zero or very close to zero. Or you can just do the clipping math in clip space and never have to worry about it. No post-clipping vertex can have a W of zero, because the clip box for each vertex is based on being in the closed range (-W, W). And if W is 0, then the closed range is an empty set, and thus the vertex is not on that range.

Also, negative values of W are outside of the clipping space. The closed range (-W, W) is inverted where W is negative, but the meaning of the range itself is not. Consider a W of -1; the range becomes (1, -1). There are no numbers that are simultaneously greater than 1 and less than -1. Therefore that space is empty.

And yet, division by a negative W can still land NDC points in the [-1, 1] NDC-space range, where they will not be clipped if you didn't clip them beforehand.

• Also, W < 0 for points behind the camera. So if you divide by W first, you then cannot tell whether a point/primitive was behind the camera or in front of it. Nov 26, 2017 at 3:05
• Last fact seems most important to me Nov 28, 2017 at 12:46
• But I doubt it's true. Could you prove it or provide an example? Nov 28, 2017 at 14:44
• @Nolan: The point (0, 0, 0, -1). Divide by -1, and it's in the [-1, 1] range. But it can't be in the range of [1, -1], since that is an empty set. Nov 28, 2017 at 15:10
• You can't get point (0, 0, 0, -1) after multiplying by the projection matrix. It requires initial point have w coordinate equal 0 or have weird projection planes like negative near or far behind near. Nov 28, 2017 at 16:50

Clipping could be done in normalised device coordinates as all primitives with z-coordinates outside -1 to 1 are outside the clipping planes. However, there is no reason not to do it in clip coordinates by considering z-coordinates from -w to w.

Theoretically it possible. However it seems there is performance increase when doing the clipping in clip coordinates. By first comparing z-coordinates before perspective division it saves time by not computing perspective division for the clipped primitives. This means less division operations. This favourable as floating point division can take a few processing cycles.

Refer also to the answer in this related question