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Geometric Algorithms in GIS

Geometric Algorithms in GIS. GIS Software Dr. M. Gavrilova. 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. GIS Software. GIS software: ArcInfo GeoSQL SmallWorld

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Geometric Algorithms in GIS

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  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 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 Line Geo-Coding Labels & Attributes

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

  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: • 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 Customapplication 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 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 Nonlinear regression and minimization • 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

  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.html • 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

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