Mesh simplification
Reducing a mesh's polygon count while keeping its shape, to build LOD chains or lighten heavy models.
The classic method is the quadric error metric (Garland and Heckbert, 1997): repeatedly collapse the edge whose removal introduces the least shape error, measured as the sum of squared distances to the original faces. The result is a sequence of ever coarser versions — the discrete LODs an engine switches between as the object recedes from the camera.
The pitfalls are the silhouette, which betrays simplification first, and UV seams and material boundaries that must not collapse without the texture sliding. Modern systems push the idea to its limit: Nanite in Unreal Engine 5 (2021) builds a hierarchy of simplified clusters and chooses the level of detail per small patch rather than per whole object.