The same torus, three ways, identical light. Left and centre are the exact mesh in your screenshot — 24×12 quads, 576 triangles. Smooth normals fix the shading but the outline stays a polygon. Only the analytic surface has no outline to break. ← back to the stage
faceted shading + faceted silhouette
the screenshotsmooth shading, faceted silhouette
still polygonalexact surface, exact normal
no silhouette errorInterpolating normals across a face hides the shading discontinuity, so the body looks round. The edge against the background is still made of straight segments, and that is exactly what reads as "corners" on a large, slowly moving shape.
Killing a visible facet means roughly quartering its screen size, so you need ~4× the triangles per halving of error. A silhouette that survives a close-up needs tens of thousands of triangles for one torus — and it breaks again the moment you zoom.
One fullscreen triangle and a length(q) - r per step. Resolution-independent: zoom to a pixel and it is still exact.
The trade is that cost scales with pixels, not with objects.