Index accelerating complex feature queries and geometric computations?

As far as I know, the index on geospatial database only optimizes lookup of features, not computation themselves, eg, it will acceleration intersection between a large number of polygons with a small number of vertices, but will not accelerate much with a lower number of polygons with the same amount of total vertices.

Besides splitting the polygons, am I missing something on geospatial databases practices to achieve great performance on operations (eg, intersection, nearest) against polygons with a large number of vertices ?