# DIVERGENT REASONINGS AND DIALOGUES OF THE DEAF: WHY ...

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Wednesday, March 28, 2012

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Changjoo Kim

Lecture 5: Vector Data Model

Geography 373 Fall, 2006

Vector Data model

1 10/9/2006

nHow to represent simple features as point, line, and areas? How the computer “see” the features and their spatial relationships? àVector data model 1. Vector data uses points and their x,y coordinates 2. Geometric objects and their spatial relationships are organized into digital data files that the computer can access, interpret, and process. (Georelational data model)

Changjoo Kim

Vector Data

3 10/9/2006

nGeospatial data is represented in the form of x, y coordinates nThe basic units of spatial information arepoints, arcs, and polygons nEach of these units is composed simply as a series of one or more coordinate points, for example, a line is a ordered collection of related points, and a polygon is a ordered collection of related lines nTIGER (Topologically Integrated Encoding and Referencing), ArcView Shapefile, ArcInfo coverage, DLG, CAD drawing 5 Changjoo Kim10/9/2006

Contents of Lecture

nVector Data nTopology nSpaghetti Data Model nArcnode Data Model nVector vs. Raster nData Transformation nData Combination

Changjoo Kim

Georelational Data model

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nSpatial (location) + Attribute (description) component nUse synchronized ID to link the two components nTo eliminate the problem of data synchronization, objectbased data model is developed.

Changjoo Kim

Dimensionality and property

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n0 dimensional objects Point:geometric location with a set of coordinates Node:topological junction n1 dimensional objects Line segment (vector):a direct line between two points having length Link:direct connection between two nodes üdirected link String:sequence of line segments Chain:directed sequence of nonintersecting line segments with nodes at each end Arc:curve string Ring:sequence of any line segments with closure n2 dimensional objects Simple polygon:an area defined by an outer ring without inner rings Complex polygon:an area defined by an outer ring with inner rings

Changjoo Kim

6 10/9/2006

1

Digital Line Graphs

nDigital vector representations of cartographic information derived from USGS maps and related sources nDepending on scale, the following layers (or categories of feature type) may be available Public Land Survey System (PLSS), boundaries, transportation, hydrography, hypsography, survey control and markers, vegetative surface cover nThree primary types of DLG data and 1:25,000Large Scale(7.5 minute):1:20,000 ,1:24,000 , scale Intermediate Scale(1:100,000 scale) Sm all Scale(1,2,000,000 scale) nSource: http://edc.usgs.gov/products/map/dlg.html 7 Changjoo Kim10/9/2006

Vector Data Representation

X, Y Coordinates (Lat, Lon) in Point

Set of Nodes (Open Path, Line)

Set of nodes where begin and ending node are same (Closed path, Polygon)

nPreserve Topology nAttributes will be saved in a separate file in georelational model Changjoo Kim

9 10/9/2006

Topology nTopology in mathematics deals withgeometric propertieswhich remain invariable under certain transformation such as stretching or bending (Massey 1967) nTopology in GIS is generally defined as thespatial relationshipsbetween adjacent or neighboring features nA GIS topology is a set of rules and behaviors that model how points, lines, and polygons share geometry For example, adjacent features, such as two counties, will share a common edge 11 Changjoo Kim10/9/2006

Digital Line Graphs

nLargescale (7.5 minute) DLG Boundary, Hydrography and Transportation layers (Dancyville, TN)

Changjoo Kim

Vector Data Issue

nScaledependent scale)Polygon (largescale) to point (small E.g. city, stream in large/ small scale map nTopological error Effects of tolerance on topological cleaning E.g. snapping

nComplex data structure Arcnode data model RDBMS

Changjoo Kim

1

Adjacency and Incidence

Changjoo Kim

6

4

3

5

nAdjacency matrix

1 112 13 14 11 01 0 1 12 00 1 0 13 10 0 0 14 01 1 0

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10 10/9/2006

nIncidence matrix 1 2 3 4 5 6 11 11 0 1 0 0 12 0 1 1 0 1 0 13 1 0 1 0 0 1 14 0 0 0 1 1 1

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2

Topology nTo manageshared geometry (better data quality) Constrain how features share geometry For example, adjacent polygons, such as parcels, share edges; street centerlines and the boundaries of census blocks share geometry nTo define and enforcedata integrity rules No gaps should exist between parcel features, parcels should not overlap, road centerlines should connect at the endpoints nTo supporttopological relationship queries and navigation (enhance GIS analysis) Have the ability to identify adjacent and connected features, find the shared edges, and navigate along a series of connected edges

Changjoo Kim

Topology Components

Changjoo Kim

point n o d e line segment link directed link string

chain

Spaghetti Data Model

a rc

ring

13 10/9/2006

sim p le polygon

complex polygon 15 10/9/2006

nViewed as raw digital data nOneforone translation of the analog map nEach entity is a single record coded as x, y coordinates nNo details of logical relationships between objects the line shared by two adjacent polygons is recorded separately in the computer spatial relationships are only implied nEfficient for cartographic display nAt first, GIS used vector data and cartographic spaghetti structures

Changjoo Kim

17 10/9/2006

Topological Relationships

nConnectivity:chains are connected at which nodes nDirection:defines a “from node” and a “tonode” of a chain nAdjacency:polygons are on the left and which are on the right side of a chain nInclusion:simple spatial objects (node, chain, smaller polygon) are within a polygon 14 Changjoo Kim10/9/2006

Vector Data Model

nSpaghetti data model No topology Graphical elements nArcnode data model Topological data model Require additional data files to store the spatial relationships (line meets correctly? Polygons are closed properly?)àbetter data quality Spatial relationships

Changjoo Kim

Arcnode Data Model

16 10/9/2006

nVector data evolved the arc/node model in the 1960s nAn area consist of lines and a line consists of points, in the arc/node model nThe topological vector model uses theline (arc)as a basic unit nAreas (polygons) are built up from arcs

Changjoo Kim

18 10/9/2006

3

Arcnode Data Model

nPolygon Topology Polygon, links nNode Topology Node, links nLink Topology Links, start node, end node, left polygon, right polygon nLink Coordinates Links, coordinates

Changjoo Kim

Homework

nRead Chapter 3, 4

Changjoo Kim

19 10/9/2006

21 10/9/2006

Arcnode Data Model Node Topology nPolygons: A, B, C, D nPoints: P1, P2No de Links nNodes: N1N13 nLinks: L1 L15 N9 L9,L13 Northing (Y)

Polygon Topology

Polygon Links C L6,L7, L8

9 N5L4N4 N13L12N12 Link Coordinates 8 Coordinat N15 7 N8 Link es L3 (9,2), 6L7 L11 L9 (12,2) L8 L15 5L5CN 7L13 B L6 4 AN11 N14 N6 N3L14Link Topology P 1 3L10 Li StartEnd LeftRight L2 nk NodeNode Polygon Polygon 2 N1L1N 2N9L9N10 L6 N6N7 CA 1 D Easting (X) 20 Changjoo Kim10/9/2006 0 12 3 4 5 6 7 8 910 11 12 13

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