Approximating parametric curves with strip trees using affine arithmetic

Computer Graphics Forum

Volumn 22, Issue 2, 2003, Pages 171-179

  De Figueiredo, Luiz Henrique ^a,b   Stolfi, Jorge ^a,b   Velho, Luiz ^a,b  

^a IMPA   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Distance fields; Geometric modeling; Interval arithmetic; Multi resolution

Indexed keywords

COMPUTER GRAPHICS; NUMERICAL ANALYSIS; OBJECT RECOGNITION; SURFACES; TREES (MATHEMATICS);

AFFINE ARITHMETIC; INTERVAL ARITHMETIC; PARAMETRIC CURVES;

DIGITAL ARITHMETIC;

EID: 0043160149     PISSN: 01677055     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-8659.00658     Document Type: Article

References (27)

1. D. H. Ballard. Strip trees, a hierarchical representation for curves. Communications of the ACM, 24(5):310-321, 1981.
2. J. L. D. Comba and J. Stolfi. Affine arithmetic and its applications to computer graphics. In Proceedings of SIBGRAPI'93, pp. 9-18, 1993.
3. A. Guéziec. Meshsweeper: dynamic point-to-polygonal-mesh distance and applications. IEEE Transactions on Visualization and Computer Graphics, 7(1):47-61, 2001.
4. H. Samet. The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading, MA, 1990.
5. A. Melkman. On-line construction of the convex hull of a simple polyline. Information Processing Letters, 25(1):11-12, 1987.
6. G. T. Toussaint. Solving geometric problems with the rotating calipers. In Proc. IEEE MELECON '83, pp. A10.02/1-4. 1983. Available at http://cgm.cs.mcgill.ca/~godfried/publications/calipers.ps.gz
7. O. Günther and S. Dominguez. Hierarchical schemes for curve representation. IEEE Computer Graphics and Applications, 13(3):55-63, 1993.
8. J. Hershberger and J. Snoeyink. Speeding up the Douglas-Peucker line simplification algorithm. In Proc. 5th Intl. Symp. on Spatial Data Handling, pp. 134-143. 1992. Also available as TR-92-07, CS Dept., U of British Columbia, http://www.cs.ubc.ca/tr/1992/TR-92-07
9. L. H. de Figueiredo. Adaptive sampling of parametric curves. In A. Paeth (ed), Graphics Gems V, Boston: Academic Press, pp. 173-178. 1995.
10. O. Günther and E. Wong. The arc tree: an approximation scheme to represent arbitrary curved shapes. Computer Vision, Graphics, and Image Processing, 51(3):313-337, 1990.
11. J. Stolfi and L. H. de Figueiredo. In Self-Validated Numerical Methods and Applications. Monograph for 21st Brazilian Mathematics Colloquium, IMPA, Rio de Janeiro, 1997. Available at ftp://ftp.tecgraf.puc-rio.br/pub/lhf/doc/cbm97.ps.gz
12. L. H. de Figueiredo and J. Stolfi. Adaptive enumeration of implicit surfaces with affine arithmetic. Computer Graphics Forum, 15(5):287-296, 1996.
13. L. H. de Figueiredo. Surface intersection using affine arithmetic. In Proceedings of Graphics Interface'96, pp. 168-175. 1996.
14. A. de Cusatis, Jr. L. H. de Figueiredo and M. Gattass. Interval methods for ray casting implicit surfaces with affine arithmetic. In Proceedings of SIBGRAPI'99, IEEE Press, pp. 65-71. 1999.
15. W. Heidrich, P. Slusallek and H.-P. Seidel. Sampling procedure shaders using affine arithmetic. ACM Transactions on Graphics, 17(3):158-176, 1998.
16. W. Heidrich and H.-P. Seidel. Ray-tracing procedural displacement shaders. In Graphics Interface '98, pp. 8-16, 1998.
17. R. E. Moore. Interval Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1966.
18. F.D. Crary. A versatile precompiler for nonstandard arithmetics. ACM Transactions on Mathematical Software, 5(2):204-217, 1979.
19. R. Ierusalimschy, L. H. de Figueiredo and W. Celes. Lua: an extensible extension language. Software: Practice & Experience, 26(6):635-652. 1996.
20. G.M. Ziegler. In Lectures on Polytopes. Graduate Texts in Mathematics. vol. 152, New York: Springer, 1995.
21. C. H. Papadimitriou and K. Steiglitz. Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, NJ, 1982.
22. J. B. Oliveira and L. H. de Figueiredo. Robust approximation of offsets and bisectors of plane curves. In Proceedings of SIBGRAPI 2000, IEEE Press, pp. 139-145, 2000.
23. J. Peters and X. Wu. In Optimized Refinable Surface Enclosures. Technical Report. University of Florida, 2001. Available at http://www.cise.ufl.edu/research/SurfLab/papers/02surfenv.pdf
24. D. Laney, M. Duchaineau and N. Max. A selective refinement approach for computing the distance functions of curves. In Proceedings of VisSym '01 (Joint Eurographics-IEEE TCVG Symposium on Visualization), Springer, New York, pp. 213-222. 2001.
25. S. F. Frisken, R. N. Perry, A. P. Rockwood and T. R. Jones. Adaptively sampled distance fields: A general representation of shape for computer graphics. In Proceedings of SIGGRAPH 2000, pp. 249-254. 2000.
26. B. von Herzen and A. Barr. Accurate triangulations of deformed, intersecting surfaces. Computer Graphics, 21(4):103-110, 1987 (Proceedings of SIGGRAPH'87)
27. L. Velho and D. Zorin. 4-8 subdivision. Computer-Aided Geometric Design, 18(5):397-427, 2001.