GeoWorld November 2012

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Just How Crooked Are Things? BEYONDMAPPING I n a heated presidential election month, this seems an apt title, as things appear to be twisted and contorted from all directions. But politics aside and from a "down to Earth" perspective, how might one measure just how spatially crooked things are? My benchmark for one of the most crooked roads is Lombard St. in San Francisco—it's not only crooked but devilishly steep. How might you objectively measure its crookedness? What are the spatial characteristics? Is Lombard St. more crooked than the eastern side of BY JOSEPH BERRY Colorado's Independence Pass connecting Aspen and Leadville? A Complicated Definition Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at 10 be calculated by dividing the crow-walking distance (crooked) by the crow-flying distance (straight) for an overall measurement of the path's diversion from a straight line. As shown in Figure 1, the diversion ratio for Path1 is 3.14 kilometers / 3.02 kilometers = 1.04, indicating that the road distance is just a little longer than the straight-line distance. For Path2, the ratio is 9.03 kilometers / 3.29 kilometers = 2.74, indicating that Path2 is more than two and a half times longer than its straight line. Based on crookedness being simply "not straight," Path2 is much more crooked. Need a Diversion? Figure 2 depicts an extension of the diversion ratio to the entire road network. The on-road distance from a starting location is calculated to identify a crow's walking distance to each road location (employing Spatial Analyst's Cost Distance tool for the Esri-proficient among us). A straight-line proximity surface of a crow's flying distance from the start is generated for all locations in a study area (Euclidean Distance tool) and then isolated for just the road locations. Dividing the two maps calculates the diversion ratio for every road cell. The ratio for the farthest-away road location is 321 cells / 117 cells = 2.7, essentially the same value as computed using the Pythagorean Theorem for the straight-line distance. Use of the straightline proximity surface is far more efficient than repeatedly evaluating the Pythagorean Theorem, particularly when considering typical project areas with thousands of road cells. In addition, the spatially disaggregated approach carries far more information about the area roads' Webster's Dictionary defines crooked as "not straight," but there's a lot more to it from a technical perspective. For example, consider the two paths along a road network shown in Figure 1. A simple crooked comparison characteristic could compare the "crow-flies" distance (straight line) to the "crow-walks" distance (along the road). The straight-line distance is easily measured using a ruler or calculated using the Pythagorean Theorem. The on-road distance can be manually assessed by measuring the overall length as a series of "tick marks" along the edge of a sheet of paper successively shifted along the route. Or, in the modern age, simply ask Google Maps for the route's distance. The vector-based solution in Google Maps, like the manual technique, sums all the line segments' lengths comprising the route. Similarly, a grid-based solution counts all the cells forming the route and multiplies by an adjusted cell length that accounts for orthogonal and diagonal movements along the sawtooth representation. In Figure 1. A diversion ratio compares a route's actual path distance to its straight-line distance. both instances, a diversion ratio can G E O W O R L D / N O V E M B E R 2 O 1 2 Government Special Issue

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