Cost and Pathway

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Cost and Pathway

• ORHow to
• Find the best way to get from A to B

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Introduction

• COST and PATHWAY are two very important and
  powerful functions
• A basic concept here is that of FRICTION
• Values in a cell can be considered to model the
  cost of moving over the cell
• COST computes the total cost of reaching a given
  pixel from a source pixel
• PATHWAY navigates over a cost surface to find the
  lest expensive way to get from the cost source to
  a given sink pixel

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Introduction

• THUS
• COST is made from FRICTION surfaces
• as in the cost to move over the landscape
• Swamps may cost 2x as much as grass(2x) to move
  over
• steep slopes are more expensive than flat lands
  (5x)
• roads are less expensive than non-roads (1x)
• PATHWAY finds the least cost pathway over a cost
  surface.

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The situation
Swamp 4x
Steep Cost5
Road 1
Forest 5x
Grass 2
5
Straight shot
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Maybe this is better
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Or maybe the road is better
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FRICTION?

• Friction Surface image?
• An image in which the attribute values are
  multiples of the cost to travel over the cell
• Therefore friction surfaces can not have any 0s
  (Zeros)!
• Friction surfaces can be added
• And usually are to provide Total Friction

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For example

• Trying to find the least cost pathway between A
  and B for the an ATV
• Friction surfaces
• Surface Roads 1s, otherwise 10
• Cover Grasslands 10s, Forest 50s
• Slope may be 1(flat), 25 (low), 50(steep),
  100(very steep)
• Add them up to get the total Friction layer

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Cost START
R1C0 052 52 R0C0 021 21 R1C1
0451.41464 (not 2124 46!)
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Surface
Cover
Slope
START
END
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Finding the pathway
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COST from FRICTION

• How is cost determined?
• Through the use of friction surfaces
• Friction Surface?

Attribute is friction to move over cell
COST for cell 2,2 2x1.414 2.282
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So, what is Cost?

• It is the minimum accumulated friction (or AF)
  for each cell in the image calculated from a
  starting target cell.
• AF is COST

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In Book

• Distance
• Cost of moving over friction surfaces AB
• Pathways over AB

1.4142.824
TOO EXPENSIVE to go through center
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To Compute COST

• Use the COST command ( Duh!)
• Two versions
• COSTPUSH
• COSTGROW ? is the better one
• Need a Friction surface AND a starting target
  from which accumulated costs are computed

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Pathway

• Pathway finds the least cost pathway across the
  cost surface.
• Cost surface is made from the finish point over
  friction (finish is an image with a cell1)
• Pathway is created by making an image with a
  cell1 where the pathway is to start.

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From the book
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Structure of COST
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Procedure

• Make a blank image (0) with INITIAL. Call it
  START
• Copy it to (file mgt) to FINISH
• Update START and FINISH
• Run COSTGROW from FINISH over FRICTION
• Run PATHWAY using START.

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Got to have a pattern
start
friction
cost
Finish
cost
pathway
Path
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Allocate

• You dont have to run cost from 1 target.
• For example, suppose you have a number of logging
  landings and what to find the area best served by
  each of them
• Run COSTGROW using multiple targets (landings)
• This computes the cost to reach each and every
  cell on the image.

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S0?

• Not too useful in itself since you wanted to know
  the area served by each landing.
• ALLOCATE to the rescue!!
• ALLOCATE assigns each cell to one of the landings
  based on the costs of reaching the landings.
• For this to work each landing has to have a
  unique number.

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HINTERLAND

• HNTRLAND!
• Supply and demand
• An image of the sources of widgets ( available
  at sources, else 0)
• An image of sinks of widgets ( that can be
  costumed)
• HNTRLAND then runs radial searches from each
  source filling the closest sinks until the source
  is exhausted.

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So?

• The question of how many sinks of widgets can be
  supplied from the sources is answered.
• Does not use friction - is pure distance
  dependent
• Works well with food, for example, where overland
  travel is uniform in cost and transportation can
  move in straight lins.

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Last word

• I didnt mention the non-isotropic cost surfaces
  described in the book
• That is because I have not figured out exactly
  how to use them.
• So I guess I cant hold your feet to the fire
  regarding that material