Vector Analysis
Vector data refers to points, lines, and polygons
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)
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 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
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:
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
Vector data refers to points, lines, and polygons
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)
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 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
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:
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
