{"abstract":[{"lang":"eng","text":"This paper presents an analytic formulation for anti-aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell-Netravali filter family. This enables high-quality rasterization of triangles and tetrahedra with linearly interpolated vertex values to regular and non-regular grids. A closed form solution of the convolution is presented and an efficient implementation on the GPU using DirectX and CUDA C is described. "}],"oa":1,"status":"public","date_published":"2012-05-13T00:00:00Z","conference":{"name":"EUROGRAPHICS: European Association for Computer Graphics"},"acknowledgement":"Funding was provided by the FWF grant P20768-N13.\nWe want to thank the reviewers for their insightful and helpful remarks, Hang Si for making available TetGen and Stefan Bruckner for VolumeShop.","main_file_link":[{"url":"https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/","open_access":"1"}],"volume":31,"extern":1,"citation":{"apa":"Auzinger, T., Guthe, M., &#38; Jeschke, S. (2012). Analytic anti-aliasing of linear functions on polytopes (Vol. 31, pp. 335–344). Presented at the EUROGRAPHICS: European Association for Computer Graphics, Wiley-Blackwell. <a href=\"http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x\">http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x</a>","chicago":"Auzinger, Thomas, Michael Guthe, and Stefan Jeschke. “Analytic Anti-Aliasing of Linear Functions on Polytopes,” 31:335–44. Wiley-Blackwell, 2012. <a href=\"http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x\">http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x</a>.","ama":"Auzinger T, Guthe M, Jeschke S. Analytic anti-aliasing of linear functions on polytopes. In: Vol 31. Wiley-Blackwell; 2012:335-344. doi:<a href=\"http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x\">http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x</a>","short":"T. Auzinger, M. Guthe, S. Jeschke, in:, Wiley-Blackwell, 2012, pp. 335–344.","ieee":"T. Auzinger, M. Guthe, and S. Jeschke, “Analytic anti-aliasing of linear functions on polytopes,” presented at the EUROGRAPHICS: European Association for Computer Graphics, 2012, vol. 31, no. 121, pp. 335–344.","ista":"Auzinger T, Guthe M, Jeschke S. 2012. Analytic anti-aliasing of linear functions on polytopes. EUROGRAPHICS: European Association for Computer Graphics, Computer Graphics Forum, vol. 31, 335–344.","mla":"Auzinger, Thomas, et al. <i>Analytic Anti-Aliasing of Linear Functions on Polytopes</i>. Vol. 31, no. 121, Wiley-Blackwell, 2012, pp. 335–44, doi:<a href=\"http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x\">http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x</a>."},"publisher":"Wiley-Blackwell","month":"05","publist_id":"4676","type":"conference","publication_status":"published","doi":"http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x","quality_controlled":0,"intvolume":"        31","alternative_title":["Computer Graphics Forum"],"issue":121,"page":"335 - 344","_id":"2268","day":"13","year":"2012","title":"Analytic anti-aliasing of linear functions on polytopes","author":[{"full_name":"Thomas Auzinger","last_name":"Auzinger","orcid":"0000-0002-1546-3265","id":"4718F954-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas"},{"first_name":"Michael","last_name":"Guthe","full_name":"Guthe, Michael"},{"full_name":"Stefan Jeschke","first_name":"Stefan","id":"44D6411A-F248-11E8-B48F-1D18A9856A87","last_name":"Jeschke"}],"date_updated":"2021-01-12T06:56:24Z","date_created":"2018-12-11T11:56:40Z"}