Vector Analysis

Vector data refers to points, lines, and polygons

Measuring vector data

In ArcGIS -> Calculate geometry by right-click on column and selecting ‘Calculate Geometry’.

Lines can be used to calculate:

  • Length (Sum of the distances between vertex to vertex)
    • Sum of all line segments between the start and end node
  • Shape or Sinuosity (Ratio of the length to its straight-line length)
    • An index of 1 would imply no sinuosity
    • The greater the ratio, the more sinuosity

Polygons, related to the area, can be used to calculate:

  • Length (Perimeter of the polygon, sum of distance between vertices)
    • Add the length of the lines together around the area of interest
  • Area
    • Formula = ½ * Σ yi(xi-1 - xi+1)

Buffering

In ArcGIS -> Toolbox and click under proximity to access the buffer option

Buffering involves measuring distance outward in directions from an object (point, line, or polygon) with the resulting buffer being a polygon file. Delineates protected zones around a feature to show areas of influence preformed in both vector and raster environments.

There are different types of buffering:

  • Simple buffer (uniform distance)
  • Multiple ring buffer
  • Variable buffer (based on an attribute)

Buffers often overlap – use the dissolve option to merge all buffer polygons into one polygon

Vector-Based Overlaying

Vector-based overlaying combines spatial & attribute data from two (or more) layers to create a new combination layer. Done by using boolean operators:

  • And - Intersection of 2 sets
  • Or - Union of 2 sets
  • XOr - Exclusive OR
  • Not - Difference operator

Creates regions of spatial configuration:

  • Contiguous regions (single-part polygons)
  • Fragmented regions (area-weighted polygons)
  • Perforated regions

Network Analysis

A network is a system of interconnected elements, such as edges (lines) and connecting junctions (points), that represent possible routes from one location to another. Network analysis allows us to answer questions such as:

  • What is the quickest way to get from point A to point B?
  • What fire incidents can be reached within five minutes of fire stations?
  • What market areas does the business cover?

There are two types of network analysis:

Geometric networks (directed)

  • River networks and utility networks—like electrical, gas, sewer, and water lines—allow travel on edges in only one direction at a time.
    • Elements: Edges (lines), junctions (point), sources and sink (points), ancillary Features (Points and Areas)
  • Types of analysis able to be done:
    • Flow & direction analysis
    • Upstream or downstream analysis
    • Barrier analysis
    • Schematics diagram analysis

Transportation networks (undirected)

  • Transportation networks—like street, pedestrian, and railroad networks—can allow travel on edges in both directions.
    • Elements: Edges (lines), junctions (point), and turns
    • Attributes: Time, speed, restriction for vehicles, and one-way traffic flow
  • Types of analysis able to be done:
    • Optimal route - Shortest path analysis
    • Closest facility
    • Travelling salesman optimal route (multiple stops)
    • Location allocation modelling (facility)

Network attributes are properties of the network elements that control the capacity of the network:

Interpolation

All interpolators are either:

  • Exact: interpolated surface passes through all original data points (produces data values)
    • Methods: Thiessen Polygons, Inverse Distance, and Splines
  • Inexact: does not pass through all data points (does not represent original data values)
    And:
  • Global: estimated values is a function of all the values in the data set (based on statistics – variance & regression)
    • Global function valid across entire area
    • Can be less exact, when data is not uniform
  • Local: estimated values is a function of a subset of values within the vicinity of the unknown value (consistent with Tobler’s Law)
    o Local functions capturing local details

Local methods for estimating the unknown points through interpolation.

  • Thiessen Polygons (Exact)
  • Inverse Distance (Exact)
  • Splines (Exact)

A triangular irregular network (TIN) layer is commonly an elevation surface that represents height values across an extent.

  • Digital means to represent surface morphology

Thiessen polygons assign the value of the nearest seed point for any unsampled location in an area

  • Assume homogeneity of the values within polygons boudaries

Inverse Distance Weighted Interpolation (IDW) assumes closer values are more related than further values with its function.

  • Combine the idea of proximity from Thiessen with the gradual change of trend surface
  • Main Idea – value of an attribute at an un-sampled location is inversely proportional to its distance from the estimated value
  • Can be linear or non-linear

Spline is an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.

  • Fits a piece-wise polynomial function to a neighborhood of sample points to produce a smooth surface
    • Sacrifices some measurements