URBDP 422 Urban and Regional Geo-Spatial Analysis

Lecture 2: Spatial Data Models and Structures

Lab Exercise 2: Topology

January 9, 2014

Raster Representation

Spatial Data Structures

0 1 2 3 4 5 6 7 8 90 R T1 R T2 H R3 R4 R R5 R6 R T T H7 R T T8 R9 R

Vector Representation

line

polygon

point

Vector data model–location referenced by x,y coordinates, which can be linked to

form lines and polygons–attributes referenced through unique ID number to tables–best for features with discrete boundaries

Raster data model–location is referenced by a grid cell in a rectangular array (matrix)–attribute is represented as a single value for that cell–best for continuous features

Spatial Data Structures

Raster Data

Raster Vs. Vector Structures

ADVANTAGES DISADVANTAGES

RASTER - Data input - Data storage- Modelling - Not Topological- Overlays - Accuracy- Continuous surface - Distortion

VECTOR - Efficient storage - Complex to- Discrete features perform overlay and- Topology modeling operations- Greater precision

Geographical Data in the Computer

User’sperceivedphenomenonstructure

GISrepresentationof phenomenonstructure

Databasestructure

HardwareStructure

A B C D

Principles of GISFrom Reality to Data

Features, Objects, and RelationshipsOject-Oriented Model Definitions in ArcGis

Feature A geographic representation of a real-world object on a map(such as point, line, or polygon).

Feature class A collection of geographic features with the same geometry type (such as point, line, or polygon), the same attributes, and the same spatial reference

Object Nonspatial data representation of real world phenomena and objects

Object class A collection of objects in the geodatabase that have the same behavior and the same set of attributes.

Relationship An association or link between two objects in a geodatabase. Relationships can exist between spatial objects (features in feature classes), between nonspatial objects (rows in a table), or between spatial and nonspatial objects.

Relationship classes Relationship classes define relationships between objects in the geodatabase.These relationships can be simple one-to-one relationships or more complex one-to-many or many-to-many.

Object-oriented Data Bases

Feature Object

Relationship

Topology

Topology is the term that describes the spatial relationships between points, lines and areas.

Technically it is a geometrical term, which describes the properties of an object that are unaffected by continuos distortion. You can distort a square to a parallelogram, but all four sides still connect at the corners.

If a map is distorted, some of its properties change: - distances

- angles - relative proximity

Other properties remain constant, including: - adjacencies - most other relationships, such as "is

contained in", "crosses", etc. - types of spatial objects - areas remain

areas, lines remain lines, points remain points.

Topological properties are those which remain unchanged after distortion

ArcGIS Topology

Source: ESRI 2004

How Is Topology Implemented in ArcGIS?

Topology is implemented as a set of integrity rules that define the behavior of spatially related geographic features and feature classes.

Topology rules, when applied to geographic features or feature classes in a geodatabase, enable GIS users to model such spatial relationships.

For example:-Containment (do parcel polygons overlap?)-Connectivity (are all of road lines connected?) -Adjacency (are there gaps between parcel polygons?).

Topology is also used to manage the integrity of spatial databases (i.e., coincidence between different features)

Source: ESRI 2004

Topology is used to

o Integrate feature geometry

o Validate feature geometry

o Define relationships between features

Topology in ArcGIS

Topological RelationshipsTopology is one of the most powerful information maintained in a spatial database. It is defined as the mathematics of connectivity or adjacency of points or lines that determines spatial relationships in a GIS.

The topological data structure logically determines exactly how and where points and lines connect on a map by means of nodes (topological junctions).

Topology—the spatial relationships between geographic features—is fundamental to ensuring data quality.

The computer stores this information in various tables of the database structure. A GIS manipulates, analyzes, and uses topological data in determining data relationships.

The importance of Topology

Explicit representation of real world Efficient data input and storage Efficient data retrieval and query Construction of complex data object Detection of data error Maintainance of data integrity

Topology Rules• Define valid spatial relationships

– Between features on a single feature class – Between feature classes

• 25 rules available

Examples of topology

Adjacency Connectivity Containment Point-in-Polygon Polygon-containing-Feature Intersect Dissolve Similar Digital Terrain Analysis

Parcel Contained

in Block

Shoreline land adjacent

to water

Roads connects at intersection

Examples of topology

Points Topological Rules

Polygons Topological Rules

Polygons and Lines Topological Rules

Lines Topological Rules

Lines Topological Rules

SIX New Topological Rules

http://help.arcgis.com/en/arcgisdesktop/10.0/help

Constructing TopologyRules

Every topology in the geodatabase is associated with a set of topology rules. Users define topology integrity by adding and removing rules from this set.

Cluster Tolerance The cluster tolerance is a distance range in which all

vertices and boundaries are considered identical or coincident and are snapped together during a Validate Topology process.

RanksRanks are defined at a feature class level, and they control how much the features in that class can potentially move in relation to features in other

classes when a topology is validated.

Topology Process

Create Create topologytopologyCreate Create

topologytopology

Cluster Cluster tolerancetoleranceCluster Cluster

tolerancetolerance

RanksRanksRanksRanks

RulesRules

DirtyDirtyareasareasDirtyDirtyareasareas

FixFixerrorserrors

FixFixerrorserrors

ErrorsErrorsErrorsErrors

ExceptionExceptionsExceptionExceptions

MakeMakeexceptionexception

MakeMakeexceptionexception

ValidateValidatetopologytopologyValidateValidatetopologytopology

EditEditfeaturesfeatures

EditEditfeaturesfeatures

RulesRulesRulesRules

CleanClean

TopologyTopology

CleanClean

TopologyTopology

ESRI-Denver/AGIC 2005ESRI-Denver/AGIC 2005

Validating Topology

Validate edited features using set topology rules

Evaluate rules/tolerance and generates error notifications

Snaps vertices using set cluster tolerance and ranks

Errors and Exceptions

Topology defines and validate rules. Rules are defined as part of the schema definition for a topology. When “dirty areas” in a topology are examined with Validate Topology, an error is generated for each instance of a topology rule that is determined to be invalid.

For example, if a rule is set that states buildings cannot overlap with easements, then an error will be generated for each building feature that overlaps an easement feature.

Exceptions

When resolving errors, the user always has the option of marking an individual error or a collection of errors as exceptions. There are instances when the occurrence of a defined error may actually be acceptable.

For example, if a building was actually a shopping mall, the one building overlapping several parcels would not be an error but rather an exception to the rule.

Once an error has been marked as an exception, it remains as such until it is reset back to an error. Running validate topology will not generate an error for an instance that has been marked as an exception.

Correcting Errors in the Topology

When an error is discovered during the validate topology operation, the user has three options:

- Correct the error using the Fix Topology Error tool or some other method.

- Leave the error unresolved.

- Mark the error as an exception.

The Fix Topology Error tool offers a variety of methods for resolving an error depending on the error and the feature type.

Basic Cartographic Concepts

• Scale• Resolution • Accuracy• Coordinate system• Projection

The map scale is the ratio between a distance on the map to that distance on the ground. Normally, it is expressed as representative fraction e.g. 1 : 10,000. Many other properties of the map are dependent on the map's scale.

Map Scale

Scale

– ratio of distance on a map, to the equivalent distance on the earth's surface.

• Large scale -->large detail, small area covered (1”=200’ or 1:2,400)

• Small scale -->small detail, large area (1:250,000)

– scale representation

• representative fraction (RF) 1: 63,360

• scale bar:

Miles

0 1 2

Resolution• the size of the smallest feature which can be

recognized or displayed.• related to, but not the same as, scale.• for vector data it is the size of the smallest polygon• for raster data it is the size of the pixel

– e.g. for NTGISC digital orthos is 1.6ft (half meter)• raster data can be resampled by combining adjacent

cells; this decreases resolution but saves storage

The map accuracy refers to how well it represents the spatial locations of map features.

Quantitative Accuracy • positional (horizontal) accuracy: distance of a feature in the GIS from true location on the ground (each measured with respect to same grid or graticule)• vertical accuracy: difference from true height

Qualitative Accuracy (validity)

Completeness (reliability)The extent to which repeated observations on the map produces consistent results.

Map Accuracy

Measurement of Accuracy

Usually measured by root mean square error:

the square root of the average squared errors

The rmse tells us how far points are from their true location, on average.

e12 + e2

2 + e32 +...+ en

2

n-1rmse =

where ei is the distance between the true location of point i

on the ground, and its location represented in the GIS.

ArcGIS uses a geographic data model that represents spatial information as objects, features, raster, and other data types. It integrates two GIS data models, the traditional relational data base model and an object-oriented relational model called a geodatabase.

The idea of "object-oriented" database is to organize information into the sorts of “objects" that people recognize. It brings a physical model closer to its logical model. The users work with objects of interests such as buildings, roads, and lakes.

Object-oriented Relational Data Bases

Vector Data Structure