Myths of Computer Graphics

Computer graphics textbooks teach that sampling by deterministic patterns or even lattices causes aliasing, which only can be avoided by random, i.e. independent sampling. They recommend random samples with blue noise characteristic, which however are highly correlated due to their maximized minimum mutual distance. On the other hand the rendering software mental ray, which is used to generate the majority of visual effects in movies, entirely is based on parametric integration by quasi-Monte Carlo methods and consequently is strictly deterministic. For its superior quality the software even received a Technical Achievement Award (Oscar) by the American Academy of Motion Picture Arts and Sciences in 2003. Along the milestones of more than ten years of development of quasi-Monte Carlo methods in computer graphics, we point out that the two previous statements are not contradictory.

[1]  Kurt Akeley,et al.  The accumulation buffer: hardware support for high-quality rendering , 1990, SIGGRAPH.

[2]  Jirí Matousek,et al.  On the L2-Discrepancy for Anchored Boxes , 1998, J. Complex..

[3]  R. Cranley,et al.  Randomization of Number Theoretic Methods for Multiple Integration , 1976 .

[4]  Chuck Hansen,et al.  Eurographics '97 , 1998, COMG.

[5]  G. Larcher,et al.  Walsh Series Analysis of the L2-Discrepancyof Symmetrisized Point Sets , 2001 .

[6]  James T. Kajiya,et al.  Rendering fur with three dimensional textures , 1989, SIGGRAPH.

[7]  John Platt,et al.  20.4: Displaced Filtering for Patterned Displays , 2000 .

[8]  William H. Press,et al.  Numerical recipes in C , 2002 .

[9]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[10]  Harald Niederreiter,et al.  Error bounds for Quasi-Monte Carlo integration with uniform point sets , 2003 .

[11]  Leonidas J. Guibas,et al.  Robust Monte Carlo methods for light transport simulation , 1997 .

[12]  Alexander Keller,et al.  Fast Generation of Randomized Low-Discrepancy Point Sets , 2002 .

[13]  Alexander Keller,et al.  Metropolis Light Transport for Participating Media , 2000, Rendering Techniques.

[14]  Andrew S. Glassner,et al.  Principles of Digital Image Synthesis , 1995 .

[15]  MatoušekJiří.  On the L2-discrepancy for anchored boxes , 1998 .

[16]  H. Faure.  Good permutations for extreme discrepancy , 1992 .

[17]  I. Sloan.  Lattice Methods for Multiple Integration , 1994 .

[18]  Robert L. Cook,et al.  The Reyes image rendering architecture , 1987, SIGGRAPH.

[19]  Alexander Keller,et al.  Efficient Bidirectional Path Tracing by Randomized Quasi-Monte Carlo Integration , 2002 .

[20]  P. Erdos,et al.  Studies in Pure Mathematics , 1983 .

[21]  H. Niederreiter,et al.  Quasirandom Sampling in Computer Graphics , 1992 .

[22]  S. K. Zaremba,et al.  La discrépance isotrope et l'intégration numérique , 1970 .

[23]  A. Keller.  A Quasi-Monte Carlo Algorithm for the Global Illumination Problem in the Radiosity Setting , 1995 .

[24]  Alexander Keller.  Quasi-Monte Carlo Radiosity , 1996, Rendering Techniques.

[25]  Edmund Hlawka,et al.  Discrepancy and Riemann Integration , 1990 .

[26]  A. Owen.  Randomly Permuted (t,m,s)-Nets and (t, s)-Sequences , 1995 .

[27]  H. Jensen.  Realistic Image Synthesis Using Photon Mapping , 2001 .

[28]  George Drettakis,et al.  Interactive Sampling and Rendering for Complex and Procedural Geometry , 2001, Rendering Techniques.

[29]  Alexander Keller.  The Quasi-Random Walk , 1998 .

[30]  Alexander Keller,et al.  Stratification by Rank-1 Lattices , 2004 .

[31]  Alexander Keller,et al.  Efficient Multidimensional Sampling , 2002, Comput. Graph. Forum.

[32]  Peter Shirley,et al.  Discrepancy as a Quality Measure for Sample Distributions , 1991, Eurographics.

[33]  Don P. Mitchell,et al.  Ray Tracing and Irregularities of Distribution , 2000 .

[34]  J. Yellott.  Spectral consequences of photoreceptor sampling in the rhesus retina. , 1983, Science.

[35]  John Platt,et al.  20.4: Displaced Filtering for Patterned Displays , 2000 .