Geometric Algorithms in GIS

GIS Software

Dr. M. Gavrilova

GIS System

What is a GIS system?

A system containing spatially referenced A system containing spatially referenced data that can be analyzed and converted to data that can be analyzed and converted to

new information for a specific purpose.new information for a specific purpose.

GIS SoftwareGIS software:

ArcInfoGeoSQLSmallWorld

Statistical analysis software:S-Plus Extension for ArcView GIS 3.2SpaceStat (TerraSeer)Grass GIS

GIS visualization software:ArcView, ArcGIS, Visual_Data, GIS Viewer, etc.

Extensions to Databases

Oracle Spatial

PostgresSQL

SDE

GIS Systems Overview

Traditional Relational Database

GIS Systems Overview

Spatial Processing

GIS Systems Overview

What is the difference? …

Representation

Database Query Table

GIS Query

ArcInfo

Designed by ESRL in 1969Features:

Querying relational databasesTool for statistical analysisSpecific display tools (scale change or zooming)Support for graphical formats

Features

Data collectionData representationData storageData analysis and computationConcurrency and recoveryQuery facility and optimization

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)

ArcInfo

Surface

Surface is represented as TIN or GRIDGrid has a reference to a Value Attribute TableTIN: List of Triangles, List of Associated Nodes, List of Neighboring Triangles

ObjectsObjects in ArcInfo:

PointArcPolygon

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.

ArcInfo

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

ArcView GIS

2 modules:ArcView Spatial AnalystArcView Network Analyst

Requests to the DB are written in a query-type language.

ArcView GIS

Designed by ESRIDesktop GISOriented toward data integration Used for analyzing maps – 2D

GEO/SQL Overview

Back End CapabilityLink to relational (SQL) databases or filesData modelingBase MappingSecurity and Integrity

Front End CapabilityInteractive, visual analytical performanceManipulation of data setsPresentation and output

GEO/SQL Features

Relational Database (SQL) Querying

Libraries,Images

Embedded, Linked, SQL Dictionaries

Data Formats

Raster and Vector Support

Format Handlers (loadable drivers)

GEO/SQL Features

Fixing Errors in Digitized Data

GEO/SQL Features

Storage StructuresSpatial Objects (Points, Lines, Polygons)

GEO/SQL Features

Storage StructuresNon spatial properties

Derived Objects and Geo-Coding

Line Geo-CodingLabels & Attributes

GEO/SQL Features

Spatial AnalysisBuffering

Generalization

Polygon DissolveLine Generalization

Overlay

Polygon Dissolve

GEO/SQL Features

Data Themes1. Definition2. Data Source3. Geographic Search Criterion4. Query Condition5. Graphical Style6. Labels7. Column List8. Data

GEO/SQL Features

Page Layout and Printing

Smallworld

Licensed by GE Power SystemsSmaller GIS – business solutionOO development language (Magik)Raster/vector graphicsHas intranet/internet network capabilityHigh-level query language

Extensions for querying spatial DB

OraclePostgre SQLSDE

Oracle

Index-aware operations:Contains, covers, inside, overlaps, touch, disjoint

Other:Union, difference, intersection, area, length

Oracle Spatial

Spatial Attribute Types:point, line string or polygon

Spatial Operations, Spatial Indexing

Postgre SQL

Open sourceOperations:

Triangulate, scale, polymorphic (works on different types of geometric objects)

No topological operations (adjacency is not implemented)No overlay operation

Spatial Database Engine SDEGIS CAD Custom

application3D visualization

SDE server

Data files

ArcInfo filesDBMS (spatial,CAD, graphics)

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

Statistical GIS softwareTypical GIS software does not perform the following functions satisfactory:

RobustnessReliabilityCompletenessCapability and featuresSpecific Spatial techniques for Autocorrelation and analysisSpatial hypothesis testing

S-plus featuresBasic Statistics

Summary statistics CrosstabulationsHypothesis tests• Probabilities, quantiles, and densitiesRandom number generation Bootstrap and jackknife estimation Power and Sample Size

RegressionBasic linear regression Polynomial regression Robust regression Constrained regression Logistic regression Generalized linear models Robust MM Regression Linear regression with correlated errors

Nonlinear regression and minimizationNonlinear regression with correlated errors Minimum-sum optimization for maximum likelihood and generic optimization Constrained nonlinear regression Nonlinear mixed effects

Among Other functionsMixed Effect ModelsClassificationsNonparametric regressionsSmoothing and interpolationMultivariate analysisCluster AnalysisQuality Control

S-plus graphical featuresGraphical 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 barplotsTime series plots Quality control charts Statistical model summaries and diagnostics

Advanced Data VisualizationEasy 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

S-plusWith 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 ArcViewthemes or S-PLUS data sets

SpaceStatSpaceStat:

http://www.terraseer.com/Spacestat.htmlDespite 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.

GrassGISGrassGIS:

http://grass.itc.it/statsgrass/This is an open sourse, 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 small subset of S-plus.