It looks like one object projected and blocked/cut another.
It gets worse with more distance between objects.
How to avoid this mess?
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jon doe
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In addition to @DrRiisTab answer, sometimes it may be caused by the bad viewport clipping settings. Please see related answer: http://blender.stackexchange.com/questions/4946/where-can-the-viewport-clipping-parameters-be-changed – Paul Gonet Apr 13 '16 at 12:38
1 Answers
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It seems to be a problem with the camera end clipping.
As you see it
the left cube is renderer with a proper camera clipping while the right one is rendered with a too low end clipping
As you see it

you can change the camera clipping in the properties menu while the camera is selected.
Try to increase the camera end clipping