Landing a cube on a cube-shaped button
To do that, select all four of the invisible brushes you made with CTRL and click. Now press CTRL and T to make those brushes into brush entities. Set the entities as func_brush. Set the solidity keyvalue as toggle, set start disabled as yes, and give the brush entities names just like you would name any other entity. Giving all four the same name would probably be best here.
Now set up the button or whatever triggers the cube to drop to also enable the brush entities. This will make them solid, hopefully keeping the cube from going off course. To make the brushes non-solid again, set up an output for the cube button to disable the brushes once the cube button is pressed. You may want to set the delay to 1.0 to make sure the cube remains on the button. I hope that helps.
I tweaked your advice to fit my situation. In the event someone is interested, here is what I did:
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Made a set of four func_clip_vphysics walls arrayed around the cube-shaped button slot to keep the cube from escaping (slightly larger than it to prevent the cube from possibly getting stuck as it comes in).
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Inside of those walls I set four trigger_push walls to push the cube into position and diminish unsightly bouncing off vphysics walls (overlapping the space the cube was expected to settle into, set to push inwards and downwards at 2000 power).
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Set the button to disable both sets of walls 3 seconds after being pressed (to insure the cube has had enough time to get settled into the slot).
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Set the button to enable both sets of walls 10 seconds after being un-pressed (to insure the cube has enough time to move away, in this case via excursion funnel).
The cube lands in the exact right spot every time I throw it in. Thanks again for the help.