By Jurg Andreas Stuckelberger
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Extra info for A Weighted-graph Optimization Approach for Automatic Location of Forest Road Networks
3 illustrates this 3-D approach for turnings of diﬀerent road links. Node O represents an incoming node, while Nodes A, B, C, and D represent potential intermediate control points, depending on the road direction. The 0-layer represents the link direction, from west to east, whereas the 4-layer indicates the south-to-north link. The 8- and 12-layers represent link directions from east to west and from north to south, respectively. 3 results in a left-turn switchback. In this representation of the solution space, any chains of links (walk) result in a feasible alignment of the road.
At each outgoing and incoming node, the model checks all possible directional combinations. Consequently, the solution space increases by a factor of 162 = 256. 2. 2: Curvature constraints in graph model. Link A-B is feasible whereas link B-C is not, because its road radius would be smaller than the minimum radius (rmin ). for determining whether a link is feasible or not (Fig. 2). In this study, the minimum radius has been set at 20 m for regular curves and 10 m for switchbacks. Representation of such constraints requires one physical node to be split into 16 virtual nodes.
Graph optimization takes place in this 3-D graph, and the result can then be mapped back to the 2-D grid, which represents the x, y-surface area of the real world. Although a total of 40 possible road directions exists in the 48-link model, we have regrouped them into 16 directional classes to reduce the problem size. All links connecting to the nodes in the Moore neighborhood of Ranges 1 and 2 can be assigned to one of 16 directions without errors. However, some links connecting nodes in the Moore Neighborhood of Ranges 3 and 5 (Fig.
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