Real-time Rendering of Heterogeneous Translucent Objects with Arbitrary Shapes Stefan Kinauer KAIST (Korea Advanced Institute of Science and Technology)

2 Outline ● Previous Work ● System Overview ● The Discretization ● The Diffusion Equation ● Storage Management ● Algorithm ● Results ● Performance

3 Previous Work (1/2) ● Photon Mapping ● physically accurate, but veery slow (hours per frame) ● A practical model for subsurface light transport by JENSEN H. W., MARSCHNER S. R., LEVOY M., HANRAHAN P. ● diffusion approximation for homogeneous materials (minutes per frame) ● Parallel solution to the radiative transport by SZIRMAY-KALOS L., LIKTOR G., MENHOFFER T., TÓTH B., KUMAR S., LUPTON G. ● homogeneous material (real time)

4 Previous Work (2/2) ● Precomputed radiance transfer for real- time rendering in dynamic, lowfrequency lighting environments. by SLOAN P.-P., KAUTZ J., SNYDER J. ● can handle heterogeneous material ● no dynamic material properties or geometry ● Modeling and rendering of heterogeneous translucent materials using the diffusion equation. by WANG J., ZHAO S., TONG X., LIN S., LIN Z., DONG Y., GUO B., SHUM H.-Y. ● heterogeneous material, real time and dynamic material properties ● but: restricted to simple geometry

5 System Overview ● Precompute tetrahedral structure ● Compute the incoming radiance on the surface ● Solve the diffusion equation ● PDE solved by relaxation method ● surface radiance as boundary condition ● discretised on the tetrahedral connectivity graph (Quadgraph) ● parallel on the GPU ● Display the results

6 Discretization (1/2) ● no regular grid (problematic with fine and complex geometry) ● Quadgraph ● 4-connected structure ● automatic tetrahedralization: “Variational tetrahedral meshing“ by ALLIEZ P., COHEN- STEINER D., YVINEC M., DESBRUN M. ● controlled by parameter K, the size difference between inner and near surface tetrahedra

7 Discretization (2/2) ● 0 to 3 surface face tetrahedra ●  split 2 and 3 surface face tetrahedra ● “0-tetrahedra“ == inner node ● “1-tetrahedra“ == 1 inner node + 1 surface node

8 The Diffusion Equation ● The physically motivated equation ● inner nodes: ● surface nodes: ● Finite Difference Method to discretise Eq.1 Eq.2

9 Storage Management (1/2) ● using textures ● divide each texture into surface and inner ● about 20MB for 100k vertices 32-bits integer textures 16-bits float textures

10 Storage Management (2/2) ● improve cache hit rate for 30% to 60% speedup ● divide textures into r x r blocks ● start at a seed node and fill the block by breadth-first traversal in the Quadgraph

11 The Algorithm

12 The Algorithm Eq.1 Eq.2

13 Quality of Results ● do not render the original geometry, but render the surface generated by triangulation of the surface nodes

14 Results

15 Performance ● Intel Core2Duo 2.13GHz CPU, with 2GB memory and an NVIDIA Geforce 8800GTX GPU with 768MB graphics memory

16 Questions? Video