Rendering fur with three dimensional textures
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Measuring and modeling anisotropic reflection
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Illumination in diverse codimensions
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
An efficient representation for irradiance environment maps
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Frequency space environment map rendering
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Unified Approach to Prefiltered Environment Maps
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
All-frequency shadows using non-linear wavelet lighting approximation
ACM SIGGRAPH 2003 Papers
Light scattering from human hair fibers
ACM SIGGRAPH 2003 Papers
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
Lighting and material of Halo 3
ACM SIGGRAPH 2008 Games
A photometric approach for estimating normals and tangents
ACM SIGGRAPH Asia 2008 papers
Interactive hair rendering under environment lighting
ACM SIGGRAPH 2010 papers
Exploiting visibility correlation in direct illumination
EGSR'08 Proceedings of the Nineteenth Eurographics conference on Rendering
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Environment-mapped rendering of Lambertian isotropic surfaces is common, and a popular technique is to use a quadratic spherical harmonic expansion. This compact irradiance map representation is widely adopted in interactive applications like video games. However, many materials are anisotropic, and shading is determined by the local tangent direction, rather than the surface normal. Even for visualization and illustration, it is increasingly common to define a tangent vector field, and use anisotropic shading. In this paper, we extend spherical harmonic irradiance maps to anisotropic surfaces, replacing Lambertian reflectance with the diffuse term of the popular Kajiya-Kay model. We show that there is a direct analogy, with the surface normal replaced by the tangent. Our main contribution is an analytic formula for the diffuse Kajiya-Kay BRDF in terms of spherical harmonics; this derivation is more complicated than for the standard diffuse lobe. We show that the terms decay even more rapidly than for Lambertian reflectance, going as l–3, where l is the spherical harmonic order, and with only 6 terms (l = 0 and l = 2) capturing 99.8% of the energy. Existing code for irradiance environment maps can be trivially adapted for real-time rendering with tangent irradiance maps. We also demonstrate an application to offline rendering of the diffuse component of fibers, using our formula as a control variate for Monte Carlo sampling. © 2012 Wiley Periodicals, Inc.