3.5 Proc-LOS

Proc-LOS calculates a weighted visibility index for each of the 1,442,401 possible observers in a cell. The method is as follows. For each point in the cell, place an observer there and fire a number of rays out to the range to determine how many points on the ray are visible. This method is traditional, but the amount of data processed is new. To date, about 20 cells have been processed.

How many rays are necessary? At first, we used 128 rays per point, which required 1,454,000 CPU seconds on a Sun IPC per cell. (A Sun IPC is 3---4 times slower than the newer Sun 10/30 used for many of the other experiments reported here.) If 32 rays were sufficient, then that would cut the CPU time down to 357,000 seconds per cell. (By now, these times have been considerably improved.) The sufficiency of 32 rays was shown two ways. First, the visibility index of each point in a cell was calculated with 128 rays, and again with 32 rays, and the two visibility indices correlated. Figure 5 plots a random sample of the visibility indices calculated with the two methods against each other. There's almost no difference.

However, the reason for finding visibility indices is to find the best points and place observers there. Even though on average the two methods are equivalent, they might differ on the best points. Therefore we selected the dozen points of highest visibility with the each method, and compared them, as shown in figure 6. Ten of the 12 points are common to both lists, and most points are in the same order. Therefore, 32 rays are quite sufficient.

Figure 6 shows another interesting point. The best points are well scattered around the cell, and not all adjacent to each other. This is good since it may not be necessary artificially to separate the points to get a good spread.

When the cell shown in figure 1 was processed, figure 7 resulted. There are some noteworthy observations here.

1. Visibility does not appear strongly correlated with elevation. On the one hand, the ridge in the middle is both high and visible. However, the low region in the bottom left is low and visible, while the high region near the top right is high but invisible. An explanation is that from a low, broad valley one can see the whole valley and the fronts of two ranges, while from a peak in a mountainous region one can see only the adjacent small valleys in front of the adjacent peaks.

2. The visibility index seems to sharpen features. The highly visible part of the central ridge is much narrower than the ridge itself. This method might be useful for identifying ridges and for feature recognition.

3. There are very few highly visible points. Figure 8 shows a semilog graph of the distribution of points of different visibility indices. The visibility index is scaled so that 32K means that 100% of the points within range are visible, 8K means 25%, etc. Of the 1.4 million possible observers, only about 40 can see over 1/2 of the possible targets within range. Therefore, selecting the best observers is difficult and critical.

4. The distribution of visibility indices is log-linear, like many natural statistics.

5. On the average, higher points are not much more visible. Figure 9 is a scatter plot of visibility index versus elevation for a random sample of points. There is no apparent correlation. In fact, the correlation here is -0.12. This agrees with experience, where the shoulder of a ridge may be more visible than the top.

6. Nevertheless, the best points are somewhat higher, although they are nowhere near the highest. Figure 10 shows the 100 best points' visibility and elevation plotted. Within this set, there is still no correlation between elevation and visibility. However the set has no points below 100 meters. On the other hand the set also has no points above 800 meters, even though the highest point is 1462 m.

3.5.1 Dependence of Visibility on Elevation

Whether or not the visibility index of a point is linearly correlated with its elevation, and whether that correlation is positive, depends on many factors, in a way that we don't yet understand. The factors include which cell is tested, how much ocean that cell contains, whether we count the sea-level points, whether we weight points either closer to, or farther from, the observer more highly, whether we use all the points, or only the best points, etc, etc. The most that we can say is that the correlation, on the average, is weakly positive in some cases, with a very large standard deviation.

Nevertheless, simply placing observers on the highest points is in many cases not the optimal method of covering some terrain.

3.5.2 Directional Visibility

We have extended Proc-LOS to calculate the visibility index of each point in each of several directions, and then to display the data in color. The hue of each point tells in which direction an observer could see the best. The color saturation tells how directional the visibility is, while the brightness still tells how good the overall visibility is here.

The directional visibility is quite good at highlighting terrain features such as ridges.