Interactive hair rendering and appearance editing under environment lighting
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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.