# Three-Dimensional Stopping Sight Distance Calculation Method under High Slope Restraint
## 1 Introduction  
With the vigorous development of the global transportation industry, the total length of the world's highways has been soaring, and the construction scope has also extended from urban areas to remote areas. Among them, mountainous highways have also developed rapidly. In the operation stage of mountain highways, a large number of excavation slopes and excessive longitudinal slope values limited by terrain conditions will cause different degrees of occlusion of the driver's vision during driving, affecting the driver's judgment and response to danger, endangering driving safety. Stopping sight distance (S.S.D.) is an important factor affecting driving safety. It refers to the distance traveled by the driver from the time the driver recognizes the danger ahead and takes the braking measures until the vehicle is completely stopped. Since the current highway alignment design is still a design method using horizontal and vertical separation, the national standard uses the two-dimensional horizontal sight distance value when considering the index. [PERSON] et al. pointed out that the three-dimensional road alignment, as a very important component in highway design, has not yet been practical in highway geometry design [1]. In the same way, we should calculate the more accuratespatial stereoscopic three-dimensional S.S.D. which considering the combination of horizontal and vertical sections. The calculation of sight distance is complex, involving drivers, vehicles, roads, and the environment. The related research can be divided into traditional two-dimensional sight distance optimization calculation model, graphic simulation method, geometric analysis method, and geographic information system (GIS)-based sight distance analysis [2; 3; 4]. Scholars [PERSON], [PERSON] and [PERSON] introduced a segmented cubic parabola in the study, and proposed a sight distance design method for segmented cubic parabola [5]; [PERSON] and [PERSON] used a triangulation model to describe the pavement model and proposed a method of calculating the sight distance of the driver by checking whether the driver's line of sight intersects the model [6]. [PERSON] and [PERSON] used the Monte Carlo model to calculate the three-dimensional sight distance limited risk probability for the horizontal curve and the combination of gentle slope, concave, and convex sections [7]. [PERSON] et al. proposed an optimization method for cross-sectional dimension design with limited viewing distance [8]. [PERSON] et al. analyzed the horizontal clearances of six scenarios based on the velocity prediction model and the reliability method [9]. [PERSON] et al. analyzed the over-the-horizon sight distance based on factors affecting overtaking operations and risk probabilities [10]. The research on S.S.D. has made many achievements, but there are still some challenges. [PERSON] et al. conducted a sufficiency study on the left-turn S.S.D. of the divided roads, and calculated the difference between the S.S.D. provided by the road and the required sight distance value, which pointed out safety during emergency braking of the vehicle cannot be guaranteed by the AASHTO (American Association of State Highway and Transportation Officials) 2011 Design Guide [11]. [PERSON] et al. improved the S.S.D. model by reanalyzing the whole process of braking and analyzed the influence of the night environment on the driver's visual perception. However, the research still uses the 2D computing model in the specification. Moreover, the braking deceleration during braking is simplified to a linear change process, so there is a certain error in the calculation result [12]. [PERSON] et al. used the mobile LiDAR (Light Detection and Ranging) cloud data to build a digital ground model and automatically calculated and evaluated the highway S.S.D. by constructing an algorithm. However, the drawback of this method is that it needs to process a large amount of data, making the computer overburdened and it takes a lot of time [13]. [PERSON] et al.