Of course, I see the benefit in using polygons to create 3D worlds. But I sometimes wonder if other methods exist and have been used in published computer games; perhaps even hybrid methods of 3D animation that combine polygons with some other style of rendering, so that the limitations of polygonal rendering might be overcome or just mitigated. For example, a way of rendering human bodies without jagged limbs.
Answer
A technique which comes around again and again for decades is raytracing. While usual 3d engines are based on taking a bunch of vertices in 3d space and see where they end up if transformed to 2d space through a projection matrix, raytracing engines simulate a ray of light from each screen-pixel into the scene and see where it hits a surface.
Raytracing engines usually like to show off by rendering perfect spheres reflecting their environment. While spheres and reflections are hard to do well in polygon-based engines, they are quite trivial to do with raytracing.
Unfortunately GPUs aren't optimized for raytracing, so very few games make use of this extensively, so no GPU vendors bothers to optimize for it. This chicken-egg problem prevents the method from becoming mainstream. There are a few experimental games which use raytracing-based engines, though.
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