Line Analysis

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Line Analysis

• The nature of linear features
• Attributes
• Directional Statistics
• Network Analysis
• Shortest Path

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The nature of linear features

• Typically represented as lines on a map
• Roads, rivers/streams, sewer lines
• Lines may or may not be connected
• Fault lines
• Trajectories
• Wind, migration routes
• Networks have nodes connecting features

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Examplefaults and rivers
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http//www.gisca.adelaide.edu.au/gisca/pd/mapping_
aust_pop_results.html
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Attributes of linear features

• Length
• Data need to be projected!
• Used to calculate the distance between two
  points, use the sum of segments to calculate the
  distance of a complex line

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Measuring Lines in a Raster System
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Method 1
Number of cells
Multiply by resolution of cell 50
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Method 2
Center Point Distance
1.414
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1
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Orientation and Direction

• Orientation
• East/west or north/south
• No direction implied (so no from-to)
• Mapping the orientation of fallen trees in
  Petrified National Forest to determine if a storm
  caused the trees to fall
• Measure either nominally or with angular measures
• Direction
• From one location to another
• One way streets
• Migration, shortest path routing, wind vectors

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Orientation of LINES

• Objects exhibit more than just distribution

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Orientation of LINES

• Objects exhibit more than just distribution
• Direction is often related to a force (process)

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blow-down wind direction?
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DIRECTION of LINES

• Objects exhibit more than just distribution

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Directional Statistics

• Descriptive
• sum, count, mean, max, range, variance, standard
  deviation
• Total length and Straight line length
• Ratio of the two (higher ratio implies more
  complexity in the line more curves)
• Sinuosity
• Important when curviness is a factor
• e.g., rivers

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Direction and directional mean

• Visually
• add arrows
• star or rose diagram
• Statistically calculate the directional mean of
  all vectors

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DIRECTION of LINES

• Distributions displayed as rose diagrams

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DIRECTION of LINES

• Q How to measure directionality?
• A Find the resultant vector!
• Find angle from base (theta)
• Multiply X coordinate by the cos of theta
• Multiply Y coordinate by sine of the theta
• Sum values for all coordinates

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Directional mean
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How to calculate it

• You may wonder why not just take the mean of the
  angles but this doesnt work. Why?
• If all the vectors are in the same quadrat, then
  it would be OK
• Otherwise, we need trigonometry to handle the
  angles

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For example, if I had 2 vectors, one with an
angle of 2 degrees and the other with an angle of
358 degrees. Their mean direction would be 0 or
360 degrees. If calculated mathematically, you
would get 180 degrees completely wrong!!!
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Circular variance

• Directional mean conceptually similar to
  central tendency
• Still need something
• that tells us how much
• deviation there is in
• our data
• Shows the variability
• of the directions

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Vectors that have similar direction
Vectors with similar directions resultant vector
is relative LONG and its length will be close to
n (remember the length of each vector is the same)
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Vectors with very different directions
Resultant vector will be relative short compared
to n for n vectors zig-zag effect
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Calculating circular variance

• Need to first calculate the length of the
  resultant vector (OR)

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Circular variance
Range of Sv is from 0 to 1 When length of or is
small all vectors go in different directions
then Sv is close to 1. When length of or is large
relative to n all vectors go generally the same
direction then Sv is close to 0.
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LINE PATTERNS

• Common measurements of line patterns

• Nearest neighbor distance between lines

1 - Randomly select point 2 - Draw perp. line to
each line 3 - Measure dist, calculate mean
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LINE PATTERNS

• Common measurements of line patterns

• Line intersect methods
• Draw random line or lines across map
• Note where sample line intersects coverage
• Random line that zigzags is called random walk
• Perform statistical analysis on points that
  intersect line

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LINE PATTERNS

• If lines not random, then.

• there is reason to believe a process other than
  random chance contributed to distribution

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Topology

• How lines (objects) are connected together
• Any type where we care about the connection
  streams, roads, pipelines
• Created with a connectivity matrix

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Connectivity Matrix