In both the OpenGL and Direct3D rendering pipelines, the geometry shader is processed after the vertex shader and before the fragment/pixel shader. Now obviously processing the geometry shader after the fragment/pixel shader makes no sense, but what I'm wondering is why not put it before the vertex shader?
From a software/high-level perspective, at least, it seems to make more sense that way: first you run the geometry shader to create all the vertices you want (and dump any data only relevant to the geometry shader), then you run the vertex shader on all the vertices thus created. There's an obvious drawback in that the vertex shader now has to be run on each of the newly-created vertices, but any logic that needs to be done there would, in the current pipelines, need to be run for each vertex in the geometry shader, presumably; so there's not much of a performance hit there.
I'm assuming, since the geometry shader is in this position in both pipelines, that there's either a hardware reason, or a non-obvious pipeline reason that it makes more sense.
(I am aware that polygon linking needs to take place before running a geometry shader (possibly not if it takes single points as inputs?) but I also know it needs to run after the geometry shader as well, so wouldn't it still make sense to run the vertex shader between those stages?)