Creating proximity surfaces from origin and destination and adding them yields the shortest path.

SpreadFromStart = Spread start
To 10000.00In costoftravel
Outof direction
;

SpreadFromStop = Spread stop
To 10000.00
In costoftravel
Outof direction
;

ShortestPath_InNetwork = SpreadFromStart + SpreadFromStop
;

The shortest path is delineated by the cells with the lowest value(s). The value is the actual cost of using this path. Using the Legend function this path can be derived by changing the color of the cells with the lowest value until a continuous path from origin to detination can be seen.

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Now, the shortest path can be extracted.

ShortestPath = Recode ShortestPath_InNetwork
Assigning 999 To 262…264;

262-264 were the cell values for the shortest path. A high value of 999 was the chosen for the path to distinctively separate the path cells from any other cells in the following overlay:
The extracted path can be overlayed over the study area map for visualization.

ShortestPath_OverMap = Cover BrownsPond With ShortestPath ;

MFworks – step by step

•  01 MFworks

• 02 Network Modelling

•  03 Incremental Linkage

• 04 Directional Identifier

• 05 Cost surface

• 06 Travel cost – path length

•  07 Dynamic Cost Surface

•  08 Artefacts

• 09 Map Layers Needed

•  10 Deriving Linkage

• 11 Deriving Directions

• 12 Deriving the Shortest Path

• 13 Viewing the Shortest Path

• 14 Dynamic Networks

• 15 Shortest Path I

• 16 Shortest Path II

• 17 Shortest Path I+II

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The procedure is similar to finding the shortest path through a network with no time-dependent travel cost (go there first).

First calculate the path(s) from origin to the cutoff-point(s), where the new time interval starts. In other words spread until the available time in time interval 1, depending on your starting time, has been used up. From the cutoff-point(s) in time interval 1, calculate the shortest path(s) to the destination through time interval 2. The path with the lowest value is the sought path. Join the paths.

The cell value at the cutoff-point for time interval 1added to the cell values of the shortest path in time interval 2 is the total cost for the joined path.

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Creating proximity surfaces for path(s) in time interval 2 and adding these together yield the shortest path(s) through time interval 2.

SpreadFromCutoff1_Time2 = Spread Cutoff_Point1
To 600
In costoftravel_time2
Outof direction
;

SpreadFromCutoff2_Time2 = Spread Cutoff_Point2
To 600
In costoftravel_time2
Outof direction
;

SpreadFromCutoff3_Time2 = Spread Cutoff_Point3
To 600
In costoftravel_time2
Outof direction
;

SpreadFromCutoff4_Time2 = Spread Cutoff_Point4
To 600
In costoftravel_time2
Outof direction
;

SpreadFromStop_Time2 = Spread stopTo 600
In costoftravel_time2
Outof direction
;

ShortestPath1_InNetwork_time2 =
SpreadFromCutoff1_Time2 + SpreadFromStop_Time2
;

ShortestPath2_InNetwork_time2
= SpreadFromCutoff2_Time2 + SpreadFromStop_Time2
;

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Now, the shortest path(s) can be extracted as follows:

ShortestPath_time2 = Recode ShortestPath4_InNetwork_time2
Assigning 999 To 83…85
;

For time interval 1, first add proximity surfaces, then extract path.
SpreadFromCutoff4_time1 = Spread Cutoff_Point4
To 600
In costoftravel_time1
Outof direction
;

ShortestPath_InNetwork_time1 = SpreadFromStart_Time1
+ SpreadFromCutoff4_time1
;

ShortestPath_time1 = Recode ShortestPath_InNetwork_time1
Assigning 999 To 169…171;

The extracted paths can now be joined and overlayed over the study area map for visualization.

ShortestPath_time = Cover ShortestPath_time1 With ShortestPath_time2
;

ShortestPath_OverMap_time = Cover BrownsPond With ShortestPath_time
;

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