Complexity Analysis

1. Introduction

This section presents the complexity analysis of volumetric and surface meshing operations. The results are categorized based on whether the buildings have roofs or not. The performance metrics are evaluated by measuring the time taken for different numbers of buildings.

2. Volumetric Mesh with Roof

The time taken to generate a volumetric mesh for buildings with roofs is presented below:

Number of Buildings,Time (seconds)
1,98.27
5,764.48
10,1484.52
25,3553.82

As the number of buildings increases, the time required for meshing grows significantly.

3. Volumetric Mesh without Roof

The time taken to generate a volumetric mesh for buildings without roofs is presented below:

Number of Buildings,Time (seconds)
1,58.70
5,439.00
10,895.18
25, 2063.61

Without roofs, the time required for meshing is way faster compared to meshing with roofs.

4. Surface Mesh with Roof

The time taken to generate a surface mesh for buildings with roofs is presented below:

Number of Buildings,Time (seconds)
1,0.00323
50,0.04604
100,0.07268
250,0.13117
500,0.27716
700,0.39347

The surface meshing process is significantly faster compared to volumetric meshing, even as the number of buildings increases. We can also conlude that giving multiple building is way faster that doing it separately.

5. Surface Mesh without Roof

The time taken to generate a surface mesh for buildings without roofs is presented below:

Number of Buildings,Time (seconds)
1,0.00182
50,0.02005
100,0.03326
250,0.05903
500,0.12153
700,0.17920

Removing roofs further reduces the time required for surface meshing, demonstrating that roof complexity adds considerable processing time.

6. Conclusions

From the results, we observe that:

Volumetric meshing is significantly more time-consuming than surface meshing.
Adding roofs increases the complexity and time required for both volumetric and surface meshing.
The Volume Meshing seems too be way less efficient than the Surface Meshing

These insights can guide future optimizations and improvements in the meshing process.

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