A Simple Layered RGB BRDF Model

1. Xavier Granier - Wolfgang Heidrich IMAGER/University of British Columbia A Simple LayeredRGB BRDF Model

2. Motivations • Increase the range of possible effects • For graphic content creation • Work in Color Space RBG - XYZ - LMS • Currently limited to linear reflection • Convincing and simple model • Not a full simulation • Effect as realistic as possible

3. Motivations • Wavelength effects • Interference • Colour dispersion • Investigation • Framework

4. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

5. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

6. Uniform BRDF • Phong models [Phong75,Lafortune94-97,…] • Most commonly used • Simplified models [Ward92,Schlick94,…] • Faster / Better for Global illumination • Micro-facet [Torrance67,Ashikhmin00,…] • Physically based [He91,Hanrahan93,…] • No wavelength dependent effects

7. Wavelength effects • Diffraction [Stam99,Sun00,…] • Interferences • Recursive Ray-Tracing [Hirayama00-01,…] • Full model [Icart99-00,…] • Fine Spectral representation • RGB based BRDF • Interferences + Colour dispersion

8. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

9. Approach • Semi-transparent layer • Interferences effects • Local prism configuration • One refraction index by colour component • Non-parallel layer interfaces • Colour dispersion • RGB colour space • Commonly used in image production

10. Layer configuration 0 Air 1 Layer 2 Support

11. Resulting energy from interferences Parallel layers Uncorrelated layers Interference : Phase Change

12. Color dispersion : Assumption

13. BRDF general expression • k{r,g,b} • R (reflected BRDF) • 3 (RGB) lobe-like models • T (transmitted BRDF) • 3 (RGB) lobe-like models • Ex: using Phong models

14. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

15. Reflected part • Phong

16. Transmitted part • Assumption • No absorption • Only one reflection Transmitted term

17. Main Parameters • Normally r0(k)1 (air/vacuum) • Local geometric configuration : layer-normal • Material properties : exponents - indices • Fully determined by 4-12 parameters • 2-6 Exponents (control transition smoothness) • 1-3 RGB refraction indices (rB  rG  rR) • 1 Layer size • 0-2 Normal variation (colour dispersion)

18. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

19. Diffuse case  Average along direction Similar expression Assumptions No colour dispersion Rd average reflected energy

20. Phase change for orthogonal incidence No absorption at the interface Diffuse component • Final expression

21. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

22. Diffuse component 67 - 73 nm 1 - 30 nm 1 - 210 nm

23. Layer Size Change Constant normal deviation 148-200 nm 1-30 nm 79-106 nm

24. Constant deviation Parallel Interfaces Constant deviation

25. Size / Normal correlation 1-90 nm 1-10 nm rR = 1.5 rG = 1.7 rB = 1.8

26. Overview • Previous Work • General Configuration • Glossy Case • Diffuse Case • Results • Conclusion

27. Conclusion • RGB Model • Interferences and colour dispersion • Continuous along direction • Two models • Phong - like for specularity • Diffuse • Validation • Such effects are possible in colour space

28. Future Work • With current model • Hardware acceleration (shader) • Try to fit some measured BRDF • Investigate other • Increase accuracy / More physical • Investigate colour spaces • Keep simplicity • Multi-layer

29. Acknowledgements • IMAGER/ University of British Columbia • Post-doctoral position • PIMS Post-doctoral Fellowship • Wolfgang Heidrich & Lionel Bastard • Useful comments and support

30. The End

31. Fresnel term (Schlick approximation) Reflected part • Phong reflection