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Efficient algorithms for shortest distance queries on special classes of polygons
1995
Theoretical Computer Science
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In this paper, we present efficient algorithms to solve the query version of the RMBP problem for special classes of rectilinear polygons given their oisibility graphs. ...
For the case of a chordal graph G, our algorithms give a distance which is at most one away from the actual shortest distance. ...
In this paper we are interested in solving the full-query version of the minimum link distance problem in a special class of rectilinear polygons. ...
doi:10.1016/0304-3975(94)00195-o
fatcat:qabjfilibzba5putolubcqvpq4
Page 1120 of Mathematical Reviews Vol. , Issue 96b
[page]
1996
Mathematical Reviews
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(Sridhar, Radhakrishnan] (1-OK-C; Norman, OK);
Han, K. (1-OK-C; Norman, OK);
Chandrasekharan, N. (1-LYLCH; Chicago, IL)
Efficient algorithms for shortest distance queries on special classes of polygons ...
In this paper, we present efficient algorithms to solve the query version of the RMBP problem for special classes of rectilinear polygons given their visibility graphs. ...
Walking your dog in the woods in polynomial time
2008
Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08
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We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons. ...
The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking ...
We present a polynomial-time algorithm for a special case of this problem, which is to compute the homotopic Fréchet distance between two polygonal curves in the plane minus a set of point or polygonal ...
doi:10.1145/1377676.1377694
dblp:conf/compgeom/ChambersVELLT08
fatcat:b7kuo5qnrrbwrn2n5iz7gtsndu
Page 7123 of Mathematical Reviews Vol. , Issue 97K
[page]
1997
Mathematical Reviews
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Davis, Parallelizing an algorithm for visibility on polyhedral terrain (75-84); Yi-Jen Chiang and Roberto Tamassia, Optimal shortest path and minimum-link path queries between two convex polygons inside ...
In fact, we provide the first worst-case optimal (O(nlogn) time, O(n) space) algorithm that is valid for the full class of what have been called nice metrics in the plane. ...
Page 1606 of Mathematical Reviews Vol. , Issue 92c
[page]
1992
Mathematical Reviews
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Summary: “We describe a new data structure for answering shortest path queries inside a simple polygon. ...
{For the entire collection see MR 92b:68019.}
92c:68190 68U05 68P05
Hershberger, John (1-DECSY)
A new data structure for shortest path queries in a simple polygon. Inform. Process. ...
Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time
2010
Computational geometry
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We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of polygonal obstacles. ...
The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking ...
We would like to thank the anonymous referees for their careful reading of the paper and their numerous suggestions for improvement. ...
doi:10.1016/j.comgeo.2009.02.008
fatcat:vqtemc2z6nffxd7si62be32s7u
Page 5145 of Mathematical Reviews Vol. , Issue 92i
[page]
1992
Mathematical Reviews
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First, we present a data structure using O(nlog n) storage such that a shortest path between two query points can be computed efficiently. ...
images, for a large class of object types (e.g., points, ...
Indexing Network Voronoi Diagrams
[chapter]
2012
Lecture Notes in Computer Science
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Although the existing approaches successfully utilize the network Voronoi diagram as a way to partition the space for their specific problems, there is little emphasis on how to efficiently find and access ...
The Network Voronoi diagram and its variants have been extensively used in the context of numerous applications in road networks, particularly to efficiently evaluate various spatial proximity queries ...
In [19] , Samet et al. proposed shortest path quadtree algorithm for efficient evaluation of both shortest path and kNN queries in road networks. ...
doi:10.1007/978-3-642-29038-1_38
fatcat:c7iwcvhyx5erxb23eyfirb2kq4
Computing external farthest neighbors for a simple polygon
1991
Discrete Applied Mathematics
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For a vertex p of Y, let @J(P) be the set of points on :sP that are farthest fromp, where the distance between two points is the length of the (Euclidean) shortest path that connects them without intersecting ...
Suri, Computing external farthest neighbors for a simple polygon, Discrete Applied Mathematics 31 (1991) 97-l 11. Let .+' be (the boundary of) a simple polygon with n vertices. ...
In Section 3 we prove some properties of external shortest paths, which lead us to an efficient algorithm for computing the external farthest neighbors for every vertex of the polygon. ...
doi:10.1016/0166-218x(91)90063-3
fatcat:klzdgk6rlbbjzhc2dx3u6cnotq
Polygonal path simplification with angle constraints
2005
Computational geometry
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We present efficient geometric algorithms for simplifying polygonal paths in R 2 and R 3 that have angle constraints, improving by nearly a linear factor over the graph-theoretic solutions based on known ...
The algorithms we present match the time bounds for their unconstrained counterparts. ...
Acknowledgement The authors would like to thank the anonymous reviewers for their helpful comments and suggestions. ...
doi:10.1016/j.comgeo.2004.09.003
fatcat:6xnshgwedvc7daebcvwjfphifa
Page 7483 of Mathematical Reviews Vol. , Issue 94m
[page]
1994
Mathematical Reviews
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Our algorithm takes O(n log? n) preprocessing time, O(n log” n) space and O(log” n) query time for the distance problem. ...
{For the entire collection see MR 94i:68003.}
94m:68194 68U05 52B55
Yan, Yong (PRC-HUST-C; Wuhan)
An optimal algorithm for solving collision distance between convex polygons in plane. ...
Page 3242 of Mathematical Reviews Vol. , Issue 97E
[page]
1997
Mathematical Reviews
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The paper investigates a special class of such scale spaces for three- dimensional images. ...
Summary: “We give a subquadratic (O(n*/***) time and O(n) space) algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles; previous time bounds were at least ...
Shortest path problem in rectangular complexes of global nonpositive curvature
2013
Computational geometry
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2010 pre-print arXiv:1010.0852v1 fatcat:gthqmulkkzczfcrl3ncrlv7viaOther Versions
In this paper, we present an efficient algorithm for answering two-point distance queries in CAT(0) rectangular complexes and two of theirs subclasses, ramified rectilinear polygons (CAT(0) rectangular ...
If K is a ramified rectilinear polygon, then one can construct a data structure D of optimal size O(n) and answer two-point shortest path queries in O(d(p,q)logΔ) time, where Δ is the maximal degree of ...
In this paper, we present an algorithm for efficiently solving two-point shortest path queries in CAT(0) rectangular complexes, i.e., rectangular complexes of global non-positive curvature. ...
doi:10.1016/j.comgeo.2012.04.002
fatcat:75aglel2izhzjat2uqsq74pg5e
Efficient Max-Norm Distance Computation and Reliable Voxelization
[article]
2003
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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We present techniques to efficiently compute the distance under max-norm between a point and a wide class of geometric primitives. ...
We formulate the distance computation as an optimization problem and use this framework to design efficient algorithms for convex polytopes, algebraic primitives and triangulated models. ...
We thank Kenny Hoff for his HAVOC software, Joe Warren and Scott Schaefer for providing us with dual contouring code, and the reviewers for their feedback and suggestions. ...
doi:10.2312/sgp/sgp03/116-126
fatcat:pk52og4wovcjpgmw2yyncjtopi
Computational Geometry Column 42
[article]
2001
arXiv
pre-print
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A compendium of thirty previously published open problems in computational geometry is presented. ...
We are grateful to Erik Demaine for several helpful comments. ...
Relatedly, is there a simple linear-time algorithm for computing a shortest path in a simple polygon, without first applying a more complicated triangulation algorithm? 11. ...
arXiv:cs/0108021v1
fatcat:xgoxckdbl5a7hacx54drwifute
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