{"external_id":{"arxiv":["0810.0052"]},"type":"preprint","language":[{"iso":"eng"}],"author":[{"first_name":"Matthias","last_name":"Fischer","id":"146","full_name":"Fischer, Matthias"},{"first_name":"Matthias","last_name":"Hilbig","full_name":"Hilbig, Matthias"},{"last_name":"Jähn","full_name":"Jähn, Claudius","first_name":"Claudius"},{"full_name":"Meyer auf der Heide, Friedhelm","id":"15523","last_name":"Meyer auf der Heide","first_name":"Friedhelm"},{"last_name":"Ziegler","full_name":"Ziegler, Martin","first_name":"Martin"}],"_id":"16465","date_created":"2020-04-08T08:41:52Z","status":"public","title":"Planar Visibility Counting","date_updated":"2022-01-06T06:52:50Z","user_id":"15415","citation":{"chicago":"Fischer, Matthias, Matthias Hilbig, Claudius Jähn, Friedhelm Meyer auf der Heide, and Martin Ziegler. “Planar Visibility Counting.” <i>ArXiv:0810.0052</i>, 2008.","apa":"Fischer, M., Hilbig, M., Jähn, C., Meyer auf der Heide, F., &#38; Ziegler, M. (2008). Planar Visibility Counting. <i>ArXiv:0810.0052</i>.","bibtex":"@article{Fischer_Hilbig_Jähn_Meyer auf der Heide_Ziegler_2008, title={Planar Visibility Counting}, journal={arXiv:0810.0052}, author={Fischer, Matthias and Hilbig, Matthias and Jähn, Claudius and Meyer auf der Heide, Friedhelm and Ziegler, Martin}, year={2008} }","short":"M. Fischer, M. Hilbig, C. Jähn, F. Meyer auf der Heide, M. Ziegler, ArXiv:0810.0052 (2008).","ama":"Fischer M, Hilbig M, Jähn C, Meyer auf der Heide F, Ziegler M. Planar Visibility Counting. <i>arXiv:08100052</i>. 2008.","mla":"Fischer, Matthias, et al. “Planar Visibility Counting.” <i>ArXiv:0810.0052</i>, 2008.","ieee":"M. Fischer, M. Hilbig, C. Jähn, F. Meyer auf der Heide, and M. Ziegler, “Planar Visibility Counting,” <i>arXiv:0810.0052</i>. 2008."},"publication":"arXiv:0810.0052","department":[{"_id":"63"}],"year":"2008","abstract":[{"text":"For a fixed virtual scene (=collection of simplices) S and given observer\r\nposition p, how many elements of S are weakly visible (i.e. not fully occluded\r\nby others) from p? The present work explores the trade-off between query time\r\nand preprocessing space for these quantities in 2D: exactly, in the approximate\r\ndeterministic, and in the probabilistic sense. We deduce the EXISTENCE of an\r\nO(m^2/n^2) space data structure for S that, given p and time O(log n), allows\r\nto approximate the ratio of occluded segments up to arbitrary constant absolute\r\nerror; here m denotes the size of the Visibility Graph--which may be quadratic,\r\nbut typically is just linear in the size n of the scene S. On the other hand,\r\nwe present a data structure CONSTRUCTIBLE in O(n*log(n)+m^2*polylog(n)/k)\r\npreprocessing time and space with similar approximation properties and query\r\ntime O(k*polylog n), where k<n is an arbitrary parameter. We describe an\r\nimplementation of this approach and demonstrate the practical benefit of the\r\nparameter k to trade memory for query time in an empirical evaluation on three\r\nclasses of benchmark scenes.","lang":"eng"}]}