# Determination of Point-to-Point 3D Routing Algorithm Using LiDAR Data for Noise Prediction

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## Abstract

**:**

## 1. Introduction

- (a)
- Determination of a routing algorithm that can determine direct and other indirect routes (when the direct transmission is obstructed) between a source and destination (or receiver) points.
- (b)
- The establishment of optimal or best possible routes containing the highest energy/flow is tried to be determined.
- (c)
- Consider natural propagation of energy or pressure over 3D terrain in an outdoor environment. It did not try to find out any other algorithm which compares the existing city road networks to find the shortest route between two points.
- (d)
- The algorithm is required to find out a solution customized to handle propagation problems in 3D.
- (e)
- The algorithm should be capable of handling highly detailed and accurate 3D terrain data (e.g., LiDAR data) for the accurate determination of routes.
- (f)
- The efficiency of the route determination algorithm is required to be tested in terms of optimality of solutions.
- (g)
- The algorithm developed should be useful for accurate noise prediction and applicable for other urban applications, e.g., determination of solar irradiance, urban supply line, view shade analysis, setting up the wireless tower for a location, etc.

## 2. Research Gap and Need for Point-to-Point 3D Routing Algorithm for Noise Prediction Using LiDAR Data

- Development of a novel algorithm to extract 3D shortest routes between a pair of points (source point and receiver point).
- Determination of 3D routes using unlabeled raw 3D LiDAR terrain points existing between source and receiver points.
- Determination detailed routes with highest accuracy.
- Accurate sound propagation modelling integrating noise data, and LiDAR terrain data with noise model.

**Definition of terms used:**

- Noise source: Source point of noise.
- Destination: Destination is where noise impact is about to calculate.
- Point-to-Point: It is pair of source and destination.
- Building Edges and corner: Edges of a building and its corners.
- Terrain data: Information of buildings, ground, trees, and other attributes.
- Terrain parameters: Route length and path difference.
- Ground and Non-ground points: Points on local ground levels. Points above the ground are non-ground points.
- Points of Intersection: Intersection points between lines.
- The route over the top of the building: Route determined from cutting plane technique that runs over buildings joining a noise source and noise receiver.
- The route around the sides of the building: Route determined from cutting plane technique that originates from the source and terminates at a receiving location traversing around the building.
- Reflected Route: Route determined where the route is formed after reflection from the ground or the nearby walls of the building (if any).
- Building Edges array: An array that contain building edges.
- Upward Route: A component of the route over top. It is the route from the source to the tallest building point.
- Downward Route: A component of the route over top. It is the route from the tallest building point to the destination point.
- Intersection Array: An array contains the intersection points between the building and cutting plane.
- Right side Route: Route from the source to destination point following the right side of the building.
- Left side Route: Route from the source to destination point following the left side of building.
- Tonal frequency: Short term single frequency sound.

## 3. Methodology

**Route Determination and efficacy for RGIPT campus:**The routing algorithm was also tried to be trained and tested over real LiDAR terrain data and used later for noise prediction using noise modeling. The terrain data were generated for RGIPT campus using Terrestrial Laser Scanner, point cloud data has an accuracy of up to ±3 cm (mentioned in Supplementary Section S2). RGIPT campus lies in between (latitude (26.265788), longitude (81.504372)) and (latitude (26.263355), longitude (81.515723)), as shown in Figure 2. The project site has an area of 0.33 km

^{2}. Adjoining the campus, there is a railway line, which is the primary source of noise pollution for the campus [35]. The locations for noise sources and receivers (destinations) in the RGIPT campus were ascertained. All the routes were determined between every pair or source and destination. Next, the terrain parameters were determined for every route and incorporated inside a noise propagation model for noise prediction. Efficacy of noise prediction was also tested with ground noise data for the campus.

#### 3.1. LiDAR Data Acquisition

#### 3.2. Building Corner Extraction Step 1 to Step 3

#### 3.3. Route Determination for Direct Route and Indirect Route Step 4 to Step 19

#### 3.3.1. Route over the Top (Step 4 to Step 9)

_{s}, y

_{s}, z

_{s}) and destination (x

_{d}, y

_{d}, z

_{d}) with calculated direction ratios.

_{sd}, y

_{sd}, z

_{sd}) represents any random point on the line, and these ‘x

_{sd}’, ‘y

_{sd}’, and ‘z

_{sd}’ can be put as variables.

_{1}with (a

_{1}, b

_{1}, c

_{1}), U

_{2}with (a

_{2}, b

_{2}, c

_{2}), etc. For calculating point of intersection P with DR’s (a

_{p}, b

_{p}, c

_{p})

_{p}= 0, that means the line does not intersect.

#### 3.3.2. Route around the Sides (Step 10 to Step 19)

_{s}, y

_{s}, z

_{s}) and D = (x

_{d}, y

_{d}, z

_{d}), for the source and the destination, calculate a buffer region that makes a square of a = (xa, ya, za), b = (xb, yb, zb), c = (xc, yc, zc), and d = (xd, yd, zd) shown in Figure 9a.

_{1}with (a

_{1}, b

_{1}, c

_{1}), U

_{2}with (a

_{2}, b

_{2}, c

_{2}), etc. For calculating point of intersection P with DR’s (a

_{p}, b

_{p}, c

_{p}).

_{p}= 0, that means the line does not intersect.

_{i}, y

_{i}, z

_{i}].

_{i}, y

_{i}, z

_{i}].

#### 3.3.3. Reflection Route

- (a)
- Ground Reflection: Reflection through the ground. The ground may be uniform and non-uniform. There are two cases formed, one for uniform and other for non-uniform ground. Both cases are discussed in Supplementary Section S2.3.3 (c). An example for ground reflection is shown in Figure 12a,b.
- (b)
- Wall reflection Route: Route that is calculated after reflection of noise signal from the wall of building. Procedure for wall reflection route is provided in Supplementary Section S2.3.3 (c). Result is shown in Figure 13.

#### 3.4. Determination of Terrain Parameters

- D = Direct transmission route
- D.A = Distance Attenuation
- B.A = Barrier attenuation
- λ = wavelength
- c = Speed of light
- f = Frequency
- N = Fresnel number

## 4. Results and Discussions

#### 4.1. Accuracy for Determined Principal Routes

#### 4.1.1. Route over the Top Accuracy

#### 4.1.2. Route around the Side Accuracy

#### 4.2. Accuracy of Noise Prediction

#### 4.2.1. Deviations in New Algorithm Generated Routes, Which Are Extracted Using LiDAR Data Are Compared with Routes (Having no Error) Extracted Theoretically. Deviations Are Related in Terms of Predicted Noise Levels

#### 4.2.2. Determination of Error in the Predicted Instantaneous Noise Levels

## 5. Conclusions

## 6. Future Scope

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Methodology for determination of routes extracting terrain parameter and utilization of same for noise prediction.

**Figure 2.**RGIPT project site LiDAR data were used for noise prediction leveraging point to point routing algorithm.

**Figure 3.**Summary flow chart of stepwise processing of LiDAR data for deriving a point-to-point routing algorithm for noise mapping.

**Figure 5.**(

**a**) Principal route with respect to route over the top and reflection routes (Routes are P1, P2, P3, and P4). (

**b**) Principal route with respect to route around the right side and reflection routes (Routes are P5, P6, P7, and P8). (

**c**) Principal route with respect to route around the left side and route of reflection (Routes are P9, P10, P11, and P12).

**Figure 6.**(

**a**) A Simulated area is taken for understanding the working of route determination with a pair of source and destination points, and (

**b**) “abcd” is the XZ cutting plane created between the source to find out intersecting buildings and points. Intersecting buildings are Building B, Building E, and Building F, and (

**c**) (B1, B2, B3, B4), (E1, E2, E3, E4) and (F1, F2, F3, F4) are the building corners on ground, which is calculated by the intersection of the XZ plane (that has shown in the previous figure) with the buildings. The source is denoted by “S” and destination by “D”.

**Figure 7.**(

**a**) (i1, i2), (i3, i4), (i5, i6) are the intersecting points found after the intersection of plane XZ (between S and D that has shown in the previous figure) with Building B, Building E, Building F denoted by (\). (Values in x and y-axis are in meter). (

**b**) This line j1 to i1 denotes the height of the Building B edge denoted by O1. Similarly, for other edges (j2–i2), (j3–i3), (j4–i4), (j5–i5), (j6–i6) the heights are O2, O3, O4, O5, O6. The source is denoted by “S” and Destination is denoted by “D”.

**Figure 8.**(

**a**) Route from Source(S) –j1–j3 is an upward travel path where j1 and j3 are the height points of intersection point i1 and i3 with respect to height of buildings denoted by (●). (

**b**) Route from j3–j4–D (Destination) is a downward travel path where j3 and j4 are the height points of intersection point i3 and i4 with respect to height of buildings denoted by (●).

**Figure 9.**(

**a**) “abcd” is the buffer region to define inlier and outlier buildings and the region “abfe” is the left side panel and “cdef” is the right side. Buffer region defines that Building C is an outlier and the rest are inliers. (Values in x and y-axis are in meter.) (

**b**) Planimetric view of setup that shows the building corner ground points of inlier buildings where (A1, A2, A3, A4), (B1, B2, B3, B4), (D1, D2, D3, D4), (E1, E2, E3, E4) and (F1, F2, F3, F4) are building corner ground points of Building A, Building B, Building D, Building E and Building F.

**Figure 10.**(

**a**) “abcd” shows the buffer region to select inlier and outlier buildings. The intersection points i1, i2, i3, i4, i5, i6, i7, and i8 were calculated from the intersection of the XZ plane between source and destination with the buildings. In this, the region “abfe” is considered and the distance from the right-side building points to the intersection points as (d1 = distance from B1 to i1) similarly from B3, D1, D3, E1, E3, F1 to i2, i3, i4, i5, i6, i7, and i8 are d2, d3, d4, d5, d6, d7, and d8 where S is source and D is the destination. (

**b**) “abcd” shows the buffer region to select inlier and outlier buildings. The intersection points j1, j2, j3, j4, j5, j6, j7, and j8 were calculated from the intersection of the XZ plane between source and destination with the buildings. In this, the region “cdef” is considered and the distance from the right-side building points to the intersection points as (c1 = distance from A2 to j1) similarly from A4, B2, B4, E4, F2, F4 to j2, j3, j4, j5, j6, j7, and j8 are c2, c3, c4, c5, c6, c7, and c8, where S is source and D is the destination.

**Figure 11.**(

**a**) Simulated 3D environment of route determination where green dot show the source and destination symbol (●). (

**b**) Cutting plane results for the simulated region. (

**c**) Complete route traversal on left side panel. (

**d**) Route traversal on right side panel starting from source. (

**e**) Route traversal on left side and right side.

**Figure 12.**(

**a**) In this figure, reflection point (R’) is found (triangulation exists) between a pair of source and destination, (

**b**) “S” is source and “D” is destination, R’ is new reflection point received.

**Figure 13.**“S” is source and “D” is destination and R’ is the new reflection point found on wall of building.

**Figure 14.**(

**a**) The blue route is the desired shortest route, and the rest of the yellow routes are the deviated routes. (

**b**) Graph for the accuracy of route over the top.

**Figure 15.**(

**a**) “1” is the first intersection point moving from source to destination around the sides of the building. Similarly, “2” is the second intersection point. The blue route is the desired route from the algorithm and the rest yellow routes are the deviated routes, when the first intersected point has shifted value upward and downward in the Z direction. (

**b**) Graph shows the accuracy of the route around the sides.

**Figure 17.**(

**a**) Google Earth map of RGIPT campus showing railway line (noise source) with 25 points on line, buildings and the rest area where the destination points are considered. (

**b**) Prediction of noise map of RGIPT campus due to noise sources at railway line. Noise levels are projected in DB. Source and destinations’ locations are marked with small circular points.

**Figure 18.**RGIPT campus noise map for noise source points at railway line when train is at different location and the noise receiver points (destination) are all over the RGIPT campus including buildings of different height. (

**a**) 1st instance, (

**b**) 2nd instance, and (

**c**) 3rd instance.

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**MDPI and ACS Style**

Bharadwaj, S.; Dubey, R.; Zafar, M.I.; Faridi, R.; Jena, D.; Biswas, S.
Determination of Point-to-Point 3D Routing Algorithm Using LiDAR Data for Noise Prediction. *Appl. Syst. Innov.* **2022**, *5*, 58.
https://doi.org/10.3390/asi5030058

**AMA Style**

Bharadwaj S, Dubey R, Zafar MI, Faridi R, Jena D, Biswas S.
Determination of Point-to-Point 3D Routing Algorithm Using LiDAR Data for Noise Prediction. *Applied System Innovation*. 2022; 5(3):58.
https://doi.org/10.3390/asi5030058

**Chicago/Turabian Style**

Bharadwaj, Shruti, Rakesh Dubey, Md Iltaf Zafar, Rashid Faridi, Debashish Jena, and Susham Biswas.
2022. "Determination of Point-to-Point 3D Routing Algorithm Using LiDAR Data for Noise Prediction" *Applied System Innovation* 5, no. 3: 58.
https://doi.org/10.3390/asi5030058