analytic anti-aliasing of linear functions on polytopes
DESCRIPTION
Thomas Auzinger 1 , Michael Guthe 2 and Stefan Jeschke 1,3. Analytic Anti-Aliasing of Linear Functions on Polytopes. 1 Institute of Computer Graphics and Algorithms Vienna University of Technology. 2 Department of Mathematics and Computer Science Philipps-University Marburg. - PowerPoint PPT PresentationTRANSCRIPT
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Analytic Anti-Aliasing of Linear Functions on Polytopes
Thomas Auzinger1, Michael Guthe2 andStefan Jeschke1,3
1 Institute of Computer Graphicsand Algorithms
Vienna University of Technology
2Department of Mathematics and Computer Science
Philipps-University Marburg
3 Computer Graphics Group
IST Austria
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Thomas Auzinger 2
Motivation
Sampling of 2D and 3D meshes
Mesh input Sampling Reconstruction
Our domain
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Thomas Auzinger 3
Primer on Sampling
Example test pattern:
Analytic zone plate – contains high spatial frequencies
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Thomas Auzinger 4
Naïve Sampling
Downsampling to half resolution:
Result FilterAliasing
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Thomas Auzinger 5
Filtered Sampling
Downsampling to half resolution:
Box filter Hat filter Gaussian filter
Anisotropicoversmoothing
Isotropicoversmoothing
Goodperformance
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Thomas Auzinger 6
Sampled Filtering
Stochastic filter evaluation:
1 Sample 10 Samples 100 Samples
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Thomas Auzinger 7
Filtered Sampling
Conclusions:Simple box/hat filters insufficient for high quality anti-aliasing
We allow higher order filter functionsUse radial filters to avoid anisotropic artifacts
We use radial filtersUse a lot of samples
We use analytic calculations,i.e. ‘infinitely many’ samples
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Thomas Auzinger 8
Related Work
T. Duff: Polygon scan conversion by exact convolution. 1989
Covers analytic anti-aliasing in 2D with separable polynomial filters on CPUs.
(becomes intractable in 3D, no radial filters)
J. Manson, S. Schaefer: Wavelet rasterization. 2011
Covers analytic anti-aliasing in 2D and 3D with wavelets based on the box filter on CPUs.
(restricted to box filtering and binary attributes)
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Thomas Auzinger 9
Analytic Sampling Overview
Overview:
Mesh inputSample positionsFilter supports Output
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Thomas Auzinger 10
Analytic Sampling in 2D
Filter convolution:
yyxyx d)v( )( )(
Sample locationMesh dataFilter function
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Thomas Auzinger 11
Analytic Sampling in 2D
Filter convolution:
yyxyx d)v( )( )(
Complicated integration domain
Intersection area Subdivision Integration domains
... ...,
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Thomas Auzinger 12
Analytic Sampling in 2D
Filter convolution:
yyxyx d)(v )( )( 1
yyxyx d)(v )( )( 2
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Thomas Auzinger 13
Analytic Sampling in 2D
Filter convolution:
Sample location
yyxyx d)v( )( )(
Mesh data & filter
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Thomas Auzinger 14
Analytic Sampling in 3D
Filter convolution:
yyxyx d)v( )( )(
Decomposition:
Intersection volume Subdivision Integration domains
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Thomas Auzinger 15
Analytic Sampling in 3D
Filter convolution:
yyxyx d)(v )( )( 1
yyxyx d)(v )( )( 2
yyxyx d)(v )( )( 3
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Thomas Auzinger 16
Analytic Sampling in 3D
Filter convolution:
yyxyx d)v( )( )(
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Thomas Auzinger 17
Implementation
Implementation in Direct3D 10 (2D) and CUDA C (3D).
Timings (3D): Grid
64³ 256³
Tetrahedra19k 2.5s 90s
1.9M 15.3s 216s
Hardware: GeForce 580 GTX, 1.5 GB SDRAM
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Thomas Auzinger 18
Results
Alias-free sampling of complex scenes:
2M tetrahedraat different filter radii
(shown right)
Area filtering (previous methods)
Gaussian filtering (our method)
32.52
32.52
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Thomas Auzinger 19
Results
Alias-free sampling of linear data functions:
64³ / 2k256³ / 2k 256³ / 12k
Linear color interpolation between spike base (black) and spike tip (cyan)
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Thomas Auzinger 20
Conclusions
We presented analytic anti-aliasing of polygons and polyhedra allowing for:
Linear functions on the mesh (e.g. colors, densities,…)
Higher order radial filter functions
Regular and non-regular sampling grids
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Thomas Auzinger 21
Future Work
Generalization to temporal filtering
Wavelet approach to general filters and/or data functions
Analytic rendering
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Thomas Auzinger 22
Fin
Questions?