Implement flow routing

[wkearn]

Flow routing constructs a flow network from a digital elevation model. The flow network is heavily used by the rest of TopoToolbox, so providing optimized implementations of flow routing and traversing the flow network should be a priority for the core library.

TopoToolbox represents the flow network as a topologically sorted weighted edge list, in which all of the incoming edges of a grid cell are listed before all of the outgoing edges from the same cell. The weights between zero and one represent the partitioning of the outgoing flow from a cell among its neighbors.

TopoToolbox constructs a flow network from a DEM in three phases:

1. Preprocess the DEM to remove sinks
2. Compute flow directions including routing flow through flat areas
3. Construct and topologically sort the edge list

We should probably start by implementing a single version of these three steps before filling in the other algorithms. I suggest implementing the equivalent to FLOWobj(DEM,'preprocess','carve') in the MATLAB version. This requires at least implementations of

• Sink filling (fillsinks) #7
• Flat-region identification (identifyflats) #8
• Computing the costs and sill pixels #9
• Gray-weighted distance transform (graydist) #10
• Flow routing with the gray-weighted distance transform #11
• Topological sorting #12

[wkearn]

With #72, we can implement this entire flow routing pipeline using libtopotoolbox functions, so I will close this issue. Any further improvements, additions or corrections to flow routing can be discussed in additional issues.