Conceptual Modeling of Geographic Data
The problem for geographic databases.
- Use of different terminology
- Use of different concepts of space
We propose the following framework
- Spatial concepts are structures that humans use to organize
their perception of geographic space.
- Spatial data models are formalizations of the semantics of
- Spatial data structures are implementations of spatial data
Informal conceptual tools to comprehend and structure our
perception and cognition of reality.
Different geographic applications require different spatial
- Networks for navigation tasks or utilities
- Euclidean geometry for surveying and cadastre
- Block units for census or land use mapping
Geometric Data Models
Comprehensive sets of conceptual tools to describe and structure
- Formally defined
- Widely applicable.
Examples: raster model, simplicial model
Geometric Data Structures
Detailed, low-level descriptions of structures and algorithms for
the storage and retrieval of data.
- storage utilization
Examples: quad trees, strip trees, winged edges
Remote sensing data as an example
The data source is conceptualized as a continuous measurable field
of real values ("geographic reality" [Goodchild 1990]).
Data collection is based on the geometric data model of a square
Data storage is often done in a quad tree data structure.
Geometric Data Models: Some Advanced Solutions
Models for Spatial Relations
Spatial relations are more complex than relations between standard
data types such as integers or strings.
Main problem: modeling the semantics of spatial relations.
- quantitative relations (distances, bearings, angles)
- qualitative relations (topology, cardinal directions,
Formal semantics are crucial for
- query processing (what to retrieve when a user asks for "all
cities north of Vienna?")
- query evaluation (is a query executable or has it internal
- optimization of complex spatial queries
Our investigations identified that the topological relations
between two point sets, A and B, can be described by the 9 set
intersections of the boundaries, interiors, and exteriors of A and
interior A /\ interior B interior A /\ boundary B interior A /\
I (A, B) = boundary A /\ interior B boundary A /\ boundary B
boundary A /\ exterior B
exterior A /\ interior B exterior A /\ boundary B° exterior A
/\ exterior B
Restriction: all objects have "sharp" boundaries.
Considering empty (ø) and non-empty (¬ø)
intersections, we found that we could realize
- 8 relations between two regions in 2-D
- 57 relations between two lines in 2-D
- 20 relations between a region and a line in 2-D.
Simplicial Data Model
A geometric data model for capturing complete topological
information in arbitrary dimensions.
The model is based on simplicial complexes, in particular closed
A simplex is the elementary geometric building block in a given
- 0-simplex is a point (node)
- 1-simplex is a line segment (edge)
- 2-simplex is a triangle (face)
A simplicial complex is a collection K of simplexes such that
- with every simplex, all its bounding simplexes are contained in
- the intersection of two simplexes is either empty or a simplex
A closed surface is a simplicial complex partitioning the
In practice, a closed surface is a triangulation of the plane
resulting from the complete intersection of all geometric objects
and its subdivision into simplexes.
[ Geographic Databases | What are Geographic Data? |
Properties of Geographic Data | User Interfaces and Spatial Query Languages |
Practical Issues of Geographic Databases |
Last updated on July 26, 1996.
J. Egenhofer | NCGIA
Maine | Department of
Spatial Information Science and Engineering ]