Eikonal Rendering: Efficient Light Transport in Refractive Object

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Eikonal RenderingEfficient Light Transport
in Refractive Object

• Ivo Ihrke1, Gernot Ziegler1, Art Tevs1, Christian
  Theobalt1, Marcus Magnor2, Hans-Peter Seidel1

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Outline

• Introduction
• Related work
• Image Formation Model
• Light Transport
• Implementation issue
• Result and Discussion

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Introduction

• Object with complex optical properties
• spatially varying refractive index
• Cause inhomogeneous focusing of light.
• Become visible as beautiful surface and volume
  caustic

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Introduction cont.

• Contribution
• Provide a general framework
• To jointly reproduce the effects below in
  real-time on commodity graphics hardware.
• Varying refractive index, arbitrary BRDF,
  view-independent single-scattering effect,
  translucent object in scattering participating
  media

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Related Work

• Approximate refraction effect
• In real-time on GPU Wyman 2005
• On a special processor Ohbuchi 2003
• In a CPU-based ray-tracerWald et al 2002
• Rendering realistic caustics
• off-line and high quality backward
  ray-tracingArvo 1986
• Photo mappingJensen et al. 2001
• Scattering
• Subsurface scatteringMerten 2003
• Light propagation
• Eikonal and transport equation , main postulate
  of geometric opticsBorn and Wolf 1999

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Image Formation Model- General Image Formation

• Account for emission, reflection, absorption,
  scattering
• denote radiance on the ray c that is
  scattered, emitted , reflected, into eye.
• is background radiance
• is the absorption of light at
  position t
• xc(t) position vdc/dt ray direction

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General Image Formation -cont.

• ? Ls due to inscatter
• Lr reflected into eye
• Le emitted into eye
• ? is the Fresnel reflection factor
• Locality of Lc

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General Image Formation -cont.

• p the scattering phase function
• dE? local differential radiance
• fr BRDF term

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IFG-Simplified Image Formation

• Too complex to evaluate in real-time
• Make two assumption
• Light originates from a discrete number of light
  source
• For each point, only a discrete number of
  incoming light ray

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Light Transport

• Including two parts
• Propagation of viewing ray
• Light transport
• Governing equations are derived from
• Ray equation of geometric optic
• Born and Wolf 1999

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Light Transport- Viewing Ray Propagtion

• The equation describe the motion of a light
  particle in a field n of inhomogeneous
  refractive indices
• Derived from eikonal equation
• The motion of a particle along the gradient of
  the eikonal solution

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Viewing Ray Propagtion -cont.

• Rewritten as below
• Use Euler forward scheme

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Light Transport -Modeling Light Sources

• Model a light source with
• Three dim. vector field of local light direction
  l(x)
• Scalar filed of differential irradiance value
• Use adaptive wavefront tracing to compute l(x)
  and

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Modeling Light Sources -cont.

• A wavefront is an iso-surface of constant travel
  time of light.
• Light ray is normal to wavefront.

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Modeling Light Sources -cont.

• l(x) ?
• traveling directions of the particle
• ?
• area of wavefront patches

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Modeling Light Sources -cont.

• The pre-computation of the three-dim. light
  distribution includes 4 steps
• Wavefront propagation
• Irradiance computation
• Wavefront refinement
• Voxelization of the local light direction and
  differential irradiance values

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Wavefront Propagation

• The propagation of light is similar to eye rays
  propagation.
• re-parameterize the former equation.

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Irradiance Computation

• The irradiance computation is based on the
  intensity law of geometric optics.
• In an infinitesimal tube of ray the energy stays
  constant.
• ?

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Wavefront Refinement and Voxelization

• To obtain a continuous volumetric representation
  of the light distribution
• Wavefront patches have to voxelized.
• If a patch area slides through a voxel without
  touching it with one of its corner,
• This patch will be unsampled.
• ? Use wavefront refinement

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Implementation Issue

• 1.Input Data Format
• Input scenes are stored as a set of 3D volume
  textures.
• Refractive index distributions can be derived
  directly from the implicitly function of the
  object
• Some texture also contain spatial varying RGB,
  boundary indicator , BRDF parameter

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Implementation Issue -cont.

• 2.Light Simulator
• Wavefront is represented as a particle system.
• Use the 2D-parameterization of the patch list
  texture to produce a
• planar wavefront --- directional light source
• Spherical wavefront --- point light source.
• The propagation of the wavefront through the
  scene and logging into the output 3D volume is
  perform in 3 subsequent steps.

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Implementation Issue -cont.

• Patch List Update
• For every time step, update the patchs position
  and direction.
• Patch List Voxelization
• Into 3D-output volume for irradiance and
  direction
• Patch List Tessellation Analysis
• Divergence tessellation stay below a minimum
  sampling bound
• Patch termination apply energy threshold to
  eliminate the patch
• 3. View Renderer

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Video time

• Taking a break and see the video!

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Conclusions

• We present a fast and versatile method to render
  a variety of sophisticated lighting effects in
  real time.
• The pre-computation took around 90 minutes for
  600 frames.
• AMD Dual Core Athlon 2.6GHz, Nvidia GeForce 8800
  GTX and 768 of video ram
• 25fps at a resolution of 800 x 600 pixels