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### Spatial DataWhat is special about Spatial Data?

### Converting from one type of data to another.--very common in spatial analysis

### Models for Spatial Data:Raster and Vector

### Hopefully, you now have a better understanding of what is special about spatial data!

Briggs Henan University 2012

What is needed for spatial analysis?

- Location information—a map
- An attribute dataset: e.g population, rainfall
- Links between the locations and the attributes
- Spatial proximity information
- Knowledge about relative spatial location
- Topological information

Topology --knowledge about relative spatial positioning

Topography --the form of the land surface, in particular, its elevation

Briggs Henan University 2012

Berry’s geographic matrix

Berry, B.J.L 1964 Approaches to regional analysis: A synthesis . Annals of the Association of American Geographers, 54, pp. 2-11

1990

time

2000

2010

geographic

associations

geographic

distribution

geographic

fact

Briggs Henan University 2012

Types of Spatial Data

- Continuous (surface) data
- Polygon (lattice) data
- Point data
- Network data

Briggs Henan University 2012

Spatial data type 1: Continuous (Surface Data)

- Spatially continuous data
- attributes exist everywhere
- There are an infinite number locations
- But, attributes are usually only measured at a few locations
- There is a sample of point measurements
- e.g. precipitation, elevation
- A surface is used to represent continuous data

Briggs Henan University 2012

Spatial data type 2: Polygon Data

- polygons completely covering the area*
- Attributes exist and are measured at each location
- Area can be:
- irregular (e.g. US state or China province boundaries)
- regular (e.g. remote sensing images in raster format)

*Polygons completely covering an area are called a lattice

Briggs Henan University 2012

Spatial data type 3: Point data

- Point pattern
- The locations are the focus
- In many cases, there is no attribute involved

Briggs Henan University 2012

Spatial data type 4: Network data

- Attributes may measure
- the network itself (the roads)
- Objects on the network (cars)
- We often treat network objects as point data, which can cause serious errors
- Crimes occur at addresses on networks, but we often treat them as points

See: Yamada and Thill Local Indicators of network-constrained clusters in spatial point patterns. Geographical Analysis 39 (3) 2007 p. 268-292

Briggs Henan University 2012

1: Analyzing Point Patserns (clusterirg and dispersion)2: Analyzing Polygons (Spatial Autocorrelation and Spatial Regression models)3Surface analysis: nterpolation, trend surface analysis and kriging)

Which will we study?Point data

(point pattern analysis: clustering and dispersion)

Polygon data*

(polygon analysis: spatial autocorrelation and spatial regression)

Continuous data*

(Surface analysis: interpolation, trend surface analysis and kriging)

*in the fall semester

Briggs Henan University 2012

Briggs Henan University 2012

Converting point to continuous data:interpolation

Briggs Henan University 2012

Interpolation

- Finding attribute values at locations where there is no data, using locations with known data values
- Usually based on
- Value at known location
- Distance from known location
- Methods used
- Inverse distance weighting
- Kriging

Simple linear interpolation

Known

Unknown

Briggs Henan University 2012

Converting point data to polygons using Thiessen polygons

Briggs Henan University 2012

Polygons created from a point layer

Each point has a polygon (and each polygon has one point)

any location within the polygon is closer to the enclosed point than to any other point

space is divided as ‘evenly’ as possible between the polygons

A

Thiessen or Proximity Polgons(also called Dirichlet or Voronoi Polygons)Thiessen or Proximity Polygons

Briggs Henan University 2012

How to create Thiessen Polygons

2. Draw perpendicular line at midpoint

1. Connect point to its nearest (closest) neighbor

3. Repeat for other points

4. Thiessen polygons

Briggs Henan University 2012

Converting polygon to point data using Centroids

- Centroid—the balancing point for a polygon
- used to apply point pattern analysis to polygon data
- More about this later

Briggs Henan University 2012

Using a polygon to represent a set of points: Convex Hull

- the smallest convex polygon able to contain a set of points
- no concave angles pointing inward
- A rubber band wrapped around a set of points
- “reverse” of the centroid
- Convex hull often used to create the boundary of a study area
- a “buffer” zone often added
- Used in point pattern analysis to solve the boundary problem.
- Called a “guard zone”

Briggs Henan University 2012

two alternative methods for representing spatial data

Briggs Henan University 2012

river

Real World

house

trees

Raster Representation

Vector Representation

point

line

polygon

Briggs Henan University 2012

Raster Model

area is covered by grid with (usually) equal-size, square cells

attributes are recorded by giving each cell a single value based on the majority feature (attribute) in the cell, such as land use type or soil type

Image data is a special case of raster data in which the “attribute” is a reflectance value from the geomagnetic spectrum

cells in image data often called pixels (picture elements)

Vector Model

The fundamental concept of vector GIS is that all geographic features in the real work can be represented either as:

points or dots (nodes): trees, poles, fire plugs, airports, cities

lines (arcs): streams, streets, sewers,

areas (polygons): land parcels, cities, counties, forest, rock type

Because representation depends on shape, ArcGIS refers to files containing vector data as shapefiles

Comparing Raster and Vector ModelsBriggs Henan University 2012

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Raster modelImage

Land use (or soil type)

Each cell (pixel) has a value between 0 and 255 (8 bits)

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Briggs Henan University 2012

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Vector Model.

- point (node): 0-dimensions
- single x,y coordinate pair
- zero area
- tree, oil well, location for label
- line (arc): 1-dimension
- two connected x,y coordinates
- road, stream
- A network is simply 2 or more connected lines
- polygon : 2-dimensions
- four or more ordered and connected x,y coordinates
- first and last x,y pairs are the same
- encloses an area
- county, lake

y=2

Point: 7,2

x=7

Line: 7,2 8,1

Polygon: 7,2 8,1 7,1 7,2

Briggs Henan University 2012

Using raster and vector models to represent surfaces

Briggs Henan University 2012

Representing Surfaceswith raster and vector models –3 ways

- Contour lines
- Lines of equal surface value
- Good for maps but not computers!
- Digital elevation model (raster)
- raster cells record surface value
- TIN (vector)
- Triangulated Irregular Network (TIN)
- triangle vertices (corners) record surface value

Briggs Henan University 2012

Contour (isolines) Lines for surface representation

Contour lines of constant elevation

--also called isolines (iso = equal)

Advantages

- Easy to understand (for most people!)
- Circle = hill top (or basin)
- Downhill > = ridge
- Uphill < = valley
- Closer lines = steeper slope

Disadvantages

- Not good for computer representation
- Lines difficult to store in computer

Raster for surface representation

Each cell in the raster records the height (elevation) of the surface

105

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Raster cells with elevation value

Surface

Contour lines

Raster cells

(Contain elevation values)

Briggs Henan University 2012

Triangulated Irregular Network (TIN):

Vector surface representation

- a set of non-overlapping triangles formed from irregularly spaced points
- preferably, points are located at “significant” locations,
- bottom of valleys, tops of ridges
- Each corner of the triangle (vertex) has:
- x, y horizontal coordinates
- z vertical coordinate measuring elevation.

valley

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ridge

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vertex

Draft: How to Create a TIN surface:from points to surfaces

Thiessen4.jpg

Thiessen3.jpg

Links together all spatial concepts: point, line, polygon, surface

Briggs Henan University 2012

Using raster and vector models to represent polygons(and points and lines)

Briggs Henan University 2012

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Representing Polygons(and points and lines)with raster and vector modelsX

- Raster model not good
- not accurate
- Also a big challenge for the vector model
- but much more accurate
- the solution to this challenge resulted in the modern GIS system

Briggs Henan University 2012

Using Raster model for points, lines and polygons--not good!

For points

For lines and polygons

Line not accurate

Point “lost” if two points in one cell

Polygon boundary not accurate

Point located at cell center

--even if its not

Briggs Henan University 2012

Using vector model to represent points, lines and polygons:Node/Arc/Polygon Topology

The relationships between all spatial elements (points, lines, and polygons) defined by four concepts:

- Node-ARC relationship:
- specifies which points (nodes) are connected to form arcs (lines)
- Arc-Arc relationship
- specifies which arcs are connected to form networks
- Polygon-Arc relationship
- defines polygons (areas) by specifying which arcs form their boundary
- From-To relationship on all arcs
- Every arc has a direction from a node to a node
- This allows
- This establishes left side and right side of an arc (e.g. street)
- Also polygon on the left and polygon on the right for

every side of the polygon

from

to

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New!

Briggs Henan University 2012

Node/Arc/ Polygon and Attribute Data

Example of computer implementation

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Smith

Estate

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Attribute Data

Spatial Data

Briggs Henan University 2012

This is how a vector GIS system works!This data structure was invented by Scott Morehouse at the Harvard Laboratory for Computer Graphics in the 1960s.Another graduate student named Jack Dangermond hired Scott Morehouse, moved to Redlands, CA, started a new company called ESRI Inc., and created the first commercial GIS system, ArcInfo, in 1971Modern GIS was born!

Briggs Henan University 2012

Other ways to represent polygons with vector model

2. Whole polygon structure

3. Points and Polygons structure

- Used in earlier GIS systems before node/arc/polygon system invented
- Still used today for some, more simple, spatial data (e.g. shapefiles)
- Discuss these if we have time!

Briggs Henan University 2012

Vector Data Structures: Whole Polygon

Whole Polygon (boundary structure): list coordinates of points in order as you ‘walk around’ the outside boundary of the polygon.

- all data stored in one file
- coordinates/borders for adjacent polygons stored twice;
- may not be same, resulting in slivers (gaps), or overlap
- all lines are ‘double’ (except for those on the outside periphery)
- no topological information about polygons
- which are adjacent and have a common boundary?
- used by the first computer mapping program, SYMAP, in late 1960s
- used by SAS/GRAPH and many later business mapping programs
- Still used by shapefiles.

Topology --knowledge about relative spatial positioning

-- knowledge about shared geometry

Topography --the form of the land surface, in particular, its elevation

Briggs Henan University 2012

A 3 4

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Whole Polygon:illustrationData File

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Briggs Henan University 2012

Vector Data Structures: Points & Polygons

Points and Polygons: list ID numbers of points in order as you ‘walk around’ the outside boundary

- a second file lists all points and their coordinates.
- solves the duplicate coordinate/double border problem
- still no topological information
- Do not know which polygons have a common border
- first used by CALFORM, the second generation mapping package, from the Laboratory for Computer Graphics and Spatial Analysis at Harvard in early ‘70s

Briggs Henan University 2012

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Points and Polygons:IllustrationPoints File

Polygons File

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Briggs Henan University 2012

Monday, we will begin talking about Spatial Statistics

Briggs Henan University 2012

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