Neither of your examples shows anything with
tons of spritesheets though.
I have seen really smooth stuff like:
This one was done using math as you said, so it has very little actual graphics. The effect is pretty good though, and the style works just fine.
I'm pretty sure Brigador is entirely made of sprite sheets.. well that's what it sounded like from the GDC talk...
I investigated this one. I saw a steam forum post the devs responded to. They are actually using 3d models, and then in game engine they are rendering sprites from them. I seriously doubt they are rendering 360 degrees of those animations as that would tax VRAM, but they are rendering enough of them that it is smooth enough that you don't notice. With fast paced moving objects like that, they might have gotten away with 32 directions with you not noticing at all. And the lighting is done using information in engine from those renders, such as normal maps. The cool part about rendering in engine is that they can do so at whatever resolution they need, so they get the niceness of 3d models with the workflow/performance of sprites. I'm sure it added quite a workload to make happen though. Wiki says they also used their own custom game engine.
I actually have a similar(but different) pipeline for my art. I'm using 3d models, but I'm pre-rendering them in Blender. I'm also rendering normal maps. So I get some of the same advantages they have, and I get real-time lighting as well. But I'm rendering for 1080P, so like sprite games, if you play at 4K, there is more scaling involved. It does however let me render the angles and animations I need easily enough. It takes longer in general to make a 3d model than to draw a sprite, but once the model and rig is done, animations can be made faster than in many cases of sprites. And iteration is much faster as well as I make a single change on the model and just hit the render button.
EDIT***
Found another thing, Brigador(according to a dev responding in another topic) uses 64 directions for vehicle sprites, which often gets cut almost in half for any that are symmetrical.