A Weighted-graph Optimization Approach for Automatic by Jurg Andreas Stuckelberger
By Jurg Andreas Stuckelberger
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Additional info for A Weighted-graph Optimization Approach for Automatic Location of Forest Road Networks
2003). However, 42 CHAPTER 2. ROAD NETWORK DESIGN MODELS that extension of 24 links results in only eight additional directions. Because one of our goals is to evaluate the eﬀect of diﬀerent link patterns on the road layout, we have also deﬁned and assessed a 48-link pattern (Fig. 1c), which consists of the full Range 2 neighborhood, 16 links of Range 3, and eight links of Range 5. This pattern results in a nearly homogenous distribution of 40 directions. A rectangular grid representation may cause an angular and, therefore, unrealistic road alignment because its location is represented by a series of connected grid cells.
5 become smaller than b. As a consequence, only the positive branch of the root term resulted in feasible solutions. The third case considered ﬁll angles equal to cut angles (a = 0). 8. 9. 9 are analogously applicable for negative slope gradients (η < 0). However, in these cases cut-slope and ﬁll-slope angles (φcut and φf ill ) had to be more negative than ground slope angle (η) because of geometrical constraints. When one knows the relation of wcut to wf ill , one can then calculate self-balanced cut-andﬁll volumes for each location in the project area.
Cut-slope and ﬁll-slope angles (φcut and φf ill ) had to be greater than ground slope (η) because of geometrical constraints. Here, we examined three diﬀerent cases in terms of variable a (Eqs. 6): (1) ﬁll-slope angles larger than cut-slope angles, (2) cut-slope angles greater than ﬁll-slope angles, and (3) ﬁll-slope angles equal to cut-slope angles. In the ﬁrst case, the resulting value was less than zero (a < 0). 5 was the limiting factor, and the discriminate d had to be positive (Eq. 7. 7 were positive, and both φcut and φf ill were always greater than η.