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 concepts.
- Spatial data structures are implementations of spatial data
models.
Spatial Concepts
Informal conceptual tools to comprehend and structure our
perception and cognition of reality.
Different geographic applications require different spatial
concepts:
- 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
spatial information.
- Formally defined
- Implementable
- 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.
Primary concerns
- performance
- 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
raster.
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,
approximate distances)
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
contradictions?)
- optimization of complex spatial queries
Topological Relations
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
B.
interior A /\ interior B interior A /\ boundary B interior A /\
exterior B
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
surfaces.
A simplex is the elementary geometric building block in a given
dimension:
- 0-simplex is a point (node)
- 1-simplex is a line segment (edge)
- 2-simplex is a triangle (face)
- etc.
A simplicial complex is a collection K of simplexes such that
- with every simplex, all its bounding simplexes are contained in
K
- the intersection of two simplexes is either empty or a simplex
in K.
A closed surface is a simplicial complex partitioning the
plane.
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 |
Literature ]
Last updated on July 26, 1996.
[ Max
J. Egenhofer | NCGIA
Maine | Department of
Spatial Information Science and Engineering ]