Improved Identification and Calculation of Horizontal Curves with Geographic Information System Road Layers

Hao Xu and Dali Wei

Horizontal curve data are collected or calculated by transportation the length of each particular curve class (A through F) of a seg- agencies for different purposes because there is always a demand to ment. For example, the total length of Level B curves on an HPMS generate new curve data either to improve the data quality or to extend record segment is reported; tangents and different levels of curves the data coverage. There are different approaches and technologies for are included. The reported data could not give detailed information curve data collection. The selection of methods takes into consideration on curve location, length, or radius. The curve data in HPMS also accuracy, cost, and available sources. There is, consequently, a wide cover only paved principal arterial and rural minor arterial sample interest in extracting curve information from available road network panel sections; it is optional for an HPMS database to include other data of the geographic information system (GIS). When the cost of sections beyond the limits of the sample panel. The HPMS curve GIS data extraction is much lower than the cost of other approaches, data cannot meet new requirements in traffic engineering and high- it is significant to improve the accuracy of GIS curve identification way safety. For example, accurate radius information is a mandatory and calculation. This paper analyzes errors related to existing GIS curve input for state systemic safety improvements and the highway safety calculation­ methods and introduces a new method to identify and to cal­ software of SafetyAnalyst. Transportation agencies have been col- culate horizontal curves with improved accuracy. The new method uses lecting or calculating horizontal curve data either to improve the data regression analysis of road vertex direction–location profiles to calcu­ quality or extend the data coverage. late curve radii. A freeway segment on Interstate 80 in Nevada, includ­ There are different approaches and technologies for curve data col- ing the eastbound and westbound directions, was selected to evaluate lection. Research activities were performed to extract horizontal curve the accuracy of the new method. The evaluation compared the curve data from satellite imagery (2), a GPS survey (3, 4), laser scanning (5), calculation results and the accurate curve information from project and GIS (6). The satellite imagery approach loads satellite imagery contract plans. The evaluation results proved the effect of the new pro­ into MicroStation Inroads or AutoCAD software, then the operator cedure on improving the accuracy of horizontal curve identification manually draws curves along highway centerlines, and finally the and estimation. The new method can be implemented as a GIS tool software calculates the radius of the drawn-out curves. Research was to scan GIS road networks automatically and create horizontal curve also done to develop an automatic process for curve extraction with data layers. This new method can also be used to generate curve data satellite images (7). However, the automatic approach is not widely from GPS survey data. used because of the lack of commercial tools and the uncertainty of the accuracy with differing image quality. Laser scanning can provide highly accurate survey data, but its cost is much higher Horizontal curve data are important in the design, operation, and than that of other approaches. When laser scanning is applied for performance evaluation of highway facilities, and curve data are especially significant for highway safety improvement. Curve-related data collection on a large road network, data management can also crashes, such as head-on crashes and run-off-road crashes, have be very challenging. The selection of curve data generation methods been identified as one of the emphasis areas that evolved from the normally takes into account the accuracy, cost, and existing data AASHTO Strategic Highway Safety Plan (1). Highway curve infor- sources owned by transportation agencies. While road GPS survey mation is an important component of the highway performance moni- data exist in only some transportation agencies, GIS data are avail- toring systems (HPMS) data set and has been collected and maintained able in almost all agencies. There is no data collection cost for using in each state. Curves in HPMS data sets are classified into levels of GIS to calculate curve data. GIS data are maintained by transportation A through F to describe the sharpness of a curve. Level A means that agencies and improved along with the data use, so most GIS road a curve is smooth with a large radius, while Level F means sharp networks are of good quality with relatively high accuracy. There is curves with a short radius. The reported HPMS curve data reflect wide interest in extracting curve information from GIS data. When the related cost is low, it is significant to improve the accuracy of GIS curve identification and calculation. H. Xu, Department of Civil and Environmental Engineering, College of Engineering, University of Nevada, Reno, 1664 North Virginia Street, MS 258, Reno, NV 89557. The common procedure for curve extraction from the GIS road D. Wei, Partners for Advanced Transportation Technology, University of California, network is to obtain location information of each line vertex, and Berkeley, 1357 South 46th Street, Richmond, CA 94804. Corresponding author: then to calculate road directions, to identify curve segments, and H. Xu, [email protected]. finally to calculate curve radii and lengths. One example of GIS Transportation Research Record: Journal of the Transportation Research Board, curve data extraction tools is Curvature Extension, which is a plug-in No. 2595, Transportation Research Board, Washington, D.C., 2016, pp. 50–58. tool of Esri ArcGIS software developed by the Florida Department DOI: 10.3141/2595-06 of Transportation (DOT) (8). The tool calculates curve radius and

50 Xu and Wei 51 length when a user manually identifies a curve’s start point and end the calculation are shown in Figure 1c. The curve radius can be point. The accuracy of curve identification and estimation depends converted to the degree of curve with Equation 2. highly on the user’s judgment and experience, so it is difficult to con- trol accuracy when the tool is used for curve data extraction for 180 RL= (1) a large road network. Automatic GIS curve extraction procedures π∆ and tools were developed to save data extraction effort and improve accuracy (9). The accuracy of curve data extracted by the automatic where tools is decided by the quality of the GIS data and by the calculation R = curve radius, methods used in the procedure. L = length of curve, and This paper analyzes errors related to existing GIS curve calculation Δ = central angle of curve in degrees (deflection angle), which methods and introduces a new approach to improve the accuracy of is the absolute value of PT direction in degrees minus PC curve identification and calculation. The new method uses regression direction in degrees. analysis of direction–location profiles of road segments to calculate the curve radius. A freeway segment was selected on Interstate 80  180 (I-80) in Nevada, including the eastbound and westbound directions, 100  π  18,000 5,729.57 ∆ to evaluate the new method. The evaluation compared the curve D = = ==100 (2) calculation results and the accurate curve information from project RRπ RL contract plans, which were provided by the Nevada DOT. The evalu- ation results showed obvious improvements in the accuracy of curve where D is the degree of curvature (the angle subtended by a 100-ft radius calculation. Curve extraction from GPS survey and GIS data arc along the horizontal curve). uses similar calculation methods. When data formats of GPS points and GIS line vertices can be converted one to the other, methods and tools developed for one data type can also be used for the other. Error Analysis Therefore this new procedure can also be used to generate curve data When this traditional method is used, the accuracy of the calcu- from GPS survey. The new method does not take spiral curves into lated radius is sensitive to the accuracy of the identified PC and PT account, so it cannot be used to identify and calculate spiral curves. locations. When the error with curve length is assumed to be e, the The rest of this paper is organized as follows. Error analysis of calculated radius with error can be estimated by Equation 3; the existing GIS curve calculation methods is presented next, followed error is (57.3/Δ)e. by a description of the curve identification and calculation procedure, including the improved curve identification method and the regression 180 180 180 180 analysis approach for calculating curve radii. The evaluation results RLerrore= rror = ()Le+= Le+ of the new method are presented next, and then the paper concludes π∆ π∆ π∆ π∆ with a discussion of the research and findings. 180 57.3 =+Re=+Re (3) π∆ ∆

Traditional GIS Curve Estimation where and Error Analysis Rerror = curve radius calculated by Equation 1, which includes radius error caused by curve length error; For horizontal curve extraction from GIS, the point of curve (PC) e = curve length error; and and point of tangent (PT) mileposts (MPs), curve length, and curve Lerror = curve length affected by error. radius (or curve degree) need to be estimated with available GIS road layers (10). Curve radius and curve degree are particularly When the PC and PT direction difference is less than 57.3°, the important to highway safety compared with other attributes. The length error will be amplified and will be involved in the calculated general method of curve calculation from GIS data is introduced in radius. For most situations, the direction difference of PC and PT the following section. is lower than 57.3°, so it is common to find that the radius error can be several times the curve length error. Table 1 presents an example of calculated curve errors on an eastbound I-80 segment, Eureka Principle of GIS Curve Calculation County MP 15 to MP 26, in Nevada. The errors were calculated by comparing the road contract plan data and the calculation results of The principle of existing methods is to calculate curve length and the general method. The numbers in the table show the length error curve radius with the use of curve end points (PC and PT), which being amplified and converted into the radius error. The identification are identified by the line vertex direction. An example of GIS line of PC and PT relies on a preset threshold value of the vertex direction vertices is presented in Figure 1a, and an example of vertex direc- change; for example, Li et al. used the threshold value of 1.25° in their tions is shown in Figure 1b. Red points of A, B, and C are the ends procedure (9). When the vertex direction change is higher than the of road segments, and green points are the vertices along the road threshold, it is considered as a start or end point of a curve. The offset segments AB and BC. The arrows in Figure 1b show the directions between the GIS road line and the actual road centerline exists in the of the continuous vertices. The curve length is the distance from PC GIS data. It was found that this offset error is common at the beginning to PT along the curve. The curve length can be calculated by adding or ending part of a curve, which is normally caused by the digitiza- the distances between continuous vertices of the curve or by using tion procedure when the GIS road network is created. In GIS road the directions and distance of PC and PT (9). The radius can then be layers, the curve can start before or after the actual PC or PT points. calculated with Equation 1 (10). The horizontal curve elements for No matter what threshold is selected, there are always curve lengths 52 Transportation Research Record 2595

C

C A B A B

(a)

∆

L

∆ ∆ 2 PC 2 PT (A) ∆ 90 – 90 – ∆ (B) 2 2 A B

R R

(b)

∆

(c)

FIGURE 1 GIS road vertices and curve elements for curve calculation: (a) example of vertices along GIS road segment, (b) demonstration of vertex directions along GIS road segment, and (c) horizontal curve elements.

TABLE 1 Example of Length and Radius Errors Caused by Calculation

Error (ft) by Segment ID

Type of Error 1 2 3 4 5 6 7 8 9 10

Radius 511 724 200 1,491 379 2,400 2,004 1,707 181 1,469 Distance 118 187 135 451 172 899 567 449 128 803

Note: Curve errors calculated for an eastbound I-80 segment in Eureka County, Nevada, MP 15 to MP 26. Xu and Wei 53

being over- or underestimated, which is then amplified and involved lon2 = longitude of current vertex point, in the radius error by the use of existing methods. lat2 = latitude of current vertex point, and R = earth mean radius (20,896,880 ft). The cumulative distance of each vertex can be calculated with New Method of Curve Identification Equation 5. and Calculation ddif i 1 This section introduces the new method of horizontal curve  cumulative_()ii−−1_+≥()i 1 d = (5) identification and calculation with improved accuracy. cumulative_i  0if0i =

where Preprocessing i = vertex ID; In GIS data, roads can be divided into homogeneous segments with i − 1 = previous vertex ID; unique attribute values, such as the annual average daily traffic or dcumulative_i = cumulative distance of vertex i; lane numbers. Joints of the road segments could be in the middle dcumulative_(i−1) = cumulative distance of vertex (i − 1), which is of horizontal curves, which affects the accuracy of the extracted curve cumulative of previous vertex; and information. To avoid this influence, the road segments with the same di_(i−1) = distance between vertex i and its previous vertex, route ID are connected as a continuous road. The mileposts of start vertex i − 1. and end points of the integrated road are recorded, and that informa- Each vertex’s bearing direction can be calculated with Equation 6. tion will be used to estimate MPs of curve PCs and PTs. This curve merging needs to be performed before GIS curve data extraction. Vertices along a merged continuous road are then extracted as the  sinl()at21−−sinl()at i cosl()on21lon  θ=arccos  (6) input of the following calculation procedure. The extracted vertices  sinl()on21− lonci os()lat1  should include at least the information on latitude and longitude. On the basis of calculated cumulative distance and direction of each vertex, the direction–distance profile along a GIS road can be Development of Road Location–Direction Profiles created as in the example shown in Figure 2. A Google aerial map was attached with the profile chart to demonstrate how the direc- With the vertex data extracted from the merged road network, each tion changed along a freeway segment. The northbound direction is vertex’s cumulative distance to the beginning point of a road is to be defined as °0 and the eastbound direction is defined as 90°. Use of calculated. The distance between each pair of continuous vertices is the direction–distance profile for the curve radius estimation is the calculated with Equation 4. major difference between this new method and the existing ones.

sinl()at12i sinl()at + cosl()at1  dR= i arccos   i R (4) Improved Curve Identification with Direction  iicosl()at22cosl()on − lon1  Change Calculation at Each Vertex where To identify horizontal curves and tangents, the bearing direction

lon1 = longitude of previous vertex point, of vertices needs to be compared with a preset direction threshold. lat1 = latitude of previous vertex point, However, the calculated bearing direction of continuous vertices

140 0°

120 270° 90° 100 )

80

60 Whole Direction ( °

0 0 5,000 10,000 15,000 20,000 25,000 Location (ft)

FIGURE 2 Example of direction–location profile along GIS road line. 54 Transportation Research Record 2595

100 90 80 70 ) ç 60 50 Study segment 40

Direction ( Curve 30 20 10 0 15 17 19 21 23 25 27 Milepost (a)

(b)

FIGURE 3 Demonstration of bearing direction fluctuation. fluctuates along road lines, no matter whether it is on a tangent the Figure 4 chart. The comparison shows that the new method pro- segment or a curve. One example of another I-80 eastbound segment vides a better profile to tell whether it is a curve or a tangent and the is shown in Figure 3 with an aerial picture to show the accrual road location of start and end points of curves. With the new vertex direc- and curves. The segment marked by the red circle in the chart is a tion changes, the horizontal curves can be identified with a vertex tangent segment. Its vertex directions should be a fixed value in the direction change threshold. A threshold of 2° is recommended on real world, but the vertex directions bump up and down in the GIS the basis of the bearing change distribution, as shown in Figure 5. layer. This situation may cause misidentification of curves or start This threshold allows the new procedure to detect curves accurately. and end locations. The moving average is applied to reduce the In Figure 5, it can be seen that a 2° threshold still missed some curve effect of direction fluctuation on curve identification. The width of points at the beginning or end parts of curves. Therefore, very short the moving average window should not be too short to smooth the and smooth curves may be misidentified as tangents by the new fluctuation. However, it cannot be too long, or more curve points method. However, short and smooth curves are not major concerns at the ends of curves will be missed. The average direction of five in traffic operation and safety. The missed points cause errors in PT, vertices was found to be good for curve identification. PC, and curve length, which further cause radius errors when the To improve the accuracy of identification of beginning or end existing horizontal curve calculation methods are used, as documented parts of curves, the difference between the 5-point average direction previously. This problem has been solved by the proposed linear before and the 5-point average direction after a vertex is calculated. regression method introduced in the next section. An example of The 5-point directions before and after were based on data pro- curves identified with the new method is presented in Figure 4 as cessing experience but not on an optimized running average band the orange dotted lines (named “curve”). width. The difference is used as the vertex direction change in the new method. The direction change is calculated at each vertex with Equation 7. Curve Radius Estimation by Regression Analysis of Location–Direction Profiles w w ∑∑θik+ θik− k=00k= After the horizontal curves were identified with the method introduced ∆θi = − (7) ww+ 11+ in the previous subsection, linear reference analysis was performed with the direction–location profile of each identified curve. For simple where Δθi is the direction difference at vertex i and w is the moving horizontal curves (part of a circle), the direction–location relationship average window width, valued as 4 in the study (5-point average is consistent with a linear relationship. So the relationship can be fitted including current vertex). by a linear function with regression analysis. The linear function can The direction change at each vertex of the sample eastbound seg- be expressed as Equation 8. ment of I-80 is shown in Figure 4. The direction difference between adjacent vertices used in existing methods is also demonstrated in θ=iiaxi + b (8) Xu and Wei 55

100

90

80

70

) 60 Study segment

Curve 50 Average direction difference

Direction ( ° 40 Average direction difference between adjacent vertices 30

20

10

0 15 17 19 21 23 25 27 Milepost

FIGURE 4 Comparison of vertex direction change and direction difference between adjacent vertices.

where Therefore, the degree of curve can be calculated by the constant term a of the linear function as in Equation 9. θi = bearing direction at vertex i,

xi = location of vertex i (MP number is used in study) (mi), ∆  1  a and D = 100 = 100 iia = (9) L  5,280 ft mi  52.8 a and b = constant terms of linear function. An example of the linear functions of horizontal curves on the So the curve radius (R) (ft) can be calculated with Equation 10. sample eastbound I-80 segment is shown in Figure 6. 5,729.57 5,729.57 × 52.8 302,521 According to Equation 2, the degree of curve can be calculated R == = (10) by the ratio of the direction difference over the location difference. Daa ) Direction Difference ( ç Direction Difference

Milepost

FIGURE 5 Vertex direction change threshold (28). 56 Transportation Research Record 2595

y = 99.073x – 1,590.3 y = 48.92x – 846.52 y = 53.349x – 766.3

y = 51.578x – 1,100.2 y = –75.49x + 1,375.4 y = –63.345x + 1,312.9 )

y = –41.055x + 894.66 y = 47.607x – 1,139.3 y = –58.616x + 1,020.7 Direction ( ° Direction

y = –60.52x + 1,481.6

Milepost Location (mi)

FIGURE 6 Example of linear functions of identified simple curves.

Evaluation of the New Approach accurate curve data from the Nevada DOT contract plans. Evaluation of the curve identification accuracy is summarized in the following: To test and evaluate the effect of the new method on horizontal curve identification and evaluation, the eastbound and westbound direc- • For I-80E, 10 of 11 curves were identified (91%); the missed tions of an I-80 segment—Eureka County MP 15 to MP 26 (11 mi) curve was 457.37 ft in length with a 10,000-ft radius. in Nevada—were tested. The curve calculation results with the new • For I-80W, 11 of 11 curves were identified (100%). method are shown in Table 2. These results were compared with the • The total curve identification accuracy is 95.5%.

TABLE 2 Results of Curve Calculation with Proposed New Procedure

Contract Comparison

Curve ID PC (mi) PT (mi) Length (ft) Radius (ft) PC (mi) PT (mi) Length (ft) Radius (ft) Length (ft) Radius (ft)

I-80 Eastbound: Calculation Results 1 15.49 15.90 2,162 5,470 15.48 15.91 2,304 5,500 −142 −30 2 16.01 16.39 1,978 4,614 15.99 16.38 2,030 5,000 −53 −386 3 16.71 16.95 1,292 2,856 16.66 16.95 1,554 3,000 −262 −144 4 17.05 17.24 997 3,324 17.05 17.24 1,008 3,078 −11 246 5 18.77 19.12 1,862 5,934 18.75 19.19 2,305 6,000 −442 −66 6 19.30 19.54 1,306 3,721 19.31 19.57 1,355 3,584 −49 137 7 20.14 20.41 1,432 6,173 20.12 20.47 1,833 6,000 −401 173 8 22.48 22.69 1,135 4,923 22.46 22.72 1,349 5,000 −214 −77 9 23.31 24.10 4,176 4,933 23.35 24.17 4,332 5,108 −156 −175 10 24.51 25.01 2,614 5,916 24.54 25.13 3,148 5,909 −534 7 I-80 Westbound: Calculation Results 11 15.49 15.90 2,188 5,454 15.46 15.90 2,304 5,500 −117 −46 10 15.97 16.37 2,155 5,102 15.99 16.37 2,013 4,956 142 146 9 16.65 16.94 1,517 3,114 16.65 16.95 1,577 3,044 −60 70 8 17.04 17.23 984 3,031 17.02 17.22 1,082 3,000 −99 31 7 18.20 18.46 1,391 7,781 18.16 18.48 1,706 7,500 −314 281 6 18.61 18.93 1,698 2,889 18.57 18.91 1,824 2,983 −126 −94 5 19.28 19.55 1,406 3,668 19.30 19.55 1,324 3,500 83 168 4 20.09 20.90 4,313 6,556 20.10 20.88 4,080 6,400 233 156 3 20.92 22.00 5,723 9,034 20.98 22.09 5,819 8,987 −96 47 2 23.30 24.05 3,986 4,909 23.34 24.14 4,240 5,000 −255 −91 1 24.35 25.07 3,790 6,303 24.53 25.14 3,205 6,017 585 286 Xu and Wei 57

9.00

8.00 100% curve radius with error in range of 10%

7.00

6.00 90% curve length with error in range of 5% 5.00

4.00 WB curve radius EB curve radius 3.00

2.00 Error or Retracement Value (%) Value or Retracement Error 1.00

0.00 15 17 19 21 23 25 27 Milepost

FIGURE 7 Evaluation of curve radius accuracy (WB = westbound; EB = eastbound).

Evaluation of the accuracy of the curve radius calculation is the calculated curve radius is not directly related to the value of R2. demonstrated in Figure 7. One hundred percent of the calculated Therefore, this research evaluated only the accuracy of the extracted radii were within the error range of 10%, and 90% of the radii were curve information; it did not compare the R2-values of the different within the error range of 5%. To evaluate how the new method curve segments. improved the radius calculation accuracy, the radius calculation results with the new method and with the traditional method are compared in Figure 8. Conclusion Error in the curve radius calculation can be caused by the error or offset in the GIS data. The new method applies the regression This research developed a new procedure to identify and calculate analysis to fit the direction–distance profile of each curve with a horizontal curves with GIS road network data. Errors caused by GIS linear equation. The coefficient of determination (R2) of each curve data and the traditional curve calculation method were analyzed. is different and decided by the GIS data quality. The accuracy of The new curve identification method calculates direction change Radius (ft)

Curve Segment (west to east)

FIGURE 8 Comparison of results of traditional method and new method. 58 Transportation Research Record 2595 at each vertex by comparing directions of before points and after References points. The new identification method improves the accuracy of curve identification, compared with the traditional curve identifica- 1. Torbic, D. J., D. W. Harwood, D. K. Gilmore, R. Pfefer, T. R. Neuman, tion procedure, which simply calculates the adjacent vertex direction K. L. Slack, and K. K. Hardy. Guidance for Implementation of the AASHTO Strategic Highway Safety Plan. NCHRP Report 500. Volume 7: difference. There are always errors included in the identified begin- A Guide for Reducing Collisions on Horizontal Curves. Transportation ning and end points of curves, no matter the accuracy of curve identi- Research Board of the National Academies, Washington, D.C., 2004. fication. The traditional method takes and even amplifies these errors 2. Zhao, H., J. Kumagai, M. Nakagawa, and R. Shibasaki. Semiautomatic into the calculated radius. The authors developed a new method to Road Extraction from High-Resolution Satellite Image. International Archives of Photogrammetry and Remote Sensing, Vol. 34, No. 3B, estimate curve radius by using the linear regression analysis. The pp. 406–411. new method eliminates the effect of beginning and end curve errors. 3. Imran, M., Y. Hassan, and D. Patterson. GPS-GIS–Based Procedure for The evaluation study compared the results from the new method, Tracking Vehicle Path on Horizontal Alignments. Computer-Aided Civil the traditional method, and the accurate curve data from the Nevada and Infrastructure Engineering, Vol. 21, No. 5, 2006, pp. 383–394. 4. Osei-Asamoah, A., and E. Jackson. Development of the ConnDOT DOT. The evaluation and comparison results clearly show the effect Horizontal Curve Classification Software. Report CT-2285-F-14-3. of the new procedure on improving the accuracy of horizontal curve Connecticut Department of Transportation, Newington, 2014. identification and estimation. The method can be implemented as a 5. Kim, J. S., J. C. Lee, I. J. Kang, S. Y. Cha, H. Choi, and T. G. Lee. Extraction GIS tool to scan GIS road networks automatically and create hori- of Geometric Information on Highway Using Terrestrial Laser Scanning Technology. International Archives of the Photogrammetry, Remote zontal curve data layers. The new procedure can help transportation Sensing and Spatial Information Sciences, Vol. XXXVII. Part B5, 2008, researchers to extract curve data for traffic design, operation, and pp. 539–544. safety analysis. 6. Findley, D. J., C. V. Zegeer, C. A. Sundstrom, J. E. Hummer, W. Rasdorf, The new method cannot estimate spiral curve attributes. How- and T. J. Fowler. Finding and Measuring Horizontal Curves in a Large Highway Network: A GIS Approach. Public Works Management and ever, the regression analysis approach can be extended to calcu- Policy, Vol. 17, No. 2, 2012. late spiral curves in future research by using nonlinear regression 7. Dong, H., S. M. Easa, and J. Li. Approximate Extraction of Spiraled Hori- functions for spiral curves. Curve extraction from GPS survey or zontal Curves from Satellite Imagery. Journal of Surveying Engineering, GIS data uses similar calculation methods. When data formats of Vol. 133, No. 1, 2007, pp. 36–40. 8. Geographic Information System (GIS): Curvature Extension for GPS points and GIS line vertices can be converted, one to the other, ArcMap 10.2. Florida Department of Transportation, Transportation methods and tools developed for one data type can also be used Statistics Office, Tallahassee, 2015. for the other. Therefore, the new approach introduced in this paper 9. Li, Z., M. V. Chitturi, A. R. Bill, and D. A. Noyce. Automated Identifica- can be used to process GPS survey data for curve identification and tion and Extraction of Horizontal Curve Information from Geographic Information System Roadway Maps. In Transportation Research Record: calculation. Journal of the Transportation Research Board, No. 2291, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 80–92. 10. A Policy on Geometric Design of Highways and Streets. AASHTO, Acknowledgment Washington, D.C., 2010.

This research was supported by the Nevada Department of The Standing Committee on Geographic Information Science and Applications Transportation, Traffic Safety Engineering Division. peer-reviewed this paper.