Information
- Publication Type: Journal Paper with Conference Talk
- Workgroup(s)/Project(s):
- Date: May 2012
- Journal: Computer Graphics Forum (Proceedings of EUROGRAPHICS 2012)
- Volume: 31
- Number: 2
- Location: Cagliari, Italy
- Lecturer: Thomas Auzinger
- Event: Eurographics 2012
- Conference date: 13. May 2012 – 18. May 2012
- Pages: 335 – 344
- Keywords: Polytope, Filter Design, Analytic Anti-Aliasing, Sampling, Integral Formula, Spherically Symmetric Filter, CUDA, Closed Form Solution, 2D 3D
Abstract
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.Additional Files and Images
Additional images and videos
![Fast Forward DivX: Video for the Fast Forward session (DivX encoded) (14 MB).](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Fast Forward DivX:thumb175.png)
![Fast Forward TechSmith: Video for the Fast Forward session (TechSmith encoded) (107 MB).](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Fast Forward TechSmith:thumb175.png)
![Intersection decomposition: Decomposition of the intersection volume between the spherical filter support and a input tetrahedron. The different colors denote different geometrical shapes for which a closed form solution of the integral can be obtained.](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Intersection decomposition:thumb175.png)
![Sea urchin model: Volume rendering of a sea urchin model sampled with our method. The color is linearly interpolated in the spike tetrahedra. The model consists of 2470 tetrahedra and is sampled to a grid with resolution 256³ with a Gaussian filter kernel of radius 2.3 voxels.](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Sea urchin model:thumb175.png)
![Zone plate model: Volume rendering of a zone plate model consisting of 2M tetrahedra with a Gaussian filter kernel.](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Zone plate model:thumb175.png)
Additional files
![Paper: Full paper preprint.](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Paper:thumb64.png)
![Slides: Presentation slides without the final video (5 MB).](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-Slides:thumb64.png)
![SlidesVideo: Presentation slides with the final video (20 MB).](https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/Auzinger_2012_AAA-SlidesVideo:thumb64.png)
Weblinks
BibTeX
@article{Auzinger_2012_AAA, title = "Analytic Anti-Aliasing of Linear Functions on Polytopes", author = "Thomas Auzinger and Michael Guthe and Stefan Jeschke", year = "2012", abstract = "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.", month = may, journal = "Computer Graphics Forum (Proceedings of EUROGRAPHICS 2012)", volume = "31", number = "2", pages = "335--344", keywords = "Polytope, Filter Design, Analytic Anti-Aliasing, Sampling, Integral Formula, Spherically Symmetric Filter, CUDA, Closed Form Solution, 2D 3D", URL = "https://www.cg.tuwien.ac.at/research/publications/2012/Auzinger_2012_AAA/", }