Figure 1: A high dynamic range 1024×512 environment map [Debevec 98] sampled with 3000 point lights. In this image, importance density is represented by the lightness of the background. It took 0.064 seconds on a 2.6 GHz P4 to generate this point set. Similar results using a hardware accelerated Lloyd relaxation [Hoff et al. 1999] required 1 second, while Structured Importance Sampling [Agarwal et al. 2003] took 1393 seconds. AbstractThis paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and these numbers are used to threshold the samples against the local value of the importance density. Pre-computed correction vectors, obtained using relaxation, are used to improve the spectral characteristics of the sampling pattern. The technique is deterministic and very fast; the sampling time grows linearly with the required number of samples. We illustrate our technique with importance-based environment mapping, but the technique is versatile enough to be used in a large variety of computer graphics applications, such as light transport calculations, digital halftoning, geometry processing, and various rendering techniques.

Figure 1: A high dynamic range 1024×512 environment map [Debevec 98] sampled with 3000 point lights. In this image, importance density is represented by the lightness of the background. It took 0.064 seconds on a 2.6 GHz P4 to generate this point set. Similar results using a hardware accelerated Lloyd relaxation [Hoff et al. 1999] required 1 second, while Structured Importance Sampling [Agarwal et al. 2003] took 1393 seconds. AbstractThis paper presents a novel method for efficiently generating a good sampling pattern given an importance density over a 2D domain. A Penrose tiling is hierarchically subdivided creating a sufficiently large number of sample points. These points are numbered using the Fibonacci number system, and these numbers are used to threshold the samples against the local value of the importance density. Pre-computed correction vectors, obtained using relaxation, are used to improve the spectral characteristics of the sampling pattern. The technique is deterministic and very fast; the sampling time grows linearly with the required number of samples. We illustrate our technique with importance-based environment mapping, but the technique is versatile enough to be used in a large variety of computer graphics applications, such as light transport calculations, digital halftoning, geometry processing, and various rendering techniques.

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