# Determination of Point-to-Point 3D Routing Algorithm Using LiDAR Data for Noise Prediction
## 1 Introduction  
Town planners need to determine the noise levels at various parts of a city. Noises are primarily generated due to road traffic conditions. The noise levels vary in different parts of the city with time. The sound pressure levels in noise also vary in frequencies. Accurate prediction of noise levels is important for the determination of noisy areas of the city. It is important to adopt appropriate noise management measures. The accurate prediction of noise levels is challenging. Noises are generated by vehicles on roads before their propagation to nearby locations. Noise sources can be the point, line, or area types, depending on the sizes of the source for noise. Multiple point sources constitute line and area noise sources. The road noise is an example of a linear source, while factory noise is an area source. After generating noise from sources in roads, it propagates to nearby locations to increase the noise levels of those locations. Accurate prediction of noise levels requires the determination of all the possible routes through which the noises are propagatingbefore reaching destinations (noise receiving points) [1]. The available noise modeling or mapping software (refer to supplementary literature review Section S1) try to integrate the sound pressure levels of sources, with their locations, and geometry of objects present between sources and receiver to predict the noise level at the receiving point. The time and space-based integration of noise levels for noise prediction often become very complex in a 3D real-world environment [2]. Existing models adopt various approximations in estimating the routes through which the noise can propagate. The parameters of geometry, orientation, and types of buildings (or other overground objects) are roughly incorporated into the models. Further, all possibilities of direct and indirect propagation of noise (i.e., through reflection, diffraction, etc.) are not considered. These approximations lead to inaccuracies. The majority of them fail to accurately predict the noise level outdoor at an instantaneous scale. Accurate prediction of noise level at a receiving point requires ascertainment of all noise sources, which can contribute the noises to that receiving point. The routes for the propagation of noises from noise sources to a receiving point are required to be determined. Accurate estimation of source and receiving points and related routes is dependent on terrain data input. The quality and nature of terrain data can significantly impact the technique and accuracy of route determination [3; 4; 5]. GIS and Graph theory offers different approaches for the determination of routes using a raster or vector-based approach [6; 7; 8]. In graph theory, the root node is considered as the source and the goal node as the destination. In this sense, a graph is made up of vertices (also known as nodes) connected by edges (also called links). The Greedy algorithm [9], which is a type of algorithm that finds the maximum value at every node in the graph to find the shortest route, is important in this area. Even if it finds a node with a very large value throughout the search, the greedy algorithm will take that route because it cannot return. As a result, it takes some time to find an appropriate solution. The Dijkstra algorithm [10], on the other hand, seeks to determine the quickest route from one location to another based on the least weight. This can only be used for ages that are not negative. The Bellman ford algorithm is similar to [PERSON]'s, with the exception that it can also be used for negative weight. However, it takes longer to search. There is another algorithm known as the A* algorithm, which performs the search for all existing nodes. This algorithm is the combination of the greedy and Dijkstra algorithms ([PERSON] et al., 2017) [9]. There is also an ant colony algorithm that finds the shortest route between the nest and source of food. The genetic algorithm is the most frequently used algorithm.