1. GIS Applications in Civil Engineering
Note #3 Maps as Numbers
GIS Data Structures
Xudong Jia, Ph.D., P.E.
January, 2011

2. Summary of the First Two Lectures
How do we describe geographical features?
by recognizing two types of data:
Spatial data which describes location (where)
Attribute data which specifies characteristics at that location (what, how much, and when)
How do we represent these digitally in a GIS?
by grouping into layers based on similar characteristics (e.g hydrography, elevation, water lines, sewer lines, grocery sales) and using either:
vector data model (coverage in ARC/INFO, shapefile in ArcView)
raster data model (GRID or Image in ARC/INFO & ArcView)
by selecting appropriate data properties for each layer with respect to:
projection, scale, accuracy, and resolution
How do we incorporate into a computer application system?
by using a relational Data Base Management System (DBMS)

3. Maps as Numbers Maps are represented by using numbers
Binary and Decimal System. How to convert a binary value to a decimal number or vice versa.
Hexadecimal number 00 to FF in one byte
More examples on binary and decimal conversions.

4. Maps as Numbers Two data models for maps : Vector and Raster
One data model for attributes: flat files
Raster: It is a model that contains a grid. Each grid cell is a map unit used to represent a pixel.
Cell size determines the resolution of the data.
The grid has an extent.
Each grid is owned by one feature
Features cannot be perfectly fitted into cells.
Cell’s bit depth provides a range to describe possible feature values.

5. Maps as Numbers Benefits of using Raster Model Easy to understand
Capable of rapid retrieval and analysis
Easy to draw on the screen and on computer devices which display pixels.

6. Maps as Numbers Vector Model
Composed of points that are provided by exact coordinates
Accuracy
Efficient at storing features
Able to store topological attributes for features.

7. Maps as Numbers Structuring Attributes
A flat file as show on Page 84 of the Textbook
Relational database table
A distributed database through server extensions, database engines, and data warehouse.
Data dictionary or metadata, the list of all the attributes along with all their characteristics save as a separte file or as a header of the file

8. Maps as Numbers Structuring Maps Vector Data Structures
Cartographic Spaghetti

9. Maps as Numbers
Structuring Maps
Vector Data Structures
Arc/Node Model

10. Maps as Numbers Structuring Maps Vector Data Structures
Topological Arc/Node Model
(see Page 88)

11. Maps as Numbers Structuring Maps Vector Data Structures
Triangulated Irregular Network (TIN Model)

12. TIN: Triangulated Irregular Network Surface
Maps as Numbers
TIN: Triangulated Irregular Network Surface A B C D 6 1 2 3 4 5 E F G H
Elevation points (nodes) chosen based on relief complexity, and then their 3-D location (x,y,z) determined.
Points
Elevation points connected to form a set of triangular polygons; these then represented in a vector structure.
Polygons
Attribute Info. Database
Attribute data associated via relational DBMS (e.g. slope, aspect, soils, etc.)
Advantages over raster:
fewer points
captures discontinuities (e.g ridges)
slope and aspect easily recorded
Disadvans.: Relating to other polygons for map overlay is compute intensive (many polygons)

13. Maps as Numbers Raster Data Structure
Challenging issues on mixed pixel problem,
redundant or missing data and
large storage requirement

14. Maps as Numbers Full Matrix--162 bytes 111111122222222223
Run Length Encoding
Full Matrix--162 bytes
1,7,2,17,3,18
1,7,2,16,3,18
1,7,2,15,3,18
1,6,2,14,3,18
1,5,3,18
1,3,3,18
Run Length (row)--44 bytes
This is a “lossless” compression, as opposed to “lossy,” since the original data can be exactly reproduced.
Now, GIS packages generally rely on commercial compression routines. Pkzip is the most common, general purpose routine. MrSid (from Lizard Technology)and ECW (from ER Mapper) are used for images. All these essentially use the same concept. Occasionally, data is still delivered to you in run-length compression, especially in remote sensing applications.

15. Maps as Numbers
R-Tree Encoding
See Page 92

16. Maps as Numbers Quad Tree Encoding See Page 92
Essentially involves compression applied to both row and column.
sides of square grid divided evenly on a recursive basis
length decreases by half
# of areas increases fourfold
area decreases by one fourth
Resample by combining (e.g. average) the four cell values
although storage increases if save all samples, can save processing costs if some operations don’t need high resolution
for nominal or binary data can save storage by using maximum block representation
all blocks with same value at any one level in tree can be stored as single value
3.25 3 4
3.5
2.5 2 4 5 3 4 2 4 4 4 4 1 4 2 4 3 2
store this quadrant
as single 1 1 1 1
store this quadrant
as single zero

17. Maps as Numbers
Image Pyramid and Quad Encoding
See Page 92

18. Maps as Numbers
Why Topological Matters

19. Maps as Numbers
Why Topological Matters

20. Maps as Numbers
Why Topological Matters

21. Maps as Numbers
Why Topological Matters

22. Maps as Numbers Why Topological Matters Terms: Slivers Spike
Unsnapped Nodes
Un-ended lines
Why Topological Matters

23. Maps as Numbers Why Topological Matters Terms: Slivers Spike
Unsnapped Nodes
Un-ended lines
Why Topological Matters

24. Maps as Numbers Formats for GIS Data Vector Data Formats:
HPGL – Page Description Language
PostScript - Page Description Language
PDF – Portable Documen Format , GeoPDF
AutoCAD DXF format
DIME/TIGER Format
DLG Format
KML
GML
XML

25. Maps as Numbers
Formats for GIS Data
DIME/TIGER Data Model

26. Maps as Numbers
Formats for GIS Data
DIME/TIGER Data Model (Page 100)

27. Maps as Numbers
Formats for GIS Data
DLG Model

28. Maps as Numbers Raster Data Formats TIF GIF JPEF GEOTIP PNG
Encapsulated PostScript
DEM (1:24,000 and 1:100,000)

29. Maps as Numbers Exchange Data and Data Standards
Data exchanges between Raster and Vector
Data exchanges among different GIS platforms
Data exchanges between different systsems
SDTS (Spatial Data Transfer Standards)
Open Geospatial Consortium
Open GIS Specifications