Mayur Patel
ABSTRACT
In this presentation, we survey modern discrepancy metrics and use them to estimate the quality of point sets produced from a variety of sample generators in two dimensions. Then, we calculate the actual performance of these point sets for integrating a number of signals in the unit square. Finally, we correlate the estimated performance to the observed result to determine which metrics have the greatest utility as predictors of success for computer graphics applications.
Supplemental Material
- Abdalla G. M. Ahmed, Till Niese, Hui Huang, and Oliver Deussen. 2017. An Adaptive Point Sampler on a Regular Lattice. ACM Trans. Graph. 36, 4, Article 138 (July 2017), 13 pages. https://doi.org/10.1145/3072959.3073588Google Scholar
Digital Library
- Brent Burley. 2020. Practical Hash-based Owen Scrambling. Journal of Computer Graphics Techniques (JCGT) 10, 4 (29 December 2020), 1–20. http://jcgt.org/published/0009/04/01/Google Scholar
- Per Christensen, Andrew Kensler, and Charlie Kilpatrick. 2018. Progressive Multi-Jittered Sample Sequences. Computer Graphics Forum 37, 4 (2018), 21–33. https://doi.org/10.1111/cgf.13472 arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.13472Google ScholarCross Ref
- David Paul Dobkin and Don P. Mitchell. 1993. Random-edge discrepancy of supersampling patterns, In Proceedings of Graphics Interface ’93. Proceedings of Graphics Interface ’93, 62–69.Google Scholar
- Carola Doerr, Michael Gnewuch, and Magnus Wahlström. 2014. Calculation of Discrepancy Measures and Applications. Springer International Publishing, Cham, 621–678. https://doi.org/10.1007/978-3-319-04696-9_10Google ScholarCross Ref
- Peter Hellekalek and Harald Niederreiter. 1998. The Weighted Spectral Test: Diaphony. ACM Trans. Model. Comput. Simul. 8, 1 (Jan. 1998), 43–60. https://doi.org/10.1145/272991.273008Google ScholarDigital Library
- Fred J. Hickernell. 1998a. A Generalized Discrepancy and Quadrature Error Bound. Math. Comp. 67, 221 (1998), 299–322. http://www.jstor.org/stable/2584985Google ScholarDigital Library
- Fred J. Hickernell. 1998b. Lattice Rules: How Well Do They Measure Up?Springer New York, New York, NY, 109–166. https://doi.org/10.1007/978-1-4612-1702-2_3Google ScholarCross Ref
- William J. Morokoff and Russel E. Caflisch. 1994. Quasi-Random Sequences and Their Discrepancies. SIAM Journal on Scientific Computing 15, 6 (1994), 1251–1279. https://doi.org/10.1137/0915077 arXiv:https://doi.org/10.1137/0915077Google ScholarDigital Library
- Mayur Patel. 2022. Optimizing Kronecker Sequences for Multidimensional Sampling. Journal of Computer Graphics Techniques (JCGT) 11, 1 (2 March 2022), 55–81. http://jcgt.org/published/0011/01/04/Google Scholar
- Peter Shirley. 1991. Discrepancy as a Quality Measure for Sample Distributions. In EG 1991-Technical Papers. Eurographics Association, Eurographics Association. https://doi.org/10.2312/egtp.19911013Google ScholarCross Ref
- Yong-Dao Zhou, Kai-Tai Fang, and Jian-Hui Ning. 2013. Mixture discrepancy for quasi-random point sets. Journal of Complexity 29, 3 (2013), 283–301. https://doi.org/10.1016/j.jco.2012.11.006Google ScholarCross Ref
Index Terms
- The Efficacy of Discrepancy in Computer Graphics
Recommendations
Interactive computer graphics at Ford Motor Company
SIGGRAPH '80: Proceedings of the 7th annual conference on Computer graphics and interactive techniquesOver the past fourteen years the Ford Motor Company actively pursued the development and use of interactive computer graphics in the design and manufacture of automobiles. The success of Ford's pioneering efforts in the area of minicomputer graphics led ...
Interactive computer graphics at Ford Motor Company
Over the past fourteen years the Ford Motor Company actively pursued the development and use of interactive computer graphics in the design and manufacture of automobiles. The success of Ford's pioneering efforts in the area of minicomputer graphics led ...
Teaching a Shader-Based Introduction to Computer Graphics
Recent GPU technology advances have led to dramatic changes in graphics software that let applications exploit the GPU's full power through programmable shaders. Introductory computer graphics courses should reflect these advances.
Comments