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Interactive Hair Rendering and Appearance Editing under Environment Lighting. Kun Xu 1 , Li- Qian Ma 1 , Bo Ren 1 , Rui Wang 2 , Shi-Min Hu 1 1 Tsinghua University 2 University of Massachusetts. Hair Appearance Editing under Environment Lighting. Motivation hair appearance editing

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interactive hair rendering and appearance editing under environment lighting

Interactive Hair Rendering and Appearance Editing under Environment Lighting

Kun Xu1, Li-QianMa1, Bo Ren1, Rui Wang2, Shi-Min Hu1

1Tsinghua University

2University of Massachusetts

hair appearance editing under environment lighting
Hair Appearance Editing under Environment Lighting
  • Motivation
    • hair appearance editing
    • Natural illumination
  • Challenges
    • Light integration complexity
related works
Related Works
  • Hair scattering function/models
  • Self Shadowing
    • deep shadow maps [Lokovic & Veach 2000]
    • opacity shadow maps [Kim & Neumann 2001]
    • density clustering [Mertens et al. 2004]
    • deep opacity maps [Yuksel & Keyser 2008]
    • occupancy maps [Sintorn & Assarson 2009]

[Kajiya & Kay 89]

[Zinke & Webber 07]

[Marschner 03]

[Sadeghi 10]

[d’Eon 11]

related works1
Related Works
  • Multiple scattering
    • Photon Mapping [Moon & Marschner 2006]
    • Spherical Harmonics [Moon et al. 2008]
    • Dual Scattering [Zinke et al. 2008]
  • Environment lighting [Ren 2010]
    • Model lighting using SRBFs
    • Precomputed light transport into4D tables
    • Fix hair scattering properties

hair appearance editing under environment lighting remains unsolved

light integration
Light Integration

Single scattering

  • : environment lighting
  • : self shadowing
  • : hair scattering function
light integration1
Light Integration

Single scattering

  • Approximate by a set of SRBFs [Tsai and Shih 2006]
light integration2
Light Integration

Single scattering

  • Approximate by a set of SRBFs [Tsai and Shih 2006]
  • Move T out from the integral [Ren 2010]

Problem: evaluate scattering Integral

single scattering integral
Single ScatteringIntegral
  • Previous Approach [Ren 2010]
    • Precompute the integral into 4D table
  • Our key insight
    • Is there an approximated analytic solution?
    • YES
      • Decompose SRBF into products of circular Gaussians
      • Approximate scattering function by circular Gaussians
circular gaussian
Circular Gaussian
  • SRBF (Spherical Radial Basis Function)
    • Typically spherical Gaussian
    • Widely used in rendering
      • Environment lighting [Tsai and Shih 2006]
      • Light Transport [Green 2007]
      • BRDF [Wang 2009]
  • Circular Gaussian
    • 1D case of SRBF
    • Share all benefits of SRBFs
circular gaussian1
Circular Gaussian
  • Useful Properties
    • Local approximation by Gaussian

, error < 1.3%,

    • Closed on product

center

bandwidth

circular gaussian2
Circular Gaussian
  • SRBF Decomposition

=

*

1D Longitudinal

circular Gaussian

1D Azimuthal

circular Gaussian

2D SRBF

scattering function
Scattering Function
  • Sum of three modes: R, TT, TRT [Marschner03]

R mode: Reflection (p=0)

TRT Mode:

Transmission-Reflection-Transmission (p=2)

hair fiber longitudinal angle

TT Mode:

Transmission-Transmission (p=1)

tilted angle

scattering function1
Scattering Function
  • Sum of three modes: R, TT, TRT [Marschner03]

R mode: Reflection (p=0)

hair fiber cross section

azimuthal angle

TT Mode:

Transmission-Transmission (p=1)

TRT Mode:

Transmission-Reflection-Transmission (p=2)

scattering function2
Scattering Function
  • Definition [Marschner03]
scattering function3
Scattering Function
  • Definition [Marschner03]
    • Longitudinal function : normalized Gaussian

simulates specular reflection

along longitudinal direction

scattering function4
Scattering Function
  • Definition [Marschner03]
    • Azimuthal function
      • Complex analytic functions
      • Different for each mode
        • Fresnel reflection term
        • exponential attenuation term
azimuthal functions
Azimuthal Functions
  • R mode
  • Fresnel term (Schlick’s approximation)
  • Approximated by polynomial of
azimuthal functions1
Azimuthal Functions
  • TT mode
    • Simple shape: look like Gaussian
    • approximated by 1 circular Gaussian centered at
    • Parameters fitted by preserving energy
tt mode approximation
TT mode approximation
  • : coefficient
    • set as the peak value,
  • : bandwidth
    • Preserving energy
  • : fresnel reflection
  • : attenuation function
tt mode approximation1
TT mode approximation
  • : coefficient
    • set as the peak value,
  • : bandwidth
    • Preserving energy
  • : fresnel reflection
  • : attenuation function

Precompute into 2D tables

4-th order Taylor expansion

azimuthal functions2
Azimuthal Functions
  • TRT mode:
    • Shape: sum of Circular Gaussians
      • : approximated by 3 circular Gaussians
      • approximated by 1 circular Gaussian
    • Fitted by preserving energy similar as TT mode
single scattering integral1
Single ScatteringIntegral

Analytic Integral

Circular Gaussian

Circular Gaussian

Gaussian

Cosine / Circular Gaussian

  • =: SRBF decomposition
  • : scattering func. def.
light integration3
Light Integration

Multiple scattering

[Ren 2010]

  • Spread function:
  • BCSDF: [Zinke2010]
  • Approximate scattering function similarly

Analytic Integral

performance
Performance
  • Testing Machine
    • Intel Core 2 Duo 3.00 GHz CPU, 6 GB RAM NVIDIA GTX 580
    • 720 * 480 with 8x antialias
conclusion
Conclusion
  • 1D circular Gaussian
    • Accurate and compact for representing hair scattering functions
    • Closed form integral with SRBF lights
  • New effects
    • interactive hair appearance editing under environment lighting
    • Rendering of spatially varying hair scattering parameters under environment lighting
future works
Future works
  • View transparency effects [Sintorn and Assarsson 2009]
  • Other hair scattering models
    • Artist friendly model [Sadeghi2010]
    • Energy conserving model [d’Eon2011]
  • Near-field light sources
  • Accelerate off-line hair rendering
acknowledgement
Acknowledgement
  • Anonymous Siggraph and Siggraph Asia reviewers
  • Ronald Fedkiw, CemYuksel, Arno Zinke, Steve Marschner
    • Sharing their hair data
  • ZhongRen
    • Useful discussion

Thank you for your attention.

circular gaussian vs gaussian
Circular Gaussian vs Gaussian
  • 1D Circular Gaussian
    • Defined on unit circle :
  • 1D Gaussian
    • Defined on x-axis
single scattering integral2
Single ScatteringIntegral

Outer integral

inner integral:

  • =: SRBF seperation
  • : scattering func. def.
  • Two dimensional integral over and
inner integral r mode
Inner Integral R Mode
  • Hair scattering function approx.
    • polynomial of :
  • Inner integral

Precompute into 2D tables

inner integral tt trt modes
Inner IntegralTT & TRT modes
  • Hair scattering function approx.
    • sum of circular Gaussians :
  • Inner integral

Analytic Integral

outer integral
Outer Integral

Gaussian

Smooth Function

Piecewise Linear approximation

Analytic Integral

summary of single scattering
Summary ofSingle Scattering
  • Hair scattering function approximation
    • R mode: polynomial of cosine
    • TT/TRT mode: circular Gaussian
  • Inner integral
    • R mode: 2D tables
    • TT/TRT mode: 2D tables, analytic integral
  • Outer integral
    • Piecewise linear approximation for smooth func.
    • Analytic integral.
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