Abstract
We derive a new output-sensitive algorithm for hidden surface removal in a collection ofn triangles, viewed from a pointz such that they can be ordered in an acyclic fashion according to their nearness toz. Ifk is the combinatorial complexity of the outputvisibility map, then we obtain a sophisticated randomized algorithm that runs in (randomized) timeO(n4/3 log2.89 n +k 3/5 n 4/5 + δ for anyδ > 0. The method is based on a new technique for tracing the visible contours using ray shooting.
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References
P. K. Agarwal, Partitioning arrangements of lines, I: An efficient deterministic algorithm,Discrete Comput. Geom. 5 (1990), 449–483.
P. K. Agarwal, Ray shooting and other applications of spanning trees with low stabbing number,Proc. 5th ACM Symp. on Computational Geometry, 1989, pp. 315–325.
P. K. Agarwal and J. Matousek, Ray shooting and parametric search,Proc. 24th ACM Symp. on Theory of Computing, 1992, pp. 517–526.
M. de Berg, D. Halperin, M. H. Overmars, J. Snoeyink, and M. van Kreveld, Efficient ray shooting and hidden surface removal,Algorithmica, 1994, to appear.
M. Bern, Hidden surface removal for rectangles,J. Comput. System Sci. 40 (1990), 49–69.
B. Chazelle and L. Guibas, Visibility and intersection problems in plane geometry,Discrete Comput. Geom. 4 (1989), 551–581.
F. Dévai, Quadratic bounds for hidden line elimination,Proc. 2nd ACM Symp. on Computational Geometry, 1986, pp. 269–275.
D. Dobkin and H. Edelsbrunner, Space searching for intersecting objects,J. Algorithms 8 (1987), 348–361.
H. Edelsbrunner, L. Guibas, and M. Sharir, The complexity and construction of many faces in arrangements of lines and of segments,Discrete Comput. Geom. 5 (1990), 161–196.
M. T. Goodrich, A polygonal approach to hidden line elimination,Proc. 25th Allerton Conf. on Communication, Control, and Computing, 1987, pp. 849–858.
M. T. Goodrich, M. J. Atallah, and M. H. Overmars, Output-sensitive methods for rectilinear hidden surface removal,Inform. and Comput. 107 (1993), 1–24.
L. Guibas, M. Overmars, and M. Sharir, Intersecting line segments, ray shooting, and other applications of geometric partitioning techniques,Proc. SWAT 88, Lecture Notes in Computer Science, Vol. 318, Springer-Verlag, 1988, Berlin, pp. 64–73.
R. H. Güting and T. Ottman, new algorithms for special cases of the hidden line elimination problem,Comput. Vision Graphics Image Process. 40 (1987), 188–204.
M. McKenna, Worst-case optimal hidden surface removal,ACM Trans. Graphics 6 (1987), 19–28.
K. Mulmuley, An efficient algorithm for hidden surface removal,Comput. Graphics 23 (1989), 379–388.
O. Nurmi, A fast line-sweep algorithm for hidden line elimination,BIT 25 (1985), 466–472.
M. H. Overmars and M. Sharir, Output-sensitive hidden surface removal,Proc. 30th IEEE Symp. on Foundations of Computer Science, 1989, pp. 598–603.
F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction, Springer-Verlag, New York, 1985.
F. P. Preparata, J. S. Vitter, and M. Yvinec, Computation of the axial view of a set of isothetic parallelepipeds,ACM Trans. Graphics 9 (1990), 278–300.
J. Reif and S. Sen, An efficient output-sensitive hidden surface removal algorithm and its parallelization,Proc. 4th ACM Symp. on Computational Geometry, 1988, pp. 193–200.
H. Schipper and M. H. Overmars, Dynamic partition trees,BIT 31 (1991), 421–436.
A. Schmitt, Time and space bounds for hidden line and hidden surface algorithms,Eurographics '81, 1981, pp. 43–56.
M. Sharir and M. H. Overmars, A simple output-sensitive algorithm for hidden surface removal,ACM Trans. Graphics 11 (1992), 1–11.
I. E. Sutherland, R. F. Sproull, and R. A. Schumacker, A characterization of ten hidden-surface algorithms,Comput. Surveys 6 (1974), 1–25.
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Communicated by Leonidas J. Guibas.
Work by the first author was partially supported by the ESPRIT II Basic Research Actions Program of the EC, under Contract No. 3075 (project ALCOM). Work by the second author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the NCRD-the Israeli National Council for Research and Development-and the Fund for Basic Research in Electronics, Computers, and Communication administered by the Israeli Academy of Sciences. A preliminary version of this paper appeared as part of the conference proceedings paper [17].
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Overmars, M.H., Sharir, M. An improved technique for output-sensitive hidden surface removal. Algorithmica 11, 469–484 (1994). https://doi.org/10.1007/BF01293267
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DOI: https://doi.org/10.1007/BF01293267