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

Eq.1

Eq.2

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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

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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

Eq.1

Eq.2

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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