# Deep Representation of a Normal Map for Screen-Space Fluid Rendering
## 5 Experiments and Analysis
### Discussion and Limitation  
The results generated during the training process are presented in Figure 14. At the beginning of training, the generator acts as a filter that simply changes color. As the training progresses, the fluid surface is smoothened, and colors similar to the actual normal map are created. After sufficient training, the cGAN model generates a normal map similar to the target normal map when an input normal map is supplied.  
Figure 12: Convergence of the normal constraint loss.  
Figure 13: Comparison of the generated normal map results for (**a**) training with one scene (Sphere Crown), (**b**) training with three scenes (Merging Fluid, Pouring Fluid, and Double Pouring Fluid), and (**c**) training with all scenes. The various scene types are shown in Figure 6.  
The results presented in Figure 15 were generated using the screen-space method with a narrow-range filter, the screen-space method with a bilateral Gaussian filter, the marching-cube surface-reconstruction method with an anisotropic kernel, and our method. The marching-cube image resolution was 270 \(\times\) 270 \(\times\) 270, and an anisotropic kernel and vertex normal were used. For the screen-space method, the parameters were adjusted to enable the front and back of the particles to be distinguished. While using the trained cGAN, the normal map generated by the bilateral filter screen-space method was used as the input data, and validation data not previously learned were used. The result video can be found in the supplementary material.  
As shown in Figure 16, the artifacts that are often observed with screen-space fluid rendering did not appear when our method was used. Moreover, the marching-cube surface-reconstruction method had an artifact involving aliasing owing to the limitation of spatial resolution of the marching cube. This artifact did not occur in our method because our method creates a normal map in the screen space.  
Figure 14: Left to right, the columns present input, target, and our result. (**a**) epoch 0 (**b**) epoch 5 (**c**) epoch 10.  
One of our method's limitations is that some artifacts remain for dynamic scenes where the particles are scattered. An example for such a failure is presented in Figure 17, where our method found it difficult to refine the scattered individual particles. An interesting aspect of our future work will be to investigate a hybrid method that can calculate the distribution of neighboring particles around each particle, render isolated particles via a conventional screen-space method, and render merged particles via our method.  
In addition, there is the problem in that, after training, the models can be overly dependent on the parameter values used in the training data, such as the blur scale for the bilateral Gaussian filter. This problem can be alleviated by using training data with more varied parameters.  
Figure 16: Close-ups of the rendering results for obtained using our method, the screen-space (bilateral Gaussian filter) method, and the surface reconstruction method.  
Figure 15: Comparison of the rendering results.