Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Generating antialiased images at low sampling densities
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Antialiased ray tracing by adaptive progressive refinement
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Spectrally optimal sampling for distribution ray tracing
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
New upper bounds in Klee's measure problem
SIAM Journal on Computing
Offline maintenance of planar configurations
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Computing half-plane and strip discrepancy of planar point sets
Computational Geometry: Theory and Applications
Statistically optimized sampling for distributed ray tracing
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Antialiasing through stochastic sampling
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
An improved illumination model for shaded display
Communications of the ACM
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Concept learning with geometric hypotheses
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Consequences of stratified sampling in graphics
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
A photon accurate model of the human eye
ACM SIGGRAPH 2005 Papers
A (slightly) faster algorithm for klee's measure problem
Proceedings of the twenty-fourth annual symposium on Computational geometry
A (slightly) faster algorithm for Klee's measure problem
Computational Geometry: Theory and Applications
The rhombic dodecahedron map: an efficient scheme for encoding panoramic video
IEEE Transactions on Multimedia
Algorithmic construction of low-discrepancy point sets via dependent randomized rounding
Journal of Complexity
Statistical measures of two dimensional point set uniformity
Computational Statistics & Data Analysis
Hardness of discrepancy computation and ε-net verification in high dimension
Journal of Complexity
A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting
SIAM Journal on Numerical Analysis
Spherical Q2-tree for sampling dynamic environment sequences
EGSR'05 Proceedings of the Sixteenth Eurographics conference on Rendering Techniques
Constructing low star discrepancy point sets with genetic algorithms
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Uniform point sets and the collision test
Journal of Computational and Applied Mathematics
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Patterns used for supersampling in graphics have been analyzed from statistical and signal-processing viewpoints. We present an analysis based on a type of isotropic discrepancy—how good patterns are at estimating the area in a region of defined type. We present algorithms for computing discrepancy relative to regions that are defined by rectangles, halfplanes, and higher-dimensional figures. Experimental evidence shows that popular supersampling patterns have discrepancies with better asymptotic behavior than random sampling, which is not inconsistent with theoretical bounds on discrepancy.