Towards a true vario-scale structure supporting smooth-zoom

Abstract

This paper presents the first true vario-scale structure for geographic information: a delta in scale leads to a delta in the map (and smaller scale deltas lead to smaller map deltas until and including the infinitesimal small delta) for all scales. The structure is called smooth tGAP and its integrated 2d space and scale representation is stored as a single 3d data structure: space-scale cube (ssc). The polygonal area objects are mapped to polyhedral representations in the smooth tGAP structure. The polyhedral primitive is integrating all scale representations of a single 2d area object. Together all polyhedral primitives form a partition of the space-scale cube: no gaps and no overlaps (in space or scale). Obtaining a single scale map is computing an horizontal slice through the structure. The structure can be used to implement smooth zoom in an animation or morphing style. The structure can also be used for mixed-scale representation: more detail near to user/viewer, less detail further away by taking non-horizontal slices. For all derived representations, slices and smooth-zoom animations, the 2d maps are always perfect planar partitions (even mixed-scales objects fit together and form a planar partition). Perhaps mixed-scale is not very useful for 2d maps, but for 3d computer graphics it is one of the key techniques. Our approach does also work for 3d space and scale integrated in one 4d hypercube.