“Analytic antialiasing with prism splines” by McCool
Conference:
Type:
Title:
- Analytic antialiasing with prism splines
Presenter(s)/Author(s):
Abstract:
The theory of the multivariate polyhedral splines is applied to analytic antialiasing: a triangular simplex spline is used to represent surface intensity, while a box spline is used as a filter. Their continuous convolution is a prism spline that can be evaluated exactly via recurrence. Evaluation performance can be maximized by exploiting the properties of the prism spline and its relationship to the sampling grid. After sampling, digital signal processing can be used to evaluate exactly and efficiently the sampled result of any analytic spline filter in the span of the box spline basis used as the original analytic filter.
References:
1. Amanatides, John. Ray Tracing with Cones. Computer Graphics (SIGGRAPH ’84 Proceedings), 18(3): 129-135, July 1984.
2. Catmull, Edwin E. A Hidden-surface Algorithm with Antialiasing. Computer Graphics (SIGGRAPH ’78 Proceedings), 12(3):6-11, August 1978.
3. Dahmen, Wolfgang, Charles A. Micchelli, and Hans-Peter Seidel. Blossoming Begets B-spline Bases Built Better by B- patches. Math. of Comp., 59(199):97-115, July 1992.
4. de Boor, Carl, Klaus H611ig, and Sherman Riemenschneider. Box Splines. Academic Press, 1994.
5. Duff, Tom. Polygon Scan Conversion by Exact Convolution. In Jacques Andr6 and Roger D. Hersch, editors, Raster Imaging and Digital Typography, pages 154-168. Cambridge University Press, 1989.
6. Feibush, Eliot A., Marc Levoy, and Robert L. Cook. Synthetic Texturing using Digital Filters. Computer Graphics (SIG- GRAPH ’80 Proceedings), 14(3):294-301, July 1980.
7. Fong, Philip and Hans-Peter Seidel. An Implementation of Multivariate B-spline Surfaces over Arbitrary Triangulations. In Proceedings of Graphics Intelface ’92, pages 1-10, May 1992.
8. Goodman, T. N. T. Polyhedral Splines. In Collection: Computation of Curves and Sulfaces (Puerto de la Cruz, 1989), volume 307 of NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., pages 347-382. Kluwer Acad. Publ., Dordrecht, 1990.
9. Grant, Charles W. Integrated Analytic Spatial and Temporal Anti-aliasing for Polyhedra in 4-space. Computer Graphics (SIGGRAPH ’85 Proceedings), 19(3):79-84, July 1985.
10. Gr~nbaum, Branko. Convex Polytopes. John Wiley & Sons, 1967.
11. Heckbert, Paul S. and Pat Hanrahan. Beam Tracing Polygonal Objects. Computer Graphics (SIGGRAPH ’84 Proceedings), 18(3):119-127, July 1984.
12. Kajiya, James T. and Mike Ullner. Filtering High Quality Text for Display on Raster Scan Devices. Computer Graphics (SIGGRAPH ’81 Proceedings), 15(3):7-15, August 1981.
13. Max, Nelson L. Antialiasing Scan-line Data. IEEE Computer Graphics and Applications, 10(1): 18-30, January 1990.
14. McCool, Michael D. Analytic Signal Processing for Computer Graphics using Multivariate Polyhedral Splines. PhD thesis, University of Toronto, Department of Computer Science, 1995. Also available as Technical Report CS-95-05 from the University of Waterloo, Department of Computer Science, or from ftp: //dgp. utoronto, ca:/pub/mccool
15. Unser, Michael, Akram Aldroubi, and M. Eden. B-spline Signal Processing. IEEE Transactions on Signal Processing, 41(2):821-848, February 1993.
16. Watt, Alan and Mark Watt. Advanced Animation and Rendering Techniques. Addison-Wesley, 1992.
