Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Digital halftoning
Information-based complexity
Numerical methods and software
Numerical methods and software
Physically based lighting calculations for computer graphics
Physically based lighting calculations for computer graphics
Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Hierarchical Poisson disk sampling distributions
Proceedings of the conference on Graphics interface '92
A fast shadow algorithm for area light sources using backprojection
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Fast computation of shadow boundaries using spatial coherence and backprojections
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Optimally combining sampling techniques for Monte Carlo rendering
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Shading models for point and linear sources
ACM Transactions on Graphics (TOG)
Direct illumination with lazy visibility evaluation
Proceedings of the 26th 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
Proceedings of the 1999 conference on Graphics interface '99
Comments on the Nature of Automatic Quadrature Routines
ACM Transactions on Mathematical Software (TOMS)
Metropolis Light Transport for Participating Media
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Soft Shadow Maps for Linear Lights
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
EGWR'99 Proceedings of the 10th Eurographics conference on Rendering
A theory of monte carlo visibility sampling
ACM Transactions on Graphics (TOG)
Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Many key problems in computer graphics require the computation of integrals. Due to the nature of the integrand and of the domain of integration, these integrals seldom can be computed analytically. As a result, numerical techniques are used to find approximate solutions to these problems. While the numerical analysis literature offers many integration techniques, the choice of which method to use for specific computer graphic problems is a difficult one. This choice must be driven by the numerical efficiency of the method, and ultimately, by its visual impact on the computed image. In this paper, we begin to address these issues by methodically analyzing deterministic and stochastic numerical techniques and their application to the type of one-dimensional problems that occur in computer graphics, especially in the context of linear light source integration. In addition to traditional methods such as Gauss-Legendre quadratures, we also examine Voronoi diagram-based sampling, jittered quadratures, random offset quadratures, weighted Monte Carlo, and a newly introduced method of compounding known as a difficulty driven compound quadrature.We compare the effectiveness of these methods using a three-pronged approach. First, we compare the frequency domain characteristics of all the methods using periodograms. Next, applying ideas found in the numerical analysis literature, we examine the numerical and visual performance profiles of these methods for seven different one-parameter problem families. We then present results from the application of the methods for the example of linear light sources. Finally, we summarize the relative effectiveness of the methods surveyed, showing the potential power of difficulty-driven compound quadratures.