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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