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Rendering Along the Hilbert Curve

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Advances in Modeling and Simulation

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Abstract

Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L’Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert curve superimposed on the raster of pixels of an image, we achieve noise characteristics that are desirable with respect to the human visual system, especially at very low sampling rates. As compared to the state of the art, our simple algorithms neither require randomization, nor costly optimization, nor lookup tables. We analyze correlations of space-filling curves and low discrepancy sequences, and demonstrate the benefits of the new algorithms in a professional, massively parallel light transport simulation and rendering system.

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Authors and Affiliations

  1. NVIDIA, Fasanenstr. 81, 10623, Berlin, Germany

    Alexander Keller, Carsten Wächter & Nikolaus Binder

Authors
  1. Alexander Keller
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  2. Carsten Wächter
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  3. Nikolaus Binder
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Corresponding author

Correspondence to Alexander Keller .

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Editors and Affiliations

  1. Randwick, NSW, Australia

    Zdravko Botev

  2. NVIDIA, Berlin, Germany

    Alexander Keller

  3. University of Waterloo, Waterloo, ON, Canada

    Christiane Lemieux

  4. Rennes Bretagne-Atlantique, INRIA, Rennes Cedex, France

    Bruno Tuffin

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Keller, A., Wächter, C., Binder, N. (2022). Rendering Along the Hilbert Curve. In: Botev, Z., Keller, A., Lemieux, C., Tuffin, B. (eds) Advances in Modeling and Simulation. Springer, Cham. https://doi.org/10.1007/978-3-031-10193-9_16

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