Steven F. Ashby Center for Applied Scientific Computing Month DD, 1997

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

• Previous Work
• System Overview
• The Discretization
• The Diffusion Equation
• Storage Management
• Algorithm
• Results
• Performance

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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)

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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

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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

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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

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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

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The Diffusion Equation

• The physically motivated equation
• inner nodes
• surface nodes
• Finite Difference Method to discretise

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Storage Management (1/2)

• using textures
• divide each texture into surface and inner
• about 20MB for 100k vertices

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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

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The Algorithm
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The Algorithm
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Quality of Results

• do not render the original geometry, but render
  the surface generated by triangulation of the
  surface nodes

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Results
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Performance

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

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Questions?
Video