Thomas Auzinger
, Michael Guthe, Stefan Jeschke
Analytic Anti-Aliasing of Linear Functions on Polytopes
Computer Graphics Forum (Proceedings of EUROGRAPHICS 2012), 31(2):335-344, May 2012. [
Paper]
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).
Fast Forward TechSmith:
Video for the Fast Forward session (TechSmith encoded) (107 MB).
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.
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.
Zone plate model:
Volume rendering of a zone plate model consisting of 2M tetrahedra with a Gaussian filter kernel.
Additional files
Paper:
Full paper preprint.
Slides:
Presentation slides without the final video (5 MB).
SlidesVideo:
Presentation slides with the final video (20 MB).
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/",
}