2

Multi-Dimensional GIS

• Have examined points, lines and polygons as components of a 2 dimensional (2D) map space

• Is this representation adequate?

• Real World is 4D comprising:

• Length (x), Width (y), Height/Depth (z) and Time (t)

• A 2D representation may be difficult to visualise

(eg. rationalising human settlement with shape of the land surface)

• A 2D representation may require expert interpretation

(eg. reconstructing the landscape from contours)

• A 2D representation may not explain the situation

(eg. current distribution of retail outlets depends on the historical development of an area)

• Ideally a GIS should be able to take account of z and t

3

The Third Dimension

• Within GIS we are usually concerned with terrain modelling

• This model reflects a continuous variation of a z value over a two-dimensional surface (x and y)

• Just occasionally this may not represent a physical terrain, but a variable such as population density or temperature

• Techniques of analysis and visualisation

• Digital Elevation Model (DEM)

– The generic term used for a terrain model in the USA, because of the way the data is collected in that country.

• Digital Terrain Model (DTM)

– The generic term elsewhere. A DTM will often contain information beyond simply the height of the land, for example breaks of slope, aspect etc.

• The extent to which terrain modelling functionality is integrated into GIS varies

• For some applications a fully 3D representation may be required

• There are various mechanisms used to collect the 'z' values

4

Acquiring Elevation Data

• Ground survey using traditional surveying techniques (eg. levelling, total station)

• Global Positioning Systems (GPS)

– but the height (z) accuracy of GPS is relatively poor

• Stereoscopic sources:

– Photogrammetry (analogue, analytical, digital)

– Stereo satellite imagery (eg. SPOT)

• RADAR (eg. SRTM)

• LIDAR / Laser Altimetry (ground, air- or space-borne)

• SONAR (for bathymetry)

• Digitising maps or plans – Need more than just contours

– Spot-heights

• Existing Digital Data – Global databases (primarily sourced from USA)

– National databases

5

Lattice Structure (Altitude Matrices)

• Data values represented by the lattice intersections

• Lattice points can be regularly sampled using photogrammetric methods

• The classic USGS DEM

• But for irregularly sampled data interpolation is required

• Other shapes of lattice can be used (eg. triangular, hexagonal), and these may have advantages for some analyses, although are rarely implemented in commercial software

6

More on Lattices

• Problems with lattice structure:

– Fixed resolution gives rise to over-sampling in areas with little elevation change and under sampling elsewhere

– Large amounts of redundant data stored in areas of uniform terrain

– Exaggerated emphasis along lattice axes for certain derived results (eg. line of sight maps)

• Progressive sampling techniques (Makarovic, 1973)

– Use greater resolution lattice in areas of more complex relief

– Reduce lattice resolution is areas of unchanging / simpler relief, allowing less data to be stored

Makarovic, B., 1973, Progressive sampling methods for digital elevation models. ITC Journal, 3, 397-

416.

7

Grid Structure (Raster)

• Data values are allocated over the entire spatial extent of the cell

• Interpolation techniques must be used to build this structure with respect to height values

• Thus an issue if used as a primary data structure

• Used for the rapid production of slope and aspect maps

8

Triangulation Structure (Triangulated Irregular Network or TIN)

• Based on original data points, therefore accuracy is not lost through a process of interpolation

• Because the original data points are retained, complete flexibility of coverage is possible, with the ability to store more information in areas of complex relief

• The TIN structure was developed by Tom Poiker (See Peucker et. al., 1978)

• Triangulation is usually achieved using the Delaunay Triangulation algorithm

Peucker, T, R.J. Fowler, J.J. Little and D.M. Mark (1978) The triangulated irregular network.

Proceedings American Society of Photogrammetry: Digital Terrain Models (DTM) Symposium, St. Louis, Missouri May 9 - 11, 1978. (Falls Church, VA, American Congree on Surveying and Mapping and the American Society of Photogrammetry and Remote Sensing pp 516-540.

9

More on TINs

• Shapes other than triangles could be used, but triangles are simplest = most desirable

• TINs are attractive because it is simple and economical

• Fits well within vector GIS:

– Triangles = Polygons (with attributes of SLOPE, ASPECT and AREA)

– Composed of:

• Three Points (with attributes of HEIGHT)

• Three Edges (with attributes of SLOPE and DIRECTION)

• TINs represent sharply-changing fluvially-eroded landscapes better

• More rounded, glacially-eroded landscapes would be better represented by interpolation methods, which have a naturally smoothing effect.

• Triangles work best in areas with sharp breaks of slope (eg. along ridge lines, where the edges can be aligned along the break)

10

TIN Storage

• TINs can be stored either as triangles or points

• Storing by points is more compact

• Either maintains the topology of the network

• Peucker’s original structure was as points

• BOTH structures are required to deal with different applications (eg. slope analysis needs triangles, whereas contouring needs points)

• As long as efficient inter-conversion routines exist, either will do for primary storage

• Note that some systems (eg. ArcInfo) effectively store both

1. BY TRIANGLE 2. POINTS & NEIGHBOURS

11

Creating a TIN

• TINs are usually created from either: – dense arrays of points, captured regularly – contour lines

• Identifying significant points is critical to a compact and representative TIN

• Use one of the following algorithms:

• Fowler & Little (1979) Algorithm

Identifies peaks, pits, passes, ridge and channel points by comparing each point’s height with its neighbours. Complex algorithm; results vary between type of landscape; fine tuning required to work well

• Very Important Point (VIP) Algorithm

Performs a local significance test on each point in turn (as against F&L, which looks for major features of the terrain). Better where few surplus points are removed (because it is local) and less satisfactory on curved surfaces, rather than sharply changing relief

• Drop Heuristic

Heuristics operate by iterating to a “best” scenario. Each point is temporarily deleted, the effect of its loss measured and then restored. Once all points have been examined, the one with least effect is removed permanently. Can be time-consuming. Best solution is to allow algorithm to locate significant points which are not in the original data set; it may suggest better points on your air photo!

12

Delaunay Triangulation

• Selected points must be connected into triangles

• “Fat” triangles (with all angles close to 60o) is preferred. Ensures that any point within a triangle is as close as possible to a vertex, which are the accurate height values

• Several methods - Delaunay (1934:Fr) generally works well

• By definition: three points only form a Delaunay triangle if, and only if, the circle which passes through them contains no other points

• Alternative definition involves the creation of thiessen polygons (dual of delaunay), by connecting each point to its nearest neighbour. The vertices are permanently connected if their theissen polygons share an edge

• The term convex hull is applied to the smallest polygon which can contain all of the vertices within the Delaunay network

• Build the network by either:

• Starting at the convex hull and work inwards

• Start at the two closest points (which, by definition, must be linked) and work outwards

• Problems: triangles are not hierarchical (c.f. morton encoding). Cannot be aggregated, and if divided they are no longer “fat”

DELAUNAY, B. (1934) Sur la sphere vide. Bulletin of the Academy of Sciences of the USSR, Classe des Science Mathematiques et. Naturelles (8) 793-800

13

Delaunay Triangulation Demo

• http://donar.umiacs.umd.edu/quadtree/points/ delaunay.html

• Any questions abt these triangles?

14

Radial Sweep Triangulation

• Alternative to Delaunay Triangulation

• After Mirante & Weingarten (1982)

• The centroid of the data is selected as the starting point

• From this point, the bearing and distance of all other points are calculated

• These records are sorted by bearing

• A radiating line to each point is established

• Long, thin triangles are formed by linking the current point to the previous point

• This process sweeps outwards to the convex hull

• The concavities which have been formed around the convex hull are next filled with triangles

• A back-filling operation is then undertaken to “fatten” the triangles, by comparing a triangle with its neighbours

• This process iterates until a further iteration produces no changes

• Although apparently complex, the algorithm uses “linked lists” which are computationally fast

• Mirante, A and N. Weingarten (1982). The radial sweep algorithm for constructing triangulated irregular networks. IEEE Computer Graphics and Applic, 2 (3) 11-21

15

Points and Contours as a DTM

• Other simple and common methods of displaying terrain data

• Spot Heights - irregular x,y locations with a height attached

• Contours (or isolines)

• Traditional methods for displaying the terrain on a 2D map

• Contours also represent a further data model for the storage of terrain data

• Digital representation usually obtained by digitising or scanning pre-existing maps

• Thus, probably the most common digital terrain representation

• Contours can be easily constructed by capturing spot-heights from, for example, photogrammetric sources

• Contours really also need spot-heights to give an effective model

– Contours are the 'mass points'

– Spot Heights should relate to 'critical' height values

16

Visualisation

• Use of computer graphics techniques enhanced for the portrayal of landscapes

• Viewing Conditions

– Viewing position and direction

– Lighting Model (time of day, time of year, latitude)

– Sky and Cloud Model

– Modifiers for Weather and Environmental Conditions

• Rendering Process

– Geometric transformation (map 3D onto 2D)

– Depth Cueing (convincing the brain that a 3D image is being viewed)

– Hidden Surface Removal (simplifying the model by accurately removing what cannot be seen)

– Texturing (perhaps adding a 'natural' landscape)

– Shading (continuous tones eg. Gourand or Phong shading; ray tracing)

– Shadowing

– Atmospheric Attenuation (loss of contrast and red light relative to blue)

– Anti-Aliasing (making diagonal lines look straight)

• Output – Screen

– Paper

– Frame Buffer (for animation / video)

• Can be a slow process

17

DTM Applications I

• Topographic Mapping

Describe landscape; storage of elevation data in national databases

• Civil Engineering

Highway engineering; earthworks; cut-and-fill; route planning

• Planning

Siting of buildings, dams, particularly locating "undesirable" objects (eg. Storage tanks, windmills), tourism planning

• Hydrographic / Bathymetric Mapping

Small-scale charts (SONAR / echo-sounder depths), off-shore structure planning (eg. Pipelines, oil-rigs)

• Mining Engineering

Mine / extraction planning, volumetrics.

• Geological / Geophysical Mapping

Modelling strata, terrain-strata intersections give outcrop locations mining. Sparse input data (eg. bore-holes). Modelling of faults.

• Geomorphology

Analysis and comparison of terrains / land-forms. Slope. Aspect erosion. Hydrology, run-off calculations

18

Terrain Model Examples

19

Terrain Model Examples

20

DTM Applications II

• Archaeology

Allocating finds to layers of occupation; under-water archaeology

• Simulation / Visualisation

Flight simulators (advanced terrain models), artificial landscapes (fractalisation); Computer graphics, animation.

Environmental impact studies, landscape design, architectural design. Context for thematic and satellite image data. Input variable and display medium for simulation models.

• Military Engineering [Lots of Money !]

Battlefield planning, aircraft mission planning, route planning. Weapons and missile guidance systems (eg. Cruise - terrain following).

Optimal siting of weapons / defence systems (eg. ground-to-air missile launchers, RADAR).

Siting communications (establishing areas liable to signal loss based on line-of-sight).

• Mobile telephony

Siting transmitters on the basis of line-of-sight. Network planning, creating reception maps.

21

From 2.5D to 3D

• 3D represents a continuous x,y,z volume

• Geography relates to the surface of the earth (from every x,y location there is only one z value)

• Within GIS we talk about this surface representation as 2.5D

• Do we actually need volume?

• Continuum is ‘x’ (fully 3D) is required for some applications:

- Geology - Archaeology

- Oceanography - Atmospheric Studies

- Environmental Modelling (soils, hydrology etc)

• Not strictly “Geographical” Information Systems?

• But the need is there, and we would have difficulty separating GIS from other Environmental Information Systems

• Full 3D may be required when GIS is used in:

- Geomorphology - Engineering - Architectural Modelling - Representation of, for example, multi-storey buildings, motorway interchanges

• Commercial GIS do not yet deal with 3D

22

Three Dimensional Structures

Extensions of 2D rasters (field-based):

• Voxels – a 3D pixel

• Oct-trees (Samet, 1990) – a 3D quadtree

Vector and Mathematical Models:

• Boundary Representations (b-reps); TINs are a form of b-rep

• Edge-based models

• 3D networks

• Non-Uniform Rational B-Spline (NURBS)

• Non-manifold 3D structures (eg. DeFloriani and Hui, 2003)

• Constructive Solid Modelling (based on combining simple geometries to build more complicated ones)

• Application Domains:

– Computer Graphics (non-topological)

– Computer Games (can be topological)

– CAD (usually topological, CSG and boundary representations)

– GIS

– Computational Geometry (usually highly specialised)

23

3D Example

• British Geological Survey: Bathymetry of the Firth of Forth

24

So Why Time?

• To locate any geographical entity precisely, we need x, y, z and t

• Because things change over time:

– Populations move

– Buildings are extended / demolished / rebuilt

– Crime patterns change

– Even landscapes erode !

• Time is not just history, it's important in geography too

• Geographical information is time as well as space-specific (Hägerstrand, 1970)

• Mapped data = theme + location + time (Sinton (1978) in Harvard Papers)

• Time is (particularly) important

– In LIS (cadastral applications)

– Facilities Management (AM/FM) applications

25

What might we want?

• Query on the basis of specific dates

• Query on the basis of arbitrary dates

• Periodic update

• Summarise changes over a defined period

OK, so how do we handle time...

AN ATTRIBUTE !

• Attach a time-stamp to operations and geographical elements (points, lines polygons)

• This allows, for example:

– all of the gas pipes laid before 1940 to be displayed

– patterns to be displayed in terms of earthquake epicentres

• But what else might be required?

Approaches to Handling Time

Pipe Id Type Diameter Condition Installed

100213 Cast Iron 25 cm OK 12-JAN-1945

100214 Cast Iron 25 cm Poor 01-MAY-1961

100215 Plastic 50 cm Good 10-APR-1987

100216 Plastic 25 cm Good 30-JAN-1994

100217 Lead 5 cm Poor 01-JAN-1900

100218 Copper 2 cm OK 31-MAR-1975

Locational Data

(ie. lines)

26

Handling Time in GIS

• There needs to be different approaches to the handling of time

• In the simplest case, time can be handled as "just another Attribute" stored in the RDBMS

• Time usually means "Date and Time", or just "Date"

• Store as a Creation or Modification Time (often both).

• This simplistic view assumes that the spatial location of the feature does not change

• Fine if data modelling process suggests it is appropriate; simple case therefore easily implemented. No special requirements for the GIS package.

• But is this adequate?

• Consider what happens if we wish to reconstruct the network as it looked in 1948. Mains will have been replaced since, how do we distinguish between extensions to the network and replacement mains?

• Requires further attributes...

27

Spatio-Temporal Problem

28

So what is the Problem?

• Where does the present go when it becomes the past? (Wittgenstein)

• There is a BIG problem in dealing with

time as an attribute...

THE PAST • You can deal with the latest state and

attach a time-stamp to each entity, but when you change that entity the record of any previous change is lost

• "Tell me how many gas mains were laid in 1949" will not take account of replaced mains

• How do you deal with changes to the geometry

– location in space of an object changes over time (pipes may be re-routed)

– changes in the topological relationships of the objects (new pipes may be connected to old ones at various points)

• You get one (or at best a few) snap-shots. Changes are over-written or discarded

• The semantics of change cannot be deciphered

29

Handling Changing Geometry

• It is possible to use attributes to record changing spatial location too

• Only the simplest cases however

• Consider the need to record changing parliamentary boundaries

Line Id Created Deleted

A 01-JAN-1923

B 01-MAY-1941 31-DEC-1961

C 01-JUN-1979 30-APR-1987

D 01-JAN-1994 31-DEC-1996

E 01-JAN-1997

F 31-MAR-1975

• While the linework is maintained, the required 'state' must be explicitly built, including the topology

• Have to be very careful how the line segments are digitised and recorded

• This simple model above doesn't necessarily take account of areas transferring from one constituency to another or overlapping lines

• Thus, this is not an ideal situation

A

B

C D E

Solid lines show the

geometries which

currently exist

F

30

1. Original road

2. Road rerouted (1931) 3. Widened to cope with increased traffic (1972)

Example requiring a Complex Spatio-Temporal

Representation

4. Carriageway replaced (1980)

5. Carriageway replaced (1981)

6. Gas pipe laid (1983)

7. Water pipe repair (1985)

8. Junction added to gas pipe (1987)

9. Carriageway replaced (1988)

10. Road narrowed as a traffic calming measure (1990)

11. Telephone trunking installed (1995)

12. Cable TV installed (1998)

13. Carriageway replaced (1999)

14. Gas pipe repair (1999)

15. Pedestrian Crossing installed (2001)

Road Maintenance Database

16. Pavements relaid (2001)

31

The Complexities of Time

32

Alternative Approaches to Handling Time

• Versioning is the ability to be able to restore the database to its state at any time in the past

• Versioning requires significant additions to the fundamental data model of any GIS

• Versioning is well developed in those GIS systems which have been influenced by CAD (eg. Smallworld, see Newell and Theriault's work)

• Versioning intervals may be discrete rather than arbitrary events

• Object models provide for a sophisticated handling of time (Spatio-Temporal Objects)

• Full temporality is therefore problematic

• No commercial GI systems handle this level of sophistication

33

Conclusions

• For many applications, GIS needs to be able to handle additional dimensions

• A "2.5D" representation solves some problems

• These layer-based approaches are widely implemented in the commercial software

• However some applications need a fully 3D representation

• There are no commercial GIS packages which allow a fully 3D representation

• Terrain data is widely available and has the advantage of being able to be captured by automated methods

• Time is also important

• The sophistication of representation is dependent on the requirements of the application

• Applications may require changes of attribute, location and / or topology to be recorded

• Most commercial GIS do not have a very sophisticated representation of time, but most applications probably don't require this

34

References

Worboys, M.F. and Duckham, M. (2004) GIS: A Computing Perspective, Second Edition, Boco Raton, CRC Press.

Langran, G. (1992) Time in Geographical Information Systems. London, Taylor and Francis.

Peuquet, D. (1999) Time in GIS and geographical databases. Chapter 8 in Longley, P, Goodchild, M.F., Maguire, D.J. and Rhind, D.W. Geographical Information Systems (2nd edition), Volume 1, 91-103. Chichester, Wiley.

Raper, J. (1989) Three Dimensional Applications in Geographical Information Systems. London, Taylor & Francis.

Raper, J. (2000) Multidimensional Geographic Information Science. London, Taylor & Francis.

Raper, J., and Kelk, B. (1989) Three-Dimensional GIS in GIS: Principles and Applications, (Volume I, chapter 20) edited by D. Maguire, M. Goodchild, and D. Rhind (Wiley).

Wachowicz, M. (1999) Object-Oriented Design for Temporal GIS. Taylor and Francis. London.

Wachowicz, M. and Healey, R.G. (1994) Towards temporality in GIS. Innovations in GIS, vol 1, 105-115. London, Taylor & Francis.

Gold, C (2005) Data structures for dynamic and multidimensional GIS Proceedings 4th ISPRS Workshop on Dynamic and Multi-dimensional GIS, pp 36-41

35

SpatMod: General Conclusions

• In this module, we have seen how:

– we might consider modelling the real world

– different forms of geographical data are stored

• We have looked at the principles of database management applied to both spatial and attribute data

– Seen how relational systems are now ubiquitous and that object-oriented systems have their place

– We have not looked at storing spatial data in dbms, that will come in Advanced Spatial Database Methods option

• We have examined: – rasters, quad-trees, morton encoding

– vectors, topology

– some three-dimensional structures

– the importance of time

• In the practicals, we have used SQL to query both attribute and spatial data

• You need to fill any gaps with your reading

"Yes raster is faster but raster is vaster and vector just seems more corrector" -- Dana Tomlin

36

Questionnaires

• I value the feedback you give in questionnaires, and regularly make changes because of it

• Questionnaires are now seen widely across the University, so please use them sensibly

• Please think about what you have enjoyed and what you have learned, as well as what you haven't enjoyed

• Don't pan the course just because you didn't like the format of the handouts!

• Re-read the Course Outline, there you will find:

– Learning Objectives

– Key References

• Assessments should be returned within three weeks

• Feedback is:

– Written

– Verbal

– And not just what I tell you

– Also about telling you what you should expect (so-called feed forward)