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Interactive Hair Rendering and Appearance Editing under Environment Lighting

This paper presents a novel approach to interactive hair rendering and appearance editing that accounts for dynamic environmental lighting. We address the challenges related to natural illumination and light integration complexity, proposing a circular Gaussian model for hair scattering functions. Our method allows for the manipulation of hair appearance in real-time, providing a more realistic representation of hair's interaction with light. We evaluate the performance of our technique against existing models and highlight its advantages in accuracy and computational efficiency. Our findings aim to enhance artist-friendly tools in computer graphics.

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Interactive Hair Rendering and Appearance Editing under Environment Lighting

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  1. 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

  2. Hair Appearance Editing under Environment Lighting • Motivation • hair appearance editing • Natural illumination • Challenges • Light integration complexity

  3. 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]

  4. 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

  5. Light Integration Single scattering • : environment lighting • : self shadowing • : hair scattering function

  6. Light Integration Single scattering • Approximate by a set of SRBFs [Tsai and Shih 2006]

  7. 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

  8. 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

  9. 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

  10. Circular Gaussian • Useful Properties • Local approximation by Gaussian , error < 1.3%, • Closed on product center bandwidth

  11. Circular Gaussian • SRBF Decomposition = * 1D Longitudinal circular Gaussian 1D Azimuthal circular Gaussian 2D SRBF

  12. 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

  13. 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)

  14. Scattering Function • Definition [Marschner03]

  15. Scattering Function • Definition [Marschner03] • Longitudinal function : normalized Gaussian simulates specular reflection along longitudinal direction

  16. Scattering Function • Definition [Marschner03] • Azimuthal function • Complex analytic functions • Different for each mode • Fresnel reflection term • exponential attenuation term

  17. Azimuthal Functions • R mode • Fresnel term (Schlick’s approximation) • Approximated by polynomial of

  18. Azimuthal Functions • TT mode • Simple shape: look like Gaussian • approximated by 1 circular Gaussian centered at • Parameters fitted by preserving energy

  19. TT mode approximation • : coefficient • set as the peak value, • : bandwidth • Preserving energy • : fresnel reflection • : attenuation function

  20. 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

  21. 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

  22. Single ScatteringIntegral Analytic Integral Circular Gaussian Circular Gaussian Gaussian Cosine / Circular Gaussian • =: SRBF decomposition • : scattering func. def.

  23. Light Integration Multiple scattering [Ren 2010] • Spread function: • BCSDF: [Zinke2010] • Approximate scattering function similarly Analytic Integral

  24. Results

  25. Results

  26. Results

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

  28. 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

  29. 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

  30. 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.

  31. Circular Gaussian vs Gaussian • 1D Circular Gaussian • Defined on unit circle : • 1D Gaussian • Defined on x-axis

  32. Single ScatteringIntegral Outer integral inner integral: • =: SRBF seperation • : scattering func. def. • Two dimensional integral over and

  33. Inner Integral R Mode • Hair scattering function approx. • polynomial of : • Inner integral Precompute into 2D tables

  34. Inner IntegralTT & TRT modes • Hair scattering function approx. • sum of circular Gaussians : • Inner integral Analytic Integral

  35. Outer Integral Gaussian Smooth Function Piecewise Linear approximation Analytic Integral

  36. 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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