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Importance Sampling Spherical Harmonics
Author(s) -
Jarosz Wojciech,
Carr Nathan A.,
Jensen Henrik Wann
Publication year - 2009
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01398.x
Subject(s) - spherical harmonics , wavelet , haar wavelet , precomputation , computer science , rendering (computer graphics) , sampling (signal processing) , bidirectional reflectance distribution function , wavelet transform , algorithm , mathematics , computer vision , discrete wavelet transform , mathematical analysis , optics , computation , physics , filter (signal processing) , reflectivity
In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a by‐product of the sampling procedure we produce a multi‐resolution representation of the density function as either a spherical mip‐map or Haar wavelet. By exploiting this implicit conversion we can extend the method to distribute samples according to the product of an SH function with a spherical mip‐map or Haar wavelet. This generalization has immediate applicability in rendering, e.g., importance sampling the product of a BRDF and an environment map where the lighting is stored as a single high‐resolution wavelet and the BRDF is represented in spherical harmonics. Since spherical harmonics can be efficiently rotated, this product can be computed on‐the‐fly even if the BRDF is stored in local‐space. Our sampling approach generates over 6 million samples per second while significantly reducing precomputation time and storage requirements compared to previous techniques.