Variable-scale Topological Data Structures Suitable for Progressive Data Transfer: The GAP- face Tree and GAP-edge Forest

This paper presents the first data structure for a variable scale representation of an area partitioning without redundancy of geometry. At the highest level of detail, the areas are represented using a topological structure based on faces and edges; there is no redundancy of geometry in this structure as the shared boundaries (edges) between neighbor areas are stored only once. Each edge is represented by a Binary Line Generalization (BLG)-tree, which enables selection of the proper repre- sentation for a given scale. Further, there is also no geometry redundancy between the different levels of detail. An edge at a higher importance level (less detail) does not contain copies of the lower-level edges or coordinates (more detail), but it is represented by efficiently combining their corresponding BLG trees. Which edges have to be combined follows from the generalization computation, and this is stored in a data structure. This data structure turns out to be a set of trees, which will be called the (Generalized Area Partitioning) GAP-edge forest. With regard to faces, the generalization result can be captured in a single tree structure for the parent-child relationships—the GAP face-tree. At the client side there are no geometric computations necessary to compute the polygon representations of the faces, merely following the topological references is sufficient. Finally, the presented data structure is also suitable for progressive transfer of vector maps, assuming that the client maintains a local copy of the GAP-face tree and the GAP-edge forest.