Simple Distance and Functional Distance: Friction Surfaces, Barriers, and Impedance (Especially for GATE-Geospatial 2022)

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1. Simple Distance

Until now, we have calculated distance between point locations in a map or along the grid cells of a linear object. We may want to know the distance between a single point location on a map and all other possible locations. In raster this is done by producing a series of concentric rings, one grid cell in diameter, around the starting grid cell. Each ring is essentially one grid cell away from the preceding ring. The result of such a distance measure, assuming the surface is completely uniform is called isotropic surface.

Figure Shows Isotropic Surface Around a Point

It is not always necessary to measure distances across a surface starting with a point as the origin. We may wish to measure the distance from a linear or polygonal object to all other locations on the map. That is possible with the same isotropic surface concept.

This Figure Shows Distance Flowchart

Figure – Distance flowchart: Notice how the distance operation is modified based on its source or starting place. This source might be a point, a line, or a polygonal object. The result of measuring from a starting place to all other places on the map is called a travel map.

2. Functional Distance

Functional distance is a measure of space based on how that space is used, rather than its absolute measurement. Functional distance recognizes that you don՚t always want to know exactly how near or how far, but rather what traveling that distance might cost you in time, money, calories, or even just emotional distress.

You can base functional distance on these kinds of factors:

  • Expenditure of fuel, based on how long it takes to travel a distance
  • How much a trip cost
  • How much wear and tear you put on your vehicle?
  • How much stress the trip puts on the travelers

These factors can influence functional distance measurements:

  • The ruggedness of the terrain
  • Whether the roads are well maintained
  • The amount and direction of wind

The purpose to calculating the functional distance is to estimating the cost for travelling on isotropic surface.

We need to consider two basic concepts when looking at functional distance:

Diagram Shows Two Basic Concepts of Functional Distance

Friction Surfaces

Friction is a force that is created whenever two surfaces move or try to move across each other. A barrier is a physical structure which blocks or impedes something. In other case rather isolated conditions or discrete obstacles called barriers interface with movement across a surface.

Barriers

Barriers are of two kinds:

Diagram Shows Two Ways of Barriers

I. Absolute Barriers

Absolute barriers prevent or redirect movement. For ex. Fenced areas, lakes, etc. though absolute barriers are preventing movement; they may be permeable with points of access through which travel is permitted. For example, Bridge over stresses.

1. Premble (prevent the movement)

2. Impermeable (restricted access such as bridge across the river)

II. Relative Barriers

Relative barriers are much like friction surfaces. The difference between friction surfaces and relative barriers is relative barriers acquire a cost for movement from once place to another.

Figure Shows Examples of Relative and Absolute Barriers

Impedance

A measure of the amount of resistance, or cost, required to traverse a path in a network, or to move from one element in the network to another.

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