If you look at many of the celestial objects in the Solar system, they have a giant impact crater on their polar regions. I believe that there is a few articles about low angle impacts with massive objects and the borderline between whether a object survives the impact, or is completely obliterated.
I would suggest that the "pinching" effect could be somewhat explained like this. One solution would be to have the graphics algorithm place a giant crater covering the worst of this effect with the center of the crater placed on the center of the worst of the pinching "effect". When done in this manner, those line would appear as ejecta rays eminating from said crater. Even a class M world such as Earth has these readily identifiable objects (take a look at the crater shaped lake in Quebec, Canada on any map).