# Spacecraft and Asteroid Thermal Image Generation for Proximity Navigation and Detection Scenarios
## 3 Results
### Asteroid Case
#### 3.2.1 Geometry and Materials  
Two geometry models are considered: the 800K faces model and the 3M faces model. Both models have corrupted geometry, where for corrupted geometry, we consider all unrealistic sudden changes in face normals and face deformations; some examples of corrupted geometry are reported in Figure 13. Thus, starting from the 800K model, the first step is to clean the geometry to perform a smooth thermal simulation. Figure 12: Radiance field \(q_{fc}\) (**left**) infrared image black and white image (**right**). Figure 13: Ryugu 800K model corrupted geometry region. A fast approach to cleaning the geometry is to apply a smoothing filter to the whole asteroid using Blender sculpting modifiers. Although the result is perfect for the mesh generation for the thermal analysis, there is an evident loss in the terrain detail as reported in Figure 14; therefore, this solution is retained just to check and test the numerical setup of the thermal simulation, but it is discarded for the final output, as the goal is to retain all the terrain details to produce an image close to the real one as much as possible. Analyzing the 3M model, no differences can be spotted in Figure 15 but given the smaller faces, the 3M better approximate the terrain curves and details, easing the meshing phase of the simulation. On the other hand, as for the 800K model, corrupted geometry is still present, and it is actually worse, as the smaller faces increase details also in the errors of the geometry as shown in Figure 16.  
Since the goal is to produce a realistic image, it is decided to use the 3M model, as it provides a more accurate mesh. To clean the geometry without losing too much detail, a weighted paint smoothing filter is applied just on the corrupted regions. This method is a Blender sculpting technique, and consists in painting the region that must be  
Figure 16: Ryugu 3M model corrupted geometry regions. Figure 14: Original Ryugu 800K model (**left**) and with smoothing filter applied (**right**). Figure 15: Ryugu 800K model (**left**) and 3M model (**right**). smoothed with a color that is proportional to the smoothing strength, so the hottest color corresponds to a heavy smoothing and the cold colors to a lighter one. All the regions that have been healed are reported in Figure 17, where it is possible to see all the regions with corrupted geometry. The final result is reported in Figure 18; from the picture, it is possible to verify that the realism of the geometry is retained, and at the same time, the geometry is clean enough to be meshed for the thermal analysis. The number of cells on the Ryugu exterior face is increased in the snapping parameters to overcome radiation illness of the linear system produced in the finite volume discretization process. Due to the low conductivity of the asteroid regolith, at the surface of Ryugu, where radiation and diffusion are combined, radiation overcomes diffusion for each cell at that surface. This creates instability due to the big oscillations caused by the errors in the temperature field that are elevated to the power of four in the code. To better clarify the problem, the code is benchmarked with a cube of 12 m and with different mesh discretizations. The analysis of such a problem is out of the scope of the research work, but in conclusion, reducing the cell size and using relaxation is enough to stabilize the algorithm. Given the problem though, different mesh resolutions were tested to verify the results were correct at least from a numerical point of view. The final simulation is single material, and it is run in steady-state mode; moreover, to avoid losing convergence in the first steps, the simulation is started with a high conductivity value at 270 W m\({}^{-1}\) K\({}^{-1}\). In this way, the diffusion contribution in the finite volume discretization is larger than the radiation term and the simulation can start in a smoother way.