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Interactive Hair Rendering and Appearance Editing under Environment Lighting

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### 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

- Motivation
- hair appearance editing
- Natural illumination
- Challenges
- Light integration complexity

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 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

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 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

- 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 Gaussian

- Useful Properties
- Local approximation by Gaussian

, error < 1.3%,

- Closed on product

center

bandwidth

Circular Gaussian

- SRBF Decomposition

=

*

1D Longitudinal

circular Gaussian

1D Azimuthal

circular Gaussian

2D SRBF

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 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 Function

- Definition [Marschner03]

Scattering Function

- Definition [Marschner03]
- Longitudinal function : normalized Gaussian

simulates specular reflection

along longitudinal direction

Scattering Function

- Definition [Marschner03]
- Azimuthal function
- Complex analytic functions
- Different for each mode
- Fresnel reflection term
- exponential attenuation term

Azimuthal Functions

- R mode
- Fresnel term (Schlick’s approximation)
- Approximated by polynomial of

Azimuthal Functions

- TT mode
- Simple shape: look like Gaussian
- approximated by 1 circular Gaussian centered at
- Parameters fitted by preserving energy

TT mode approximation

- : coefficient
- set as the peak value,
- : bandwidth
- Preserving energy

- : fresnel reflection
- : attenuation function

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 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 ScatteringIntegral

Analytic Integral

Circular Gaussian

Circular Gaussian

Gaussian

Cosine / Circular Gaussian

- =: SRBF decomposition
- : scattering func. def.

Light Integration

Multiple scattering

[Ren 2010]

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

Analytic Integral

Performance

- Testing Machine
- Intel Core 2 Duo 3.00 GHz CPU, 6 GB RAM NVIDIA GTX 580
- 720 * 480 with 8x antialias

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

- 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

- 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

- 1D Circular Gaussian
- Defined on unit circle :
- 1D Gaussian
- Defined on x-axis

Single ScatteringIntegral

Outer integral

inner integral:

- =: SRBF seperation
- : scattering func. def.
- Two dimensional integral over and

Inner Integral R Mode

- Hair scattering function approx.
- polynomial of :
- Inner integral

Precompute into 2D tables

Inner IntegralTT & TRT modes

- Hair scattering function approx.
- sum of circular Gaussians :
- Inner integral

Analytic Integral

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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