Exporting and visualization

After completing the triangulation and mesh refinement process, the resulting meshes are exported and visualized to evaluate the accuracy and quality of the generated terrain models. This section presents the visualizations of the final meshes, which were created using both lambda functions and GPS data.

The meshes were exported in the MSH format, which is compatible with Gmsh, a popular open-source finite element mesh generator with a built-in CAD engine and post-processor, making it ideal for visualizing and assessing the quality of the generated meshes. The following images illustrate the mesh structures after the application of contour constraints and re-triangulation.


1. First lambda function

The first set of images shows the mesh generated using \(z(x, y) = \sqrt{r^2 - (x - x_0)^2 - (y - y_0)^2}\) which produces a half-sphere:

constrained lambda 1
Figure 1. 3D mesh after re-triangulation (lambda function 1)

constrained lambda 1 side
Figure 2. 3D mesh after re-triangulation (lambda function 1) side view

2. Second lambda function

The next set of images depicts the mesh generated using \(z(x, y) = sin(x) + cos(y)\), which creates a wave-like terrain surface:


constrained lambda 2
Figure 3. 3D mesh after re-triangulation (lambda function 2)

constrained lambda 2 side
Figure 4. 3D mesh after re-triangulation (lambda function 2) side view

3. GPS data

This set of images presents the mesh generated from GPS data corresponding to the tile with coordinates (x, y) = (33809, 23527) at zoom level 16, which includes the location at longitude 5.7232 and latitude 45.1835, located in Grenoble, France:n the mesh.


constrained grenoble 16 1
Figure 5. 3D mesh after re-triangulation (GPS data zoom 16)

constrained grenoble 16 2
Figure 6. 3D mesh after re-triangulation (GPS data zoom 16) side view

Here’s the visualization of the mesh generated from GPS data corresponding to the same location, but with a zoom of level 15, which provides a broader view of the terrain but with lower elevation detail.


constrained grenoble 15 1
Figure 7. 3D mesh after re-triangulation (GPS data zoom 15)

Here’s the result for a tile in Strasbourg City Center, France (latitude: 48.582380 and longitude 7.748242 at zoom 16) which corresponds to a very flat area:


constrained strasbourg 16
Figure 8. 3D mesh after re-triangulation (GPS data Strasbourg zoom 16)

Here at zoom 15


constrained strasbourg 15
Figure 9. 3D mesh after re-triangulation (GPS data Strasbourg zoom 15)

4. Conclusion

These visualizations confirm the effectiveness of the methods used for mesh generation, contour constraint application, and triangulation refinement, resulting in high-quality, accurate terrain meshes suitable for further simulation or analysis.


Next: Handling and merging multiple tiles


References