Project presentation for my MS Exam on April 09, 2010.

1. Real Time Visual Simulation of Smoke on the GPU By Muhammad S. Karim MSCS Student Department of Computer Science The University of New Mexico

2. Introduction & Motivation HORVATH, C., AND GEIGER, W. 2009. Directable, high-resolution simulation of fire on the GPU. ACM Trans. Graph. 28, 3, 1-8. Used in creating visual effects in “Harry Potter and the Half Blood Prince”. Uses a incompressible, inviscidNavier-stokes equations for fluid flow. Pursuing as part of an Individual Study project with Dr. Joe Kniss.

3. The Project and Goal Starting with an implantation of the following: FEDKIW, R., STAM, J., AND JANSEN H. W. 2001. Visual Simulation of Smoke. In proc. of ACM SIGGRAPH 2001. Based on: Stam, J. 1999. Stable Fluids. In SIGGRAPH 99. Goal is to pursue the real-time implementation using GPU specific vertex & fragment processing features. Images from [FEDKIEW 2001]

5. Simulation Algorithm, inside a 3D grid:

6. Step 1: Add Forces (Buoyancy,Vorticity)

7. Step 2: Advect Velocity Field

8. Step 3: Solve for intermediate pressure term.

9. Step4: Project velocity field to make the field divergence free.

10. Step 5: Apply boundary conditions to Velocity & Pressure fields.

12. Simulation Algorithm Steps 1.b Add back Vorticity Confined Force to the velocity field: Curl(u) Shader + = Fvort u’(t) u(t)

13. Simulation Algorithm Steps 2. Advect Velocity field: (Semi-Lagrangian Advection) Move back along the vector back a timestep. Pick a vector by Tri-linear interpolating the 6 neighboring cells from the 3D texture. Set this computed value to the current cell.] Benefits: ‘Stable’ field, avoid “blow-ups”, GPU friendly. Shader u’(t) u(t)

14. Simulation Algorithm Steps 3. Compute field Pressure (for the next projection step): u(t) Solve for p Shader Shader Iterative Jacobi Solver Div(u) p(t) after N Jacobi Iterations (I use 30-40)

15. Simulation Algorithm Steps 4. Project Velocity field: Using Helmholtz-Hodge decomposition. (To ensure 0 divergence). Any vector field u* can be uniquely decomposed as the following equation where u has 0 divergence: - = Grad ( p(t) ) u(t) u (t+1)

16. Simulation Algorithm Steps 5. Apply boundary conditions: Based on ‘fixed-grid’, fluid confined to the grid. a. Velocity goes to zero on the boundary (no-slip condition). b. Pressure derivative goes to zero on the boundary. (Neumann pressure condition). Draw 4 lines along the boundary on each slice of the 3D texture GPU Implementation Draw a quad on the front (z=0) and another on the back (z=slices-1) of the 3D texture

17. Simulation Algorithm Steps 6. Advectthe scalar fields (Density & Temperature) Similar to velocity field advection. Dissipate the scalar fields based on time. Shader ρ(t) Shader u(t) T(t)

18. Volume Rendering a. Slice the grid region from the viewer’s point-of-view. b. Render each slice from front-to-back order. c. Use the “under” operator to composite (blend) the slices to make the final images of the smoke region. I used the polygon slicing algorithm implemented in a vertex shader exactly described in: Ref “Real-time Volume Graphics” – Engel et. al. Ch-3.5. Demonstration from my program showing 2 slices

19. Volume Rendering (more…) Implemented volumetric shadows using the Half-Angle Slicing technique by Kniss et al. 2003. Ref: Kniss, J., S. Premo e, C. Hansen, P. Shirley, and A. McPherson. 2003. "A Model for Volume Lighting and Modeling." IEEE Transactions on Visualization and Computer Graphics 9(2), pp. 150–162. Using a 2D light buffer to accumulate opacity at each slice, the use as a shadow map

20. Some Results Self-shadowing the smoke volume produces more realism. Smoke volume transparency is computed based on the smoke density values computed in the grid. No self-showing inside the volume With self-showing inside the volume

21. Closing Remarks and Demo I used 64 x 64 x 64 grids in the Demo, higher resolution provides finer details. I also used a fixed grid, will possibly explore techniques to move the fluid out of the box. Practical and possible to use in real-time applications with mid-high end GPUs.