Abstract
We present an algorithm for the hidden-surface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, κ. Our algorithm obtains a trade-off between these two components, in that its running time is O(r(n 1+1/r+κ)), where 1≤r≤log n is a tunable parameter. By using this method while adjusting the parameter r “on the fly” one can achieve a running time that is O(n log n+κ(log n/log(1+κ/n))). Note that when κ is Θ(n), this achieves an O(n log n) running time, and when κ is Θ(n 1+ε) for any positive constant ɛ, then this achieves an O(κ) running time, both of which are optimal.
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This author's research was supported by the National Science Foundation under Grant CCR-8810568 and by the NSF and DARPA under Grant CCR-8908092.
This author's research was supported by the Office of Naval Research under Grants N00014-84-K-0502 and N00014-86-K-0689, and the National Science Foundation under Grant DCR-8451393, and the National Library of Medicine under Grant R01-LM05118. Part of this research was carried out while this author was visiting the Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, California.
This author's research was partially supported by the ESPRIT II Basic Research Actions Program of the EC, under contract No. 3075 (project ALCOM).
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Goodrich, M.T., Atallah, M.J., Overmars, M.H. (1990). An input-size/output-size trade-off in the time-complexity of rectilinear hidden surface removal. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032067
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DOI: https://doi.org/10.1007/BFb0032067
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