Fig. 1. Particle approximation for a two-dimensional problem. defined by Fig. 2. SPH simulation flow. tunable parameter [102]. This method forces particles near each other to move with close velocity and conserves angular and lin- ear momentum approximately by dumping the particle velocity [102] by using Fig. 3. Rendering method overview. Fig. 4. Depth map created using the Ray Casting procedure. 3.2.2. Screen space curvature flow To achieve a better-looking result, [14] proposed a Curvature Flow Approach based on [103], which smoothes sudden changes in curvature between particles. As the viewpoint is constant, the smoothing effect can be applied by moving the depth value z pro- portionally to the curvature, as defined by Fig. 5. Result of the blur in the depth map. Fig. 6. Result of the normal estimation. The z component of the divergence is always zero, because z is a function of x and y, being kept constant when x and y are also maintained constant. So Fig. 7. Final render result. CPU and GPU computation times and their respective speedups for each test case. Table 1 Fig. 8. Initial configuration of the 3D dam break. Fig. 9. Initial configuration of the 3D drop case. Fig. 11. Rendering of the water drop scene. Fig. 10. Time profile of CPU and GPU versions. Fig. 12. Rendering of the dam break scene. Fig. 13. Rendering with different numbers of smoothing iterations: 25 (left), 50 (middle) and 100 (right). Fig. 14. Variations on the fps given the number of smoothing iterations. The tes! was performed with 500k particles and 1000 x 1000 image resolution. Variations on the fps given image resolution and number of particles for static and dynamic scenes. Fig. 15. Comparison between rendering percentage time and number of particles. Rendering time for a single frame of our method compared to commercial softwares with different particle numbers. Fig. 16. Rendering result of the 3DS Max 2019 (left), our method (middle), and the Realflow (right) for a fluid with 1M particles. As each commercial software uses a different particle based method to simulate the fluid, the input particles position may differ from each other.
![Fig. 2. SPH simulation flow. tunable parameter [102]. This method forces particles near each other to move with close velocity and conserves angular and lin- ear momentum approximately by dumping the particle velocity [102] by using](https://figures.academia-assets.com/117820269/figure_002.jpg)
![Fig. 4. Depth map created using the Ray Casting procedure. 3.2.2. Screen space curvature flow To achieve a better-looking result, [14] proposed a Curvature Flow Approach based on [103], which smoothes sudden changes in curvature between particles. As the viewpoint is constant, the smoothing effect can be applied by moving the depth value z pro- portionally to the curvature, as defined by](https://figures.academia-assets.com/117820269/figure_004.jpg)
