A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes
The numerical calculation of integrals is central to many computer graphics algorithms such as Monte-Carlo Ray Tracing. We show that such methods can be studied using Fourier analysis. Numerical error is shown to correspond to aliasing and the link between properties of the sampling pattern and the...
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| Language: | en-US |
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2011
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| Online Access: | http://hdl.handle.net/1721.1/67677 |
| _version_ | 1826211936454311936 |
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| author | Durand, Frédo |
| author2 | Computer Graphics |
| author_facet | Computer Graphics Durand, Frédo |
| author_sort | Durand, Frédo |
| collection | MIT |
| description | The numerical calculation of integrals is central to many computer graphics algorithms such as Monte-Carlo Ray Tracing. We show that such methods can be studied using Fourier analysis. Numerical error is shown to correspond to aliasing and the link between properties of the sampling pattern and the integrand is studied. The approach also permits the unified study of image aliasing and numerical integration, by considering a multidimensional domain where some dimensions are integrated while others are sampled. |
| first_indexed | 2024-09-23T15:13:45Z |
| id | mit-1721.1/67677 |
| institution | Massachusetts Institute of Technology |
| language | en-US |
| last_indexed | 2024-09-23T15:13:45Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | mit-1721.1/676772019-04-11T03:07:06Z A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes Durand, Frédo Computer Graphics Numerical Analysis Integration Fourier Monte-Carlo Aliasing Rendering Ray Tracing The numerical calculation of integrals is central to many computer graphics algorithms such as Monte-Carlo Ray Tracing. We show that such methods can be studied using Fourier analysis. Numerical error is shown to correspond to aliasing and the link between properties of the sampling pattern and the integrand is studied. The approach also permits the unified study of image aliasing and numerical integration, by considering a multidimensional domain where some dimensions are integrated while others are sampled. 2011-12-14T19:45:12Z 2011-12-14T19:45:12Z 2011-12-14 http://hdl.handle.net/1721.1/67677 en-US MIT-CSAIL-TR-2011-052 6 p. application/pdf |
| spellingShingle | Numerical Analysis Integration Fourier Monte-Carlo Aliasing Rendering Ray Tracing Durand, Frédo A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes |
| title | A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes |
| title_full | A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes |
| title_fullStr | A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes |
| title_full_unstemmed | A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes |
| title_short | A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes |
| title_sort | frequency analysis of monte carlo and other numerical integration schemes |
| topic | Numerical Analysis Integration Fourier Monte-Carlo Aliasing Rendering Ray Tracing |
| url | http://hdl.handle.net/1721.1/67677 |
| work_keys_str_mv | AT durandfredo afrequencyanalysisofmontecarloandothernumericalintegrationschemes AT durandfredo frequencyanalysisofmontecarloandothernumericalintegrationschemes |