# Determination of Point-to-Point 3D Routing Algorithm Using LiDAR Data for Noise Prediction
## 1 Introduction
The noise due to interference with buildings and other structures cannot be visualized in 2D noise maps. Two-dimensional noise maps do not provide enough information for calculating the efficiency of noise mitigation measures due to the effect of barriers, building insulation material, etc. There were also limitations in capturing accurate and dense terrain information for different noise prediction models. The limitations of models can be overcome using high-resolution 3D LiDAR data, which come in the form of the point cloud (X, Y, Z). This technique can produce accurate digital terrain data of the wide-area in quick time [1]. The terrain data are required to be processed to extract terrain features such as building, ground, and other overground objects. These are then required to be processed for the determination of terrain parameters for noise propagation modeling. The determination of terrain parameters requires the estimation of all routes for the propagation of noise between source and destination pairs. When there is no direct route noise undergoes diffraction from the top of barriers, and sides of the barrier. Noise can also reach the noise receiver (destination) after reflections from the ground or wall. Once all-terrain parameters are determined, they can be incorporated in the noise prediction model with noise data for the prediction of noise levels at noise receiver (destination) points. Thus, there is a need for the determination of a routing algorithm between any pair of points (source and receiver points). Accurate route determination is dependent on the quality of 3D terrain data. Hence, a routing algorithm is required to use 3D LiDAR point data for accuracy. Once all possible routes are efficiently be determined, these can be used for accurate noise prediction and used for other urban applications. There are different algorithms for determination of shortest route between two points. These routing algorithms primarily work in 2D environments. Largely, the routing algorithms are used to determine the shortest route between two points in cities. Typically, in a city environment all routes are required to be laid down between any pair of points before routing algorithm can determine the shortest route. Every route is defined by all the points or vertices (in X and Y) and the vectors joining the points making the individual routes. Routing algorithms attempt to determine the shortest of all established routes in 2D. However, the issue is that the existing algorithms primarily work when routes are delineated in 2D. Establishment of routes require digitization of terrain and route data. Initial abstraction of route is the prerequisite for any routing algorithm. Inaccuracy in delineation of routes causes ineffective determination of the shortest route. Further, in the case of sound propagation modelling, sounds propagate through principal routes following the physics of propagation. The shortest routes for sound propagation work in 3D similar to the 2D shortest route discussed above. For sound propagation modeling, actual propagation routes are not limited in the 2D plane. In a real scenario, from the source point there are many routes that are possible. However, out of them, there are certain shortest routes in different directions, which form the set of principal routes. Existing algorithms are not customized to the need of these computations. The computation requires the determination of all principal propagation routes from the source point to any specific destination point. Unlike the existing routing algorithm, sound waves do not follow the network of previously laid down streets. Route determination requires extraction of all routes in 3D between the source and destination points. Once the 3D routes are determined, the algorithm is required to find the shortest route for propagation of sound waves.