With a focus on mobile and web mapping, we propose several algorithms for on-the-fly generalization of point data, such as points of interest (POIs) or large point collections. In order to achieve real-time performance we use a quadtree. With their hierarchical structure and progressive levels of detail, indexes of the quadtree family lend themselves as auxiliary data structures to support algorithms for generalization operations, including selection, simplification, aggregation, and displacement of point data. The spatial index can further be used to generate several measures on the relative point position and proximity of points, neighborhood, clusters, local and global density, etc. Using the tiles of the tree structure, such measures can be efficiently generated and updated. These measures can then serve to make educated guesses on the density and proximity of points across a series of map scales, and thus enable to control the operation of the generalization algorithms. An implementation of the proposed algorithms has shown that thanks to the quadtree index, real-time performance can be achieved even for large point sets. Furthermore, the quadtree data structure can be extended into a storage structure, which can be used to store pre-computed generalizations; thus, a desired level of detail can simply be retrieved from storage.