The Properties of Geographic Data

• Geometry + meaning
• Operations define the semantics
• Uneven distribution, uneven density, varying sizes
• Multiple spatial reference systems
• Geometry often complex (holes, separations, aggregates, spikes, networks).

Map "Algebra" (Dana Tomlin)

• Boolean operations (and, or, etc.)
• Buffer zone

• Need for same resolution, alignment, orientation
• User interfaces

Vector Data Model

• Represents "objects" through their boundaries (and interiors).
• Elementary data types: point, line, region.
• Arbitrarily complex spatial objects as aggregates.
• Geometric consistency constraints.
• Records topology explicitly to guarantee consistent query processing.

Geometric Data Types

• Generally applicable (no exceptions).
• Formal definitions of values and functions of data types.
• Possible within finite resolution.
• Geometric consistency.
• Attributes and non-geometric operations.

• Multiple representations
• Spatio-temporal
• Real-time

Querying of Spatial Data: Topological Relations

• Binary topological relations modeled as intersections of objects' boundaries and interiors (4-intersection).
• Properties are invariant under topological transformations.
• Considering empty and non-empty values, 16 relations are defined.
• If objects are homogeneously 2-dimensional, simply connected, eight relations can be realized in R2.

Topological Relations with Regions and Lines

• Intersections of interiors, boundaries, and exteriors (9-intersection).
• Out of 512 combinations, 36 topological relations can be realized between two lines in R2, 19 between a line and a region.

9-Intersection as basis for:

• Inferences through composition (e.g., for query processing):

A inside B, B meets C -> A disjoint B.

• Definition of spatial similarity through conceptual neighborhoods.
  
  
• Definition of natural-language-like spatial terms.
  
  
• Cross-language spatial queries.