Conceptual Modeling of Geographic Data

The problem for geographic databases.

We propose the following framework

Spatial Concepts

Informal conceptual tools to comprehend and structure our perception and cognition of reality.

Different geographic applications require different spatial concepts:

Geometric Data Models

Comprehensive sets of conceptual tools to describe and structure spatial information.
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
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.
Formal semantics are crucial for

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

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:
A simplicial complex is a collection K of simplexes such that
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 ]