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Using the Triangulation Method to Map a Scene

I once mentioned to someone that I had used the "Triangulation Method" to map a complicated scene by hand one time when I couldn't get a Total station to the scene. They looked at me like I had three heads. I told them that I'd show them how I did it, so here it is.

The intersection in question incorporated a traffic circle approximately 100 feet in diameter, with four roads leading into/out of it at odd angles. Two photos of the circle with the approximate locations of the four roads are shown below:

A Scene Photo, 51Kb FIGURE 1

Another Scene Photo, 51Kb FIGURE 2

I mapped more than I actually needed, partly to see how well it would come out. The first step was free-handing a pretty good diagram of the scene, and deciding on reference points (I used about 33 points for most of this scene), which I dotted with spray-paint. Then I drew the connections I wanted to measure on my sketch, trying to keep triangles as near equilateral as possible, with some overlap in point locations. My completed field sketch is shown below (Road A is toward the top of the sketch):

The Scene Sketch, 52Kb FIGURE 3

In addition to these distances, I measured the road and lane widths a ways away from the circle as well as the heading of each road, using a compass set on the pavement between the yellow lines. Adding a few more data points than are shown here down each road made the final drawing easier. Reviewing scene photos helped get all the road-lines correct.

Then I went to Autocad-LT. I don't recall which points I started with, but one can start with ANY two points. For this demonstration, I'll begin with Points #20 and #22, which I measured to be 29.8 feet apart, so start by drawing a line that long. These two points were at corners of the traffic island at the entrance to Road A (shown in the foreground of both photographs of the circle). Then the distance from Points #20 and #22 to Point #23 were measured to be 45.2 and 42.6 feet respectively, so I'll draw circles with those radii from their respective origins. They will overlap at point #23. Figure 4 shows that first line and these first two circles, locating the first three points in my picture. (I had to touch up all the Autocad drawings by hand a bit to make them clearly legible to the scanner.)
Figure 4, 26Kb FIGURE 4

This process of drawing circles (or arcs) of known radii from previously located points simply repeats itself, until you've worked back to the beginning, or to the end of your area of interest. Figure 5 shows the just-completed island drawn with radiused corners, and also shows point #19 (on the circle's inner radius) being located based on the known locations of points #20 and #22:
Triangulating One Point, 12Kb FIGURE 5

After all the labelled points were mapped, I used the drawing functions in Autocad to connect the dots. Radii on the island corners were estimated, and sign locations were indicated. The final product (Figure 6), including possible paths of travel for the two vehicles involved, came out looking something like this (Road A is to the lower left of the drawing):
Final Scene Drawing, 26KbFIGURE 6

Aerial Shot, 26Kb[NOTE ADDED 12/2004: Overhead photographs are more readily available now than they were 10 years ago. The final drawing above compares reasonably well with a photo of the area, shown to the right.]
[NOTE ADDED 11/2009: Aerial photos are even better now! here's a link to this intersection on googlemaps. The latest aerial photography is amazing in comparison to the vintage stuff shown on this page. You'll notice that I rotated NORTH slightly, as compared to the online maps.]]

This method proved itself better suited to this sort of large, many-curved scene than the rectangular coordinate method, though with a total station I would have taken three times as many points to make the autocad portion go faster. A second (or third) set of hands, and long steel tapes would improve accuracy over the roller wheel used for this scene (and perhaps make taking extra points possible), though I was quite pleased with the results. This method was somewhat time-intensive. I estimate that the method described here required 20% more people-hours on-scene than a Total-station documentation would have required, and about 60 to 80% more time at the computer transfering that information to the final drawing. I would not hesitate to use it again, if more modern methods were not available.

I have heard of one-person range-finding systems available from surveyor supply companies (among others) which incorporate two stationary reference markers and a measuring head, for about $300. The operator places the measuring head at the point of interest and reads off the distance to each of the two reference points. A mapping process such as that undertaken here would then be required, I'd expect. I have heard that a 15mph breeze can severely affect some of these systems, though, so be careful out there!

Copyright 1998, 2020 by Wade Bartlett
Mechanical Forensics Engineering Services, LLC.

This page created 21-OCT-1998
Last edited 04-AUG-2020