UNIT 42 - TEMPORAL AND THREE-DIMENSIONAL REPRESENTATIONS
Compiled with assistance from John H. Ganter, University of
Pennsylvania
A. INTRODUCTION
- although the vast majority of GISs currently work only in
two dimensions, across the plane, certain applications
require the addition of other dimensions, namely time or
elevation/depth
- most geological applications require a consideration
of attributes in the vertical dimension as well as
the horizontal ones
- temporal variations are important in many economic
and social studies
- oceanographic and meteorological models need to
consider variations both in the vertical and the
temporal dimensions
- this unit will look briefly at how these additional
dimensions can be incorporated into GISs
B. VERTICAL DIMENSION ("3D")
- there are two very different ways of looking at
representations of the vertical dimension (normally
called the third dimension) in GIS
- the most commonly recognized is a data structure where a
z value (normally elevation) is recorded as an attribute
for each data point (x,y)
- these z values can be used in a perspective plot to
create the appearance of 3 dimensions
- this is not true three dimensional representation
and is often referred to as "2 1/2 dimensions"
overhead - Perspective plot - Tiefort Mountains, CA, same
data used for graphics in Unit 11
- these 2 1/2D plots are an attractive way of displaying
topography and other continuous surfaces from DEMs or
TINs
- perspective plots can be computed from any
viewpoint
- additional layers can be "draped" over the surface
using color
- "artist's impressions" can be created by converting
classes (e.g. of land cover) to simulated trees,
etc.
- with powerful computers, it is possible to animate
2 1/2D plots to create simulations of flying over
topography
- "LA the Movie" was created by Jet Propulsion
Lab, Pasadena CA, by draping a Landsat scene
over a DEM of LA, then simulating the view from
a moving aircraft
- true three dimensional representations store data in
structures that reference locations in 3D space (x,y,z)
- here z is not an attribute but an element of the
location of the point
- this permits data to be recorded at several points
with equal x and y coordinates, e.g., soundings in
the ocean or atmosphere, geologic logs of wells
- true 3D representations allow:
- visualization of volumes
- is difficult to understand volumes when they
are represented by several orthographic
projections
- modeling of volumes
- algorithms for spatial analysis of volumes are
simpler if the data is in a volumetric form
Uses of 3D representations
- 3D representations of spatial information have several
important applications:
- designing major developments such as mines,
quarries, dams and reservoirs
- geologic exploration
- scientific explanation of three dimensional
processes such as ocean currents
- here don't necessarily know what is being
sought
- therefore, the structure of the representation
can constrain the types of analyses that are
performed and what is found
C. CHARACTER OF THE PHENOMENON
- a major determinant of the type of representation used is
the 'phenomenon-structure' itself
- three dimensional phenomena have several characteristics:
Distribution
1. Continuous
- present in some quantity in all places
- e.g. land, stratigraphic or piezometric surface
- similar to 2D raster representations
2. Discrete
- distinct objects which occupy specific locations
- e.g. lithology, ore bodies, tunnels, caves
- similar to 2D vector objects
Topological complexity
- how the object is composed
- this has a major effect on the data structure used
overhead - Topological complexity
1. Compound (One class)
- composed of identical smaller objects
- well casing or well log
- ore body composed of smaller bodies
2. Mixed (Multiple classes)
- composed of smaller, dissimilar objects
- mine composed of shafts, adits, etc. which are
hierarchically-arranged either adjacent to, or
wholly within each other
3. Interpenetrating (Multiple phenomena)
- mixed, but objects may share subsets of each other's
volumes
- large-scale structural geology
- karst features intersecting with the water
table and geologic structures
Geometric complexity
- degree to which the representation is irregular or
convoluted
- involves questions of:
Accuracy
- how much is required?
- design applications (e.g. tunneling) - must be
highly accurate
- prospecting or science applications - general
relations may be more important
Precision
- resolution of measurement and detail of analysis
- often depends on scale of examination and nature of
phenomenon
- may have to filter and generalize to reduce storage
and computation burden
D. METHODS OF REPRESENTATION
- specific approach taken is a function of:
- user's needs and capabilities
- character, distribution and complexity of phenomenon
- characteristics of the data available, or the means
to collect it
2 1/2 dimensions
1. Single-valued surfaces
- single z (elevation) value for each coordinate pair
- usually continuous distributions
- topologic complexity is low
- geometric complexity can be high
- defines a surface with no thickness
- usually displayed with isolines
- geometrically 3-D, but topologically 2-D
- suited to visualization and some modeling
- available in many mapping and statistical packages
2. Multi-valued surfaces and volumes
- more than one z-value for each x,y pair
- usually continuous distributions
- topological complexity is low
- geometric complexity can be high
- can be displayed with isolines
- may become difficult to comprehend
- often subjected to geostatistical analysis in
prospecting and scientific research
- not as widely available in turnkey systems
True three dimensional representations
1. Boundary representations (B-reps)
overhead - B-Rep of a Cave Passage
- objects are defined as polyhedra bounded by planes
or faces
- can be displayed with hidden line removal for
easier comprehension
- each object can be represented by a number of:
faces - flat planes, usually triangular (a
mixture of rectangles and hexagons on the
overhead)
edges - define the edges of the faces (3 per
triangular face)
points - define the ends of the edges (2 per
edge)
- suited to discrete objects
- topological complexity can be high
- geometric complexity can be high
- well suited to design, some exploration and
explanation applications
- widely available in CAD systems
- the TIN is a type of B-rep, constrained to be
single-valued (i.e. one value of z for every
x,y)
- requires a powerful user-interface to construct
combinatorially-complex objects
- each part of the B-rep (planes, edges, points)
must be carefully and consistently defined for
each application in order to maintain validity
- performance degrades rapidly with high geometric
complexity
2. Spatial occupancy enumeration (SOE)
overhead - SOE of a Mine/Quarry
- volume is divided into cubes or voxels
- can have on (full) or off (empty) status
- or, can have attribute values
- vertical resolution is often different (higher) from
horizontal resolution, e.g. modeling the atmosphere
- objects can be displayed as positive (casts) or
negative (molds)
- suited to discrete objects or continuous
distributions
- combinatorial complexity can be very high
- geometric complexity can be high, within limits
of voxel resolution
- suited to exploration and explanation applications,
also analytical operations in design
- some systems exist for mine modeling, also
medical applications
- usually produced by converting from B-reps (similar
to converting vectors to rasters in 2D)
- properties like mass, volume and surface area are
quickly computed as Boolean operations or voxel
counts
- these can be indexed using octtrees (also octrees)
overhead - Octree
- is an extension of the quadtree concept to 3
dimensions
- cells are numbered by starting on one level and
using the same pattern as a quadtree, then
moving up a level and continuing with the same
pattern but numbering from 4 to 7
Summary
- these 3D representations are relatively new, so there is
little collective experience on how to implement them in
the earth sciences and engineering
- it may be easiest to utilize technology developed in
other fields (mechanical engineering, medicine) and adapt
to needs
- however, the needs of medical imaging are different
from earth science
- medical imaging technology is not designed for
modelling, it does not need analytical tools
for abstraction and interpretation that earth
science applications do
- medical imaging is time dependent (it is
usually necessary to track moving objects
between one 3D image and the next) while many
earth science applications do not require this
E. TIME DEPENDENCE
- time dependence adds a third dimension to spatial data,
just as the vertical dimension does
- Hagerstrand (1970) has used the vertical dimension
to visualize movement in human systems - movements
in the plane become trajectories in three dimensions
suggested overhead - Time dependence as a third dimension
based on Hagerstrand model (not supplied, see for example
Haggett, P., A.D. Cliff, A. Frey, 1977, Locational
Models, Edward Arnold, London, p. 16)
- computer science deals with time dependence of records in
databases
- records may be valid only for limited times
- the geographical cases are more complex - objects may
have limited existence, but may also move, change shape,
and change attributes
- similarly to the 3D case, the set of database models for
time dependent data has not been fully developed
Possible models
1. boundaries of reporting zones change through time
2. attributes of objects change through time
- define a limited number of time "slices", and
store the attributes as separate tables for each
time slice
- if attributes are needed between time slices,
interpolate
3. shapes of objects change through time
- define time slices, and store the objects at each
slice
- may be difficult to identify objects from one
time slice to the next because objects may
coalesce or split - e.g. kelp beds in the ocean
off the coast of California
- may be easier to avoid identifying objects, and
store classified but unrelated rasters at each
time - equivalent to the SOE or voxel solution
to 3D data
- alternatively, use a 3D space with the vertical
dimension as time, populated by 3D objects, e.g. the
lines in Hagerstrand's diagrams - equivalent to B-
reps
- attach attributes to these objects
- if the attributes change through time, we have
a problem similar to that of continuously
varying attributes on transportation networks
Summary
- the main issue is the extent to which objects should be
identified - either in 2 or 3D
- solutions vary from one extreme of no objects to the
other of fully 3D objects:
- no objects at all - voxels
- e.g. remotely sensed images
- objects at each time slice, but unrelated from one
time to another - layers
- objects at each time slice, related or tracked from
one time to another - related layers
- objects defined continuously in the time dimension -
3D objects
- e.g. individual space-time travel behavior
REFERENCES
Bouille, F. 1976. "A Model of Scientific Data Bank and Its
Applications to Geological Data," Computers and
Geosciences 2: 279-291.
Carter, J.R. 1988. "Digital Representations of Topographic
Surfaces: An Overview," in American Congress on Surveying
and Mapping and American Society for Photogrammetry and
Remote Sensing, Technical Papers 5:54-60.
Ganter, J.H. 1989. "A Comparison of Representations for
Complex Earth Volumes," Auto-Carto 9: Proceedings of the
Ninth International Symposium on Computer-Assisted
Cartography, Baltimore, MD.
Hagerstrand, T., 1970. "What about people in Regional
Science?" Papers, Regional Science Association 24:7-21.
Discusses the concept of space-time prisms in human
spatial behavior.
Kavouras, M. and S. Masry, 1987. "An Information System for
Geosciences: Design Considerations," Auto-Carto 8:
Proceedings of the Eighth International Symposium on
Computer-Assisted Cartography, ASPRS/ACSM, Falls Church,
VA, pp. 282-291.
Langran, G., 1989. "A review of temporal database research
and its use in GIS applications," International Journal
of Geographical Information Systems 3(3):215-32. Can
research on time dependence in databases help in
representing the effects of time in GIS data?
Langran, G. and N.R. Chrisman, 1988. "A framework for
temporal geographic information," Cartographica 25(3):1-
14. Discusses models for representing temporal change in
GIS.
Mark, D.M. and J.A. Cebrian, 1986. "Oct-trees: A Useful Data-
Structure for the Processing of Topographic and Sub-
Surface Data," ACSM/ASPRS Technical Papers 1:104-113.
Raper, Jonathan. Three Dimensional Applications in GIS,
Taylor and Francis, New York. A collection of papers on
the developing technology of 3D GIS.
Requicha, A.A.G. 1980. "Representations for Rigid Solids:
Theory, Methods and Systems," ACM Computing Surveys
12:437-464.
DISCUSSION AND EXAM QUESTIONS
1. You are directed to build a 3-D representation for (a) a
civil engineer; (b) a petroleum geologist; (c) a
hydrogeologist; (d) a meteorologist. What kinds of
questions might you ask each specialist about their job and
what they want from the representation?
2. How do the distributions considered by each of the
individuals (above) compare?
3. What would be the advantages and limitations of surface
representations, B-reps and SOE in different disciplines and
applications?
4. Many people have assumed that the problems of moving from
2D to 3D in GIS are comparable to those of moving from 2D to
time-dependent 2D. Do you agree?
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Last Updated: August 30, 1997.