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Based on this article "PDF: Extensions to least-cost path algorithms for roadway planning (Chaoqing, Jay, dan Mandy 2002)" (Click on link for PDF).

Whether least cost path tool used in ArcGIS software is already using anisotropic accumulated surface?

If so, why in determining the cost surface, the slope of the data used is the result of the 3D slope analysis?

Whereas based "ArcGIS Help sources" equation used is as shown below:

ArcGIS help

Whereas the anisotropic equation-accumulated surface, the formula used is the Euclidean Distance formula.

If anyone can explain what alogarithm used for the analysis of least cost path in ArcGIS softwere?

Extension:

In this case, I want to find the shortest path between two points through the terrain surface. Technical criteria that must be fulfilled is, "the slope should be less than 5%" when I compare with other software by hand through contour lines such as AutoCAD, Surpac. the results are very different. see the picture below

enter image description here

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    I beleive that you are mixing to seperate tools. You might use slope surface as detailed above as the ost surface to compute the least cost path; you may also use other inputs as well; thus it might be useful if you specify what is that you are asking: Is it about the slope calculation or the least-cost path? – dof1985 Apr 17 '15 at 19:16
  • in this case, i want to find the shortest path between 2 point through the terrain surface. technical criteria that must be fulfilled is, "the slope should be less than 5%" when I compare with other softwere by hand through contour lines such as AutoCAD, Surpac. the results are very different. so the point is, i'm asking about cost surface algorithm used in ArcGIS.. – Faizalprabowo Apr 17 '15 at 19:30
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One thing that should be mentioned, is that the Least-Cost-Path is computed as, literally, the least cost path, and not as th Shortest Path. Also cited from ArcHelp for Cost Distance Analysis:

The cost distance tools are similar to Euclidean tools, but instead of calculating the actual distance from one location to another, the cost distance tools determine the shortest weighted distance (or accumulated travel cost) from each cell to the nearest source location

Thus, the output you have recieved chose a path which follow the rule of the lowest cumulative slope. Yet, it is longer than the other path you have obtained (red one).

To compute Euclidean Distane in arcmap, you may want to use the Euclidean Distance Tool; that is to say that arcmap do provide an algorithm to compute anisotropic distance (cost surface). Yet it ignores other obstacles, such as: cliffs, rivers, or from other costs such as: slopes.

Than, you should use the path distance which is similar to the cost distance tool, i.e. taking slopes as costs; but also consider euclidean distance as a factor while generating a cost surface and calculating a least-cost (this time, also shortest) path. As in:

The path distance tools are similar to the cost distance tools in that both determine the minimum accumulative travel cost from a source to each cell location on a raster. However, path distance not only calculates the accumulative cost over a cost surface, it does so while compensating for the actual surface distance that must be traveled and for the horizontal and vertical factors influencing the total cost of moving from one location to another. The accumulated cost surface produced by these tools can be used in dispersion modeling, flow movement, and least-cost path analysis.

Regarding the slope constraint: you can assign NoData (set Null in field caluclator) for each cell with a slope >= 5%. That will prevent a path from being generated through those cells.

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