Spherical Harmonic Lighting of Wavelength-dependent Phenomena Clifford Lindsay, Emmanuel Agu Worcester Polytechnic Institute (USA)

Introduction  Modeling of Light Interference As A BRDF  Compactly Store Surface Response and Hemispheric Light Contribution In Terms Of Spherical Harmonic Coefficients  Evaluation of Light And Reflection Is Done on GPU  Working With Spectral Color Space Instead of RGB

Spherical Harmonics We can then use these coefficients to reconstruct an approximation to the original signal We can use spherical harmonics to approximate the original, where c i is a vector of SH coefficient Spherical harmonics is a set of basis functions defined in spherical coordinates

Interference Factors that Affect Light Interference :  Refractive index and thickness of the thin film  Refractive indices of the media 1 & 2  Incident Angle  and incident SPD (Spectral Power Distribution)

Spectral BRDF Just Like Regular BRDFs (but different)  Rendering equation  Function of 4 angles (incident, reflection)  Conservative What’s Different?  Different Color Interaction  Different Material Interaction  Different Viewer Interaction (non-reciprocal)

Previous Work in S.H.  Diffuse Reflection Maps, Hanrahan, Ramamoorthi, 2001  Physically Based BRDFs, Westin 1992  Isotropic BRDFs with SH Maps, Hanrahan, Ramamoorthi, 2002  Arbitrary BRDFs, Kautz et al, 2002  Radiance Transfer, Glossy Surfaces, Self-shadow, and Interreflection, Sloan et al, 2002

Our Approach Two Stage Approach: 1. Pre-computation 2. Render   

Pre-computation Total Light Contribution: BRDF Response:  Texture map based all possible view vectors  Set of coefficients approximating total light contribution

GPU V,T,B Vertex Processor Fragment Processor Texture Map, f i Uniform Var, L i Rendering:  Index Texture Map Based on view V  Summing the coefficients for final contribution  Add ambient, diffuse, Fresnel for additional realism

Conclusion  Real-time rendering of complex materials previously available to offline renderers (ray tracers)  Data and Data structures that are GPU friendly  Evaluation of Spherical Harmonics is a linear operation  Increased realism with Image Based Lighting and accurate BRDFs with GPU acceleration

Results