EXAMPLE 2 

 AN ASYMMETRICAL, BELL-SHAPED RIDGE 

 THREE SEGMENTS 



Quality score (t) was originally described (fig. 4) as an aggregate of 11 planar 

 regions over flow (F) and stability (S) of gap-graded road materials, a strongly seg- 

 mented descriptor (Lee, and others 1973, fig. 14). The objective here was to smooth 

 the figure and minimize the number of segments in the descriptor. Although the problem 

 is an unusual one, its solution serves admirably to demonstrate descriptor segmentation. 



From figure 4, it can be seen that opposite sides of the ridge differ substantially 

 in slope so that an asymmetrical, flat-topped, bell-shaped curve would be required to 

 describe the cross-section at any point in S while rounding the junctures of planes. 

 A relatively simple descriptor alternative involves segmentation of the (S ,F) -regions 

 as shown, with left and right orientation lines. Note that the lines are parallel to 

 their respective sides of the ridge and lie one unit in F closer to the ridge center. 

 This permits use of a single, but different, sigmoid cross section to represent and 

 smooth the corners of each segment, left and right. The sigmoids will peak at their 

 respective orientation lines and will be functional over a constant distance from them 

 (left or right as appropriate). The constant will vary by side as needed. Since the 

 ridge is flat-topped, it will have a value of t = 10 everywhere in the center segment. 



SEGMENTS 



LEFT ►|-«-CENTER-»-|-« RIGHT >» 



30 25 20 15 10 5 



FLOW,(F) 



Figure 4. — Quality of gap-graded road materials: segmented planar form. 



5 



