Create the perfect stream network ?

[MalardArnauld]

I am searching a way to "hydrologically" connect upstream points to a unique downstream outlet by creating an optimized stream network as pictured below...

The cummulated lenght of the stream lines should be minimized.

Otherwise the stream network should remains confined within a defined polygon...

I only know the input points (red) and the output (green) and the polygon. There is no other constraints

Does anyone know how to do it ?...

I searched on the web all the morning but without succeed

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[MarkBoucher]

Are you doing this regardless of the topography?

[MalardArnauld]

Yes.
In the first time I do not take the topography into consideration
I just want to join the input points to the outlet by the shortest drainage network

Do you have any idea how to do that ?

[MarkBoucher]

Arnauld,

I assume you want the flows to follow a drainage network because you say, "I just want to join the input points to the outlet by the shortest drainage network." There are tools in Arc Hydro for doing this. You need Spatial Analyst to use Arc Hydro.

If you install the correct version of HEC-GeoHMS for your version of Arc Map, you will also install the correct version of Arc Hydro. Both are free. If you haven't used Arc Hydro, it can take some time to understand it. I've written a post here (http://forums.arcgis.com/threads/53316-Why-can-t-I-define-a-stream-network) that summarizes the steps I use. There are other posts in the forums that could also help you become familiar with Arc Hydro. One is a thread I started to post solutions in one place : http://forums.arcgis.com/threads/48100-ArcHydro-Problem-Solvers.

As for a drainage network, if you have a polyline dataset of the existing pipe network and also polylines at bridges (where the DEM might rise higher than the creek), Arc Hydro can "burn" these into to the DEM (lower it where these polylines are). You can use a stream (creeks/rivers/streams) polyline dataset, but I usually don't use all the lines in the stream layer because they don't always follow the terrain as well as the DEM. An intersect of the stream layer and roads can help me find bridge/culvert crossings. In flat areas, however, you may need to do a lot of "training" for the flow paths to be defined correctly and in those cases the stream layer might be best to use.

In the process you will create a flow direction grid (fdr). The fdr is the basis for the rest of the processing in Arc Hydro. You may not need to go any further in the Arc Hydro processing steps for what you want.

Using the fdr and the Arc Hydro flow path tracing tool in the Arc Hydro toolbar you can get traces of the flow paths from points you click in the watershed to the outlet.  If the fdr is correct, the traces will be the lines that join the "input points to the outlet by the shortest drainage network".  You could then convert those lines to features using a menu command in the Draw tool bar.

Hope this helps.

Mark