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I have not been able to find how you can activate an arbitrary clip plane before rendering geometry (like glClipPlane() functionality in OpenGL).
Does an API for this exist in Irrlicht or is it something which I will need to write custom rendering code to accomplish?
I think you want to call ICameraSceneNode::setNearValue(). That will adjust the near clip plane of the view frustum. Before rendering, objects are tested against the view frustum. If they are outside the frustum box, they are not normally rendered.