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Computational geometry in the parallel external memory model

Nodari Sitchinava
<span title="2012-07-01">2012</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xxmn5ensyfflpngqtirzbea3re" style="color: black;">SIGSPATIAL Special</a> </i> &nbsp;
also contain low-latency caches and load data from shared memory in blocks -cache lines -larger than a single word.  ...  In this article we present an overview of the geometric problems that can be solved in parallel and I/O-efficiently in the PEM model.  ...  We will describe the two approaches using the problem of orthogonal line segment intersection reporting as a running example: given a set of axis-aligned line segments, report all pairs of segments that  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2367574.2367578">doi:10.1145/2367574.2367578</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3luy25yq35ef7n5r3ha6gaydmu">fatcat:3luy25yq35ef7n5r3ha6gaydmu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171101215312/http://www.algoparc.ics.hawaii.edu/~nodari/pubs/12-sigspatial.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/31/80/3180a27d1e77c7e7eed7b536d1e74cad5547cdd0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2367574.2367578"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Computation of the Hausdorff distance between sets of line segments in parallel [article]

Helmut Alt, Ludmila Scharf
<span title="2012-07-17">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that the Hausdorff distance for two sets of non-intersecting line segments can be computed in parallel in O(^2 n) time using O(n) processors in a CREW-PRAM computation model.  ...  Each segment set is assumed to be intersection free.  ...  All above mentioned line segment intersection parallel algorithms utilize the segment tree data structure [6] , which is also used in this paper and is described in section 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1207.3962v1">arXiv:1207.3962v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/awpwwsytrfahddfbv7tk2ed2om">fatcat:awpwwsytrfahddfbv7tk2ed2om</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1207.3962/1207.3962.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1207.3962v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

An Optimal Worst Case Algorithm for Reporting Intersections of Rectangles

Bentley, Wood
<span title="">1980</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5jlmyrayyrdazh5awdlsoec77q" style="color: black;">IEEE transactions on computers</a> </i> &nbsp;
In this paper we investigate the problem of reporting all intersecting pairs in a set of n rectilinearly oriented rectangles in the plane.  ...  Index Terms-Computational geometry, geometric intersection problems, optimal algorithms, range searching, VLSI design rule checking.  ...  line segments, report all pairwise edge intersections.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tc.1980.1675628">doi:10.1109/tc.1980.1675628</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qkawskomnzd7dcl6n7ddas4jnu">fatcat:qkawskomnzd7dcl6n7ddas4jnu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160112221515/http://www.itseng.org/research/papers/topics/VLSI_Physical_Design_Automation/Physical_Verification/DRC/Geometric_Intersection_Problems/1980-Bentley.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e9/9d/e99dd4160e9fc384b15a118317128ab873263aa1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tc.1980.1675628"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Locus Example

Gheorghe Sorta
<span title="">2010</span> <i title="Zigotto Printing &amp; Publishing House, Galati"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/k4n6jpu3wfapzhw7ikzehrdbnq" style="color: black;">GeoGebra</a> </i> &nbsp;
the lines of a given triangle and the other two vertices on the other two lines.  ...  In the present paper I set out to exemplify the way in which GeoGebra can be used to solve a classic locus problem, namely the loci of the centers of symmetry of a rectangle with two vertices on one of  ...  Draw a parallel to the Oy axis from M building the point in which it intersects the BC line segment. Rename this point N.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://doaj.org/article/70abff62cb35474eb323ca4f1a2d8e86">doaj:70abff62cb35474eb323ca4f1a2d8e86</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7omepjgjlffqxmp6s7pr6vqgea">fatcat:7omepjgjlffqxmp6s7pr6vqgea</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180421191251/https://ggijro.files.wordpress.com/2011/07/10-exemplu-de-loc-geometric_sorta.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d1/63/d16368feb8f38c66ee156a901dd1ea94e4062306.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Analytic Visibility on the GPU

T. Auzinger, M. Wimmer, S. Jescke
<span title="">2013</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p2lpq6bugfcqxk44anrm6yki4m" style="color: black;">Computer graphics forum (Print)</a> </i> &nbsp;
Building on recent works in computational geometry, we present a new edge-triangle intersection algorithm and a novel method to complete the boundaries of all visible triangle regions after a hidden line  ...  All stages of the method are embarrassingly parallel and easily implementable on parallel hardware.  ...  The check marks in row out show which intersection points are reported as visible edge segments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/cgf.12061">doi:10.1111/cgf.12061</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vdgtjxjngvc45kwzrmw6rl2vbu">fatcat:vdgtjxjngvc45kwzrmw6rl2vbu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130909121456/http://www.cg.tuwien.ac.at/research/publications/2013/Auzinger_2013_AnaVis/Auzinger_2013_AnaVis-Paper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f1/e9/f1e96226fa72bed87ec4f93479e5f8112f8c35c5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/cgf.12061"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Space-Efficient Plane-Sweep Algorithms [article]

Amr Elmasry, Frank Kammer
<span title="2016-04-22">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also give a simple algorithm to enumerate the intersections of n line segments that runs in O((n^2/s^2/3) · s + k) time, where k is the number of intersections.  ...  When the segments are axis-parallel, we give an O((n^2/s) ·^4/3 s + n^4/3·^1/3 n)-time algorithm for counting the intersections, and an algorithm for enumerating the intersections that runs in O((n^2/s  ...  Another question is if it is possible to get around with the extra logarithmic factors in the running times of the problem of enumerating the general and the axis-parallel linesegments intersections.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.01767v2">arXiv:1507.01767v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7divs57smzdjdgsqtokx6nhek4">fatcat:7divs57smzdjdgsqtokx6nhek4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200906064836/https://arxiv.org/pdf/1507.01767v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b8/2f/b82fb1a4b5c67caa5b3fcc442456b53e742d7c96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.01767v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Geometric Algorithms for Private-Cache Chip Multiprocessors [chapter]

Deepak Ajwani, Nodari Sitchinava, Norbert Zeh
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
For the second group of problems-orthogonal line segment intersection reporting, batched range reporting, and related problems-more effort is required.  ...  To obtain nearly optimal algorithms for these problems, we introduce a parallel distribution sweeping technique inspired by its sequential counterpart. ⋆  ...  using orthogonal line segment intersection reporting as an example.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-15781-3_7">doi:10.1007/978-3-642-15781-3_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tmjpjij3fvf6rhsvkpc4dqywka">fatcat:tmjpjij3fvf6rhsvkpc4dqywka</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200320223103/https://researchrepository.ucd.ie/bitstream/10197/9902/2/ajwani_esa10.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/af/a7/afa742e3d2d51d2d76914ba5821b2dabc43e5ecb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-15781-3_7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Space-Efficient Plane-Sweep Algorithms

Amr Elmasry, Frank Kammer, Marc Herbstritt
<span title="2016-12-02">2016</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6u44dxxc6ffsdc6pb66slxylg4" style="color: black;">International Symposium on Algorithms and Computation</a> </i> &nbsp;
We also give a simple algorithm to enumerate the intersections of n line segments that runs in O((n 2 /s 2/3 ) • lg s + k) time, where k is the number of intersections.  ...  When the segments are axis-parallel, we give an O((n 2 /s) • lg 4/3 s + n 4/3 • lg 1/3 n)-time algorithm that counts the intersections and an O((n 2 /s) • lg s • lg lg s + n • lg s + k)-time algorithm  ...  Counting Axis-Parallel Line-Segments Intersections Given a set of n axis-parallel (horizontal or vertical) line segments in the plane, we want to count the intersection points among these line segments  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.isaac.2016.30">doi:10.4230/lipics.isaac.2016.30</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isaac/ElmasryK16.html">dblp:conf/isaac/ElmasryK16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b4e5pjwgk5gtjamfwujmdcxjji">fatcat:b4e5pjwgk5gtjamfwujmdcxjji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220205180633/https://drops.dagstuhl.de/opus/volltexte/2016/6800/pdf/LIPIcs-ISAAC-2016-30.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/df/29/df2916c49c2e00ecb3f88b689af2a43475e99d88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.isaac.2016.30"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

I/O-Optimal Distribution Sweeping on Private-Cache Chip Multiprocessors

Deepak Ajwani, Nodari Sitchinava, Norbert Zeh
<span title="">2011</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t3x4vqewrncrfgn2wu7cafsbsq" style="color: black;">2011 IEEE International Parallel &amp; Distributed Processing Symposium</a> </i> &nbsp;
denotes the number of elements that fit in a cache line, and denote the sizes of the input and output, respectively, and sort ( ) denotes the I/O complexity of sorting items using processors in the PEM  ...  As a tool for developing geometric algorithms in this model, a parallel version of the I/O-efficient distribution sweeping framework was introduced recently, and a number of algorithms for problems on  ...  OPTIMAL ORTHOGONAL LINE SEGMENT INTERSECTION REPORTING As discussed in Section IV, the orthogonal line segment intersection algorithm of [16] achieves the optimal I/O complexity of O(sort ( ) + / ) I  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdps.2011.106">doi:10.1109/ipdps.2011.106</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ipps/AjwaniSZ11.html">dblp:conf/ipps/AjwaniSZ11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ryuwmi3x2fbqhlhuolpwao2wju">fatcat:ryuwmi3x2fbqhlhuolpwao2wju</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922031423/https://web.cs.dal.ca/~nzeh/Publications/pem_geometry_ipdps11.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cb/28/cb288696b3503d59d3e15a97da47eaa32947f75c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ipdps.2011.106"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Parallel Optimal Weighted Links [chapter]

Ovidiu Daescu
<span title="">2001</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper we consider parallel algorithms for computing an optimal link among weighted regions in the 2-dimensional (2-D) space.  ...  We present a CREW PRAM parallel algorithm and a coarse-grain parallel computer algorithm.  ...  that allows to quickly report the segments intersected by a query line.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45545-0_75">doi:10.1007/3-540-45545-0_75</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kmpqvwmczrgnrchtwr6djha45y">fatcat:kmpqvwmczrgnrchtwr6djha45y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180730144750/https://link.springer.com/content/pdf/10.1007%2F3-540-45545-0_75.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2a/46/2a4650484cf6e408c6a222615bdafa76f7ad38ee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45545-0_75"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Tile Count in the Interior of Regular 2n-gons Dissected by Diagonals Parallel to Sides [article]

Richard J. Mathar
<span title="2009-11-17">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The manuscript reports on the number of tiles up to the 78-gon.  ...  The regular 2n-gon (square, hexagon, octagon, ...) is subdivided into smaller polygons (tiles) by the subset of diagonals which run parallel to any of the 2n sides.  ...  */ double t = lines[lidx].inters(split.lines[slidx], t2) ;if ( isinf(t) ) /* no action if parallel, since in the current problem these segments are distinct */ They do intersect: mark position t for splitting  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0911.3434v1">arXiv:0911.3434v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tfmza4ja6rchtbivlbrdsb4wp4">fatcat:tfmza4ja6rchtbivlbrdsb4wp4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200914094321/https://arxiv.org/pdf/0911.3434v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2c/c6/2cc679a8e2a3d46daf371b7aa31c7be0ccb31119.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0911.3434v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Dynamic C-oriented polygonal intersection searching

Ralf Hartmut Güting
<span title="">1984</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fbkexx2qg5anljkxraobuswdq4" style="color: black;">Information and Control</a> </i> &nbsp;
The intersection searching problem is studied for such objects, namely: Given a set of c-oriented polygons P and a c-oriented query polygon q, find all polygons in P that intersect q.  ...  This suggests that the c-oriented solution be used in appropriate areas of application, for instance, in VLSI-design.  ...  LINE SEGMENT INTERSECTION SEARCHING The c-oriented LSI searching problem is: Given C, a set of C-oriented line segments L and a C-oriented query line segment lq, find all line segments in L which intersect  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-9958(84)80011-x">doi:10.1016/s0019-9958(84)80011-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rnmez7ohebb7zg2fzzunhusn6u">fatcat:rnmez7ohebb7zg2fzzunhusn6u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190415174939/https://core.ac.uk/download/pdf/81145164.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ee/52/ee528afb720cab30a9707eb7ef1ddf65fdbfe1ed.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0019-9958(84)80011-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Algorithms for Reporting and Counting Geometric Intersections

Bentley, Ottmann
<span title="">1979</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5jlmyrayyrdazh5awdlsoec77q" style="color: black;">IEEE transactions on computers</a> </i> &nbsp;
In this paper we extend their work by giving algorithms that count the number of such intersections and algorithms that report all such intersections.  ...  An interesting class of "geometric intersection problems" calls for dealing with the pairwise intersections among a set of N objects in the plane, These problems arise in many applications such as printed  ...  Lauther for pointing out a bug in the original presentation ofAlgorithm 2.2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tc.1979.1675432">doi:10.1109/tc.1979.1675432</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pl2mjw5skjecbnxy4dteugvjk4">fatcat:pl2mjw5skjecbnxy4dteugvjk4</a> </span>
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Page 7258 of Mathematical Reviews Vol. , Issue 87m [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
preprocessing, the inter- section of a query line segment and an arrangement of n lines is solved in time O(log n +t), where t¢ is the number of intersecting lines reported.  ...  It is shown that the intersections of the line segments that form a so-called hammock can be found in time O(nlogn +k), where k is the number of intersections reported.  ... 
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External-memory algorithms with applications in GIS [chapter]

Lars Arge
<span title="">1997</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We also discuss an algorithm for the reb/blue line segment intersection probleman important subproblem in map overlaying.  ...  orthogonal line segment intersection problem we illustrate the distribution-sweeping and the buffer tree techniques which can be used to solve a large number of important problems.  ...  The Orthogonal Line Segment Intersection Problem The orthogonal line segment intersection problem is that of reporting all intersecting orthogonal pairs in a set of N line segment in the plane parallel  ... 
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