1 SG, 9.2%, 180 fps 3 SGs, 6.0% , 76 fps 5 SGs, 3.4 %, 55 fps 7 SGs, 2.0% , 36 fps 9 SGs, 1.1% , 27 fps 1 ASG 11 SGs, 0.54% , 22 fps 13 SGs, 0.26% , 19 fps 15 SGs, 0.11% , 17 fps 1 ASG, 0.10% , 125 fps reference Figure 1 : Comparison of the SG (Spherical Gaussian) based approximation with the ASG (Anisotropic Spherical Gaussian) based approximation in rendering a highly anisotropic metal dish, under an environment light and two local lights. The BRDF of the metal dish is approximated by different number of ASGs or SGs in different images. Notice the superior property of ASGs over SGs. The result generated by 1 ASG already matches the path-traced reference well (with a L 2 error of 0.10%), and achieves a high framerate of 125 fps, while, to achieve a similar quality, more than 10 SGs are required, but with much lower framerates (19 fps for 13 SGs or 17 fps for 15 SGs). The L 2 error and the framerates for each configuration are also given in the corresponding subtitle. We present a novel anisotropic Spherical Gaussian (ASG) function, built upon the Bingham distribution [Bingham 1974] , which is much more effective and efficient in representing anisotropic spherical functions than Spherical Gaussians (SGs). In addition to retaining many desired properties of SGs, ASGs are also rotationally invariant and capable of representing all-frequency signals. To further strengthen the properties of ASGs, we have derived approximate closed-form solutions for their integral, product and convolution operators, whose errors are nearly negligible, as validated by quantitative analysis. Supported by all these operators, ASGs can be adapted in existing SG-based applications to enhance their scalability in handling anisotropic effects. To demonstrate the accuracy and efficiency of ASGs in practice, we have applied ASGs in two important SG-based rendering applications and the experimental results clearly reveal the merits of ASGs.
Recently, Xu et al. REF introduced a representation called anisotropic spherical gaussian (ASG), which is efficient and effective in representing anisotropic spherical functions, such as anisotropic BRDFs and visibilities.
Anisotropic spherical Gaussians
TOGS
Mathematics Computer Science