1. Geometric Algorithms in GIS
GIS Software
Dr. M. Gavrilova

2. GIS System What is a GIS system?
A system containing spatially referenced data that can be analyzed and converted to new information for a specific purpose.

3. GIS Software GIS software: ArcInfo GeoSQL SmallWorld
Statistical analysis software:
S-Plus Extension for ArcView GIS 3.2
SpaceStat (TerraSeer)
Grass GIS
GIS visualization software:
ArcView, ArcGIS, Visual_Data, GIS Viewer, etc.

4. Extensions to Databases
Oracle Spatial
PostgresSQL
SDE

5. GIS Systems Overview
Traditional Relational Database

6. GIS Systems Overview
Spatial Processing

7. GIS Systems Overview What is the difference? … Representation
Database Query Table
GIS Query

8. ArcInfo Designed by ESRL in 1969 Features:
Querying relational databases
Tool for statistical analysis
Specific display tools (scale change or zooming)
Support for graphical formats

9. Features Data collection Data representation Data storage
Data analysis and computation
Concurrency and recovery
Query facility and optimization

10. Diagram Graphical display and interaction with the user (ArcEdit)
Map editing tools (ArcPlot)
Network management (optimal paths) (Network)
Layers overlaying (Overlay)
Underlying data structure (ArcScan)

11. ArcInfo

12. Surface Surface is represented as TIN or GRID
Grid has a reference to a Value Attribute Table
TIN: List of Triangles, List of Associated Nodes, List of Neighboring Triangles

13. Objects Objects in ArcInfo:
Point
Arc
Polygon
More complex objects: graphs, sequence of arcs. Can be described in a specific language.
For instance, a route can be defined within a graph or a network, having specific attributes, a set of roads, a city block can also be represented.

14. ArcInfo
Map queries: after a Map is created, a different coverage (highways, regions, elevation, etc…)

15. ArcView GIS
2 modules:
ArcView Spatial Analyst
ArcView Network Analyst
Requests to the DB are written in a query- type language.

16. ArcView GIS Designed by ESRI Desktop GIS
Oriented toward data integration
Used for analyzing maps – 2D

17. GEO/SQL Overview Back End Capability Front End Capability
Link to relational (SQL) databases or files
Data modeling
Base Mapping
Security and Integrity
Front End Capability
Interactive, visual analytical performance
Manipulation of data sets
Presentation and output

18. GEO/SQL Features Relational Database (SQL) Querying Libraries,Images
Embedded, Linked, SQL Dictionaries
Data Formats
Raster and Vector Support
Format Handlers (loadable drivers)

19. GEO/SQL Features
Fixing Errors in Digitized Data

20. GEO/SQL Features Storage Structures
Spatial Objects (Points, Lines, Polygons)

21. GEO/SQL Features Storage Structures Non spatial properties
Derived Objects and Geo-Coding
Labels & Attributes
Line Geo-Coding

22. GEO/SQL Features Overlay Polygon Dissolve Spatial Analysis Buffering
Generalization
Overlay
Polygon Dissolve
Line Generalization
Polygon Dissolve

23. GEO/SQL Features Data Themes 1. Definition 2. Data Source
3. Geographic Search Criterion
4. Query Condition
5. Graphical Style
6. Labels
7. Column List
8. Data

24. GEO/SQL Features
Page Layout and Printing

25. Smallworld Licensed by GE Power Systems
Smaller GIS – business solution
OO development language (Magik)
Raster/vector graphics
Has intranet/internet network capability
High-level query language

26. Extensions for querying spatial DB
Oracle
Postgre SQL
SDE

27. Oracle Index-aware operations: Other:
Contains, covers, inside, overlaps, touch, disjoint
Other:
Union, difference, intersection, area, length

28. Oracle Spatial Spatial Attribute Types:
point, line string or polygon
Spatial Operations, Spatial Indexing

29. Postgre SQL Open source Operations:
Triangulate, scale, polymorphic (works on different types of geometric objects)
No topological operations (adjacency is not implemented)
No overlay operation

30. Spatial Database Engine SDE
GIS
CAD
3D visualization
Custom application
SDE server
Data files
DBMS (spatial, CAD, graphics)
ArcInfo files

31. Statistical GIS software
There are a number of Software that is being used for statistical analysis of spatial data.
S-Plus Extension for ArcView GIS 3.2
SpaceStat (TerraSeer)
Grass GIS

32. Statistical GIS software
Typical GIS software does not perform the following functions satisfactory:
Robustness
Reliability
Completeness
Capability and features
Specific Spatial techniques for Autocorrelation and analysis
Spatial hypothesis testing

33. S-plus features Nonlinear regression and minimization Basic Statistics
Nonlinear regression with correlated errors
Minimum-sum optimization for maximum likelihood and generic optimization
Constrained nonlinear regression
Nonlinear mixed effects
Among Other functions
Mixed Effect Models
Classifications
Nonparametric regressions
Smoothing and interpolation
Multivariate analysis
Cluster Analysis
Quality Control
Basic Statistics 
Summary statistics
Crosstabulations
Hypothesis tests•
Probabilities, quantiles, and densities
Random number generation
Bootstrap and jackknife estimation
Power and Sample Size
Regression
Basic linear regression
Polynomial regression
Robust regression
Constrained regression
Logistic regression
Generalized linear models
Robust MM Regression
Linear regression with correlated errors

34. S-plus graphical features
Graphical feature of the software
Time series charts: high-low-open- close and candlestick
Combined vertical/horizontal error bar charts
Multiple x-y pair plots
Nonlinear curve fitting plots
2-D plots: area plots, barplots, boxplots, density plots, dot charts, histograms, pie charts, and more
Scatterplot extensions: scatterplot matrices, linear fits, smooth fits, vary symbol color and size, text as points
3-D plots: point clouds, surface plots, contour plots, color image plots, 3-D barplots
Time series plots
Quality control charts
Statistical model summaries and diagnostics
Advanced Data Visualization 
Easy control of axis scales
Pop-up descriptions for data values
2-D and 3-D graph palettes for easy plotting
Multiple simultaneous 3-D rotation views
2-D projections in 3-D space
Multiple graphs per page with auto-formatting
Interactive 3-D view angle specification
Interactive observation identification
Multiple, user-defined color maps

35. S-plus
With the S+SpatialStats module:
Spatial autocorrelation a to assess global association for the values of a variable as a consequence of their location
Build neighbor weight matrices based on adjacency as well as distance between sampling units
Local spatial association can highlight clusters of data spatially correlated
Supports Moran's I index and Geary's c measures of correlation
Spatial regression to depict relationships between variables for each spatial unit, given a neighbor weight matrix
Model variables may be selected from ArcView themes or S-PLUS data sets

36. SpaceStat SpaceStat: http://www.terraseer.com/Spacestat.ht ml
Despite solid indications that spatial effects matter, much empirical work that uses spatial data still fails to take its distinctive characteristics into account. Until SpaceStat, there was no comprehensive software package that covered a reasonable range of techniques in spatial statistics and spatial econometrics.
SpaceStat provides tools for the creation of spatial weights matrices, exploratory spatial data analysis and spatial econometric analyses
SpaceStat was first released in 1991, and since then was updated 4 times. In 2002, SpaceStat joined forces with TerraSeer.
ClusterSeer 2 evaluates disease clusters and non-disease events such as crime or sales data. You can determine whether a cluster is significant, where it is located, and when it arose, providing insight into the origin, causes, and correlates of the event.
BoundarySeer is the premier product for the detection, description and analysis of geographic boundaries. It detects patterns in your data and then tests them statistically. Aside from edge detection, most GIS do not provide any boundary analysis techniques.

37. GrassGIS GrassGIS: http://grass.itc.it/statsgrass/
This is an open source, language-based software, which allows in-house development of spatial tools that can be used to manipulate data that must be represented by unconventional statistical systems.
All of its functionality is essentially a subset of S-plus.

38. Conclusion
Rich variety of software appeared in the last 10 years to deal with spatial data, statistical analysis, and database queries on complex geometric objects.
Future directions include web- based, server- based distributed database with hierarchical data representation and advanced visualization capabilities