Discussion Topology Reading - University of Colorado …€¦ · Topology Reading Discussion By:...

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Topology Reading Discussion By: Emily R. Shelton, Kc Meredith, Mark Pollich, Jeremy Belasquez, and Keeley Rideout.

Transcript of Discussion Topology Reading - University of Colorado …€¦ · Topology Reading Discussion By:...

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Topology Reading DiscussionBy: Emily R. Shelton, Kc Meredith, Mark Pollich, Jeremy Belasquez, and Keeley Rideout.

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What is Topology?“Topology is used to describe the relationship between objects.”

The term has many uses:

● Theory or model of features in space.● Allowing features to share geometry.● Set of editing tools for integrated

features.● Set of validation rules.● Navigating between features using their

topological relationships.

Wissler & Christopherson pg 1

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What is Topology?

http://www.esri.com/news/arcnews/summer02articles/arcgis-brings-topology.htmlhttp://warpinghistory.blogspot.com/2012_11_01_archive.html

There are topologies that affect the geometry of features based on the location of other features, sometimes in other feature classes.

Wissler & Christopherson pgs 4 & 5

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Wissler and Christopherson: Arc-Node ModelThe arc-node model manifests itself in GIS data as a specialised data structure that supports analysis functions. Elements of the structure include arcs (or lines) with it’s beginning and end points (nodes). Nodes are not independent from arcs, and arcs always begin and end with nodes.

http://www.geo.hunter.cuny.edu/aierulli/gis2/lectures/Lecture2/lecture2.html

Node

Wissler & Christopherson pg 2.

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Problem SetsAn example (from Wissler and Christopherson) would be if you are trying to get to a destination (way-finding). A network is an interconnected set of arcs representing possible paths for the movement of resources from one location to another.

This example uses a road network. There is a starting point (origin), and an ending point (destination).

The example uses blue for nodes, red for arcs (and their directions), and green polygons formed by the arcs. The software can analyse a series of trials to get from the origin to the destination by moving along the arcs, connected by nodes.

Wissler & Christopherson pgs 3 and 4.

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Problem SetsRelationships include (modeled by ESRI):● Connectivity: the attachment of objects● Contiguity: the identification of adjacent polygons by

recording the left and right polygon of each arc.● Area Definition: a closed area defined by a boundary.

Wissler & Christopherson pg 4

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Other UsesTopology can be grouped into two broad areas:-Support spatial analyses: can include using connectivity for network analysis, area definition to determine containment, and contiguity for neighborhood analysis. -Support database development: knowledge of topological conditions in data can be used to discover structural problems with the feature database. It can also be used to automate feature creation and ensure feature integration. Wissler & Christopherson pg 4

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Topology in the GeodatabaseIn ArcGIS, the topology is maintained on top of the geodatabase. Topology is built on the data structure of the geodatabase. It’s found in ArcCatalog has a database object within the geodatabase. This example shows where topology data would be.

Wissler & Christopherson pg 6

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Parameters that Define TopologyTopologies are used to store 3 important sets of parameters and some internal feature layers:-Cluster Tolerance: specifies distance at which all vertices or boundaries are considered coincident. There is a single tolerance established for the topology. Vertices that fall within this tolerance are snapped together, called validation.

Wissler & Christopherson pg 7

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Parameters that Define Topology-Ranks: defined at the feature class level and determine how many features in that class can move relative to features. Lower ranked features snap to higher ranked features during validation. This shows that the positional accuracy was higher in some features versus others.

Wissler & Christopherson pg 7

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Parameters that Define Topology-Topological rules: these rules define for a topology to control the allowable relationships of features within a feature class and between features in different feature classes. During development, users can add or remove rules from a set. This example states the rule that “land parcels must not overlap.” Features are then checked to make sure they are not in violation. During validation, cracking and clustering occur. Vertices are inserted at an intersection during cracking. Clustering involves snapping vertices together within a cluster tolerance. After validation, feature class will report any violations or errors that occurred.

Wissler & Christopherson pg 8

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Wissler and Christopherson Questions -Does topology affect both raster and vector data? And is it possible to ascribe rules to raster data?

W. and C. did not mention raster data in their article, however, we have an answer! Vector data focuses on the geo feature, while the raster focuses on the location, hence generalisation occurs through raster data. The rules do apply. In overlay, for example you look for features (vector) in the location (raster). Vector overlay is complex, but raster overlay is quick and simple. -Although topology appears simple, how can you decipher the topology features within the database feature class?

From the slide prior, we would use topology in the geodatabase. Topology files are located within the feature class, keeping the attributes and topology connected. http://dusk2.geo.orst.edu/arc/265gif/comp3.gif

Both picture and first question’s answer.

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Wissler and Christopherson Questions-With the “no overlapping” rule, I must refer to a real world situation. In the Sino-Indian border dispute, how should one go about the “no overlapping” rule? Both countries lay claim to this area, so there would be overlap when one is showing the land for India/China. Does one simply make a third category of disputed land? How else might one go about this?

In this case, validation would tell you this area is in violation of the rules, or you could create a polygon out of this region, and use the “boundary must align with [India polygon] and [Pakistan polygon]” to make sure it agrees with the rules, and could potentially call it [Kashmir polygon]. https://tiananmenstremendousachievements.wordpress.

com/2013/04/30/amid-improving-sino-indian-ties-border-stand-off-baffles-the-experts/

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Wissler and Christopherson Questions-How did topological rules come to be and which ones do GIS scientists often neglect?

The creation of topology came about in 1736 by Swiss mathematician Leonhard Euler in Königsberg (now Kaliningrad, Russia). Konigsberg had a seven bridge problem (the city is both on the island and on the sides of the river). Townspeople wanted convenience, and to only cross the bridge once. Euler replaced city landmasses with vertices and bridges with arcs, connecting them. This is the creation of the arc-node topology. GIS uses the “line” topology connection, these other connections are, according to W. and C., not used, or seldom used.

http://www.esri.com/news/arcuser/0401/topo.htmlhttp://www.esri.com/news/arcuser/0401/conundrum.html http://en.wikipedia.org/wiki/Network_topology#mediaviewer/File:NetworkTopologies.svg

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Theobald

Non-Topological Data Structures.● Relationships among adjacent features are implied, but

are not formally enforced and clearly defined.● Errors like cartographic spaghetti, dangles, polygons

slivers, etc. are products of generalization seen in “unstructured” data.

Above: ibis.colostate.edu/webcontent/IBIS/websptray/bluecontent/userguide/layervector/htmlRight: gisdepaul.edu/sewang/teachinggeog/GIS_representation.htm

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Topological data structure (TDSs“By requiring a node at the intersection of two linear features, planar topology is enforced and results in a single set of non-overlapping features.” -Theobald

● Nodes mark the intersection between linear features forming-essentially- topological junctions, or markers.

● By defining “from” and “to” nodes L/R polygons are specified.

● This defines relationships between polygons, and in turn, all areas.

● Having clearly defined areas enables advanced spatial analyses encompassing adjacency, connectivity, and containment. eg: directional data analysis of land parcels.www.esri.com/industries/surveying/community/data_model

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More Pros of TDS● The explicit data structure of topology enables faster

processing speed for spatial analyses.● Smaller file sizes because shared vertices of adjacent

polygons are not stored twice.● TDS were developed with the intended purpose of

providing an thorough and automated way of cleaning up data entry errors and confirming data.

○ All lines are first digitized (boundaries merged, nodes placed, etc), then topological rules are enforced to identify self-intersecting polygons, dangles, slivers/gaps, open polygons, etc.

http://support.atlibase.com/manual/in/611b/html

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Why not TDS?

www.geog.ucsb.edu/~jeff/gis/data_models1.html

● Non-topological data structures can be drawn and edited faster.

○ TDS is delayed in graphic display time because geographical features are not stored sequentially, and must be extracted from different data structures or files.

● Complex features, like self-intersecting transportation routes (bus routes) cannot be represented in ‘directional’ TDS, only ‘complex’ TDS systems.

○ Interpreted as an “error”, ie: self-intersecting polygon directional TDS

● TDS is time consuming as topological tables must be created and errors must be corrected for adequate performance of spatial analysis.

● TDS does not store in shapefiles which are easy to copy, and do not require importing or exporting. Shapefiles are ubiquitous.

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Why not TDS?● TDS storage still remains large requiring additional files

to store topological data.● Although storage was of a concern in the past, storage

constraints are no longer a concern.● GIS user requirements have also changed.● Non-topological data structures are easier to manipulate

and analysis because the map representation corresponds more closely to the real world.

● Topological constraints: points, lines and polygons may be required to coincide, or lines may not connect to other lines “dangles”, in the real world, etc.

○ eg: building footprints, & cul de sacs.○ Each real-life element adding complexity and time to

improving the logistical consistency and clarity of the data.

https://ahiglobal.wordpress.com/catagory/community/page/2/https://www.e-education.psu.edu/geog160/html

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Spatial Relations

Topology best known spatial relation type, but alsoProximal: distance between geographical features(direction based queries are common in GIS, but proximal relations are not stored typical stored in topologic data structure)

Directional: above & below and cardinal directions between features

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Connectivity“Defining connectivity solely on the basis of topological adjacency is inadequate” (695)ex: Movement of animals from spatially disjunct habitats

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Graph TheoryTheobald: Provides a basis for a generalised approach to describing spatial relationships. -Not strictly limited topologically adjacent features - potentially all features can be connected

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Graph Theory

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ButtenfieldTransmitting Vector Data Across the Internet

The Problems with Transmitting Vector data:

1. Vector files tend to be large and increase unpredictably: Issue for Transmission Time and Data Storage

2. Content and Topology change with resolution: Issue for reducing data ‘packet’ size

Fig. 1. Hydrographic features at several levels of resolution (Source: USGS Topographic Maps)

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Objectives for Progressive Transmission

1. To insure delivery of original data and without excess data for the

user.

2. To have user control of resolution before download.

3. To protect logical consistency which insures delivered data retains

detail consistency with original file (Attributes,

Spatial/Topological).

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Pre-Processed Data● At the server, data is partitioned into subfile

‘packets’ by the RDP algorithm, through:

Dividing the original vector into halves, then

continue subdividing the parts of the original data

● BUT subdivision will stop at a pre-determined

threshold distance for anchor lines

● AND the pre-processed data will be stored in

Ballard Tree Strips, which each strip increasing

in detail

Fig. 2. Hierarchical subdivision by RDP and multi-resolution storage in a Ballard strip tree

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Transmitting the Vectors● When a client initiates a transmission, the server

relays “packets” that contain every strip organized into one row of the “strip tree” (see right image).

● Efficiency is achieved by:○ transmitting only the anchor coordinates of a strip○ newly partitioned strips are transmitted in UNIX

dif operation style ● Packets with partitioned strips are transmitted

last and without previously sent unpartitioned strips, creating more detail while conserving data storage.

● Strips are identified by a 5-digit code:○ 1st two digits correspond to vertical location (aka

the level of resolution)○ last three digits provide correct sequencing

● The user or client can control the transmissionButtenfield, page 7

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Modifications to Preserve Topology● First Method

○ In the strip tree model, a collection of convex hulls replace Minimum Bounding Rectangles to preserve topology through the transmission without altering RDP partitioning.

○ Precedent - Saalfeld■ Argument 1: displacement of coordinates is caused by generalization■ Argument 2: convex hull of the line will always encompass the RDP

displacement ■ Conclusion: correct original vector will lead to the convergence of RDP

to create right topological solution● The gist of the first method:

○ convex hulls operate linearly, preserving topology, accuracy and detail during construction.

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Modifications to Preserve Topology● Second Method

○ Tests the strip tree using the first method○ Determines how intersecting convex hulls affect anchor lines (cross vs. converge)○ ‘dirty bit’ is added to strip ID to identify possible conflicts

● Third Method○ During transmission, the presence of a ‘dirty bit’ creates new process:

■ Right and left partitions of ‘dirty bit’ strips continually resends until topographic accuracy is achieved

■ This results in added detail, possibly beyond the requested amount, to ensure resolutions to topographic conflicts

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Java Implementation“Jekyll & Hyde”● Jekyll refers to a Java server application

○ subdivides RDP in a hierarchy○ creates convex hulls○ works through parity check (analyzes ‘dirty bit’ issues)○ saves partitions in strip tree database

● Hyde refers to a client application○ interface ○ keeps track of data transmission○ saves local database○ operates within a JAVA-supported internet browser

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Questions-Could it be effective to convert a file to raster to send it, and then convert it back to vector after receiving it?

● “Raster transmission and subsequent vectorization may distort geometric length and local density of detail, introducing unpredictable errors and uncertainty. Coordinate positions of topologically significant points may shift or disappear” (Buttenfield, pg. 4).

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Questions-Can you walk us through an example of what this looks like with all the advantages and limitations laid out?

● Advantages: “Progressive transmission includes preservation of geometric properties, particularly line length and local density of detail; inclusion of attributes and metadata matching the feature resolution as transmitted; topological consistency; and user control over the level of transmitted detail, over termination of progressive transmission, and about local storage options” (Buttenfield, pg. 13).

● Disadvantages: “the current procedures have been tested only on single polyline packets contained in small geographic databases.” (Buttenfield, pg. 13).

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Questions-It seems like the RDP method of subdividing the vector data into packets results in packets of varying size. For example, in Figure 2 the red packet seems much larger than the blue or white packets. What determines the final packet size? Are there any implications for this variability in packet size, such as big jumps in resolution as the packets are delivered or problems with it being difficult to get some packets small enough for transmission?

● What determines final packet size? Subfile packets contain “at a minimum, strip identifier number, the coordinate endpoints, the maximum deviation on either side of the anchor line, and three pointer fields. Other geometric characteristics may be recorded, for example number of coordinates in the original string, or length. Attributes and metadata may be attached to each strip” (Buttenfield, pg. 6).

● Implications for varying ‘packet’ size? Possibly transmission efficiency and resolution details

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ConclusionThrough these articles, we have learned how to incorporate topology into GIS, how to connect data, the variety of different types of topological rules and connections. The use of topology is important because it keeps all feature classes, all attributes, and all geodatabases in synchronise.

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BibliographyFeature 1.1: http://warpinghistory.blogspot.com/2012_11_01_archive.html Feature 1.2: http://www.esri.com/news/arcnews/summer02articles/arcgis-brings-topology.html Feature 1.3: http://www.geo.hunter.cuny.edu/aierulli/gis2/lectures/Lecture2/lecture2.htmlFeature 1.4 : http://dusk2.geo.orst.edu/arc/265gif/comp3.gifFeature 1.5: https://tiananmenstremendousachievements.wordpress.com/2013/04/30/amid-improving-sino-indian-ties-border-stand-off-baffles-the-experts/Feature 1.6: http://www.esri.com/news/arcuser/0401/conundrum.htmlFeature 1.7: http://en.wikipedia.org/wiki/Network_topology#mediaviewer/File:NetworkTopologies.svg

Wissler, C., & Christopherson, G. (2007, January 1). Topology and Topological Rules: Geometric Properties Maintained in Spatial Databases. GIS in Natural Resources.

Theobald DM. (2001) Topology Revisited: Representing Spatial Relations. International Journal of GIScience, 15(8): 689-705.

Buttenfield BP. 2002 Transmitting Vector Geospatial Data across the Internet. Proceedings, GIScience2002. Berline: Springer Verlag Lecture Notes in Computer Science #2478: 51-64.