---
_id: '2268'
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. '
acknowledgement: |-
  Funding was provided by the FWF grant P20768-N13.
  We want to thank the reviewers for their insightful and helpful remarks, Hang Si for making available TetGen and Stefan Bruckner for VolumeShop.
alternative_title:
- Computer Graphics Forum
author:
- first_name: Thomas
  full_name: Thomas Auzinger
  id: 4718F954-F248-11E8-B48F-1D18A9856A87
  last_name: Auzinger
  orcid: 0000-0002-1546-3265
- first_name: Michael
  full_name: Guthe, Michael
  last_name: Guthe
- first_name: Stefan
  full_name: Stefan Jeschke
  id: 44D6411A-F248-11E8-B48F-1D18A9856A87
  last_name: Jeschke
citation:
  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>'
  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>.
  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>.
  short: T. Auzinger, M. Guthe, S. Jeschke, in:, Wiley-Blackwell, 2012, pp. 335–344.
conference:
  name: 'EUROGRAPHICS: European Association for Computer Graphics'
date_created: 2018-12-11T11:56:40Z
date_published: 2012-05-13T00:00:00Z
date_updated: 2021-01-12T06:56:24Z
day: '13'
doi: http://dx.doi.org/10.1111/j.1467-8659.2012.03012.x
extern: 1
intvolume: '        31'
issue: 121
main_file_link:
- open_access: '1'
  url: https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/
month: '05'
oa: 1
page: 335 - 344
publication_status: published
publisher: Wiley-Blackwell
publist_id: '4676'
quality_controlled: 0
status: public
title: Analytic anti-aliasing of linear functions on polytopes
type: conference
volume: 31
year: '2012'
...