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Shortest paths in simple polygons with polygon-meet constraints
2004
Information Processing Letters
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We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. ...
The algorithms are linear, both in time and space, in terms of the complexity of the two polygons. ...
Convex target polygon In this case, the problem can be considered as a special case of the general touring polygons problem (general TPP) studied by Dror et al. [3] . ...
doi:10.1016/j.ipl.2004.04.010
fatcat:2vthzqpxvzc4zfznlquzwyepxm
Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane
2020
Discrete & Computational Geometry
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We first give an O(n 4 log 3 n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colours with n corners in total. ...
We study the following separation problem: Given a collection of pairwise disjoint coloured objects in the plane with k different colours, compute a shortest "fence" F, i.e., a union of curves of minimum ...
This work was initiated at the workshop on Fixed-Parameter Computational Geometry at the Lorentz Center in Leiden in May 2018. ...
doi:10.1007/s00454-020-00232-w
fatcat:txszq35blvcpjkbnn3hlthczvy
Intégrale, Longueur, Aire
1902
Annali di Matematica Pura ed Applicata
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ongueurs des segments ou des aires des polygones. ...
Dc BoIs R~YMO~D (*) est donc un cas particulier de la d6finition classique~ m~me en dtendant comme je l'ai fait le sens du mot in-t~grale. ...
Consid6rons un ligne polygonale P inscrite dans cette courbe. ...
doi:10.1007/bf02420592
fatcat:frwlqoy53fbbzmfon5sgtxh5g4
Thiessen Polygons
[chapter]
2017
Encyclopedia of GIS
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When there are multiple convex polygons in the same constraint relation, the complement of one convex polygon can be affected by the complements of all the other convex polygons. ...
In constraint databases, any concave polygon or polygon with holes has to be divided and represented by multiple convex polygons. ...
The LTIS database contains the following information for use in our analysis: • Accidents ı In general, it records the total duration (measured in [Event-Hrs] ) affected by all accidents on a given day ...
doi:10.1007/978-3-319-17885-1_101387
fatcat:gzp2stwscbcf7eupd3h6eztjri
Optimal patrolling of fragmented boundaries
2013
Proceedings of the 25th ACM symposium on Parallelism in algorithms and architectures - SPAA '13
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These two fundamental types of strategies were studied in the past in the robotics community in different theoretical and experimental settings. ...
Our main contribution is a proof that the optimal solution to the patrolling problem is attained either by the cyclic strategy, in which all the robots move in one direction around the curve, or by the ...
Unsurprisingly, many general watchman route problems are NP-hard (e.g. watchman tours of simple polygon with holes, suggested in [7] and corrected in [13] ), touring a sequence of non-convex polygons ...
doi:10.1145/2486159.2486176
dblp:conf/spaa/CollinsCGKKKMP13
fatcat:ijqaqcelfzb7da63yh62dpzlku
Foundations
[chapter]
2011
Methods of Geometry
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The image f[D] of the domain is called the range off.
Preserved and invariant properties In many apphcations, a function maps its domain D into itself. ...
The intersection of any family of convex point sets is convex. ...
For example, 2 is an upper bound for the set S of values f(x) = x 2 /(l + x 2 ), indicated by the dotted hne in figure B.l. ...
doi:10.1002/9781118032787.ch2
fatcat:6ft5vaghbratrgvyxj6mhppppu
The Genesis of Architectural Space
2021
Építés - Építészettudomány
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This valuable writing – although published in Hungarian as a series of journal articles or in copied version – is hardly known to the architectural profession.2 The English version published here helps ...
Space" is a concise summary of Gyula Hajnóczi's spatial theory research that offers a thorough overview also for less experienced researchers in architectural theory. ...
but convex, i.e. turn in a full-bodied, "articulated" way. ...
doi:10.1556/096.2021.00010
fatcat:qgitm7iiifcq3dbvugu5woyc6y
Topology building and random polygon generation
1994
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This problem translates directly to polygon nesting in computational geometry: given a set of polygons, find their nesting structure. ...
In order to test and verify the time complexity of our polygon nesting algorithm, we present an algorithm that generates x-monotone polygons uniformly at random over a vertex set of n points. ...
Then they partitioned the convex polygonal line into convex chains and further partitioned the convex chains into the x-monotone polygonal lines. ...
doi:10.14288/1.0051255
fatcat:qhttfsy4vnhmdevvielxu6scze
Subject Index Volumes 1–200
2001
Discrete Mathematics
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, 2215, 2955, 5032, 5222, 5322, see also
Eulerian tour
trails, 4690, 5064
Euler (cont.) ...
, see n-convex d-convexity, see n-convexity d-covered, see n-covered d-critical, see n-critical d-cube, see n-cube D-cycle, 1442 d-dimensional, see n-dimensional d-disjunct, see n-disjunct d-distance, ...
convex bodies, 1950 convex bodies, Wilson, 88, 255, 514, 601, 1376 convex bodies, , 1490 convex bodies, , 1570 convex bodies, , 2526 convex bodies, , 2568 convex bodies, , 2691 857, 1137, 1200, 1305 ...
doi:10.1016/s0012-365x(00)00471-4
fatcat:znxg54q6ifgutnhzj3urcw455y
Full Issue PDF
2019
Canadian field-naturalist
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We thank the Ontario Reptile and Amphibian Atlas for making a vast amount of data available in the public domain and the hundreds of volunteers who have taken the time to submit their observations to those ...
MacDonald, whose expertise and knowledge of all things amphibious was instrumental to the success of this project in the early days. ...
We determined the home range of individuals by calculating the 100% minimum convex polygon (MCP) using the genmcp function in GME, which provides the smallest possible convex polygon that encompasses all ...
doi:10.22621/cfn.v132i2.2199
fatcat:izcs3k7qtvfofo5pa6iltgztti
Parts of visual form: computational aspects
1995
IEEE Transactions on Pattern Analysis and Machine Intelligence
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A representation of parts for recognition requires that they be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy ...
Neckbased parts arise from narrowings in shape, or the local minima in distance between two p o i n ts on the boundary, while limb-based parts arise from a pair of negative curvature minima which h a ve ...
fence. ...
doi:10.1109/34.368189
fatcat:7dyauhzs6zdnvlptymotf3xjem
Proceedings of the IX International Workshop on Locational Analysis and Related Problems
[article]
2020
arXiv
pre-print
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The International Workshop on Locational Analysis and Related Problems will take place during January 30-February 1, 2019 in C\'adiz (Spain). ...
Previous meetings took place in Segovia (September 27-29, 2017), M\'alaga (September 14-16, 2016), Barcelona (November 25-28, 2015), Sevilla (October 1-3, 2014), Torremolinos (M\'alaga, June 19-21, 2013 ...
polygonal chain. ...
arXiv:2002.08300v1
fatcat:g3nupnp2kfb7fnjno45nx2kvym
Elements of Mathematics: A Problem-Centered Approach to History and Foundations
[article]
2022
Zenodo
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In general, naïve theory in mathematics is a term referring to a mathematical theory that employs natural language to describe its objects of study. ...
Many terms in a naïve theory are not defined with mathematical rigor, and thus the theory is prone to "excesses," possibly leading to inconsistencies. ...
If Q participates in a polygonal path for C, then this path can be split into the union of two polygonal paths, one for C 1 and the other for C 2 . ...
doi:10.5281/zenodo.6080520
fatcat:7cxkxhgpevgvnf7pe3irxrh7xy
Non-parametric Spatial-Domain Algorithm for Analysis and Mapping of Urban Scenes Using 3D Point Clouds
[article]
2016
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With half of the current seven billion people living in urban areas, urbanization most certainly will continue in the future. ...
Such a steep urbanization growth curve requires and justifies the growing interest not only in urban sustainability but also in sustainable development in general, which explains the growing interest as ...
Figure 5 - 5 Figure 5-16 Detected polygons and recognized windows in a facade. (a) Detected polygons. ...
doi:10.11575/prism/27122
fatcat:oi2b6apmjrhz5cgpuqixkvr5ee
An Invitation to Tensor-Triangular Geometry
2017
Notices of the American Mathematical Society
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Embark on a playful mathematical tour, aided by Lisl Gaal's illustrations of familiar scenes and whimsical triggers for the imagination. ...
Along the way, find fruit stands arranged using polynomial multiplication, checkerboard tablecloths sewn with patterns of primes in a two-dimensional number system, and deceptive cats revealing that simple ...
C y n t h i a D w o r k , H a r v a r d U n i v e r s i t y , Privavy in the Land of Plenty (AMS Josiah Willard Gibbs Lecture). ...
doi:10.1090/noti1594
fatcat:ciebsoei5faltj5zoyfg3ewlfi
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