Fast approximation to spherical harmonics rotation

ABSTRACT

We present a fast and simple approximation of spherical harmonic rotation which decreases the asymptotic complexity and achieves a speedup of four to six in practical applications. The rotation procedure's simplicity allows implementation in a pixel shader of standard graphics hardware. The main idea is to replace the general spherical harmonic rotation matrix by its truncated Taylor expansion, resulting in a sparse matrix. We show applications in global illumination (radiance interpolation) and GPU-based real-time shading (normal mapping on surfaces with arbitrary BRDFs illuminated by low-frequency environment lighting). Although the rotation approximation is accurate only for small rotation angles, we show this is not a serious limitation in our applications.

REFERENCES

• 1: Jan Kautz , Peter-Pike Sloan , John Snyder, Fast, arbitrary BRDF shading for low-frequency lighting using spherical harmonics, Proceedings of the 13th Eurographics workshop on Rendering, June 26-28, 2002, Pisa, Italy
• 2: Jaroslav Krivanek , Pascal Gautron , Sumanta Pattanaik , Kadi Bouatouch, Radiance Caching for Efficient Global Illumination Computation, IEEE Transactions on Visualization and Computer Graphics, v.11 n.5, p.550-561, September 2005 [doi>10.1109/TVCG.2005.83]
• 3: Peter-Pike Sloan , Ben Luna , John Snyder, Local, deformable precomputed radiance transfer, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
        I.2.10 Vision and Scene Understanding

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Fast Fourier transforms (FFT)

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

General Terms:
Algorithms, Design, Theory