Vario-scale data structures supporting smooth zoom and progressive transfer of 2D and 3D data

This paper introduces the concept of the smooth tGAP structure represented by a space-scale partition, which we term the space-scale cube. We take the view of 'map generalization is extrusion of data into an additional dimension'. For 2D objects the resulting vario-scale representation is a 3D structure, while for 3D objects the resulting vario-scale representation is a 4D structure. This paper provides insights in: 1. creating valid data for the cube and proof that this always possible for the implemented 2D tGAP (topological Generalized Area Partition) generalization operators (line simplification, merge, and split/collapse), 2. obtaining a valid 2D polygonal map representation at arbitrary scale from the cube, 3. using the vario-scale structure to provide smooth-zoom and progressive transfer between server and client, 4. exploring which other possibilities the cube brings for obtaining maps having non-homogenous scales over their domain (which we term mixed-scale maps), and 5. using the same principles also for higher dimensional data; illustrated with 3D input data represented in a 4D hypercube.