OD Matrix

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#1 Leeroy Posted 06 March 2010 - 08:54 PM

Leeroy

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Hey everyone,

i have to make a project with ArcGIS 9.3. I have to find out which of 18 Places in a road network is the central one. I want to use the OD Cost Matrix. Practically it works. The result is right. I also built a model with the model builder. But my big problem is that I do not find something theoretically because I also have to explain the whole thing.

1) What is the OD Matrix
2) How does it work
3) How can you use it
4) Which algorithm is important for that
5) etc.

Every thing would be very helpful!

Thank you very much!
Sorry for my bad english but my mother tongue is german!

Best regards

Thomas

#2 dsl Posted 06 March 2010 - 11:12 PM

dsl

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I can't guarantee my answer will be the correct one but I'll give it a shot. An OD Matrix is just a matrix of the distances between your objects where the diagonal is zero since the distance to an object and itself is going to be zero:

obj 1 obj2 obj3
obj1 0 5 10
obj2 5 0 6
obj3 10 6 0

I'm not sure how the central object is going to be calculated, but presumably it is going to be the place that is the shortest distance to all the other places. As with the central feature calculation, but using network distance rather than euclidean distance. The ESRI Guide to GIS Analysis part 2 is a good reference for that.

Which algorithms are you referring to? Assuming you mean algorithms to calculate the shortest path between each object on your road network, then I'm not sure which one ESRI uses. A common "simple" one is dijkstra's. That wikipedia page talks about graphs, but you can think of your road network as a graph where the intersections are vertices and the roads are edges. One way streets are edges that go in one direction.

Hope that helps.

Cheers,
David

#3 dsl Posted 07 March 2010 - 07:47 PM

dsl

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Also, just noticed something. If you are familiar with python, and want to see how ESRI calculates the central feature using euclidean distance. You can go to your ArcGIS installation, then the ArcToolbox\Scripts\CentralFeature.py file. On my computer this is: C:\Program Files\ArcGIS\ArcToolBox\Scripts\CentralFeature.py.

Cheers,
David

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