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

Abstract

This paper introduces the concept of the smooth topological Generalized Area Partitioning (tGAP) structure represented by a space-scale partition, which we term the space-scale cube. We take the view of ‘map generalization as extrusion of data into an additional dimension’. For 2D objects the resulting vario-scale representation is a 3D structure, while for 3D objects the result is a 4D structure.

This paper provides insights in: (1) creating valid data for the cube and proof that this is always possible for the implemented 2D tGAP 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.

The proposed new structure has very significant advantages over existing multi-scale/multi-representation solutions (in addition to being truly vario-scale): (1) due to tight integration of space and scale, there is guaranteed consistency between scales, (2) it is relatively easy to implement smooth zoom, and (3) compact, object-oriented encoding is provided for a complete scale range.

Keywords:

• 3D modelling
• 3D visualization
• generalization
• geographic information systems
• Internet GIS

Acknowledgements

This research is supported by the Dutch Technology Foundation STW (project numbers 11,300 and 11,185), which is part of the Netherlands Organisation for Scientific Research (NWO) and partly funded by the Ministry of Economic Affairs.

We would like to thank the anonymous reviewers for their concise reading and very constructive comments, which have improved the paper. Also thanks to Rod Thompson for proofreading the paper and suggesting numerous improvements. The authors would further like to thank Dirk de Jong, European Patent Attorney at Vereenigde, for the inspiring questions and discussions during the process of writing the patent claim for the method and system description of true vario-scale maps (patent pending nr. OCNL 2006630). All (remaining) errors are the sole fault of the authors.

Notes

1. A simple polygon is strictly convex if every internal angle is strictly less than 180° (so not equal to 180°).

2. In case of a concave object, this is then first decomposed into its convex parts, similar to the 2D approach.