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Infrastructures
, Volume 6 (1) – Dec 24, 2020

/lp/multidisciplinary-digital-publishing-institute/procedure-for-the-identification-of-existing-roads-alignment-from-ejK8V09hR1

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- 10.3390/infrastructures6010002
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infrastructures Article Procedure for the Identiﬁcation of Existing Roads Alignment from Georeferenced Points Database Giuseppe Cantisani * and Giulia Del Serrone Department of Civil, Constructional and Environmental Engineering, University of Rome La Sapienza, Via Eudossiana 18, 00184 Rome, Italy; giulia.delserrone@uniroma1.it * Correspondence: giuseppe.cantisani@uniroma1.it Abstract: The aim of this research is to look for an automated, economical and fast method able to identify the elements of an existing road layout, whose original geometric design could date back to distant ages and could have undergone major modiﬁcations over the years. The analysis has been directed towards the Italian two-lane rural roads; the national public company ANAS made available its graph, obtained from high-performance surveys, that represents about 90% of these roads’ network. The graph is made up of a collection of georeferenced points but does not recognize or describe the geometric elements making up the roadway. Consequently, it has been necessary to design and develop an original procedure, subsequently implemented in a programming platform, able to identify the characteristics of the several parts, which constitute the reference axes of the existing roads. This research focuses on the horizontal geometry assessing the coherence, consistency and homogeneity of the roads’ layout, through the ex post application of the regulatory model for the design veriﬁcation. If road sections are identiﬁed in which some conditions are not signiﬁcantly met, further investigation should be conducted in order to ensure road safety and to plan any road upgrading activities. Keywords: road-alignment identiﬁcation; horizontal geometry; road consistency; design veriﬁcation; automated procedure Citation: Cantisani, G.; Del Serrone, G. Procedure for the Identiﬁcation of Existing Roads Alignment from 1. Introduction Georeferenced Points Database. 1.1. Context and Aim of the Work Infrastructures 2021, 6, 2. https:// The safety assessments for newly built roads can be carried out according to the dx.doi.org/10.3390/infrastructures6 guidelines of the design standards. In Italy, speciﬁcally, the Ministerial Decree dated 5.11.2001 [1], referring back to the road classiﬁcation of the Highway Code [2], deﬁnes the constructive, technical and functional characteristics of each type of road; with regard to Received: 12 November 2020 Accepted: 22 December 2020 these features, it imposes prescriptions for the design and veriﬁcation of the geometric Published: 24 December 2020 elements and their composition, so that the road users’ movement takes place regularly and safely. Publisher’s Note: MDPI stays neu- The veriﬁcation of the design accuracy includes the road consistency examination. tral with regard to jurisdictional claims The road consistency is the characteristic of the infrastructure that makes it suitable to meet in published maps and institutional road user expectations and implies that the geometric successive elements are coordinated afﬁliations. in order to produce harmonious and homogeneous driver performance and to not generate incorrect and, sometimes, unsafe driving behavior [3–5]. The rules that guide road design should ensure that a driver is spontaneously induced to adopt a driving behavior that is congruent with the real characteristics of the road. It is Copyright: © 2020 by the authors. Li- the case of the “self-explaining roads” [6,7], which are deﬁned as roads where drivers per- censee MDPI, Basel, Switzerland. This ceive and recognize the features of the infrastructure they are driving on and “instinctively” article is an open access article distributed know how to behave [8]. Since the driver ’s behavior is directly related to the perception of under the terms and conditions of the the route he/she is following, a designer should make the road as readable as possible, so Creative Commons Attribution (CC BY) as to guide the user in the behavioral choices to be adopted, suitable to deal with even the license (https://creativecommons.org/ licenses/by/4.0/). most dangerous situations [9–11]. Infrastructures 2021, 6, 2. https://dx.doi.org/10.3390/infrastructures6010002 https://www.mdpi.com/journal/infrastructures Infrastructures 2021, 6, 2 2 of 16 Many studies have found that some design choices, violating the user ’s expectations, can negatively affect his/her behavior [12–15], by inducing the disoriented driver to change his/her usual driving choices and leading him/her to have risky driving behavior. The inadequacy of the technical characteristics of the road can be detected under sev- eral aspects, including, for example, unsuitable adhesion values of tire-asphalt pavement interface to guarantee the transfer of dynamic actions, geometric horizontal alignments design or conditions of the environment surrounding the infrastructure insufﬁcient in ensuring a correct perception of the route, especially for occasional users. Design, construc- tion, but above all maintenance problems are often the cause or contributing cause of high levels of accidents on many road networks. Therefore, it is necessary to investigate in more detail what the role of the infras- tructure may be in the occurrence of accidental events, in order to assess what type of countermeasures can be implemented to ensure higher safety standards. In particular, in order to be conducted, evaluations related to the consistency of the technical characteristics of existing roads, require data that correctly represent the geometric characteristics of the infrastructures; such data are often not accessible, not updated or do not have the accuracy and precision required to perform the analysis to be carried out. In light of the above, the identiﬁcation of the plano-altimetric geometrical characteris- tics of the existing roads is still a topic of great interest in the ﬁeld of civil and transportation engineering. Considering these problems, the objective of this research is looking for an automated, economical and fast procedure able to identify the elements of a road lay- out belonging to an existing and operating road network. In particular, the horizontal geometry—and, more speciﬁcally, the continuous trend of curvatures—is especially needed in order to perform the ex post application of some standard design rules and assess the coherence, consistency and homogeneity of the road infrastructure. There are no shared and reliable methodologies that establish how this activity should be carried out, for the purpose of performing road safety analyses and for the maintenance of the infrastructure. Although much research has presented techniques and procedures suitable to obtaining useful data from surveys, no methods are available for the extraction of the reference axis (it means a continuous and coordinated line, composed by basic elements mathematically described, like in the design process of a new track) of an existing road section. Thus, the aim of this work and the proposed contribution to the state of the practice is to overcome the described lack. 1.2. State of the Practice In general, in order to overcome the lack of information about the existing road networks, a lot of energy has been spent in research aimed at obtaining the geometry of the compositional elements of the layout from different sources. Various attempts were made to obtain information regarding the horizontal and vertical alignment both from aerial and satellite georeferenced images, both from road maps of geographic information systems, and from data collected with positioning sensors on mobile systems and vehicles. There are many road geometry relief techniques to date, which can be divided into static and dynamic ones, depending on the instrumentation used to obtain the data. Among the static procedures, the following may be enumerated: - Fully automated acquisition methods that extract horizontal curve data directly from road maps in GIS environment [16,17]. - Automatic identiﬁcation of road geometry from digital vector data [18]. Among the dynamic ones, on the other hand, it is worth mentioning: 1. Detection systems using mobile mapping system (M.M.S.) technology. These are widely appreciated both for their versatility and for their low operating costs. In general, M.M.S. are made up of vehicles equipped with different instruments, properly integrated with each other: a satellite navigation device, an Inertial Navigation System (INS) and an odometer [19–22]. In speciﬁc cases, the “Digital Highway Data Vehicle” (DHDV) has been used, an integrated system through which three Euler angles, the Infrastructures 2021, 6, 2 3 of 18 1. Detection systems using mobile mapping system (M.M.S.) technology. These are widely appreciated both for their versatility and for their low operating costs. In gen- eral, M.M.S. are made up of vehicles equipped with different instruments, properly Infrastructures 2021, 6, 2 3 of 16 integrated with each other: a satellite navigation device, an Inertial Navigation Sys- tem (INS) and an odometer [19–22]. In specific cases, the “Digital Highway Data Ve- hicle” (DHDV) has been used, an integrated system through which three Euler an- gles, the driving speed and the vehicle acceleration were measured to perform the driving speed and the vehicle acceleration were measured to perform the survey survey in a rigorous way [20,23]. Another instrumented vehicle able to collect pave- in a rigorous way [20,23]. Another instrumented vehicle able to collect pavement ment condition and asset data and not only geometric information is the van auto- condition and asset data and not only geometric information is the van automatic matic road analyzer (ARAN) [24]. road analyzer (ARAN) [24]. 2. Global Navigation Satellite System (GNSS) with GPS receivers mounted on trains 2. Global Navigation Satellite System (GNSS) with GPS receivers mounted on trains [25–27] [25–27] or vehicles travelling at almost constant speeds, instrumented with vertical or vehicles travelling at almost constant speeds, instrumented with vertical gyroscopes gyroscopes and gyro compasses able to provide information on the vehicle positions and gyro compasses able to provide information on the vehicle positions (x, y, z (x, y, z coordinates) and orientations (angle of pitch, roll and yaw) [28–32]. In some coordinates) and orientations (angle of pitch, roll and yaw) [28–32]. In some cases, case vehicle s, vehpositions icle position have s hbeen ave been recor recorded d via ed via smartphone smartphone [33]. [33]. The describe The described d techniques techniques are gen are generally erally effici ef ent ﬁcient and v and alid valid for ac for quiring a acquiring dataa sedataset t but, once the necessary points for the definition of the road geometry have been collected, there but, once the necessary points for the deﬁnition of the road geometry have been collected, comes the n there comes eed to dev the needeto lop develop a rapida an rapid d economic and economic procedu pr rocedur e that a ellows to ea that allows sily to a easily nd pre- and cisely obt precisely ain obtain the geometric the geometric definit deﬁnition ion of the of the plan plano-altimetric o-altimetric road la roadyout layout tha that t shoul should d be be mathematically formalized through simple and continuous geometric elements. mathematically formalized through simple and continuous geometric elements. The above-mentioned studies and the proposed techniques, in fact, are able to obtain The above-mentioned studies and the proposed techniques, in fact, are able to obtain points and to determine the coordinates of the track, but they do not manage to deﬁne a points and to determine the coordinates of the track, but they do not manage to define a continuous curvature graph (or a continuous reference line), which is useful to conduct continuous curvature graph (or a continuous reference line), which is useful to conduct safety evaluation by means of the ex post application of the design veriﬁcations. Only safety evaluation by means of the ex post application of the design verifications. Only in in some cases, they can efﬁciently identify circular curves with their radii and straight some cases, they can efficiently identify circular curves with their radii and straight lines, lines, but they cannot represent the reference road axis in the traditional design way as a but they cannot represent the reference road axis in the traditional design way as a suc- succession of straight lines, circular arcs and clothoids. cession of straight lines, circular arcs and clothoids. Over the years, multiple algorithms, able to identify in an automated way the circular Over the years, multiple algorithms, able to identify in an automated way the circular arcs and the straight lines, have been built; the most successful method is that of the arcs and the straight lines, have been built; the most successful method is that of the least least squares ﬁtting of the points of the road axis. The most widely used and easily squares fitting of the points of the road axis. The most widely used and easily implementa- implementable algorithm is the least squares circle ﬁtting, able to estimate radius, angle at ble algorithm is the least squares circle fitting, able to estimate radius, angle at the center the center and arc length with high accuracy; as can be seen in Figure 1, it can minimize and arc length with high accuracy; as can be seen in Figure 1, it can minimize the devia- the deviations between the computed curve and the original points [34]. tions between the computed curve and the original points [34]. Figure 1. A least square circle ﬁtting example. Figure 1. A least square circle fitting example. The least squares regression method is a technique aimed at determining an analytical The least squares regression method is a technique aimed at determining an analyti- function that approximates a set of values without necessarily passing through the points cal function that approximates a set of values without necessarily passing through the themselves. In fact, if the data come from experimental measurements and are, therefore, points themselves. In fact, if the data come from experimental measurements and are, affected by measurement or instrument errors, or if the data quality is not very accurate therefore, affected by measurement or instrument errors, or if the data quality is not very (few signiﬁcant ﬁgures), then it is appropriate to approximate to least squares rather than accurate (few significant figures), then it is appropriate to approximate to least squares interpolate. In particular, the function found must be the one that minimizes the sum of rather than interpolate. In particular, the function found must be the one that minimizes the squares of the distances between the points and the plotted curve [35]. the sum of the squares of the distances between the points and the plotted curve [35]. As an implementation of the aforementioned algorithm, an iterative least squares circle ﬁtting algorithm has been proposed, which iteratively searches for circumferences approximating the available data, changing the center and radius of the arc from time to time, until the smallest possible differences between the input data and the originated output are achieved [28]. Another similar method, useful for searching the characteristic parameters of horizontal curves, generates from the calculation of each circle that can be drawn using all the triplets of non-aligned points, reducing iteratively the distance between the circle and the complete set of points, using a minimization method [36]. Infrastructures 2021, 6, 2 4 of 16 In general, the algorithms developed through the least squares ﬁtting method have tried to evaluate the reliability and accuracy of the results obtained, considering the errors due to the surveying GPS instrumentation [32,37,38]. Other approaches deﬁned by data collected from inertial measurement units ﬁtted to road vehicles have also been used for radius measurement, including the kinematic method, the geometry method, the lateral acceleration method and the chord offset method [20,39]: The kinematic method plans to use the longitudinal speed (v) and centrifugal accelera- tion (a) values, directly obtained from the dataset provided by the vehicle, according to the following formula: R = (1) The geometry method involves linear approximation of the vehicle’s trajectory be- tween one measurement point and the next one—linearization made possible by the high data sampling frequency—and calculates the curve radius through the reciprocal of the curvature: 2 2 dy 1 + dx R = ; (2) d y dx The lateral acceleration method uses the data of super-elevation, side friction factor and speed to calculate the corresponding radius: R = (3) 127(q + f ) According to the chord offset method, the chord length (L) and the offset between the chord and the arc midpoint (M) are measured through the vehicle’s trajectory; using these parameters, it is possible to calculate the radius of the curve: L M R = + (4) 8M 2 In order to identify of the starting and ending points of the circular arcs; instead, the heading angle trends have been studied and their linear variation has been determined [20,39]. Finally, it is worth mentioning that several authors have used a completely different method from what was exposed so far to recreate the road geometry; this method involves the interpolation of raw data, acquired to identify the road layout, through polynomial curves and/or splines [29,30,40,41]. In contrast to some previous research, which are based on the B-spline approxima- tion [30,42,43], the proposed method utilizes a data ﬁtting process. The least square regression is an optimization technique that allows to ﬁnd a function, represented by an op- timal curve, that is as close as possible to a set of data. Other similar procedures have been implemented in these years to automatically identify all horizontal geometric elements and produce recreated alignment geometry for existing roads and railways [29,44,45]. 2. Materials and Methods As anticipated, the objective of the analysis entails in the deﬁnition of a methodology able to recognize the reference axis, which means the road layout composing elements as a succession of straight lines, circular arcs and clothoids. This is important and necessary for a more general purpose, which consists in the preventive safety evaluation offered by existing roads, through procedures based on the veriﬁcation criteria of safety conditions referred to the road geometry. It should be noted that, for example, on Italian roads in 2018, road accidents with injuries to persons were 172,553, with 3334 victims and 242,919 injured (see Figure 2). Infrastructures 2021, 6, 2 5 of 18 2. Materials and Methods As anticipated, the objective of the analysis entails in the definition of a methodology able to recognize the reference axis, which means the road layout composing elements as a succession of straight lines, circular arcs and clothoids. This is important and necessary for a more general purpose, which consists in the preventive safety evaluation offered by existing roads, through procedures based on the verification criteria of safety conditions Infrastructures 2021, 6, 2 5 of 16 referred to the road geometry. It should be noted that, for example, on Italian roads in 2018, road accidents with injuries to persons were 172,553, with 3334 victims and 242,919 injured (see Figure 2). Ac- Accidents and injuries are progressively decreasing on urban roads and freeways, while cidents and injuries are progressively decreasing on urban roads and freeways, while they they are increasing on rural roads. are increasing on rural roads. Figure 2. Road accidents, deaths and injuries for different road categories. Source: Italian National Figure 2. Road accidents, deaths and injuries for different road categories. Source: Italian National Institute of Statistics—Istat (2018). Institute of Statistics—Istat (2018). Given the high accident rate found on single-carriageway rural roads, which are Given the high accident rate found on single-carriageway rural roads, which are more suitable for studying and understanding the behavior of users in relation to the more suitable for studying and understanding the behavior of users in relation to the char- characteristics of the road, it was decided to focus the research on single-carriageway acteristics of the road, it was decided to focus the research on single-carriageway high- highways outside urban perimeters. ways outside urban perimeters. Since the Italian state roads are spread throughout the national territory and about Since the Italian state roads are spread throughout the national territory and about Infrastructures 2021, 6, 2 6 of 18 90% of this network is managed by the company ANAS S.p.A., the choice of the road 90% of this network is managed by the company ANAS S.p.A., the choice of the road network to analyze has fallen on the roads managed by this company, shown in Figure 3. network to analyze has fallen on the roads managed by this company, shown in Figure 3. Figure 3. Geographical representation of the road network managed by ANAS S.p.A. as of 10 October 2019. Figure 3. Geographical representation of the road network managed by ANAS S.p.A. as of 10 Oc- tober 2019. The company ANAS S.p.A. has shared with the authors its road graph, realized by means of high-performance surveys and composed of three-dimensional geographical The company ANAS S.p.A. has shared with the authors its road graph, realized by coordinates. The network graph is, therefore, made up of georeferenced points, but it means of high-performance surveys and composed of three-dimensional geographical co- does not recognize or describe the geometric elements making up the road. Thus, it ordinates. The network graph is, therefore, made up of georeferenced points, but it does not recognize or describe the geometric elements making up the road. Thus, it was neces- sary to design and develop an original procedure, subsequently implemented in a pro- gramming platform, aimed at identifying the different geometric elements that constitute the planimetric road layout. Therefore, the research essentially consists of a new approach proposed with the aim to reconstruct the horizontal road alignment by using traditional design elements such as straight lines, circular arcs and transition curves. The first difficulty met has been the processing of a huge amount of raw data, specif- ically the georeferenced points in space. The first research step has been looking into fil- tering and sorting the vertices of the road graph to obtain an ordered set of geographical coordinates to be connected. Once the heading direction graph was constructed, it has been necessary to clean the data from repetition and inaccuracy and then smooth the resulted line through the appli- cation of a moving average filter, as the values were affected by measurement or instru- ment errors. The Savitzky–Golay filter used is a digital low-pass filter that allows to make the data trend more continuous; it is applied to a series of data points in order to decrease the signal noise without deforming the signal. The subsets of consecutive data points are fit- ted using a low order polynomial with linear least square method, so the convolution of all the polynomials is then obtained [46]. The data, having a set of n {xj, yj} points, where j = 1, 2…n, and x is an independent variable, whereas y is an observed value, can be repre- sented with a set of m convolution coefficients Ci; the effect of convolution can be ex- pressed as a linear transformation: Infrastructures 2021, 6, 2 6 of 16 was necessary to design and develop an original procedure, subsequently implemented in a programming platform, aimed at identifying the different geometric elements that constitute the planimetric road layout. Therefore, the research essentially consists of a new approach proposed with the aim to reconstruct the horizontal road alignment by using traditional design elements such as straight lines, circular arcs and transition curves. The ﬁrst difﬁculty met has been the processing of a huge amount of raw data, specif- ically the georeferenced points in space. The ﬁrst research step has been looking into ﬁltering and sorting the vertices of the road graph to obtain an ordered set of geographical coordinates to be connected. Once the heading direction graph was constructed, it has been necessary to clean the data from repetition and inaccuracy and then smooth the resulted line through the application of a moving average ﬁlter, as the values were affected by measurement or instrument errors. The Savitzky–Golay ﬁlter used is a digital low-pass ﬁlter that allows to make the data trend more continuous; it is applied to a series of data points in order to decrease the signal noise without deforming the signal. The subsets of consecutive data points are ﬁtted using a low order polynomial with linear least square method, so the convolution of all the polynomials is then obtained [46]. The data, having a set of n {x , y } points, where j j j = 1, 2, . . . , n, and x is an independent variable, whereas y is an observed value, can be represented with a set of m convolution coefﬁcients Ci; the effect of convolution can be expressed as a linear transformation: Infrastructures 2021, 6, 2 7 of 18 i=(m1)/2 m + 1 m 1 Y = C y j n (5) j å i j+i 2 2 ()/ i=(m1)/2 𝑚+ 1 𝑚− 1 𝑌 = 𝐶 𝑦 ≤ 𝑗 ≤𝑛 − (5) 2 2 ()/ Three inputs are necessary to execute a Savitzky–Golay ﬁlter: the signal (x), the polynomial Three inputs or are nec der (ke)ssar and y to execute its frame a Sav length itzky (f–G ); in olay fi Figur lter: e 4 th ,e s an igna example l (x), the can pol-be seen. ynomial order (k) and its frame length (f); in Figure 4, an example can be seen. Figure 4. Figure Example of 4. Example a smooth of a smoothing ing technique o technique btained by app obtained lying a low-pass filter. by applying a low-pass ﬁlter. Consequently, a data mining effort has been made to write a code able to automati- Consequently, a data mining effort has been made to write a code able to automatically cally approximate the heading direction signal and generate a new trend, through which approximate the heading direction signal and generate a new trend, through which it has it has been easier to search for the starting and ending points of the sections with zero been easier to search for the starting and ending points of the sections with zero curvature. curvature. Subsequently, using the vertices falling within the starting and ending points of each Subsequently, using the vertices falling within the starting and ending points of each constant curvature element, a least square regression has been implemented in a different constant curvature element, a least square regression has been implemented in a different code, in order to automatically ﬁnd centers and radii of the circular arcs, analyzing from code, in order to automatically find centers and radii of the circular arcs, analyzing from time to ti time to me t time he devia the deviation tion standards. standards. A linear least square problem is [47]: A linear least square problem is [47]: ( ) 𝑚𝑖𝑛 𝑓 𝑥, 𝑟 (6) , 2 min f (x, r) (6) x,r å j j=1 where 𝑓 (𝑥, 𝑟 ) is the “residual”, 𝑓 (𝑥, 𝑟 ) = |𝑥 − 𝑎 | −𝑟 (7) The optimal values of the original variables x,r can be recovered from the formulae: x = y , i = 1,2, … , n r = y +x x (8) Once the geometrical parameters were known, two other programming codes have been written to construct in an automatic and rapid way the curvature graph and the de- sign speed profile, according to the Italian road design guidelines. This procedure will be described below and Highway n. 4 (S.S. n. 4) will be reported as a case study. 3. Results The main obtained results refer to the application to the case study of the “Strada statale n. 4 Via Salaria”. This is an Italian state highway (HWY); it is a single carriageway highway for most of its route, presenting one lane per each travel direction, but it falls into the category of dual carriageway urban road in its first part (near to Rome city center). It, therefore, follows that this infrastructure is characterized by many various geometrical elements, changing gradually from urban highway to mountain road. Infrastructures 2021, 6, 2 7 of 16 where f (x, r) is the “residual”, f (x, r) = x a r (7) j j The optimal values of the original variables x, r can be recovered from the formulae: x = y , i = 1, 2, . . . , n r = y + x x (8) i n+1 Once the geometrical parameters were known, two other programming codes have been written to construct in an automatic and rapid way the curvature graph and the design speed proﬁle, according to the Italian road design guidelines. This procedure will be described below and Highway n. 4 (S.S. n. 4) will be reported as a case study. 3. Results The main obtained results refer to the application to the case study of the “Strada statale n. 4 Via Salaria”. This is an Italian state highway (HWY); it is a single carriageway highway for most of its route, presenting one lane per each travel direction, but it falls into the category of dual carriageway urban road in its ﬁrst part (near to Rome city center). It, Infrastructures 2021, 6, 2 8 of 18 therefore, follows that this infrastructure is characterized by many various geometrical elements, changing gradually from urban highway to mountain road. Once the graph of the road network has been acquired form the company ANAS, the Once the graph of the road network has been acquired form the company ANAS, the 3D geographical information of the road of interest has been extrapolated, in terms of x, 3D geographical information of the road of interest has been extrapolated, in terms of x, y y and orthometric elevation coordinates. Thanks to the east and north coordinates in the and orthometric elevation coordinates. Thanks to the east and north coordinates in the WGS 84 UTM zone 32N Reference System, and the elevations in meters above sea level WGS 84 UTM zone 32N Reference System, and the elevations in meters above sea level (m.a.s.l.), the planimetric and then altimetric layout of the road have been reconstructed. (m.a.s.l.), the planimetric and then altimetric layout of the road have been reconstructed. Conventionally the direction of the distance has been taken from point A to point B, Conventionally the direction of the distance has been taken from point A to point B, linking Rome to Ascoli Piceno, as it can be seen in Figure 5: linking Rome to Ascoli Piceno, as it can be seen in Figure 5: Figure 5. Graph of the HWY 4 from A to B. Figure 5. Graph of the HWY 4 from A to B. The plan reconstruction, as a succession of straight and curved elements, has been carried out in stages through the implementation of a programming code. Initially, a denser discretization of the axis was carried out, measuring the distances between two consecutive vertices and dividing the segments longer than 6 m. For each point the Cartesian coordinates, the elevation, the identification code, the azimuth of the segment linking the i-th point to the next one (see Figure 6), the slope (m) and the y-inter- cept (q) of the straight line passing between the 2 above points, the partial length and, lastly, the distance have been tabulated, as shown in Table 1. Figure 6. Example of Azimuth: heading angle from the magnetic north. Infrastructures 2021, 6, 2 8 of 18 Once the graph of the road network has been acquired form the company ANAS, the 3D geographical information of the road of interest has been extrapolated, in terms of x, y and orthometric elevation coordinates. Thanks to the east and north coordinates in the WGS 84 UTM zone 32N Reference System, and the elevations in meters above sea level (m.a.s.l.), the planimetric and then altimetric layout of the road have been reconstructed. Conventionally the direction of the distance has been taken from point A to point B, linking Rome to Ascoli Piceno, as it can be seen in Figure 5: Infrastructures 2021, 6, 2 8 of 16 Figure 5. Graph of the HWY 4 from A to B. The plan reconstruction, as a succession of straight and curved elements, has been The plan reconstruction, as a succession of straight and curved elements, has been carried out in stages through the implementation of a programming code. carried out in stages through the implementation of a programming code. Initially, a denser discretization of the axis was carried out, measuring the distances Initially, a denser discretization of the axis was carried out, measuring the distances between two consecutive vertices and dividing the segments longer than 6 m. For each between two consecutive vertices and dividing the segments longer than 6 m. For each point the Cartesian coordinates, the elevation, the identiﬁcation code, the azimuth of point the Cartesian coordinates, the elevation, the identification code, the azimuth of the the segment linking the i-th point to the next one (see Figure 6), the slope (m) and the segment linking the i-th point to the next one (see Figure 6), the slope (m) and the y-inter- y-intercept (q) of the straight line passing between the 2 above points, the partial length cept (q) of the straight line passing between the 2 above points, the partial length and, and, lastly, the distance have been tabulated, as shown in Table 1. lastly, the distance have been tabulated, as shown in Table 1. Infrastructures 2021, 6, 2 9 of 18 Figure 6. Example of Azimuth: heading angle from the magnetic north. Figure 6. Example of Azimuth: heading angle from the magnetic north. Table 1. Information related to each vertex of the graph. Table 1. Information related to each vertex of the graph. E N Q i Azimuth m q Partial Length Distance Partial (m) (m) (m) (°) y = mx + q (m) (m) E N Q i Azimuth m q Distance Length 790,885.2 4,654,322.3 24.79 1 22.8 2.4 2,769,909.0 1.286 0.00 (m) (m) (m) ( ) y = mx + q (m) (m) 790,885.7 4,654,323.4 24.776 2 22.6 2.4 2,749,917.0 1.289 1.29 790,885.2 4,654,322.3 24.79 1 22.8 2.4 2,769,909.0 1.286 0.00 790,886.2 4,654,324.6 24.763 3 22.4 2.4 2,738,193.8 1.290 2.57 790,885.7 4,654,323.4 24.776 2 22.6 2.4 2,749,917.0 1.289 1.29 790,886.7 4,654,325.8 24.756 4 22.5 2.4 2,740,488.4 1.289 3.86 790,886.2 4,654,324.6 24.763 3 22.4 2.4 2,738,193.8 1.290 2.57 790,886.7 4,654,325.8 24.756 4 22.5 2.4 2,740,488.4 1.289 3.86 790,887.2 4,654,327.0 24.737 5 22.3 2.4 2,723,133.1 1.292 5.15 790,887.2 4,654,327.0 24.737 5 22.3 2.4 2,723,133.1 1.292 5.15 790,887.7 4,654,328.2 24.723 6 21.9 2.5 2,686,229.1 1.294 6.44 790,887.7 4,654,328.2 24.723 6 21.9 2.5 2,686,229.1 1.294 6.44 790,888.2 790,888.2 4,654,329.4 4,654,329.4 24.726 24.726 7 7 21.8 21.8 2.5 2, 2.5 672,991.9 2,672,991.9 1.295 1.295 7.74 7.74 790,888.7 4,654,330.6 24.712 8 21.5 2.5 2,648,700.0 1.300 9.03 790,888.7 4,654,330.6 24.712 8 21.5 2.5 2,648,700.0 1.300 9.03 790,889.1 4,654,331.8 24.697 9 21.3 2.6 2,626,662.2 1.305 10.33 790,889.1 4,654,331.8 24.697 9 21.3 2.6 2,626,662.2 1.305 10.33 790,889.6 4,654,333.0 24.692 10 21.1 2.6 2,608,805.8 1.306 11.64 790,889.6 4,654,333.0 24.692 10 21.1 2.6 2,608,805.8 1.306 11.64 Once the azimuth (or heading angle) of each segment that composes the graph has Once the azimuth (or heading angle) of each segment that composes the graph has been calculated, its trend and the elevations have been represented in a diagram as a been calculated, its trend and the elevations have been represented in a diagram as a func- function of the distance, as shown in Figure 7: tion of the distance, as shown in Figure 7: Figure 7. Heading direction and elevation trends along the HWY 4. Figure 7. Heading direction and elevation trends along the HWY 4. Subsequently, the Savitzky–Golay filter was applied to the heading angle trend for the purpose of smoothing the data, to increase their precision without distorting the signal tendency. The results of this filtering process are shown in Figure 8, for the highway section used as an example, from the distance 40 km to the distance 55 km: Infrastructures 2021, 6, 2 9 of 16 Subsequently, the Savitzky–Golay ﬁlter was applied to the heading angle trend for the purpose of smoothing the data, to increase their precision without distorting the signal tendency. The results of this ﬁltering process are shown in Figure 8, for the highway section Infrastructures 2021, 6, 2 10 of 18 used as an example, from the distance 40 km to the distance 55 km: Infrastructures 2021, 6, 2 10 of 18 Figure 8. Heading direction graph, compared to moving average filter ‘sgolayfilt’ type of the HWY Figure 8. Heading direction graph, compared to moving average ﬁlter ‘sgolayﬁlt’ type of the HWY 4—from the distance 40 km to the distance 55 km. 4—fr Figure 8. om the Head distance ing direct 40 ion g kmrto aph, com the distance pared to 55 m km. oving average filter ‘sgolayfilt’ type of the HWY 4—from the distance 40 km to the distance 55 km. Subsequently, again by means of the programming code, a further method to deter- Subsequently, again by means of the programming code, a further method to deter- mine the starting and ending points of the straight lines has been developed, through the Subsequently, again by means of the programming code, a further method to deter- mine the starting and ending points of the straight lines has been developed, through the analysis of the heading angle. A straight line has constant heading all the way along it, so mine the starting and ending points of the straight lines has been developed, through the analysis of the heading angle. A straight line has constant heading all the way along it, in the distance–heading direction diagram, it is possible to identify in each plateau the analysis of the heading angle. A straight line has constant heading all the way along it, so so in the distance–heading direction diagram, it is possible to identify in each plateau the elements with zero curvature. On the contrary, the circular arcs are represented by linear in the distance–heading direction diagram, it is possible to identify in each plateau the elements with zero curvature. On the contrary, the circular arcs are represented by linear variations of the heading angle; conventionally, positive slope of the heading angle trend elements with zero curvature. On the contrary, the circular arcs are represented by linear variations of the heading angle; conventionally, positive slope of the heading angle trend corresponds to right-handed curves; the negative slope corresponds to left-handed variations of the heading angle; conventionally, positive slope of the heading angle trend corr curves. When esponds to there are right-handed linear v curves; ariationthe s with negative a positslope ive slope corr imm esponds ediately to follo left-handed wed by curves. corresponds to right-handed curves; the negative slope corresponds to left-handed variations with a negative slope, or vice versa, in which no section with a zero slope is When there are linear variations with a positive slope immediately followed by variations curves. When there are linear variations with a positive slope immediately followed by interposed, the points of reverse curvature can be identified at the vertices of the cusps. with a negative slope, or vice versa, in which no section with a zero slope is interposed, the variations with a negative slope, or vice versa, in which no section with a zero slope is Circular arcs with a length shorter than 45 m were excluded from the analysis, be- points interposed, the points o of reverse curvatur f reverse c e can u be rvat identiﬁed ure can be at id the entifie vertices d at the vertices of th of the cusps. e cusps. cause they can be too short to carry out a reliable analysis, and the length may depend on Circular arcs with a length shorter than 45 m were excluded from the analysis, be- Circular arcs with a length shorter than 45 m were excluded from the analysis, because excessive signal variations, not effectively smoothed by the application of the filter de- cause they can be too short to carry out a reliable analysis, and the length may depend on they can be too short to carry out a reliable analysis, and the length may depend on excessive scribed above. excessive signal variations, not effectively smoothed by the application of the filter de- signal variations, not effectively smoothed by the application of the ﬁlter described above. Figure 9 shows, between the distance 40 km and 55 km, the identification of the start- scribed above. Figure 9 shows, between the distance 40 km and 55 km, the identiﬁcation of the ing points of the straight lines in red, the ending points in green and the points of reverse Figure 9 shows, between the distance 40 km and 55 km, the identification of the start- starting points of the straight lines in red, the ending points in green and the points of curvature in cyan. ing points of the straight lines in red, the ending points in green and the points of reverse reverse curvature in cyan. curvature in cyan. Figure 9. Identification of straight line starting and ending points and points of reverse curvature of the HWY 4—from the distance 40 km to the distance 55 km. Figure 9. Identification of straight line starting and ending points and points of reverse curvature Figure 9. Identiﬁcation of straight line starting and ending points and points of reverse curvature of of the HWY 4—from the distance 40 km to the distance 55 km. the HWY 4—from the distance 40 km to the distance 55 km. Once the coordinates of the starting and ending points of the straight sections have been identified, the starting and ending points of the circular arcs have also been defined, Once the coordinates of the starting and ending points of the straight sections have been identified, the starting and ending points of the circular arcs have also been defined, Infrastructures 2021, 6, 2 10 of 16 Once the coordinates of the starting and ending points of the straight sections have been identiﬁed, the starting and ending points of the circular arcs have also been deﬁned, dividing each linear variations of the heading angle into ﬁve equal parts. The search of the geometric parameters of the elements—i.e., the radii and the coordinates of the centers of the arcs, the length of the straight lines—has been carried out by analyzing only the vertices falling in the central 3/5 of the different sections. The remaining areas—between the straight lines and the arcs or between two successive arcs—have a curved trend and have not been investigated due to the possible presence of transition curves inside the path (or in any case they can belong to the gaps where the trajectory of the vehicle used for the survey has made a progressive steering to enter the circular curve). Once the vertices of the graph, corresponding to each geometric element, were known, the following features for the straight lines have been deﬁned, as shown in Table 2: the length, the mean and the deviation of the azimuth, the starting and ending point in east and north coordinates. Table 2. Information related to straight lines. L Es Ns Ee Ne (m) ( ) (m) (m) (m) (m) (m) S.L. 1 205.52 19.17 0.58 2,313,937.5 4,651,583.2 2,313,870.0 4,651,389.1 S.L. 2 68.64 25.65 0.59 2,313,998.1 4,651,718.7 2,313,968.6 4,651,656.8 S.L. 3 79.56 27.58 0.53 2,314,072.8 4,651,861.9 2,314,036.0 4,651,791.4 S.L. 4 259.91 23.39 0.38 2,314,209.1 4,652,169.7 2,314,105.9 4,651,931.2 S.L. 5 20.36 38.45 0.09 2,314,311.8 4,652,333.7 2,314,299.1 4,652,317.8 S.L. 6 105.43 15.86 0.44 2,314,403.7 4,652,552.1 2,314,374.9 4,652,450.7 S.L. 7 12.95 22.07 0.01 2,314,448.1 4,652,676.4 2,314,443.3 4,652,664.4 S.L. 8 119.66 24.32 0.20 2,314,382.7 4,653,143.4 2,314,432.0 4,653,034.3 S.L. 9 340.07 18.06 0.85 2,314,476.8 4,653,938.4 2,314,371.3 4,653,615.2 S.L. 10 218.78 91.24 0.24 2,315,295.8 4,654,341.2 2,315,077.1 4,654,345.9 The vertices of the graph that fall within the starting and ending points of a circular arcs were used to calculate the center and radius of each circumference, using a code that implements a least squares circle ﬁtting algorithm. Table 3 shows the east and north coordinates of the center and the value of the radii of the circular arcs, the deviations, the east and north coordinates of the starting and ending points of each element, the lengths of the arcs and the values of the angles at the center: Table 3. Information related to circular arcs. Ec Nc R Es Ns Ee Ne L (m) (m) (m) (m) (m) (m) (m) (m) (m) (rad) C.A. 1 2,314,485.9 4,651,399.3 578.3 0.04 2,313,943.0 4,651,598.5 2,313,961.1 4,651,642.2, 47.30 0.08 C.A. 2 2,313,038.2 4,652,397.5 1165 0.10 2,314,079.7 4,651,875.5 2,314,099.2 4,651,916.5 45.39 0.04 C.A. 3 2,314,581.2 4,652,045.8 389.5 0.26 2,314,223.7 4,652,201.1 2,314,278.3 4,652,290.9 105.34 0.27 C.A. 4 2,314,143.7 4,652,503.7 236.6 0.39 2,314,330.1 4,652,357.9 2,314,367.8 4,652,427.3 79.33 0.34 C.A. 5 2,315,098.3 4,652,369.9 717.6 0.15 2,314,411.2 4,652,577.3 2,314,435.5 4,652,644.9 71.88 0.10 C.A. 6 2,314,120.3 4,652,837.3 364.3 0.25 2,314,473.0 4,652,746.9 2,314,460.6 4,652,967.5 224.53 0.62 C.A. 7 2,314,926.2 4,653,387.6 596.8 0.33 2,314,349.3 4,653,235.8 2,314,345.5 4,653,526.4 293.57 0.49 C.A. 8 2,315,049.6 4,653,733.4 611.5 0.81 2,314,547.7 4,654,083.5 2,314,923.2 4,654,331.0 460.79 0.75 The research ﬁndings consist of a procedure composed by three sequential phases, as described below. 3.1. Geometrizing Horizontal Alignment of an Existing Road Layout As shown in Figure 10, the Italian highway S.S. n. 4 has been completely geometrized by a succession of curves and straight lines; all the circumferences obtained by the pre- Infrastructures 2021, 6, 2 12 of 18 Infrastructures 2021, 6, 2 12 of 18 The research findings consist of a procedure composed by three sequential phases, The research findings consist of a procedure composed by three sequential phases, as described below. as described below. Infrastructures 2021, 6, 2 11 of 16 3.1. Geometrizing Horizontal Alignment of an Existing Road Layout 3.1. Geometrizing Horizontal Alignment of an Existing Road Layout As shown in Figure 10, the Italian highway S.S. n. 4 has been completely geometrized As shown in Figure 10, the Italian highway S.S. n. 4 has been completely geometrized by a succession of curves and straight lines; all the circumferences obtained by the previ- viously described method, implemented in the original programming code, have been by a succession of curves and straight lines; all the circumferences obtained by the previ- ously described method, implemented in the original programming code, have been im- imported ously descr into ibed method, implemented in the the CAD (Computer-Aided orig Design) inal progr envir aonment. mming code, have been im- ported into the CAD (Computer-Aided Design) environment. ported into the CAD (Computer-Aided Design) environment. Figure 10. Circumferences obtained by fitting the circular arcs of the road. Figure 10. Circumferences obtained by ﬁtting the circular arcs of the road. Figure 10. Circumferences obtained by fitting the circular arcs of the road. Figure 11 shows an example of a circumference computed by the circle fitting proce- Figure 11 shows an example of a circumference computed by the circle ﬁtting proce- Figure 11 shows an example of a circumference computed by the circle fitting proce- dure implemented in the code, in which the points used for the least squares arc evalua- dure implemented in the code, in which the points used for the least squares arc evaluation— dure implemented in the code, in which the points used for the least squares arc evalua- tion—and the center and radius coordinates definition obtained as a result—are repre- and the center and radius coordinates deﬁnition obtained as a result—are represented in tion—and the center and radius coordinates definition obtained as a result—are repre- sented in red (the curve obtained is in black): red (the curve obtained is in black): sented in red (the curve obtained is in black): Figure 11. Least square circle fitting for the center and radius coordinates definition. Figure 11. Least square circle ﬁtting for the center and radius coordinates deﬁnition. Figure 11. Least square circle fitting for the center and radius coordinates definition. To test the accuracy of the results, after calculating the characteristic parameters of the circular arcs and the straight lines through the least square ﬁtting, a qualitative comparison between the project axis obtained and the road layout, obtained from GIS basemaps, has been done. Even if it is not possible to consider Figure 12 as a quantitative validation, it can be noted that the two trends are overlapped in the entire distance considered. Infrastructures 2021, 6, 2 13 of 18 To test the accuracy of the results, after calculating the characteristic parameters of the circular arcs and the straight lines through the least square fitting, a qualitative com- parison between the project axis obtained and the road layout, obtained from GIS base- Infrastructures 2021, 6, 2 12 of 16 maps, has been done. Even if it is not possible to consider Figure 12 as a quantitative val- idation, it can be noted that the two trends are overlapped in the entire distance consid- ered. Figure 12. A qualitative comparison between the calculated project axis and the road layout got Figure 12. A qualitative comparison between the calculated project axis and the road layout got from from a GIS basemap and a zoom of the HWY 4—from the distance 40 km to the distance 55 km. a GIS basemap and a zoom of the HWY 4—from the distance 40 km to the distance 55 km. 3.2. Curvature Graph 3.2. Curvature Graph Once the calculation of the planimetric elements parameters has been completed, the curvature graph of the entire road layout has been subsequently constructed through an- Once the calculation of the planimetric elements parameters has been completed, other original code. Conventionally, the right-hand curves have been positioned above the curvature graph of the entire road layout has been subsequently constructed through the reference (zero-curvature) line, assuming as positive the direction from point A to another original code. Conventionally, the right-hand curves have been positioned above point B, while the left-hand curves have been positioned below. The transition zones, be- the longin refer g neit ence her t (zer o th o-curvatur e straight line e) s nor line, toassum the circular arc ing as positive s, have been treated the direction as variable from point A to point curvature elements, in order to connect elements having different curvatures. B, while the left-hand curves have been positioned below. The transition zones, belonging Figure 13 shows the curvature graph for the segment taken as an example between neither to the straight lines nor to the circular arcs, have been treated as variable curvature the distance 40 km and 55 km: elements, in order to connect elements having different curvatures. Infrastructures 2021, 6, 2 Figure 13 shows the curvature graph for the segment taken as an example 14 of 18 between the distance 40 km and 55 km: Figure 13. Curvature graph of the HWY 4—from the distance 40 km to the distance 55 km. Figure 13. Curvature graph of the HWY 4—from the distance 40 km to the distance 55 km. 3.3. Design Speed Profile Once the curvature graph has been defined, an additional code has been imple- mented to calculate the design speed profile. The calculation follows the indications of the Italian Ministerial Decree 5 November 2001 [1] according to which: The speed is constant all along the curve extension, and when the radius is less than a characteristic one (R2.5), it is determined by some graphs in the guidelines. 1. On straight lines, on circular arcs with radius bigger than R2.5 and on clothoids, the design speed tends to the upper limit of the speed range; the acceleration spaces re- sulting from the exit from a circular curve and the deceleration spaces for the en- trance to a curve are only limited to the elements considered. 2. The acceleration and deceleration values are 0.8 m/s . 3. It is assumed that the longitudinal slopes do not influence the design speed. The transition distance DT is the length in which the speed, according to the accepted theoretical model, passes from the value sd1 to sd2, of two consecutive elements. DT [m] is given by the following expression, where Δ𝑠 is the difference between sd1 and sd2 [km/h], 𝑠 ̅ is the average speed [km/h]: Δ𝑠 ∗ 𝑠 ̅ (9) 𝐷𝑇 = 12.96 ∗ 𝑎 The result of the calculation is shown in Figure 14: Figure 14. Design speed profile of the HWY 4—from the distance 40 km to the distance 55 km. Infrastructures 2021, 6, 2 14 of 18 Infrastructures 2021, 6, 2 13 of 16 Figure 13. Curvature graph of the HWY 4—from the distance 40 km to the distance 55 km. 3.3. Design Speed Proﬁle Once the curvature graph has been deﬁned, an additional code has been implemented 3.3. Design Speed Profile to calculate the design speed proﬁle. The calculation follows the indications of the Italian Once the curvature graph has been defined, an additional code has been imple- Ministerial Decree 5 November 2001 [1] according to which: mented to calculate the design speed profile. The calculation follows the indications of the The speed is constant all along the curve extension, and when the radius is less than a Italian Ministerial Decree 5 November 2001 [1] according to which: characteristic one (R ), it is determined by some graphs in the guidelines. 2.5 The speed is constant all along the curve extension, and when the radius is less than a characteristic one (R2.5), it is determined by some graphs in the guidelines. 1. On straight lines, on circular arcs with radius bigger than R and on clothoids, the 2.5 1. On straight l design speed ines, on tends circ to ular the arcs upper with r limit adiusof bigg the er t speed han R2.5 range; and onthe clotacceleration hoids, the spaces design speed tends to the upper limit of the speed range; the acceleration spaces re- resulting from the exit from a circular curve and the deceleration spaces for the sulting from the exit from a circular curve and the deceleration spaces for the en- entrance to a curve are only limited to the elements considered. trance to a curve are only limited to the elements considered. 2 2. The acceleration and deceleration values are 0.8 m/s . 2. The acceleration and deceleration values are 0.8 m/s . 3. It is assumed that the longitudinal slopes do not inﬂuence the design speed. 3. It is assumed that the longitudinal slopes do not influence the design speed. The transition distance DT is the length in which the speed, according to the accepted The transition distance DT is the length in which the speed, according to the accepted theoretical model, passes from the value s to s , of two consecutive elements. DT [m] is d1 d2 theoretical model, passes from the value sd1 to sd2, of two consecutive elements. DT [m] is given by the following expression, where Ds is the difference between s and s [km/h], given by the following expression, where Δ𝑠 is the difference between sd1 and s d1d2 [km/h] d2, s is the average speed [km/h]: 𝑠 ̅ is the average speed [km/h]: Ds s Δ𝑠 ∗ 𝑠 ̅ DT = (9) 𝐷𝑇 = (9) 12.96 a 12.96 ∗ 𝑎 The result of the calculation is shown in Figure 14: The result of the calculation is shown in Figure 14: Figure 14. Design speed profile of the HWY 4—from the distance 40 km to the distance 55 km. Figure 14. Design speed proﬁle of the HWY 4—from the distance 40 km to the distance 55 km. After performing the described three sequential phases, a complete representation of the geometric elements composing the planimetric road layout, as well as the theoretical design speed trend along the alignment, is made available. This kind of representation is useful when performing the safety analyses and, ﬁrst of all, the ex post application of the regulatory model for the design veriﬁcation. In this way, the procedure allows us to identify the sections where in-depth assessments have to be focused: if there are road sections in which some theoretical design conditions are not met signiﬁcantly; in fact, further investigation should be conducted, especially when these sections also show other critical conditions related to safety or functional indicators (accident rates, heavy trafﬁc conditions, black spots and so on). As a general remark, the proposed assessments can be useful to pursue strategical and managing actions aimed at planning any road upgrading activities and at improving road safety performances. 4. Conclusions The research carried out was aimed at implementing an automated, fast and economi- cal procedure to identify the horizontal geometry of existing two-lane rural roads, based on the data obtained from the road graph of the network. In particular, it has been necessary Infrastructures 2021, 6, 2 14 of 16 to search for methods and algorithms capable of identifying the reference axes, such as in the design process of new tracks, which have to be mathematically described as simple and as continuous geometric elements (circular curves, clothoids and straight lines). Using semi-automated procedures, implemented in a programming platform, the following main steps have been developed: Representation of the heading direction as a function of the distance, on the basis of the 3D spatial coordinates of the vertices of the road graph. Application of a Savitzky–Golay ﬁlter to the heading angle trend, with the purpose of smoothing the data and in order to identify straight line starting and ending points and points of reverse curvature. Analysis of the vertices falling within each element range and determination of the azimuth and length of the straight lines, of the radii and of the lengths of the circular arcs, by the application of a least square ﬁtting procedure. Identiﬁcation of the transition zones between the constant curvature elements (treated as clothoids) to compose a continuous curvature diagram. Once the curvature graph has been deﬁned, calculation of the design speed proﬁle by the implementation of an additional code. The proposed method can be useful to analyze the technical characteristics of existing roads, especially in order to perform the ex post application of the regulatory models for the design veriﬁcation. In particular, it allows us to perform road consistency analysis or to recognize other relevant effects in the road–user behavior interaction, such as the violation of: All these analyses are intended to assess Minimum and maximum lengths of each element with constant curvature, in relation to the drivers’ correct perception of the road layout. Correct succession of straight lines and circular arcs, or of two circular elements, in order to have gradual variations between their geometric characteristics. Optical, dynamic and road users’ comfort criteria of the variable curvature elements. All these analyses are intended to assess the safety conditions for existing and open to trafﬁc roads. In fact, considering the high accident rate found on the selected kind of roads, it is important to better study and understand the inﬂuence of the characteristics of the road on the users’ driving ability. Thus, the presented procedures are suitable for researchers to evaluate the effects of geometric inconsistencies on driver behaviors, as well as for practitioners (road administrators, technicians and professionals) to more easily develop the assessments on existing networks. The effective contribution of this research to the state of practice is due to the opportu- nity to extract the track geometry from surveys or databases. The curvature graph and the design speed proﬁle can be rapidly obtained, especially if the raw data are properly stored; the entire analysis process (starting from the data ﬁltering to the ﬁnal diagrams) can be uploaded and performed in a few hours. The short time needed is suitable for an extensive and systematic application of the methodology. In fact, it will be possible to implement a code capable of quickly verifying the compliance of existing road layouts with the current design standards, in order to identify the sections that most differ from an optimal geometric conﬁguration. Author Contributions: Conceptualization, G.C. and G.D.S.; methodology, G.C.; software, G.D.S.; validation, G.C. and G.D.S.; formal analysis, G.C.; investigation, G.D.S.; data curation, G.C. and G.D.S.; writing—original draft preparation, G.D.S.; review and editing, G.C. and G.D.S.; supervision, G.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: 3rd Party Data. Infrastructures 2021, 6, 2 15 of 16 Acknowledgments: We thank the national public company ANAS for making its graph available and for the technical support. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. 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Infrastructures – Multidisciplinary Digital Publishing Institute

**Published: ** Dec 24, 2020

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